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= 37.5 kN). Such load has been chosen for the analysis because the mean value of cracking shear force during the experiment was Vcr= 38 kN.While observing the σ11 stress values distribution in analyzed beams (see ) it is possible to notice the differences among them. The stream of σ11 stresses and neutral axis position changes according to a/d. More precisely it may be observed on the basis of the comparison presented in . In the beam S4 tensile stress in the bottom part of the cross section C-C is lower and compressive stress in the upper part of the cross section A-A is higher as compared to others beams. But the differences in obtained test results are seen the most clearly when comparing the maximum principal stress distribution in analyzed beams (see ). The visualization of maximum principal stress looks quite different in beam S4 of the lowest shear span-to-depth ratio compared to other beams S5, S3, S2. This difference points out that in short beams, the mode of failure changes. It causes other cracks propagation, especially diagonal cracks propagation, and higher load carrying capacity. The beams of a/d |
⩾ 2.5 make up very similar maximum principal stress values distribution. These beams can be treated as slender beams and therefore their shear failure process has the same character.The shear span-to-depth ratio a/d is the primary parameter that significantly affects the shear failure mechanism in flexural concrete members reinforced longitudinally and without transverse reinforcement. If a/d is greater than 2.5, an inclined tensile crack penetrates the entire depth of the compression zone and causes a diagonal tensile failure. On the other hand, if a/d is less than 2.5, compression crushing occurs in the upper region of the compression zone, which is called a shear-compression failure. Due to the difference in the failure mechanism, the shear strength of slender beams with a/d greater than 2.5 and that of beams with a/d less than 2.5 should be studied separately.The load carrying capacity of reinforced concrete beams without stirrups depends on shear span-to-depth ratio because the failure mechanism changes in accordance to this parameter. Further basic research should be encouraged to analyze the diagonal crack propagation process in longitudinally reinforced concrete members without transverse reinforcement.The results of numerical simulations presented in the paper show the differences in maximum stress distribution according to a/d. The performed numerical analysis seems to be promising, although it was performed using very simple linear elastic model, and points that investigated problem is worth to deal with. The authors would like to improve numerical analyses by simulating the diagonal crack evaluation as described in Detachment folding, growth mechanism and seismic potential in the Jammu Sub-HimalayaThe Surin Mastgarh anticline (SMA) marks the active deformation front in the northwest Sub-Himalaya near Jammu. The southern limb of the SMA is not truncated by an emergent thrust, unlike other frontal folds along the Himalayan front. We investigate the structural data, deformation pattern, and seismic potential of the SMA using field surveys and re-interpretation of seismic profile. Strath profiles along the Chenab and the Munavar Tawi river valleys indicate active growth of the SMA by layer parallel shortening, and limb rotation accompanied by flexural slip, suggesting an early phase of its development. Lateral migration of the southern limb suggesting limb lengthening and bending at the hinge are the dominant mechanisms of fold amplification with strain localization at the fold core above the floor thrust tip. Bending moment faulting at the hinge led to the formation of crestal grabens or lakes in the southeastern section of the SMA. Our results suggest the existence of a weak, less viscous layer beneath a brittle sedimentary detachment. The SMA initiated as a detachment fold and sequentially deformed by passive roof thrusting. Therefore, the seismotectonic model of the Jammu Sub-Himalaya is different from that of the central and eastern Himalaya.The ∼2500 km long Sub-Himalayan deformation front of the Himalayan arc is characterized by anticlines associated with emergence of the south-verging Himalayan Frontal Thrust (HFT), otherwise named as the Main Frontal Thrust (MFT) (). The HFT is an updip representation of the Main Himalayan Thrust (MHT) decollement which releases most of the accumulated interseismic strain during large-to-great earthquakes (The structural pattern of frontal anticlines in the northwest Jammu Sub-Himalayan deformation front is, however, quite different. In the western, central and north-eastern parts of the Himalaya, the emergence of the HFT or MFT at the deformation front has been well-documented through paleoseismological studies (). But in the northwest Jammu Sub-Himalaya, the HFT is not emergent at the surface, and therefore remains blind (West of the Beas river in the Jammu Sub-Himalayan zone defined here between the Ravi and the Jhelum rivers, surficial mapping and cross sections revealed the existence of ∼200-km-long and continuous Surin Mastgarh Anticline (SMA) (). The boundary between the SMA and the alluvial plain to the south is obscured by prograding alluvial fans with a gradual topographic slope which merges with the active Indo-Gangetic foreland basin ( suggested that, individual folds cannot exceed a lateral growth threshold of ∼8 km without producing an emergent thrust front (). However, the SMA running for a length of ∼200 km contradicts the model if the SMA is assumed to represent a single individual continuous fold structure. Southeast of the SMA, the Janauri anticline grows in a discontinuous en echelon pattern with an emergent frontal thrust (). Several structural models put forth by researchers have variously explained the deformation pattern of the SMA. A positive flower structure model was proposed for the SMA (). Subsequently, another model of tip-line folding suggesting the emergence of a thrust fault/tip-line fault at the core or crestal region of the SMA has also been proposed (Sup. ). The tip-line fault was interpreted to be southward-vergent creating a triangular zone at the deeper central region of the anticline. The anticline was mentioned as a ‘blind thrust anticline’ in a later study (). Further, a simple fold model without a thrust ramp based on folding of terraces along Chenab valley has also been proposed recently, advocating the possibility of a back-thrust at the core region of SMA (). Due to the absence of a well-constrained geometry of the blind ramp at depth, they estimated the horizontal shortening across the SMA since terrace abandonment by using the excess area method (), in which the area of the anticline section under the terrace envelope and the depth of the detachment plane were taken into account. Furthermore, more recent balanced cross-section and terrace restoration studies along the Ujh river valley suggests that the SMA is a SW-directed wedge and duplex thrust structure (). The inference was based on the terrace geometry of the Ujh river section, where sub-horizontal to southward tilting, vertically uplifted terraces in the northern limb and southward tilting terraces in the southern limb were observed.Even though multiple studies have produced various structural models for the SMA, there still remains a lack of consensus due to the along-strike variation of its complex structure and vast length. The present study area is located within the seismic gap of the 1905 Kangra and 2005 Kashmir earthquakes. To understand the seismic potential associated with the SMA, it is necessary to understand its surface and subsurface geometry. Though most of the earlier works were model-driven, published a viable model based on field evidences from the Ujh river section. Our work focused on the western section of the Jammu Sub-Himalaya, where we provide a suitable structural model for the SMA between the Chenab and the Munavar Tawi rivers. Additionally, we investigated study sites across the SMA along the Tawi, the Ujh, the Bhini, the Ravi and the Chakki river valleys to look into the along-strike variation of SMA. We used high resolution satellite imageries, detailed field based geological and geomorphological mapping, and deformation pattern of strath terraces across the SMA, integrated with published seismic reflection profile of the study area (). Our results and observations suggest that the SMA is an actively growing detachment fold modified by passive roof thrusting. Furthermore, a paleoseismological trench was also excavated across a potential fault scarp along the western segment of SMA mountain front to evaluate the potential emergence of HFT in the region (Sup. The Jammu Sub-Himalaya broadly consists of two tectono-stratigraphic regions, viz., the inner Sub-Himalaya in the north, and the outer Sub-Himalaya in the south (A). The Inner Sub-Himalaya is the deformation belt between the Main Boundary Thrust (MBT) and the Medlicott Wadia Thrust (MWT) which consists of the faulted and folded Sirban Limestones, the Subathu, the Murree, and units of the Lower Siwalik. The outer Sub-Himalaya consists of the Siwalik folded units lying to the south of the MWT (A). An exploratory seismic survey by the ONGC shows a prominent surface reflection, which is inferred to be the decollement surface at a depth of ∼8 km underlain by the Neo-Proterozoic Sirban Limestones (). However, in the neighboring region east of the Beas river, a shallow detachment depth is inferred at 4.5 km (). The depth of the detachment associated with the plate boundary Main Himalaya thrust is inferred to significantly increase in the Jammu Sub-Himalaya (The northern limb of the SMA in the Jammu region is overthrusted by the Mandili Kishanpur Thrust (MKT), which juxtaposes the Murree Formation against the Siwalik Formation (). The MKT, the Reasi Thrust (RT), and other equivalent thrusts to the east, as well as the Kotli Thrust (KT) and the Balakot-Bagh Fault to the NW are collectively referred to as the MWT by ), the RT places the Neo-Proterozoic Sirban Limestone (Great Limestone), the Middle Eocene Subathu, and the Oligocene Murree Formations over the Neogene Siwalik Formation (). At several locations in the Riasi and Katra areas, the Sirban Limestone overlies the tilted and folded Upper Quaternary Vaishnodevi calcareous gravels (The SMA varies in trend from WWN-ESE between the Munavar Tawi and the Chenab rivers, which changes to NW-SE between the Chenab and the Ravi rivers (A). The anticline forms a re-entrant near the town of Akhnoor, where it exhibits a structural bend leading to a change in strike. For the purpose of our study, we divide the SMA into northwestern section (between the Munavar Tawi and the Chenab rivers) and southeastern section (between east of Chenab and Ravi rivers) based on the change in structural trend (E-W to NW-SE) and the presence or absence of small extensional basins or lakes along the SMA axis (A). Two lakes Mansar and Surinsar were observed in the southeastern section of the faulted SMA axis. However, lakes are absent in the northwestern section where the SMA axis appears un-faulted (). Along the axial trace of the SMA, several gas seepages, potential salt springs, and oil shores have been reported by the ONGC, and oil exploration drillings have been conducted near the Surinsar village (). Along-strike of the SMA's southern forelimb at the exit of the Munavar Tawi river valley near the Line of Control, prograding fan deposits ensuing from the Sub-Himalayan zone characterized the deformation front. The SMA fold axis comprises rocks of the Lower Siwalik occupying the fold core with steep dips of 75–80° bounded by the Middle and Upper Siwaliks in either of the limbs dipping at 70-15°. (). The upper Siwalik beds appear discontinuous in the northern limb as the northern limb being shorter than the south. To the northern limb of SMA we have discontinuous presence of syncline (Geomorphic landforms along the Chenab and the Munavar Tawi rivers were mapped in the laboratory using Cartosat-1A stereo-pair imageries (∼2.5 m spatial resolution), 30 m Digital Elevation Models (DEM) of Shuttle Radar Topographic Mission (SRTM) and Advanced Land Observing Satellite (ALOS), Google Earth, and Survey of India topographic maps of 1:50,000 scale. We surveyed the strath terraces preserved along the Chenab and the Munavar Tawi rivers with Real Time Kinematic GPS (RTK GPS) (). River profiling was done in Rivertools v4.0, maps were prepared in ArcGIS v10.0 and Global Mapper v13, illustrative work was done in Adobe Illustrator vCS5.With respect to the elevation of the current river grade, the uplifted strath terraces were mapped and named from youngest (T0) to oldest (T3). The term ‘strath’ is defined as the erosional base of a terrace (). It is characterized by a sub-horizontal erosional base, commonly carved into bedrock, and overlain by a thin cover of alluvium, whereas, ‘bedrock’ is described as any substrate upon which a river valley develops. Strath is generally overlain by soft and poorly-consolidated sediments. The incised strath terraces in the study area vary in height from 11 to 68 m across the study area. The underlying bedrock in this case are Siwalik rocks.Several bedding parallel fault scarps were mapped using Cartosat-1A stereo-pair image analysis, both on the northern and southern limbs along the SMA. These fault scarps were surveyed with RTK DGPS. North-facing scarps were observed on the northern limb of SMA, whereas south-facing scarps were observed on its southern limb. Along the western end of SMA, at the mountain front along the Munavar Tawi river, a ∼5 km long putative fault scarp parallel to the regional structure was mapped (In this study, we re-interpret a previously published seismic profile across the SMA by using structural data from the field, surface geology, and geometry of the strath terraces in the study area and suggest a new deformation model that better fits the field observations. B shows the NW-SE striking seismic reflection profile at the core of SMA. The seismic section consists of data up to a depth of 6-s seismic travel time and about 6 km horizontal distance across the anticline core. The seismic section shown in B depicts depth-wise subsurface heterogeneity due to structural or stratigraphic variation along individual units as reflectors. At a depth of ∼8 km (3.5–4.0 s horizontal marks), the seismic section shows a prominent undulating layer which we interpret as detachment-1. An incompetent, ductile basal unit (Subathu Formation) thickened in the core of the fold at between 2.5 and 3.5 s, with no visible thrust ramp. The detachment-1 defines the downward termination of the fold. Beneath that, stacked structural ramps seem to extend downward from the horizontal mark of 3.5–5.5 s, suggesting a duplex structure at a depth between detachment-1 and a second possible detachment surface referred to as the detachment-2. The stack of Pre-Tertiary thrust ramps terminates at detachment-1. The dips of the Formations inferred from the reinterpreted seismic section are as follows. The Middle and the Lower Siwalik Formations at the crest region show a dip of 56°, whereas, that of the Upper Murree Formation is about 50°. The dip of the Lower Murree and the Subathu Formations ranges between 40 and 45°.The strath terraces extending between the Riasi town on the northern limb and the Akhnoor town on the southern limb were mapped on the basis of their geometry and elevation with respect to the current river grade ( inset). Three sets of strath terraces (T1, T2, and T3) preserved along the Chenab river flowing transversely to the SMA were mapped with RTK DGPS.The Chenab river and terrace profiles were projected on a NE-SW strike normal to the SMA fold axis using MATLAB ( inset). On the northern limb of the SMA, T1 and T2 dip northward (B), however, on the southern limb both dip southward with a fore tilt of ∼0.28° and 0.83°, respectively. In the Akhnoor region, near the southern inflection zone or fold boundary, the T2 strath lies on left bank of the Chenab river at a height of 11 m (). However, upstream of the Chenab river (i.e., north of the Akhnoor region), close to the hinge zone, the strath terrace incision is at 47 m (T1) and 68 m (T2). The strath terraces are tilted away from the core of the SMA to follow the respective dip direction of the underlying folded Siwalik strata.West of the Chenab re-entrant, the Munavar Tawi river dissects the SMA (). A detailed investigation could only be conducted on the terraces preserved on the forelimb of SMA because of international border restrictions. Three levels of terraces, T0, T1, and T2, are preserved along the Munavar Tawi river (A). The strath height of T2 is 14 m which overlies the Siwalik strata that dips 20° south and composed of broad gravel units with sand-silt interbeds or lenses (A inset). The dip direction of the underlying consolidated Siwalik bedrock (20° S) and inclination of the fluvial gravel cover sediments of the T2 terrace are the same. This relationship is well observed on the eastern bank of the Munavar Tawi river along the Indian side of the Line of Control (LoC). However, in the Siwalik bedrock and the overlying sediments, a minor step-like feature is observed, which indicates the flow of a small paleo-tributary before the last uplift event of the anticline. T1 consisting of 5 m thick, coarse to fine-grained sandy sediments intercalated by thin gritty units, lies at the height of 8 m. T0 is the flood plain, and is extensive on both banks.The underlying steeply-dipping parallel strata deform quaternary landforms near the SMA axis. Several active, discontinuous fault scarps were mapped along various segments of the SMA with RTK DGPS. (). Tectonically modified fault scarps have been observed on both the northern and southern limbs of the SMA. On the northern limb, fault scarps were noticed in three different sections from west to east, viz., between the Riasi and the Katra towns, in the Ujh-Bhini river section, and the eastern bank of the Chakki river. In the Riasi-Katra section, the vertical separation of fault scarps ranges from 6 to 15 m. In the Ujh-Bhini river section, the vertical separation is ∼20 m, and lastly, the displaced terrace preserved along the Chakki river revealed a vertical separation of ∼2–3 m. The fault scarps were quickly map-able due to the abundance of alluvial fan and quaternary terrace deposits in these sections. However, in contrast with the northern limb, the southern limb lacks extensive alluvial surfaces, making it difficult to map the faults in this region. We were only able to map two parallel fault strands of ∼1 m and 4 m on the terrace preserved along the western bank of the Tawi river. The trend of the mapped offsets is parallel to that of the underlying steeply or moderately dipping bed. The slip is dip-parallel to the underlying bedding, which suggests that slip is intrinsically controlled by bedding (e.g., flexural slip).In active fold regions, flexural slip and bending-moment faults accommodate bending-related tangential longitudinal strain arising due to folding. These secondary faults can deform landforms developing a series of sub-parallel, closely-spaced geomorphic scarps (). Active flexural-slip fault scarps are mainly developed in the portion of the limb on steeply-dipping beds close to the fold axis, whereas the bending-moment fault scarps are concentrated at the hinge region. However, bending-moment fault scarps may also form along with flexural-slip fault scarps on the fold limb as a result of progressive fold tightening and exposing of well-layered beds due to erosion. We observed higher scarps in the northern limb (back limb) on the steeply-dipping beds, but on the gently-dipping beds in the southern limb (forelimb), the scarps are either of lower relief or else absent. The older fan surfaces (Vaishnodevi Gravels) show more significant displacement due to these faults.Along-strike and parallel to the SMA axis, several prominent ridges and valley structures have been observed within the anticline (From two wells underneath the SMA core near the Surinsar region, the basal lower Murree is identified to contain organic-rich matter with over pressured shales (). Higher salinity and presence of migrating hydrocarbon in the well suggest a ductile or weak substrate. Gravity anomaly data also reveals buried or concealed salt range in the Jammu Sub-Himalayan basin (). Extra thickness of the sedimentary package without an obvious fault ramp in the seismic section above the Tertiary units (i.e., Detachment-1) and presence of an Eocambrian salt Formation () collectively suggest that the Jammu Sub-Himalaya is analogous to the Potwar Basin in Pakistan. The steep dip with tight folding and presence of seepages of oil, gas and other salt springs along the SMA axis are a few surface signatures that disclose the presence of hidden oil below the SMA (). Based on these evidences it may be interpreted that there is a weak detachment beneath the outer Jammu Sub-Himalaya region. Consequently, an incompetent lubricating medium such as evaporites or over-pressured shales may facilitate the formation of a detachment fold. Also, the Subathu or Murree Formations are made of carbonate or fine-grained shale. They may act as a ductile medium for anticline growth proposed previously (). Several observations from the SMA well data and surface geological data suggest that a weak detachment exists below the folded SMA.Crustal scale anticlines grow by slip accumulation on an underlying thrust ramp (e.g., ). However, fold growth can also occur without slip on a thrust ramp (), where distributed pure shear above a detachment plane creates a fold (). Detachment folds either grow by strain localization at the hinge and initial limb rotation followed by limb lengthening, or, a combination of moving hinge with limb rotation and duplex-cored anticline (). The continual growth of the SMA is evident from the folding of overlying terraces. The range front has forelandward-dipping strata without an emergent thrust in the southern forelimb (A), which has been revealed by trench investigation (Sup. ). The deformation pattern of strath terraces along the Chenab river valley and structural data across the SMA indicate that the deformation is concentrated at the SMA axis. The cover rocks of the SMA constitute the Lower Tertiary and Siwalik Formation folded in a more or less upright manner. If folding were a result of thrusting, then the underlying layers should not have been folded. Thus, the folding could be interpreted as a result of layer-parallel compression resulting in a flexural slip upright fold. This is also observed between the 3.5–4.0 s mark and top of the reinterpreted seismic section (B). In the Chenab river valley, the northerly surface tilt of strath terrace corresponds to the dip direction of underlying bedrock away from the SMA core (). Similar observations were also made along the Ravi, the Ujh, the Tawi, the Bhini and the Chakki river valleys. It is interesting to note that, suggested a vertically uplift of terrace (T1) in the Ujh river valley. However, we suggest that the fluvial stratigraphy preserved above the beveled strath of Middle Siwalik shows a prominent dip towards north and not in the upper sequences where terrace cover increases to heights of 40 m, as the T3 surface merges with Vaishnodevi gravels (D). The existence of linear lakes between the vertically dipping and drop-down beds along the SMA axis could possibly indicate that SMA is characterized by flexural slip on the limbs and bending-moment normal faulting at the hinge (). The bending has resulted in extensional strains on the outer arc resulting in the formation of fractures. These fractures were probably amplified by gravity gliding and erosion to form the Surinsar and Mansar lakes in the central zone, and basin in the southern zone of SMA (Based on balanced cross-section, three possible structural interpretations were proposed, viz., SW-directed duplex, NE-directed duplex, and detachment fold (). Vertically uplifted terraces in the northern limb and highly southward-tilted terraces on the southern limb favor a SW-directed duplex model. Conversely, a model of fold with a blind thrust was suggested based on folding observed in the eroded terrace surfaces along the Chenab river valley across the SMA (). In accordance to this model, the RTK-GPS measurements along the Chenab river valley terraces in this study also generate an arc-shaped profile.Due to an extensive length of the SMA (∼200 km) and along-strike variation of geometry, multiple structural models are possible. Based on our present observations and reinterpretation of the published seismic section, we propose a model of simple detachment fold that progressively grew as a result of a weak detachment in the northwestern section. However, as per the balanced cross-section model proposed by , the southeastern section of the SMA might have modified into a passive roof duplex pattern due to a ramp structure at deeper levels that lies beneath the Detachment-1 in order to accommodate further deformation (). The idea is further substantiated by the presence and absence of bending-moment normal fault scarps in the southeastern and northwestern sections along the axis of SMA suggesting initiation of a simple detachment fold. Additionally, thermochronology results reveal that the cooling ages are younger in the southeastern section of the Ujh river valley (∼1.0 Ma) and older in the northwestern section along the SMA axis towards Jammu (∼4.4 Ma) (). This suggests an along-strike variation in the geometry of SMA.). A step-like feature observed in the strath terrace section on eastern bank of the Munavar Tawi river (), as well as ridges and valleys developed in the anticline forelimb or southern limb shown in inset 1 of A further suggest foreland migration of inflection point or fold boundary of SMA. These features imply migration of active axial surface during the progressive lengthening of southern anticline limb (forelimb) to amplify the folds (). The northern limb evidently consists of several flexural slip faults close to the SMA crest. The interlayer slip, indicated by slickensides on bedding surfaces, varies along the fold limbs. A major slip occurs at or around the inflection points gradually decreasing towards the fold hinge, where the slip becomes zero (). Hinge migration involves continuous bending at successive points. This can be identified by strain measurements across the present hinge. Field evidence indicative of hinge migration are triangular gashes with extension in the fold outer arc and compression in the inner arc around the hinge zone, especially in the overturned limb. No such field evidence was observed in the present study, hence no effort for strain estimation was made. The geometry of SMA appears to be a result of layer-parallel compression without involvement of a basement fault. A closer examination of the drainage on the SMA reveals an upward propagation of intensive erosion. Several perched drainages developed on the southern forelimb and northward increasing topography suggest a fixed hinge with limb rotation and migration of fold boundary in front of the fold towards foreland (e.g., Further, a two-dimensional plot of bedding dip of the SMA forelimb and horizontal distance towards the hinge given in shows a progressive increase in dip due to early stage of limb rotation. An overturned forelimb dip of 70°–60° could be due to limb rotation about a fixed anticlinal hinge. Hence, limb rotation and flexural slip might have also contributed to growth of the SMA, especially during its initial evolutionary stage. Flexural slip might have occurred to accommodate the layer-parallel slip, with the direction of slip being away from the synclinal hinge and toward the anticlinal hinge (). The slip is maximum at the anticlinal limb but becomes zero at the hinge. However, lateral migration of southern fold boundary, and limb lengthening are the dominant processes of fold amplification. In a detachment fold, if the stratigraphic beds are well-layered, layer-parallel slip will accommodate strain in the form of flexural slip faulting in an anticline, the slip direction being towards the anticlinal hinge. Conversely, if the beds are relatively poorly-layered, then the layer-parallel slip is accommodated in the form of bending-moment normal fault or asymmetric grabens at the core, and thrust faulting towards the synclinal zone. Comparing the theory of to the SMA, the hinge zone is characterized by extension and bending which led to the formation of extensional strain on the outer arc causing extensional fractures. Steep bedding dips at the hinge zone might have supported the gravity gliding and erosion to form the Surinsar and Mansar lakes. Strong fold deformation and erosion of well-layered beds results in bending moment normal fault scarps, which can coexist with flexural slip fault scarps on the fold limb with deeper exposures. Similarly, a reverse fault at the limb of SMA accommodates layer-parallel slip (). We studied the Ujh river section of the scarp shown in D, where north-tilted quaternary deposits are observably truncated by a reverse fault (E). The structure exists south of the Baniyari syncline (Due to a stronger brittle-ductile decoupling of the detachment, deformation is localized at the SMA core. The SMA has formed over a prominent plane of weak decollement, and therefore it cannot be correlated with internal buckling. The fold has an isoclinal geometry (i.e., steep fold limbs) in the core which varies with depth along the axial surface. The inter-limb angles gradually increase with distance from the core resulting in close and open fold styles. This is a normal feature of multilayer folds (). This is very much similar to the Yakeng anticline in the Tian Shan Mountains of Central Asia, which is a detachment fold situated at the mountain front with a non-emergent thrust beneath forelimb (The detachment at a depth of ∼8 km beneath SMA implies a higher overburden and thick foreland sedimentation compared to the adjacent Janauri and Mohand anticlines east of the Beas river, where the foreland sedimentation is also 3–4 km thick (). Alternatively, a greater thickness of the sedimentary sequences above the weak detachment favors either a passive roof duplex, or outward propagation of detachment folding along the detachment (). The former model favors propagation away from the most external thrust in the floor sequence. The latter, however, favors a fixed detachment fold above a floor thrust tip, as a result of strain localization at the core region of the anticline. Conversely, analog models have shown the importance of decollement viscosity, and brittle-ductile coupling along the detachment is controlling the strain localization (). The SMA neither has an emergent or surficial fault at the forelimb (or foreland), nor a ramp fault above the detachment-1. It just has a weak detachment with focused strain localization at the core, which implies that progressive shortening is being accommodated mostly by limb rotation accompanied by flexural slip and outward propagation of detachment folding with marked vertical amplification and strain localization at the core due to layer-parallel slip between the beds of the southern limb (forelimb) and coterminous continued uplift and bending at the hinge (The absence of an emergent thrust beneath forelimb of the SMA is relative to a detachment at greater depth, thick sediment pile in the foreland and low shortening rate (). A greater thickness of foreland sediments in the Jammu Sub-Himalaya () and considerably steeper bedding dips at axial region of the SMA thus indicate the formation of a new back-thrust beneath the SMA core toward hinterland (). This process would give rise to a younger-over-older relationship in a compressional setting especially in the detachment fold model (). The thrust appears to initiate on the limbs during later stages of fold development when the limb dip is steep. The process involving the development of thrusts at later stages of multilayer folding has been demonstrated using a ‘Plasticine model’ (). A greater thickness of 6 km at the hinge further supports the initiation of thrust at later stages of fold formation. A sharp structural dissimilarity exists between the northwestern and southeastern zones of the SMA. In the northwestern section, crestal extension basins (or grabens) are absent. This section is characterized by vertically-dipping beds (). Alternatively, the southeastern section shows bending moment normal faults or crestal extension due to the presence of linear lakes (or grabens) like the Surinsar and the Mansar lakes (The SMA lacks any observable surface rupture, but records significant evidence of uplift which might be due to blind thrust-related earthquake/s and/or detachment folding with potential flexural slip scarps and bending moment normal fault scarps (). However, a detailed investigation across these mapped flexural-slip scarps and the bending moment faults is necessary for an assessment of the seismic risk associated with paleoearthquakes in this region. Relative damages from great earthquakes in the Kashmir Basin have no imprint within the SMA region (). Paleoseismological trenching across a scarp east of the Munavar Tawi river indicates no evidence of surface faulting (Sup. ). Lack of fault scarp along frontal part of the SMA suggests that the incremental strain produced during blind thrust earthquake would otherwise be accommodated by folding, bending moment fault scarp and anticline growth, similar to that of the Coalinga anticline in Southern California (Our study suggests that the SMA does not grow by slip accumulation on an underlying ramp thrust, rather by maintaining a fixed hinge with limb rotation accompanied with flexural slip at early stage, and subsequent limb lengthening and growth of southern limb towards foreland.The fold is characterized by flexural slip on the limbs and uplift-driven bending-moment faulting at the hinge zone. which has resulted in extensional strains on the outer arc resulting in formation fractures. These fractures were probably amplified by gravity gliding and erosion to form lakes in the northwestern zone and basins in the southeastern zone along the SMA axis.The proposed detachment fold model with a passive roof duplex mode of deformation is viable, and thus the seismic scenario is quite different from that of the Central Himalaya.A simple seismotectonic model, where the surface trace of the great earthquake lies at the Himalayan front as interpreted for the Central Himalaya, cannot be applied to the western part of NW Himalaya with a complicated configuration owing to the growing anticline and frontal non-emergent thrust.The flexural-slip and bending-moment fault scarps might be helpful in the seismic risk assessment associated with active folds and blind thrusts.Some of the prominent map scale folds in the Himalaya are fault propagation folds such as the asymmetrical Mohand anticline, whereas, others have formed either as a result of layer-parallel compression such as the SMA, or layer-oblique compression such as the recumbent and reclined folds in the Tethyan Himalayan sequence.AA: conceptualization, methodology, investigation, formal analysis, data curation, writing original draft, software. RLM: visualization, review and editing. SJ: investigation, resources. RJ: conceptualization, supervision, investigation, methodology, review and editing, project administration, validation, funding acquisition. VCT: investigation, visualization, review and editing. CCP: investigation, supervision. VJ: resources.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.The following is the Supplementary data to this article:Supplementary data to this article can be found online at Modelling explicit fracture of nuclear fuel pellets using peridynamicsThree dimensional models of explicit cracking of nuclear fuel pellets for a variety of power ratings have been explored with peridynamics, a non-local, mesh free, fracture mechanics method. These models were implemented in the explicitly integrated molecular dynamics code LAMMPS, which was modified to include thermal strains in solid bodies. The models of fuel fracture, during initial power transients, are shown to correlate with the mean number of cracks observed on the inner and outer edges of the pellet, by experimental post irradiation examination of fuel, for power ratings of 10 and 15 W g−1 UO2. The models of the pellet show the ability to predict expected features such as the mid-height pellet crack, the correct number of radial cracks and initiation and coalescence of radial cracks. This work presents a modelling alternative to empirical fracture data found in many fuel performance codes and requires just one parameter of fracture strain. Weibull distributions of crack numbers were fitted to both numerical and experimental data using maximum likelihood estimation so that statistical comparison could be made. The findings show P-values of less than 0.5% suggesting an excellent agreement between model and experimental distributions.Nuclear fuel modelling has been carried out for many decades in support of fuel management in many reactor systems. Recent work in the US using the BISON code now has many new capabilities of solver technology, high performance computing and multi-physics modelling There have been several previous attempts to incorporate pellet facture in fuel performance modelling. Many of these follow the approaches taken in LIFE-II Attempts to remedy this have been made by Marchal et al. To further enhance the ability to model pellet cracking, in a fuel performance context, there have been recent applications of the commercial code ABAQUS to model the explicit cracking of the pellet, along predetermined paths, through the use of cohesive zones To date modelling of stresses in solid bodies has largely been dominated by the finite element method (FEM) or, more recently, the extended finite element method (XFEM). Modelling brittle solids or brittle solids on ductile substrates can be difficult using the FEM as incorporating cracks requires damage criteria for crack nucleation and crack branching, as well as a prior decision on how many branches are allowed to form Thus far XFEM has produced some of the best results for crack growth in FEM as it has less mesh dependence as crack paths can pass through elements instead of being limited to element boundaries. However, XFEM crack growth speeds do not match observed experimental data without significant scaling of the fracture energies and branching angles tend to be smaller than experimental results The difficulties with FEM, in modelling defects in brittle solids, occur because the spatial derivatives necessary to calculate the deformed state cannot be evaluated at the discontinuities present in a damaged material. This occurs because of the use of classical partial differential equations, which leads to singularities at crack surfaces and crack tips. To circumvent this problem, peridynamics modelling, as proposed by Silling Peridynamics has great potential for application to many difficult problems in the nuclear industry. Previous work has shown that it can be applied to bonded dissimilar materials This paper applies the bond-based peridynamics method to issues related to fuel pellet fracture. Statistical information from over 170 PIE studies of crack patterns of AGR fuel were compared to a similar number of peridynamics models. This paper describes a model that is able to reproduce fracture patterns created by the first heat-up of fuel pellets. The model's predictions are then compared to Central Electricity Generating Board (CEGB) studies It is shown that the branched radial cracks observed in PIE are not formed by the growth and branching of one crack but are actually independently nucleated inner and outer surface radial cracks that coalesce.This study used the peridynamics implementation available in the molecular dynamics code LAMMPS and the calculated thermal strain of the bonds were used to load the peridynamic model. As the temperature changes are taken from pre-computed thermal profiles, from Ref. Detailed methods on the implementation of peridynamics are given elsewhere Fracture and damage is controlled by a history function μ (defined between 0 for zero damage and 1 for a failed bond), which controls the bond failure when the stretch exceeds a critical stretch value, s0. A zeroth order failure behaviour was used where the bond strength is reduced to zero, with no further strain, when the critical value s0 is reached. Considering all the bonds connected to a single point x, damage can be defined as,where Ψ(x, t) is a scalar value of damage at each material point found from the summation of all the bond failures within a volume, V, defined by a horizon, δ, surrounding that material point, where Ψ(x, t) = 1 defines undamaged material and this surrounding region defined by a horizon parameter is the source of non-locality. This is the same definition of damage found in traditional continuum mechanics we define ξ = x′ − x as the relative position of two points in the undeformed configuration and η = u(x′, t) − u(x, t) = u′ − u as the relative displacement of the two points at time t ≥ 0. To form the discrete peridynamics model we use the equation of motionIn the simplified form M is the lumped mass matrix; u¨ is the acceleration; Fsn is the external force vector, and FTn is the internal force vector. Each diagonal term of M is ρVi (where ρ and Vi is the density and volume of particle i respectively) and each component of Fsn is binVi (bin is a body force vector), leaving FTn to represent the sum of all the forces from the trusses connected to material point i, which is defined as ∑pf(upn−uin,xp−xi)ViVp. Once the element matrix has been defined, what remains is to create a mesh for the peridynamics material. It is straightforward to generate peridynamic truss meshes, this entails: placing all the material points that define your material and connecting each material point to each other material point within a sphere with a radius equal to the user-defined distance (the horizon here denoted by δ). Such a mesh in 3D can produce millions of trusses, even for a moderately-sized problem.ρy¨inVi=∑p∈Fi(‖yp−yi‖−‖xp−xi‖‖xp−xi‖)μ(t,η,ξ)ν(xp−xi)Vpyp−yi‖yp−yi‖×(s−αθ+ε˙)+∑p∈Fismin(0,csδ(‖yp−yi‖−dpi))Vpyp−yi‖yp−yi‖+bin is an expanded application of Newton's second law, where y and x are the current and initial coordinate vectors respectively. It is expanded to cover material points, which interact with a finite radius force field. There is a force that increases linearly with stretch between each pair of material points within the given horizon. When the critical stretch of a bond is reached, however, the force goes to zero in order to represent bond breaking. The force on the bond then remains at zero for the remainder of the simulation and this history dependent damage state is held by μ. The second summation in Eq. is representative of a short range contact force where cs is a force constant to prevent material point overlap (as discussed in-depth in Refs. In the modified equations of motion s is the current stretch of the bond, α in this context is the thermal expansion coefficient and ε˙ is the viscous damping term. With a pre-calculated temperature field (from Ref. ), the peridynamics model can undergo damage from thermal events similar to that in nuclear fuel during heat-up and cool-down.The bond-based peridynamics method limits the number of free elastic constants and hence forces the Poisson's ratio to 1/4 in 3D or 1/3 in 2D and also fixes the shear modulus i.e. this only allows isotropic materials to be modelled. This limitation can be removed by the use of a state-based formulation.It is not trivial to extract the stress tensor from peridynamic models as it is for FE models and hence many works do not present stresses. The hoop stresses were calculated by extraction of bond strains associated to material points, the stress tensor was then constructed and transformed to cylindrical coordinates. The stresses were then projected back onto the material points and these were then used to produce hoop stress contour plots. The theory and detailed method for the stress calculation procedure is outlined in Ref. presents the parameters used in these simulations. The bond-based material properties were typical of uranium dioxide. The Young's modulus was 194 GPa; Poisson's ratio was 0.25 and density of 10,690 kg m−3. The time-step chosen was 1.0 × 10−8 s, well below the von Neumann stability criterion. In this first model the properties were neither burn-up, nor temperature dependent, for simplicity. The fracture strain s0 is specified as a single value for the bond fracture strain and the macroscopic material fracture strain. This is because the definition of strain in peridynamics and continuum mechanics is the same. All bonds have the same fracture strain and heterogeneity that may induce nucleation of cracks would originate from numerical rounding in regions where the material is approaching the fracture strain. The geometry of the model was of an annular fuel pellet (geometry in ), a material point spacing of 2.0 × 10−4 m and a horizon distance, δ, three times larger than that. Despite the use of an explicit time stepping method the loading step was quasi-static through the use of dynamic relaxation. This is a process by which the material is loaded and then allowed to relax fully before taking the next time increment. The size of each dynamic relaxation step is chosen as a length of time it takes for a sound wave to move through (farthest distance) the specimen and return.The peridynamic models are more computationally expensive than traditional FEM. Models of just over 100,000 nodes require 3 s per explicit time step on a single 3.0 GHz Intel Xeon (2014) processor core. Parallel computation was not used despite LAMMPS ability to scale due to the modifications to the code involving thermal strain. These initial modifications were written with simplicity and not parallelism in mind and would require further development and testing to ensure correct parallel functionality. This leads to over 1 h per dynamic relaxation step; however, parametric studies were conducted in parallel as each model was independent of all others.Seventy simulations were made per power level and the statistics compared with PIE data from Ref. . The inclusion of a damping term removes the continuous oscillation of the material points, which occurs when load was applied. When these oscillations reached an amplitude with sufficient energy to break bonds the material disintegrated. The imposed damping prevented pellet disintegration but combined with positional variation, in the 6th decimal place, also made the model non-deterministic. Therefore results for a particular thermal load may sample many possible different fracture states. This damping term is possibly physically representative of internal frictions (to sound wave propagation) within the materials such as structural deviations from prefect crystals (e.g. grains). The damping term was chosen, as the smallest possible damping coefficient required to prevent pellet disintegration. The minimum resistive force was found through trial and error. shows the mechanical deformation of a single pellet modelled by simple FEM, extracted from previous studies of AGR fuel has a region of high tension, greater than a typical UO2 fracture stress (See ), on the outer rim of the pellets and fracture was therefore expected to nucleate at these positions. Such models are applied in the current study as a precomputed thermal field on the pellet for fracture studies. Additionally the noted FE models are used to compare pellet thermal expansion without fracture. shows 10 quasi-static thermal strains applied to the pellet model during the thermal ramp for 10 W g−1 final power rating. When the pellet is loaded the fracture strain is taken as the total bond strain minus thermal strain The experimental data used in this study were crack measurements in irradiated AGR fuel pellets from PIE metallographic cross-sections of the fuel. Within the report describing the dataset a FORTRAN program (FUELCRAK) was used to analyse radial crack distributions This section describes the parameter estimation for the experimental data and simulations for an assumed Weibull distribution. Included is the process of data conditioning to produce a goodness of fit to determine whether peridynamics modelling of early life fuel heat-up is representative of the available PIE data.In the case of brittle fracture a Weibull distribution is traditionally assumed. As the pellets contain no cracks, before first loading, there is no need for a minimum parameter suggesting a two parameter Weibull was appropriate. The 2-parameter Weibull probability density function is given in Eq. where the random variable is x; a is the scale parameter and b is the shape parameter. To determine the two parameters in Eq. the method of maximum likelihood for the two parameter Weibull distribution is applied.The maximum likelihood method can be used for parameter estimation when there are insufficient results to make an accurate goodness of fit ∑i=1nxibln(xi)∑i=1nxib−1b−1n∑i=1nln(xi)=0where n is the number of data points available, which may be solved for an estimate of b via procedures such as Newton–Raphson. Once b is known it can be introduced into the derivative of the log likelihood with respect to the scale parameter to find the estimate for a:To enhance the current dataset, due to the limits on the amount of data per bin described above, the estimated probability distribution were each subjected to a 1000 Monte Carlo samplings to produce a distribution appropriate for a goodness of fit test and still representative of the original data. A goodness of fit test may be applied to the conditioned data and the peridynamics models applicability was characterised by the use of a P-value of the fitted distributions, where a significance threshold of 5% is usually considered a good a fit and 1% an excellent fit.As a verification of the peridynamics method the displacements from the peridynamic pellet, deforming under thermal strain, without fracture, at 5, 10, 15, 20 W g−1 were compared to an equivalent ABAQUS FE model with identical material properties. The FE model was composed of a uniform mesh of 50 μm 3D reduced integration continuum elements (C3D8R). The results are presented in . These show excellent agreement for this verification test case with no differences observed greater than a fraction of a per cent. The difference between the FE and peridynamic models was expected to be quite small as the peridynamic bond strain was identical to macroscopic strain and the additional of thermal strain was the same for both models. shows the material points (mesh) of a typical fuel pellet fracture pattern, taken from a slice at quarter-axial pellet height. The colour (in the web version) scale depicts damage fraction (see Eq. then shows the resulting hoop stress at increasing time steps during heat-up. a shows the pellet just at the point where damage was nucleating on the inner surface but as yet none has formed on the outer surface. b–d then show snapshots of hoop stress as time increases during crack evolution. The individual cracks are difficult to see in both figures, due to mesh resolution, but schematic indicator lines have been placed on both to show the crack locations. Difficulty in seeing explicit cracks, on the edges, is probably due to a coalescence of a great number of small cracks not distinguished by this mesh compounded by the peridynamics surface softening effect mentioned in Ref. The radial centre of the pellet and the upper and lower ridges of the pellet experience a high density of damage due to the tensile stresses generated in these regions as shown in a depicts the stress state in the hoop direction. Interestingly damage initiates on the inner surface first. This was due to the geometric distortions depicted in , which generates regions of initial tension on the inner surface skin. These can just be seen as yellow/green regions in a. However, shortly after this event the tension on the outer surface nucleates a series of cracks there as well and the tensile fields at the crack tips can clearly be seen in b–c. At the same time the inner cracks very quickly arrest due to growth into regions of compressive hoop stress, again clearly visible in d shows how the outer radial cracks coalesce with the inner radial cracks. Perhaps this is the most interesting feature of the work as it shows that radial cracks do not grow from the inner surface and then branch, as might be inferred by studying their final state from PIE alone, but in fact grow as independent inner and outer cracks which coalesce presumably because the stress fields interact and draw them together. The reason they appear branched was a consequence of the fact there were always more outer cracks than inner ones to join up with. shows the distributions of cracks compared to the experimentally measured crack distribution from PIE, for 15 W g−1 peak power. Line plots were added for the predicted distributions found during maximum likelihood estimation. The parameters for which are given in shows a mean inner surface crack count of around 8 for both distributions and an outer surface crack count of 10-11 (PIE) and 11 (model). Inner crack count has an almost identical predicted crack distribution while the outer cracking simulation data was similar but with small differences. The peridynamics models predict a slightly wider spread of outer crack number. Outer crack count is considered a very important parameter when studying pellet-cladding interactions that cause stress concentrations ). The 20 W g−1 entry shows the only discrepancy between the model and PIE for the outer crack count.A detailed statistical analysis was carried out for the 15 W g−1 peak power rating. For this power the maximum likelihood method was used to fit Weibull distributions to both model results and PIE data. The fitted inner crack distributions were found to have a mean and variance that differ by less than 6 and 7% respectively. Whilst the shape parameters differ by 4.6% and the scale parameters differ by 6.2%. For the outer crack distributions the mean and variance of the distribution differ by 1.3% and 44% respectively. The outer distribution fits give shape parameters that differ by 28% and scale parameters that differ by only 0.7%. From these comparisons we can see excellent agreement for inner crack count with only some differences for the outer crack count. shows the peridynamics model distribution has its peak at the same position as the experimental data, however, it has a narrower distribution, which impacts the fit of the shape function. The fact that the means are very similar but the variance of the fits differs is plausibly due to the resolution of the model mesh, which may not capture all the small peripheral cracks on the pellet edges. However, the model results still serve as a lower bound for cracking at different power ratings.Despite the differences in the Weibull distribution shape parameter the crack surface statistics, for 15 W g−1 maximum power, show a P-value of 0.05%, for inner cracks, and a P-value of 0.47% for outer cracks. These P-values show that both the experimental and peridynamic model show a very strong statistical correlation. The P-values give some confidence that modelling of fuel for early life, through peridynamics, is appropriate and reasonably accurate noting the fact the mesh resolution may need increasing to better represent the variance in outer crack distributions.There are experimental data available from PIE studies of crack distributions, however this data does not provide a complete picture of how the fuel has fractured. It is known that the fuel cracks normal to the pin axis at mid-height From analysis of the peridynamics fracture simulation all pellets fracture in a similar manner. Whilst the number of radial cracks changed the order of damage evolved was the same. Mid-height (pin normal) cracks initiated earlier than radial cracks. The time evolution of the crack fronts for both axial and radial cracks are shown in (actual simulation). Both radial and pin normal mid-height cracks stop growing at roughly the same time, in the simulation, despite the earlier initiation of mid-height cracks. This is because normal cracking was quickly suppressed between 15 and 45% full power by the compressive stress region within the pellet centre, which was later relaxed by the radial crack growth from the outer surfaces. This radial crack growth starts at about 30% power. The axial pellet halving happens very much like previous delamination peridynamics studies Looking to the future of fuel performance modelling, this work has shown the ability to produce accurate predictions in crack density, which can feed into other models of pellet expansion and relocation, which previously depended on PIE data. Although computationally expensive it was capable of reproducing findings from PIE of early fuel life. The notable limitations for whole life fuel fracture modelling are the absence of crack healing and plastic behaviour (inclusive of irradiation; thermal creep; fuel swelling and densification) of the pellet and variation in fracture stress with changing fuel material microstructure. It is notable that we chose to use a single value for the fracture strain and this gives a good representation of the PIE data but a more accurate description could incorporate a distribution of fracture strains. This addition might also lead to the broader crack number distributions observed in PIE compared to simulated fracture patterns. Additionally, the simplification of neglecting cross crack heat conduction is acceptable when radial cracking dominates, however later in life the fuel circumferential cracking will impact the thermal profile further modifying cracking behaviour. Ideally all these extra factors should be included in future models, however, it is noted that despite the presence of some of these missing features in the current work, on low-burn-up fuel (7000 MW d tU−1), the results were surprisingly good. This work, while initially targeted at studying stress concentration sources on AGR cladding would be useful in a light water reactor (LWR) fuel context. In LWR fuel a cracked pellet may also cause increased local clad strains and a pellet fracture model, such as the one presented here, may offer insights into pellet relocation and pellet-cladding interactions. Both of these features are thus far hard to model but have a big impact on fuel performance and lead to operational fuel restrictions in LWRs and in some cases fuel failures.With respect to pellet fracture studies there is a great deal of similarity between the results found with the peridynamics simulations and those found from an analysis of low burn-up irradiated fuel.The peridynamics predictions of crack counts were good for what appears to be the domain where the damaged volume was far less than un-damaged volume. The predictions of outer crack count were better for the 10 W g−1 than the 20 W g−1 power ratings because of this effect. The inner crack counts were more similar.The models make very reasonable estimates of crack distributions and morphologies given that the models are not parameterised by the PIE data; the only experimental data used was the single fracture strain value of UO2.All the results correlate well with peak power rating and this is something that needs to be tested as the fuel burn-up increases and operational history becomes more important.Mid-height pin normal cracks were found to form and initiated before radial pellet cracks. The normal cracks were arrested on the inner surface by the strong compressive stresses there.Radial pellet cracks nucleate first on the inner surface, quickly arrest, due to the compressive hoop stress, whilst outer surface cracks nucleate independently and grow. Eventually the inner and outer radial cracks coalesce in a manner that resembles the growth of a single branched crack.Shear performance of strengthened timber beam with intermittent GFRP stripsIn this study, the timber beam was strengthened at the shear span with intermitted glass fiber reinforcement polymer (GFRP). The effect of different numbers of GFRP strips, different orientation angles of GFRP strips to the principal axis of the beam, and different warping schemes of GFRP strips on the performance of the timber beam under flexural load was investigated. The experimental shear capacity was validated using an analytical analysis. In the results, the optimum number of GFRP strips was five. The inclined stripping and fully wrapping scheme were achieved higher strengths than vertical stripping and partial schemes, respectively.Repair and rehabilitation of existing structures using fiber-reinforced polymers (FRP) have become one of the major growth areas in the construction industry. FRP sheets and plates are widely used in the strengthening of concrete and timber structures. The use of FRP bolted plated and adhesive bonding plates are also among the repair and rehabilitation methods []. FRP bolted plated approach experienced flexural and splitting failures, buckling of the plate, and fracture of bolt shear connector due to extreme slippage. Meanwhile, adhesive bonding plates faced peeling in axial, shear, and flexural, and when exposed to the environment, they experienced durability problems []. Externally bonded FRP is an appealing technique among the different strengthening and regeneration methods because of its ease and pace of installation, high reliability, and chemical and corrosion resistance []. In this method, the adhesive is used to bond the FRP plates or sheets externally to the shear or tension zone of the elements. It has been proven that using the externally bonded FRP strengthening method increases the performance of reinforced concrete (RC) beams in terms of shear and flexural []. In a research was aimed at strengthening the defected timber beams of the buildings in service such as historical buildings, Rescalvo et al. [] found experimentally that the bending capacity and stiffness of the broken timber beams can be recovered and improved by the use of pultruded laminate strips attached on the tension side of the element, CFRP fabrics U-shape wrapping the timber element ether continuous or discontinuously, or the combined use of both reinforcement solutions. The performance of the shear strengthening by FRP materials depends on the factors related to FRP properties (FRP types), FRP geometry, bond behavior between the element surface and FRP, the applied wrapping schemes, and the anchorage system. Belarbi and Acun [] found that the FRP type significantly affects the shear capacity of the strengthened RC beam. Meanwhile, the fiber orientation has no changes in the shear capacity of the strengthened RC beams [] found that fibers placed perpendicular to the existing cracks show an increase in strength and stiffness. Hoult and Lees [] found that the spacing between FRP strips displayed a markable effect on the level of strain in the strips which in turn affects the load sharing between the materials. Juvandes and Barbosa [] investigated the interfacial bond behavior between the plates and timber substrate. The results show that the highest bond strength was achieved by the smallest bonding length.The bond behavior between FRP and concrete for strengthened RC beams is well understood over the last decades. However, few studies [] have been undertaken to investigate the bond behavior of reinforced timber beams.Glued laminated timber beam (glulam) has been used for over a century as an engineered wood product in the construction and building industry []. Yellow Meranti is one of the major species available and widely distributed in Malaysia for the construction industry due to its availability and low cost. However, the cellular structure of glulam hardwood species such as Yellow Meranti is more complex where they tend to have short fiber length with very large vessels (pores). Whilst softwood relatively has a longer fiber length and presents a uniform appearance of which free from large pores. The smaller hardwood fiber in terms of fiber length and fiber diameter which was one-third on average from the size of softwood fiber would result in less load carrying capacity and consequently have lower shear strength and stiffness []. Therefore, strengthening of solid timber beam from hardwood species is seen as crucial to enhance the performance of the timber for structural usage. The failure of timber structural structures is due to insufficient configuration []. The loss of flexural stiffness “due to substantial cracking at the middle of the beam” is the most common mode of degradation for timbers. The flexural stiffness is strongly related to the shear performance of the timber beam when the aspect ratio (length to height) is relatively low. Therefore, the loss of stiffness in the timber beams is associated with a loss of shear performance as the timber degrades []. Therefore, the method of repairing and strengthening should be applied for the purpose to enhance the shear strength and load capacity of timber structures. However, shear strengthening of the timber structural member is not popular as compared with flexural and axial strengthening. In addition, most of the previous research strengthened timber beams with FRP by the fully wrapped method at the shear zone while the intermittent FRP strips have not yet been used for strengthening the tropical solid timber beams. Therefore, this study investigated the shear strengthening of tropical solid “Yellow Meranti” timber beams using intermittent GFRP strips externally bonded at the shear zone. The shear zone of the timber beam tested “under four-point loading system” was strengthened with glass fiber reinforced polymer (GFRP) with different numbers of strips, orientation angles, and warping schemes. Hence, a series of experimental tests were conducted on the timber beams to investigate the effect of each of these parameters on the failure mode, load carrying capacity, and shear capacity. The paper ends by highlighting the main findings from the current study.The physical primary test of moisture content (MC) was conducted for the Yellow Meranti timber prior to the and mechanical testing to ensure that it is in dry condition (MC ≤ 19 %) to comply with MS 544: Part 2: 2001 []. The MC was determined using 50 mm × 50 mm × 50 mm cube samples as recommended in ASTM D143 – 09 [], while the test procedures were conducted according to BS 5268–2:2002 [Moisture content was determined purposely at four circumstances which are before drying, after drying, after mechanical testing of specimens, and after four-point bending test of the beam. A commercial oven of 3 m long, 1 m width, and 1.5 m height, was used to dry Yellow Meranti timber beams that had a moisture content of>19 %. After the drying process, the moisture content of all timber beams was determined using a moisture meter to ensure desired moisture content was achieved. The average MC of 10 dried timber beam specimens selected randomly shows the consistency of MC ranging between 16.8 % and 19.1 %, with an average of 18 % and a standard deviation of 0.7 %. The timber beams were placed by stack at room temperature and humidity in a laboratory environment for stabilization of moisture content in the timber.The specimens used for the tests of the mechanical properties were cut from the Yellow Meranti dried timber. Shear block test parallel to grain was carried out in accordance with ASTM D143 – 09 []. A total of 20 specimens of 50 mm wide × 50 mm long × 63 mm high as shown in were used in the test. The small rectangular section of 13 mm high × 20 mm wide was cut out from each sample to produce shear failure during the test. Compression load was applied constantly at a rate of 0.6 mm/min using a Universal Testing Machine (UTM) until the failure of the test specimens.The tensile parallel to the grain test was carried out in accordance with BS 373:1957 []. A total of 20 specimens of 300 mm long with a cross-sectional area of 20 mm × 6 mm at the end section and 6 mm × 6 mm at the middle section were prepared and tested under tensile load as shown in . The smaller cross-sectional area at the middle section as compared with the end section was to induce tensile failure during the test. The tensile load was applied constantly at a rate of 0.6 mm/min until the failure of the test specimens using a 2.5 t Universal Testing Machine (UTM) – INSTRON 5567. The results of the ultimate tensile strength, ultimate tensile strain, and Modulus of Elasticity were recorded and analyzed.In the compression test parallel to the grain, a total of 20 specimens of 200 mm long × 50 mm wide × 50 mm height were prepared following the requirements in BS 373:1957 [The mechanical properties results of Yellow Meranti timber are summarized in . These values are utilized later in the analytical stage of this paper.Tensile test parallels to the fiber direction, and shear test parallel and perpendicular to the fiber direction were conducted for the GFRP. GFRP was fabricated from fabrics and epoxy resin by hand lay-up method. The compression molding method was used in the fabrication process by applying approximate pressure of 900 psi following BS ISO/DIS.10406–2 procedures []. In the fabrication process, the surface of the mold with a dimension of 360 mm × 360 mm was sprayed with release film for the ease of GFRP de-molding. Then, epoxy from Sikadur-330 (refer to ) was poured throughout the mold’s base followed by laying a single sheet of fiber. The fibers were pressed by a scrapper along the fiber direction. The other two layers were finally laid up over the first layer with the same process. The mold was covered using heavy steel plates and hydraulic pressure was applied until approximately 900 psi. After 24 h, the fabricated GFRP composite was de-molded and left to cure in the laboratory environment for 7 days. Before testing, the specimen was cut into the desired dimensions. A total of 6 shear specimens were cut in dimensions and geometry as shown in a. The modified Arcan fixture test rig designed by Hassan [] and originally introduced by Arcan et al. [] was used to conduct the shear test. The GFRP specimens were tested in both fiber orientations of 0 and 90 related to the loading axis, respectively. b shows the schematic diagram of the modified Arcan test fixture and the actual shear test setup is shown in c. The test was conducted using a 2.5 t Universal Testing Machine (UTM) – INSTRON 5567 with a loading rate of 2 mm/min until failure.The tensile test parallel to the fiber direction was conducted following ISO/DIS 10406–2: 2007 []. The specimens were cut in a dimension of 200 mm long × 12.5 mm wide. Aluminum plates were attached at both ends of the specimens using Sikadur-30 adhesive (refer to ) for anchoring purposes during the test. The specimens were then left in the laboratory environment for 7 days for curing before testing was carried out. Extensometer was attached to the specimens along the gauge length to measure the change in length due to the applied loading. The testing was performed with a loading rate of 2 mm/min until failure. The GFRP specimens and tensile test setup are shown in The mechanical properties results of GFRP laminate are listed in and utilized in the analytical stage of this study.A total of 30 untreated Yellow Meranti timber beams were tested under a monotonic four-point bending load setup as per ASTM D198 []. In total, 3 un-strengthened timber beams (control), and 27 strengthened timber beams were tested. For the strengthened timber beams, GFRP laminates were applied in the shear span for strengthening purposes. All timber beams dimension was made consistent at 100 mm wide × 200 mm high × 1500 mm long. In addition, the timber beams were designed to fail in shear and not in bending. To generate shear failure, the ratio of a/d should be<5 as per ASTM D198 [], where a is known as half-shear span stated by the distance between the support and the applied load, while d is the effective depth of the beam. For expecting shear failure to be in Mode II under the four-point loading setup (shear compression or shear tension failure), the ratio of a/d should be between 1.0 and 2.8 []. Therefore, the ratio of a/d in this study was taken as 1.40, which gives an equivalent, a = 280 mm.From the total of 27 strengthened timber beams specimens, they were configured with 10 different strengthening techniques. The configurations were categorized in terms of 3 main parameters, which are the coverage area (number of strips), the orientation angle of the strips, and the scheme of strips. shows the details of the shear strengthening technique configurations of the timber beams. The coverage area of the shear zone is represented by the numbers of GFRP vertical strips, which started from 2 strips and gradually increased to 7 strips, adhered at both sides of the timber beam (front and back faces). It is worth noting that adding>7strip is not applicable because the spacing between the strips became narrower. For the orientation of the angle parameter, the GFRP strips adhered on the timber surfaces at 90 and 45 to the principal axis of the beam. Finally, for the wrapping schemes, the timber beams were wrapped around the beam’s cross-section by side bonded (SB), U-jacket (UJ), and fully wrapped (FW) techniques. shows the designation of timber beams for different configurations. Three samples for the control beam and three samples for each different strengthening technique were considered to determine the average results of each beam configuration. According to the previous researches on shear and bending strength, average results of less than four samples were adopted for each reinforced sample [The unidirectional GFRP fabric was cut into the desired size and bonded to the timber beams with the Sikadur-330 epoxy-based using a wet laid-up process. Before the bonding process, the respective bonding areas on the timber beams were cleaned and marked, and the areas between the GFRP strips were covered with cloth tape in order to have a cleaner appearance for easier crack detection during the test. In the bonding method, the first layer of the epoxy-based adhesive was first applied to the timber beams. Then, the GFRP strips were attached layer by layer onto the timber surface using a putty knife to remove air bubbles. Then, the cloth tape was immediately removed after finishing the laid-up process. Finally, the timber beams were left for 7 days in laboratory condition for curing. A total of 4 strain gauges (BFLA-5-3L, Tokyo Measuring Instruments Lab Co., ltd., Tokyo, Japan) were installed at the mid-span length of each of the timber beams at the front side, top surface, and bottom surface. Furthermore, 2 more strain gauges were also installed on the surface of one of the GFRP strips at the left and right sides of each timber beam. The strain gauges were positioned in the direction of the fibers.A four-point bending load test with a clear span of 1175 mm and a shear span of 280 mm was conducted for the timber beams. The beam was centrally positioned on the steel test frame. Steel lateral bracing was used at both ends and at the front and back of the timber beam to prevent any of the horizontal movements during the test (see ). Steel bearing plates and rubber pads “between the timber beam and the steel bearing plate” were placed at both supports and the loading points to minimize the stress concentration. Three Linear Variable Displacement Transducers (LVDTs) were positioned at mid-span length of the timber beam specimen, and under the loading points to measure the vertical displacement during the test. Loading was applied constantly with a loading rate of 2 kN/min until failure using an Electro-Hydraulic jack with a 30 t load cell.The load-carrying capacity is the first term for evaluating the effectiveness of shear strengthening of the timber beams. Therefore, the load-carrying capacity was calculated from the corresponding load when there was a major failure during the test. Therefore, the maximum horizontal shear stress, τ in the timber beam is determined using the following Eq. where V is the maximum shear load, and A is cross-sectional area of the timber beam.The analysis was based on a wood-equivalent approach initially proposed by Triantafillou [] and later employed by Morales-Conde et al. []. In this study, the proposed equation was modified by introducing a coefficient related to the current parametric study. The timber beam strengthened at the shear zone was converted into an equivalent cross-section as demonstrated in c where hw and bw are the height and width of the timber beam, respectively, while hc and bc are the height and width of the GFRP section, respectively.The maximum shear stress which occurred at the middle of the section was given by Collignon expression in Eq. where Fmax is the maximum shear load, Qt,max is the maximum static moment of area, bt is the section width, and It is the moment of inertia.These parameters were then related to the different converted wrapping schemes as shown in are valid for the UJ wrapping scheme when the third part of these equations is divided by 2, while for the SB scheme the third part of these equations should be equal to zero.The modular ratio, η of the strengthened timber beam is determined using Eq. where CMOE is the modification factor of stiffness.Sincehw = hc=h where the cross-section is assumed as a rectangular section, the Eq. can be simplified and written as in Eq. where α is the angle between the longitudinal axis of the timber beam and the principal GFRP orientation.To compute the predicted shear load, Fth,max the strengthened area ratio (Af/Ashear) was combined with the composite area fraction, ρc, together with the estimated shear strength, τth. The composite area fraction, ρc, is defined as follows: and by introducing the ratio (Af/Ashear), the maximum shear stress can be written as in Eq. τth=Fth,maxQt,maxbtIt1+ηhchwρc(Af/Ashear)1+ηhwhcρc(Af/Ashear)1+ηhwhc2ρc(Af/Ashear)The timber beam will fail in shear when the overall shear strength, τth is equal to the horizontal shear strength, τd of the timber material.Then, the normalized estimated shear failure load, Fth,max of the strengthened beam cross-section is determined using Eq. Fth,max=2bthτd31+ηhwhcρc(Af/Ashear)1+ηhwhc2ρc(Af/Ashear)1+ηhchwρc(Af/Ashear)where e is defined as the ratio of shear capacity of the strengthened section to shear capacity of the un-strengthened section. It represents the efficiency of the GFRP strengthening system for the timber beam.The strengthened area ratio of (Af/Ashear) is introduced in the current research to predict the shear capacity of the strengthened timber beam in shear.For beam strengthened with different number of GFRP strips, the estimated shear capacity was calculated by changing the ratio of the strengthened area Af/Ashear. For beam strengthened with different GFRP stripping angles, the angle, α was changed either with 45 or 90. For beam strengthened with different GFRP wrapping patterns, the section width, bt, the moment of inertia, It and static moment of area, Qt,max were calculated using Eq. , according to their corresponding wrapping schemes to suit the cross-section of the beam. Eq. is valid based on the assumption that the shear failure initiates the failure mechanism on the strengthened timber beam. The ratio of maximum shear stress in the GFRP to the timber beam is equal to η, which indicates that if the shear strength of GFRP, τfrp is less than ητd, then the shear capacity of the cross-section is always controlled by the shear strength of un-strengthened timber (control). If such is the case, the normalized shear capacity of Eq. is simply equal to 2/3. The predicted shear stress of strengthened timber beam, τth was then compared with the experimental shear stress, τd.The failure mode of the un-strengthened beam (control) is shown in . The horizontal crack was following the grain of the timber resulted in slipping of the upper portion of the beam as shown from the side view in b. From close observation, a loud sound was heard when the applied load reached 147.5 kN due to the vertical crack that occurred at the shear zone of the control beam. This confirmed the design of the timber beam should fail in shear under the four-point bending load. Therefore, the timber beam was strengthened in this shear zone to increase the shear resistance. shows the failure mode experienced by the timber beams strengthened with GRFP strips. Generally, strengthening with different numbers of GFRP strips, failure mode was observed with 3 different categories which are compression failure, tensile fracture, and horizontal shear failure. Beam GF-2–90-SB failed where the crack initiated from the bottom section of the beam at both point loads and propagated towards the mid-span region. Then, total failure occurred due to the spreading of horizontal crack from the mid-span region to the end section following the timber grain along the neutral axis of the beam. This kind of failure is categorized as tensile fracture owing to bending because the shear crack was not observed at the shear zone. Meanwhile, beam GF-3–90-SB and GF-4–90-SB failed where the crack grew rapidly from the mid-span “at the neutral axis” region to the end section of the beam, which is categorized as a tensile fracture. The crack propagation caused the shifting and tearing of GFRP sheets. The GFRP sheets failed with fiber-tear failure. At the region of high bearing stress, little softening of the GFRP interface and timber occurred as demonstrated by Miller [Although prevention had been taken to reduce the bearing stress effect, crushing failure occurred near the location of the point load for beam GF-4–90-SB, GF-5–90-SB, and GF-6–90-SB. In contrast, bearing failure mode due to shear and tensile force resistance action is considered as a strong mode of failure as mentioned by Gómez and Svecova []. The combination of tensile and compression failure occurred to beam GF-5–90-SB, while beam GF-6–90-SB and GF-7–90-SB exhibited compression failure, which started from the top section before propagating to the bottom section of the beam. This failure was identified as shattering and cross-grain failure because of the high bending force at the mid-span region.The control timber beam (CB) failed under the shear failure of which implies the expected shear weakness of the beams. The purpose of strengthening the timber beam was to increase the shear capacity and to identify the changes of failure mode. From the failure mode of the strengthened timber beams shown in , it was noticeable that the mode of failure changed from horizontal shear failure to tensile fracture failure at the mid-span region together with compression failure at the points of loading. As the failure at the mid-span was still in tensile mode, therefore, strengthening using 2 to 4 GFRP strips can still ensure that the timber beam was within the under-reinforced section. However, when 5 GFRP strips were attached to the timber beams, a balanced reinforced section was considered as it had changed the failure mode. Even though the tensile failure was considered crucial, the changes to the failure mode make the strengthening at the shear zone is more consecutive. The shear zone was free from cracking at the start of the test, confirming that the failure was correlated with the bending force. In addition, no debonding was noticed for all GFRP strips which implies ideal bonding with the timber beams, while the tearing of fiber was only observed at the sliding region. Thus, it was proved in the current study that the strengthening at the shear zone was successful.On the other hand, the timber beams strengthened with a 45 angle of GFRP strips (GF-5–45-SB) failed at 268.6 kN. It was observed that the failure was due to the combined compression near the point load and tensile at the bottom mid-span section of the beam. The GFRP strips also prevented the tensile crack to initiate and propagate at the mid-span section of the beam.Overall, timber beams strengthened with 90 and 45angle of GFRP strips failed first in a tensile fracture before shifting to shear failure. This further proved that the strengthening techniques were successful where none of the timber beams failed first in shear. In addition, it was generally found that the timber beams strengthened with 45 angle GFRP strips failed due to the crushing at the location of the applied load.For timber beams strengthened by different wrapping schemes, the horizontal crack started from the left end section and propagate to the mid-span region for beam GF-5–90-UJ. This causes the beam to slip at the left end section causing the GFRP sheets to rupture before total failure was observed. Then, several debonding of the GFRP strips were noticed at total failure as the fiber followed the splitting pattern of the timber beam. The failure of beam GF-5–90-FW started with the development of horizontal crack at the mid-span region and propagated to the end section causing breaking failure of the beam. This indicates that the mode of failure can be changed from shear failure to tensile fracture failure by the different wrapping schemes. The debonding failure of GFRP strips was absent for all timber beams strengthened by the fully wrapped technique. The fully wrapped technique significantly increased the capacity of the timber beam due to the increased effective bond length at the top section. shows the comparison of the load–deflection curves between the control beam and other strengthening configurations. In the figure, it was sufficient to represent one sample from each configuration due to the consistency of the results of each configuration’s samples. a shows the comparison of the load–deflection curve between the control beam (CB) and the timber beams with various GFRP strengthening techniques. Generally, linear-elastic behavior up to a certain load was observed for all strengthened timber beams with all various numbers of GFRP strips. Then, elastoplastic behavior was observed and slightly changed to elastic behavior at the end of the test before the failure of the beams. The ultimate loading capacity was reached when a major crack occurred, followed by a large deflection with no increase in the applied load. This was also considered as a rupture at the end of the test. Based on the relationships in , the average maximum deflection for all the beams was about 28 mm. The control beam (CB) achieved an ultimate load of 147.5 kN, followed by the beam strengthened with 2 GFRP strips at 175 kN. The curves of the timber beam strengthened with 3 and 4 GFRP strips almost have the same pattern and achieved an average ultimate load of 185kN. Likewise, the curves of the timber beam strengthened with 6 and 7 GFRP strips almost behave similarly with an average ultimate load of 185 kN and 195 kN, respectively. The relationship shows that the beam strengthened with 5 GFRP strips achieved an average ultimate load of 200 kN.b shows the comparison of the load–deflection curves between the control beam (CB) and the timber beam strengthened with 45 and 90 angle GFRP strips. From the relationships, strengthening with a 45° angle GFRP strips shows linearly elastic behavior up to the proportional limit, then changes to semi-plastic as the applied load increased gradually until failure occurred. Timber beams strengthened with 45° angle GFRP strips had less stiffness than those with 90° angle although they achieved higher loading capacity after the incidence of the crack at the mid-span region of the beam. This is demonstrated that after cracking occurred, the 45° angle GFRP strips kept the beam at higher deformation by the connection of the fiber. However, the attached 90° angle GFRP strips onto the timber beams provided higher stiffness. This is because the shear failure of the timber beam is parallel to the grain (in the horizontal direction) due to its orthotropic properties as explained above in section 4.1. Thus, to prevent shear failure in timber beams, GFRP should be placed vertically because the results indicate that the shear strength of GFRP perpendicular to the grain is higher compared to the shear strength of GFRP parallel to the grain. If the GFRP is placed diagonally, it does not produce higher shear strength.c shows that the timber beams strengthened by the UJ and FW wrapping schemes behave similarly to one strengthened using the SB wrapping scheme. The relationship shows bilinear elastic behavior of the UJ and FW wrapping schemes with an increment in the ultimate loading capacity of up to 10 % as compared with the SB.a shows the relationship of the strengthened area ratio with the average shear strength of strengthened timber beams by GFRP strips. The number of GFRP strips were represented with a strengthened area ratio of (Af/Ashear). This was computed by dividing the area of the GFRP adhered to the timber beam surface by the area of the shear zone. Hence, the number of 2, 3, 4, 5, 6, and 7 GFRP strips is equivalent to (Af/Ashear) of 0.18, 0.27, 0.36, 0.45, 0.54 and 0.63, respectively.Based on the graph, there is an obvious tendency for an increase in the shear capacity due to the increase of strengthened area ratios from 0.00 to 0.45. However, there is no significant increment in the shear capacity for the strengthened area ratio from 0.45 to 0.63. Therefore, the current study suggested that GFRP with 5 strips is the optimum arrangement.As an advantage, the intermittent style of reinforcing had been exhibited to reduce the cost of material and at the same time having the same strength as the continuous one. The average shear strength of all timber beams strengthened with GFRP strips ranged between 6.78 N/mm2 and 7.94 N/mm2 with the percentage increment of between 11.0 % and 29.9 % as compared with the control beam (CB). The highest percentage difference of 29.9 % over the control beam (CB) was the timber beams with a GFRP of 0.45 strengthened area ratio.For practical purposes based on the number of GFRP strips of the strengthened timber beam as compared with the control beam (CB), the average shear strength is correlated to the modification factor,β, in accordance with the changes to the number of GFRP strips at the shear zone. The modification factor, β, can be determined by dividing the average shear strength of each number of GFRP strips by the average shear strength of the control beam (CB). Then, this modification factor is plotted in b for various strengthened area ratio of (Af/Ashear). Their relationship can be expressed mathematically in Eq. β=8.7428x4-12.671x3+5.2299x2-0.0181x+1.0if0≤x≤0.45where × represents the strengthened area ratio of (Af/Ashear).Therefore, a relation for the permissible shear grade strength from MS 544: Part 2: 2001 [where τadm is the permissible shear grade strength, τv is the shear strength parallel to the grain = 0.97 N/mm2, and K1,K2, and K4 are the modification factors taken as 1.0, and K8 is the modification factor equal to 1.1.On the other hand, timber beams strengthened with 90° and 45° angle GFRP strips achieved 29.9 % and 35 % higher average shear strength than the control beam (CB), respectively.The results from this study have good agreement with the findings by Sim et al. []. The reinforcement adhered inclined to the timber grain was preferable over the perpendicular because it improves the stiffness of the beam [The comparison between the experimental test and analytical prediction shows a good agreement as summarized in . The analytical predictions on the shear capacity of timber beams strengthened with the various number of GFRP strips were 0.8 % to 14.5 % lower than those from the experimental results.For the timber beams strengthened with 90° and 45° angle GFRP strips, the experimental results on the shear capacity of beam GF-5–45-SB were higher than beam GF-5–90-SB. In contrast with other parameters considered in this study, the predicted shear capacity was slightly overestimated for beam GF-5–45-SB as compared with beam GF-5–90-SB. The percentage difference between the experimental and analytical prediction was 14.5 % and 19.5 % for beam GF-5–90-SB and beam GF-5–45-SB, respectively, where they were also consistent with the findings by Naghipour et al. [Finally, the predicted and experimental shear capacity has almost the same pattern for all wrapping scheme techniques. Beam GF-5–90-FW achieved the highest shear capacity, while the lowest was accomplished by beam GF-5–90-SB. The percentage difference between the experimental results and analytical prediction is in the range of 9.3 % and 14.5 %.Therefore, the proposed equation can be used to predict the shear capacity of timber beams strengthened with GFRP with various arrangements and techniques as applied in the current study.This section discussed the determination of bending and shear stiffnesses for strengthened and un-strengthened timber beams (control) under flexural load. It is expected that the stiffness will increase by strengthening the timber beam using GFRP. shows the load–deflection relationship for beam GF-5–90-SB which was selected as an example to explain how to obtain the bending stiffness.From the relationship, the strengthened timber beam performed as bilinear elastic until the total failure. The initial stiffness of up to the load of 60 kN was considered for the determination of bending stiffness using Eq. where, F = P/2, L is the total span taken as 1175 mm, a is the shear span taken as 280 mm, E is the Modulus of Elasticity, Δ is the maximum deflection at mid-span, and I is the moment of inertia taken as 6.66×105 mm4.The shear stiffness, GAs of the timber beam is computed using Eq. where A is the cross-sectional area of the beam, and G is the Shear Modulus which can be determined using the following Equation:where E is the Modulus of Elasticity, and ν is the Poisson's ratio.Timber is classified as anisotropic material i.e., orthotropic but transversely isotropic. The Poisson's ratio parallel to the grain direction, -xy plane of the Yellow Meranti timber, νxy is 0.33 as confirmed by Ahmad [ shows the results of bending and shear stiffnesses of the un-strengthened timber beam (control)and those strengthened with the different numbers of GFRP strips. Generally, the strengthened timber beams achieved 26.61 % to 56.12 % higher stiffness than the un-strengthened beam (control). The strengthened timber beam with 5 GFRP strips achieved the highest shear and bending stiffnesses. This confirmed that timber beam strengthened with GFRP had enhanced the stiffness, where the same finding was also stated by Ahmad [For a better interpretation of stiffness for timber beams strengthened with the different number of GFRP strips, represents a polynomial regression of the modification factor,α, with the strengthened area ratio of (Af/Ashear). shows that the stiffness increases but is not linearly related to the ratio of (Af/Ashear). Furthermore, the stiffness decreases after the ratio of (Af/Ashear) is>0.45. Therefore, the modification factor, α , based on the stiffness strips is determined and expressed as follows:α=-5.4798x3+3.4631x2+0.6321x+1.0118for(Af/Ashear)≤0.45where × represents the strengthened area ratio of (Af/Ashear) at the shear zone. Therefore, this factor should be considered for the design of timber beam and strengthened at the shear zone using GFRP sheets to the Modulus of Elasticity of the timber material given in MS 544: Part 2: 2001 [, both bending and shear stiffnesses accomplished 37.90 % and 56.12 % higher than the control beam (CB) for timber beams strengthened with 45° and 90° angle GFRP strips, respectively. This shows that strengthening the timber beam transversely to the fiber orientation of the GFRP was able to optimally increases the initial stiffness by 19 % than the one strengthened diagonally. Remarkably, the result was somehow contradicted with the load-carrying capacity where the highest was from the timber beam strengthened with 45° angle GFRP strips as discussed previously in . Overall, strengthening the timber beams using GFRP strips at an angle of either 45° or 90°does improve the bending and shear stiffnesses. As compared to the inclined one, the transversely strengthening technique of the timber beam had higher initial stiffness, but not the overall efficiency.The strengthened timber beams with different GFRP wrapping schemes achieved a higher stiffness over the control beam (CB) as shown in . Timber beams strengthened with a fully wrapped scheme (FW) gained the highest stiffness (shear stiffness of 40,801 kN/m2 and bending stiffness of 6512 kN/mm2), followed by the U-jacket wrapping scheme (UJ) (shear stiffness of 39,454 kN/m2 and bending stiffness of 6297 kN/mm2). Meanwhile, timber beam strengthened achieved the lowest stiffness (shear stiffness of 39,307 kN/m2 and bending stiffness of 6273 kN/mm2). Besides, the types of wrapping schemes play a crucial role as the stiffness of timber beams with the FW scheme is 5 % higher than that of the UJ scheme, although the latter offered ease of installation. This indicates that overlapping of GFRP sheets for strengthening of timber beams positively affected the strength and stiffness.The strain distribution across the height of the timber beam for a selected applied load of the control beam (CB) and those strengthened with different numbers of GFRP strips are shown in . The strains were recorded for every load increment until failure was observed. Based on the plot, linear behavior was noticed at the initial stage of the applied load. Then, as the load increases, the compressive zone of the timber beam behaved partially plastic, while the tensile zone still linearly behaved. In general, all compressive strains of the strengthened timber beams displayed some decreases before the total failure, while the tensile strain extremely increases except for beam GF-6–90-SB. The variation in the strains is acceptable due to the nature of the timber itself. Based on the strain profile, as the number of GFRP strips increases, the tensile strain at failure increases until the 5 GFRP strips. Consequently, the tensile strain did not increase by adding>5 GFRP strips, where the timber beam failed in compression. Therefore, it can be assumed as an over-reinforced section.From the strain profile of timber beam strengthened with 45° angle GFRP strips, the strain linearly behaved at the initial stage of the applied load. The top fiber of the timber beam behaved partially plastic once the load reached around 120 kN. Then, once it was close to failure, the neutral axis shifted slightly down around 20 mm, and the strain at the compression zone was significantly reduced before the total failure. From close observation during the test, the strengthened timber beams suffered from tensile crack before numerous slipping across the longitudinal plane of the beam, which validated the decrease of compressive strain prior to the total failure. Besides, few GFRP strips were debonded from the timber beams due to the higher deflection which decreases the stiffness, even though becoming more ductile.From the strain profile for timber beams strengthened with different wrapping schemes, they exhibited linear strain until the applied load reached 160 kN, except for beam GF-5–90-FW, where linear performance reached the applied load of 200 kN. Curiously, by using fully wrapped (FW) schemes for strengthening purposes, the neutral axis was kept at the original location at the center of the beam’s cross-section. The results show that the tensile and compressive strains for timber beams strengthened with U-jacket (UJ) and fully wrapped (FW) schemes were lower than that achieved by the control beam (CB). This confirms that expanding the GFRP strips ahead of the side surfaces increases the stiffness of the timber beam. summarizes the tensile and compressive strains at failure for all tested timber beams. It was assumed that the timber beam failed if the tensile strain and compressive strain exceeded 0.3 % and 0.2 %, respectively.It was also observed that the strain of the GFRP at the failure of beam GF-5–45-SB was higher than the timber strain of that particular beam. This demonstrates that the load was carried instantly by the GFRP after the timber attained its ultimate strain. In addition, the strain of GFRP at the failure of beam GF-5–45-SB was higher than that of beam GF-5–90-SB, which demonstrated a better load transfer and at the same time showing an effective strengthening technique.To meet the fundamental design requirements, structural members must be designed with proper ductility characteristics. It was estimated that the capacity of the timber beams in this study was improved by strengthening them using GFRP strips so that it offers significant ductility prior to failure.Beam GF-5–90-SB was considered as a typical example to discuss the effect of GFRP on its ductility. In this study, two methods were employed to estimate the ductility index. First, the deflection and energy method as suggested by Yusof [] was adopted, and second, using deflection method with means of the yield point, value of elastic limit, and the ultimate point from the load–deflection curve. As an example, for ductility estimation, the maximum elastic load, the ultimate load corresponding to their deflection, and the estimated yield load were defined from the load–deflection curve for beam GF-5–90-SB as shown in , the elastic load of 120.3 kN, yield load of 169.6 kN, and ultimate load of 217 kN have corresponding deflections of 6.24 mm, 9.88 mm, and 25.59 mm, respectively. Based on the deflection method, the ductility index was estimated by dividing the deflection at ultimate load with the deflection at yield load. Meanwhile, based on the energy method, the energy under the curve was first determined from the generated equation of the best fitting curve.The equation of ductility index, μE,based on energy is applicable for the strengthened timber beam with GFRP used by Ahmad et al. [where Wtotis the total energy equal to 4094.83 Nm which is calculated from the area under the curve between Δ = 0 mm and Δ = 25.59 mm. Meanwhile We is equal to 357.62 Nm which is calculated from the area under the curve between Δ = 0 mm and Δ = 6.24 mm.The ductility indexes for timber beams strengthened with GFRP strips are given in . Based on the results, the ductility index based on the energy method was found to be much higher than the deflection method. shows the effect of the ductility index with the number of GFRP strips on the strengthened timber beams. It was observed that the accomplished ductility at the ultimate load of strengthened timber beams increases with an increase in the number of GFRP strips for both methods. Apart from that, strengthened timber beams with a ratio of (Af/Ashear) = 0.45 expected peak ductility index using both methods. It was also found that the ductility index from the energy method was in parallel with those obtained by Ahmad [], while the ones based on the deflection method was in agreement with those obtained by Al-tamimi et al. [On the other hand, higher deflection achieved by timber beam strengthened with 45° angle GFRP strips in which exposed higher ductility than the 90° angle GFRP strips and also the control beam (CB). Meanwhile, the diagonal strengthening to the longitudinal axis of the timber beam achieved a slightly greater ductility index than the vertical strengthening.For the different wrapping scheme methods, the ductility index using both energy and deflection methods suggested that all types of wrapping schemes are more ductile than the control beam (CB). Also, the ductility index increases by increasing the sides of the GFRP wrapping.The main purpose of this study is to improve the shear performance of the Yellow Meranti timber beam by externally strengthening using GFRP strips. The following conclusions had been drawn from the study:All timber beams strengthened with GFRP strips performed linearly elastic up to a certain load level, followed by elastoplastic behavior, and finally changed to nearly elastic before failure.The optimum number of GFRP strips attached at the shear zone on the timber beams was found to be effective with 5 strips with a strengthened area ratio of 0.45, as the ultimate load and shear capacities were significantly increased, and the mode of failure changed from horizontal shear failure to tensile fracture and compression failure.Timber beams strengthened with 45° GFRP strips were accomplished ultimate load and shear capacity of 4 % higher than those strengthened with 90° GFRP strips.The fully wrapping (FW) scheme strengthening method on the timber beam achieved 6 % and 2.6 % higher shear capacity as compared with the SB and UJ schemes, respectively.Timber beam strengthened with GFRP strips improved the shear capacity, stiffness, and ductility of up to 41 %, 62.05 %, and 3.5 %, respectively as compared with control beam (CB).An analytical approach for estimating the shear capacity of strengthened timber beam was successfully developed with only 0.8 % to 19.5 % percentage difference with the experimental results.Mohammed Yahya Mohammed Al-Fasih: Supervision, Writing – review & editing. Nor Izzah Mokhtar: Supervision, Writing – review & editing. Yusof Ahmad: . Izni Syahrizal Bin Ibrahim: Supervision, Writing – review & editing. Shukur Abu Hassan: Supervision, Writing – review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.A finite element program for on-line life assessment of critical plant componentsAn on-line structural safety evaluation system (BOSSES) has been developed over the years at Bhabha Atomic Research Centre (BARC), India, which is capable of assessing the damage due to creep and fatigue in critical plant components. The system acquires plant transients in real time and processes them to evaluate the stress, temperature and damage distribution in the components and provides information through a visual module. The aim of the paper is to briefly describe the details of the damage assessment methodology adopted by BOSSES with some case studies of real life plant components.The issue of remaining life prediction has attracted considerable attention in the power generation industry Several researchers have stressed the need to develop a life prediction methodology to address the various aspects of failure mechanisms. Sakurai et al. describes some typical features of the program. Some case studies of components from heavy water plants and thermal power plants are provided in Sections , respectively. In addition to the on-line deterministic damage assessment module, BOSSES also has a probabilistic module for calculating the on-line probability of failure of components due to various mechanisms such as creep, fatigue and erosion–corrosion, etc., and it is described in Section In recent years considerable progress has been made in research on the behaviour of defect-free structures and structures containing defects at elevated temperature. Developments have been made both in structural analysis techniques and in methods for collecting relevant material data. For the assessment of defects in plant that operates in the creep range under cyclic loadings, creep–fatigue interaction is the failure mechanism. Hence a prediction method for the accumulation of damage due to creep and fatigue throughout their lifetime is important for remaining life assessment of components. The early approaches to high temperature life assessment describe methodologies that were based on defect-free assessment codes, i.e., ASME code case N-47 (Now, it is known as Section-III, Subsection-NH) ASME code case N-47 was the first design code to formally embrace the concept of linear damage summation as a method of predicting material failure at high temperature, consisting of a fatigue (Miner’s cycle summation) component and a creep (Robinson’s creep time summation) component. The French code RCC-MR incorporates many of the concepts of ASME N-47, but with modified stress analysis procedures. The British R5 procedure According to the conventional method, when any component is subjected to cyclic loading under high temperature and pressure environment, failure is assumed to occur when the summation of damage fractions due to fatigue and creep becomes unity. In this method, one calculates separately the damage due to the fatigue and creep and linear damage summation rule is used. Miner’s cycle summation is used to calculate fatigue damage and Robinson time summation is used for creep . Let σ1, |
σ2, … , |
σn, are the maximum applied stress intensities for n1, |
n2, … , |
nn number of cycles. S1, |
S2, … , |
Sn are the corresponding stress amplitudes. Corresponding to these stress amplitudes, N1, |
N2, … , |
Nn are the allowable cycles calculated from the S–N diagram (). The fractional damage due to fatigue is calculated asSimilarly, σm1, |
σm2, … , |
σmn are average values of equivalent stresses applied for hold times t1, |
t2, … , |
tn, respectively. Corresponding to these stresses, T1, |
T2, … , |
Tn are the creep rupture lives calculated from the creep rupture time curve of the material for the given operating temperature (). The fractional damage due to creep is calculated asThe creep rupture life of the material is expressed by the equation: T |
= |
Aσ−v, where A and v are material constants.Here, linear damage summation rule is used. The component will fail ifwhere f |
= 0.3 for carbon and low alloy steels and f |
= 0.5 for austenitic and high alloy steels.Creep–fatigue interaction tends to be a low cycle phenomenon. Once a significant dwell time is included, it takes a long tome to accomplish the 105 plus cycles needed to get into the high cycle regime. Consequently, low cycle fatigue is commonly dominated by crack propagation, with crack initiation taking place early in the life. The flowchart for the assessment of damage by fracture mechanics based method for components with defects is shown in . From the assumption that crack growth governs creep/fatigue damage accumulation, several research workers have developed theories based on tracing the process of a crack, growing by the twin mechanics of creep during dwell periods and by a Paris type law based on fracture mechanics during rapid cycling. This approach assumes that damage is represented by the crack depth a. The cyclic crack growth is then added to the creep crack growth during the dwell period (thold) to calculate the total growth per transient as (a) R5 method: If conditions during the transient are in the linear static range, cyclic crack growth would be calculated using Paris’s law:where ΔKeff is an effective stress intensity range adjusted for crack closureR5 gives the following empirical expressions for q:where R is the ratio of minimum and maximum values of stress intensity factors, i.e., Kmin/Kmax. If the strain ranges falls in elasto-plastic range, ΔKeff then is replaced by ΔJeff (J being Rice’s path independent integral used as a loading parameter in elastic–plastic fracture mechanics).where Eamb and ET are Young’s moduli at ambient temperature and working temperatures, respectively.(a) Use of C∗integral for steady state condition: It is based on the assumption that a cracked body is subjected to a steady loading at elevated temperature and the load has been applied for sufficiently long time for steady state creep to engulf the remaining ligament. The stress and strain rates of the component are related by creep constitutive equation, which is analogous to the relationship between plastic stain and stress in the sub-creep temperature regime. In the analogy, strain is replaced by strain rate and the stress coefficient is replaced by the creep stress coefficient and the plastic strain hardening constant is replaced by creep strain rate hardening constant. The integral C∗ is defined analogous to Rice’s J-integral asC∗=∫ΓW∗dy-Ti∂u˙i∂xdswhereW∗=∫0ε˙ijσijdεij,where Γ is the line contour, W∗ is the strain energy density associated with the point stress and the strain rate ε˙ij. Ti is the traction in i-direction, ∂ui∂x is the gradient of velocity components in x-direction, ds is the incremental length of contour. The C∗ integral can be also explained in terms of energy release rate (per unit time).(b) Use of C(t) integral for transient condition: The crack tip stress fields under small scale creep can be characterized by a time dependant C(t) integral, whose value is determined along a contour taken very close to the crack tip, i.e.,It may be noted that C(t) is the same as C∗, but its value is determined close to crack tip within a region where the creep strain dominates over the elastic strains. C∗ is only valid as a measure of creep crack load once a stationary state has been reached. In the transient phase of stress redistribution leading to the steady state, C(t) is more appropriate criterion. Since C(t) is generally larger than C∗, ignoring the transient phase can underestimate the severity of creep induced crack growth. Transient conditions are usually important under repeated loading conditions, where new high stresses are reestablished at the beginning of each cycle. A criterion to know whether transient conditions need to be considered is to compare the cycle period, tcyc, with the Reidel transition time (c) R5 method: In this method, the reference stress is calculated as, σref |
= |
σyP/PL where is the yield stress of the material, P is the applied load and PL is the limit load at which stress in the net section at the cracked location reaches yield stress. Under different combination of loads and moments, the reference stress can be calculated by finite element modeling of the component or using Handbook solutions where C1 and n1 are the creep strain rate coefficient and hardening exponents, respectively. The C∗ integral can be represented aswhere R′=ΔKeffσref2 and ε˙ref is the reference strain rate evaluated using. The crack growth rate due to creep can be expressed in terms of C∗ integral aswhere D and ϕ are material constants. To know that steady sate creep condition has been achieved, the stress redistribution time tred is evaluated using the equation, tred=K2EC∗, where K is the stress intensity factor and E is Young’s modulus. In case of transient creep condition, the C(t) integral is evaluated using Reidel’s approximation, i.e., and C(t) integral is used in the creep crack growth equation instead of C∗.(d) API-579 method: This method is also based on calculation of reference stress and use of C∗ and C(t) integral. The only difference is that these are to be evaluated using the specified expressions given in the document and the stress intensity factor and reference stresses for different geometries have to be calculated using the appendices of API-579 (e.g. Appendix C for stress intensity factor K, Appendix D for reference stresses and Appendix F for creep and fatigue material properties). The time tred is calculated astred(ai,ci)=0.91[K(ai,ci)]2(nBN+1)·EY·C∗(ai,ci),where ai and ci correspond to crack depth and crack width for a semi-elliptical surface crack, EY is Young’s modulus at mean temperature of the cycle, K is the stress intensity factor and nBN is the Bailey–Norton coefficient evaluated at the reference stress in the current load increment. C∗ and C(t) are evaluated asC∗(ai,ci)=εref˙1-Dbc-Daci[K(ai,ci)]2σrefandC(t)(ai,ci)=C∗(ai,ci)tred(ai,ci)tinBN-3nBN-1+1,where ti is the cycle time, Dbc is the local creep damage before initiation of crack and this is computed using the net section stress considering the pre-crack loading history. Dac is the local creep damage after initiation of crack and this is computed using the reference stress (Appendix D of API-579) considering the post-crack loading history. The creep crack growth rate is computed using the equation dadt=D·[C(t)]μ where D and μ are creep crack growth rate constants for the material.The various modules of the BARC on-line structural safety evaluation system (BOSSES) are explained through a flowchart in . The transient acquisition module collects the plant transients, e.g. pressure, temperature and flow rate, at certain time intervals through a data acquisition system interfaced to a PC. In on-line fatigue–creep monitoring, the conversion of plant transients to the temperature/stress responses in the structure is one of the most important tasks. The technique generally used is Green’s function technique (GFT). This is a method, which transforms the plant transients to temperature/stress responses using a predetermined transfer function. The primary advantage of this method is the less computation time. However, the GFT has a number of limitations. Strictly the GFT cannot be applied to the nonlinear analysis because of the inherent assumptions of linear superposition. The GFT provides information on some predetermined points of the structure. If the number of points is increased, the computation time also increases. Various investigators, e.g. Chen and Kuo To overcome the limitations of GFT and also to utilize the computing power of modern computers, the present system BOSSES employs on-line finite element technique to compute temperature transients and the thermal stresses in the structure due to fluctuation of the process transients. The system can take care of the variations of heat transfer coefficient and can provide whole-field information. The damage evaluation module finds out the fatigue usage factor, creep damage and fatigue–creep interaction effect. Various algorithms are available for cycle counting in an irregular stress history. The most widely used is the rain-flow cycle counting technique. The stress time history is converted to stress frequency spectrum using the rain-flow cycle algorithm as introduced by Socie There are different types of heavy water plants in India depending upon the type of process used. The heavy water plant Tuticorin is based on a mono-thermal process whereas the heavy water plant Kota is based on a bi-thermal process of heavy water production. In the mono-thermal process, the feed gas is taken usually from a fertilizer plant in the form of synthesis gas mixture (73% H2 and 24.4% N2, rest other gases). The gas is passed through a drier and purification column to remove impurities. The cooled gas is then introduced into the exchange column. Subsequently further processing produces heavy water. In this type of plant, the drier unit is subjected to regular thermal cycling.There are usually two drier vessels, which operate in tandem. The flow diagram of gases from and to the two drier vessels along with the sensor signals for BOSSES is shown in . The drier vessel performs four different functions, i.e., service, regeneration, cooling and standby. The operation stage is typically 8 h of duration. The total time for regeneration, cooling and standby is also 8 h. During operation, the temperature of the process gas entering into the vessel is around 0 °C. In the regeneration, it is heated to around 185 °C and it is cooled down again to around −2 °C during cooling operation. The drier is exposed to fatigue damage due to this thermal cycling. As the maximum temperature (i.e., 185 °C) is low, creep effect is not significant. The objective of the on-line monitoring system is to calculate the stress and thermal transients seen by the drier nozzle and then to calculate the fatigue damage over the period of monitoring. This value of fatigue damage can be extrapolated to know the life to which the component can be operated safely. The finite element (FE) models of the top and bottom end of the drier vessel (with nozzles) used for computation of material temperature; stress and damage in BOSSES are shown in . The typical plant transients of various parameters as acquired by the data acquisition system are plotted in BOSSES computes the material temperature, stress and damage due to fatigue at all the Gauss points of the FE models and stores the information for further use by the plant operator. A typical computed information history for a shell-nozzle junction of the bottom end of drier vessel is shown in . Similarly, FE model of some of the components of a bi-thermal process heavy water plant (i.e., heavy water plant Kota) are shown in . The computed stress (von Mises equivalent stress in MPa) and damage (i.e., usage factor due to fatigue) contour at any instant of time (e.g., after 16 h of online data processing) is shown in , respectively. From the damage information, one can easily estimate the remaining life of a component assuming that the design life of the component is over when the total damage fraction becomes unity. In the following section, various information regarding stress and damage state of some components of a thermal power plant as computed by BOSSES are provided.In a thermal power plant, high energy piping, boiler headers, turbine rotors, casings, steam chests, valves, etc., are the most critical components subjected to creep and fatigue damage under service conditions. To prevent any unforeseen outages of the plant due to steam leakage preceded by crack formation leading to plant unavailability and down-time cost, it is necessary to generate some information on localized degradation due to various damage mechanisms in real-time basis. For this purpose, BOSSES has been implemented in two units of a coal-fired power plant (each unit generates 210 MW). The units are in service for approximately 10 years. The main steam pressure and temperatures are approximately 140 kg/cm2 and 535 °C, respectively. The corresponding pressure and temperature in the hot reheat lines are 34 kg/cm2 and 535 °C, respectively. Some of the components under monitoring are superheater outlet header, reheater inlet and outlet header and the hot reheat pipe bends, etc. The material of these headers and pipe bends is ASME SA 335 P22 (a low alloy ferritic steel).The finite element models of some of the components monitored by BOSSES are shown in . The actual plant transients used by BOSSES are main steam pressure, temperature and flow and similar parameter in other circuits such as hot and cold reheat lines. Some of the plant transients of the thermal power plant (e.g. main steam pressure, temperature and flow) are shown in , respectively. It may be noted that the piping load is an important loading on a component apart from internal pressure and thermal stresses.The piping loads on a component are evaluated by carrying out stress analysis of the whole piping loop (with associated supports and restraints) using various types of straight and bend pipe finite elements due to various load such as dead weight, pressure and thermal loads. The layout of such a piping loop (where the hot reheat piping bend is a part) is shown in and the associated piping loads computed on both ends of the pipe bend are shown in With all the loads known, BOSSES evaluates the material temperature, stress and damage (due to creep and fatigue) in all the components. The computed values of material temperature, maximum stress intensity and damage history at a shell-nozzle junction of a superheater outlet header of the thermal power plant are shown in . Similarly, one can obtain the whole-field information on stress and damage in a component at any instant of time and as an example, the stress and damage contours of the hot reheat pipe bend after 24,000 h of on-line computation are shown in , respectively. Calculation procedure of crack growth due to creep and fatigue are described in Section . In the following section, some details of creep and fatigue crack growth for a hot reheat pipe bend is described.The geometrical details of the pipe bend are given as: internal radius = |
rj |
= 224 mm; external radius re |
= 254 mm; average radius = |
rm |
= 239 mm; bend radius = |
Rc |
= 1500 mm; thickness = |
h |
= 30 mm; initial crack size a0 |
= 0.5, 0.1 and 1.5 mm; c0/a0 |
= 3Nomenclature for loading: pressure = |
P; bending moment = |
M2 |
= |
M (in-plane). The nomenclature for various geometrical parameters of the pipe bend is provided in . The different postulated crack configurations used in the analysis are shown in . The details of stress intensity factor and limit load calculation used by BOSSES for the pipe bend are described in the following section. The variation of stress intensity factors (at bottom and side end of the semi-elliptical crack) and limit load ratios (i.e., ratio of reference stress to the material yield stress) for four cases (Cases 1–4 as shown in ) with initial crack size to thickness ration are plotted in , respectively. The stress intensity factors for different crack configurations were calculated using RCC-MR A16 procedure. The nominal stresses were evaluated using on-line FE analysis for the combined internal pressure and in-plane bending moment acting on the elbow. The stress intensity factor is expressed asK=σ0i0+σ1i1ah+σ2i2ah2+σ3i3ah3+σ4i4ah4πa,where a is crack depth and σ0 and σ1 are the derived stresses and calculated in the following way for different crack configurations with nominal longitudinal membrane stress (σ1m), nominal circumferential stress (σ2m), nominal longitudinal bending stress (σ1b), nominal circumferential bending stress (σ2b) and internal pressure P. The stresses for various crack configurations of the pipe bend are given as:For circumferential crack (internal): σ0 |
= |
σ1m |
− |
σ1b |
+ |
P and σ1 |
= 2σ1b.For circumferential crack (external): σ0 |
= |
σ1m |
+ |
σ1b and σ1 |
= −2σ1b.For longitudinal crack (internal), σ0 |
= |
σ2m |
− |
σ2b |
+ |
P and σ1 |
= 2σ2b.For longitudinal crack (external), σ0 |
= |
σ2m |
+ |
σ2b and σ1 |
= −2σ1b. are obtained from the tables provided for straight pipes with corresponding crack configurations in A16. σ2, σ3 and σ4 are the stresses corresponding to second- to fourth-order nonlinear stress distributions across the thickness and are neglected in this analysis. The reference stress can be evaluated using modified limit load option or elasto-plastic stress option of A16. Both the options are used here and the maximum among the two limit loads is selected for further calculation. The crack growth computed by BOSSES for various crack configurations with initial crack size of 1.5 mm are shown in where on-line computation has been carried out for a period of 24,000 h of plant operation. The maximum crack growth is for the longitudinal semi-elliptical crack at external surface of the intrados of the pipe bend. Once, the damage fraction and crack growth are known, BOSSES can estimate the life consumed for the component for the entire service life using suitable extrapolation techniques. As an example, the life for the hot reheat pipe bend under consideration has been extrapolated for a service life of around 12 years and is plotted in the form of a bar chart in . Life consumed by the pipe bend for both conventional and fracture mechanics based methods are shown in the above figure. This information is available for all the critical components of a thermal power plant and serves as an important information base for scheduling and prioritizing maintenance of various components.The crack growth due to creep and fatigue depends upon the stress intensity factor, C∗ integral, etc., of the assumed cracked configurations and the methods to evaluate them are already described in Section . The method to incorporate them in the calculation of various state probabilities of pipe bend will be described here. On the other hand, the erosion–corrosion rate depends upon the process parameters such as fluid velocity, pH, temperature and oxygen content Fe3O4+3(2-b)H+=3Fe(OH)b(2-b)++(4-3b)H2O,whereb=0,1,2,3.The equilibrium constants Kb are calculated as Kb=[Fe(OH)b(2-b)+]/[H+](PH2)1/3, where [Fe(OH)b(2-b)+] is the concentration of bth ferrous ion, [H+] is that of hydrogen ion and PH2 is the partial pressure of molecular hydrogen gas. The corrosion rate depends upon two factors, i.e., (a) Oxide dissolution: This rate is governed by the Arrhenius relationship: Rk |
= |
R0 |
exp(−Ek/RT), where Ek |
= activation energy = 31,580 cal/mol, R0 |
= 9.55 × 1032 |
atoms/cm2 |
S, T |
= fluid temp in K, R |
= universal gas constant = 2 cal/mol/K.(b) Mass transfer based on oxide dissolution: This transfer rate is given by: RMT |
= |
K(CS |
− |
CB), wheremass transfer coefficient=0.0791(DO2/d)(Ud/n)x(n/DO2)0.335, (d |
= inner diameter of pipe, U |
= flow velocity, n |
= kinematic viscosity, x |
= 0.54 for fully turbulent flow)oxygen diffusivity = 7.4 × 10−8T (2.6 × 18)0.5/(290)0.6surface concentration of ferrous ions=∑[Fe(OH)b(2-b)+]=∑Kb[H+](PH2)1/3). To find out the erosion–corrosion rate, various process parameters (such as flow velocity, pH, temperature, etc.) are used. (a) S = success (depth of corrosion less than 0.125t),(c) L = leak (depth of corrosion 0.45–0.8t),(d) R = rupture (depth of corrosion beyond 0.8t),where t is thickness of the component (e.g. a pipe). The various state transition rates used in the Markov model (Different limit state functions to calculate the state transition rates for a pipe are shown in Notations: rate = erosion–corrosion rate in mm/year; T |
= time of inspection (usually 10 years); Pop |
= operating pressure; Pf |
= failure pressure (defined as in Shell-92 model The state transition probabilities are calculated using first-order reliability methods (FORM). The calculation procedure followed in Markov model is briefly described here. Once the state transition rates are known, one can set four differential equations, one for each state, as follows:dSdt=-ϕS+ωF+μL;dFdt=ϕS-(λF+ρF+ω)F;dLdt=λFF-(ρL+μ)L;dRdt=ρFF+ρLL.In vector form these equations can be rewritten asThe eigen-values are determined by solving the fourth-order polynomial equation given bywhere I is the identity matrix. All the expressions of the corresponding eigen-values, eigenvectors and the integration constants are calculated. shows the variation of different state probabilities due to erosion–corrosion damage in the feed water pipe with increasing plant operational time (using an offline calculation), using the parameter values given in shows the on-line calculation of various state probabilities over time of 2 years due to creep and fatigue crack growths in the reheat pipe bend (The prevailing approach of the plant operator to estimate the need for inspection (i.e., inspection schedule) is often on the basis of offline inspection and past operation and maintenance (O&M) experience. Such an approach results in frequent inspection of problem-free equipments and many times critical shell-nozzle junction are overlooked due to lack of detailed information. The application of the present system helps in making realistic decisions to schedule maintenance intervals on certain selected components and hence it can be used to save lot of resources. The system can be merged with existing O&M planning and scheduling activities for efficient plant management and thus provide a cost effective solution. The system can also be used to rank various components of the plant based on the ‘Risk’ associated with their failure (Risk is defined as the product of probability of failure and consequences of that failure mechanism). Such a risk-based monitoring should be a part of the overall concept of risk-based life management of different plant components.Elastic properties of tantalum carbide (TaC)Elastic properties of TaC have been investigated experimentally and by model calculations. The elastic stiffness coefficients c11=597(11) GPa and c44=153(2) GPa were determined on a (100)-oriented disc-shaped monocrystal at room temperature using a plane-wave ultrasound method. The corresponding theoretical values (c11=621(3), c44=166.8(3) GPa) agree within 4 and 8%, respectively. Therefore, we are confident that the predicted value for c12 is equally accurate, and this allows the prediction of the Bulk and Young's moduli and the Poisson ratio. Data published earlier are critically reviewed and predictions concerning the possibility to synthesize extremely incompressible carbides are made.The physical and chemical properties of group IV and V transition metal carbides (TMC) are of interest for basic research and several technological applications. Industrial applications of the carbides are cutting tools and hard coatings because of their great strength, hardness and durability Tantalum carbide crystallizes in the NaCl type structure (B1, space group Fm3¯m) and it has been found that large deficiencies in carbon content are tolerated without changing the structure type Hence, our aim was to redetermine experimentally elastic stiffness coefficients of TaC and to complement these experimental values with data from ab initio total-energy calculations. These data are compared to values published earlier for TaC in order to obtain a consistent set of elastic coefficients. This is a prerequisite to establish systematic dependencies of structure-property relationships of TMC on their composition.Tantalum carbide discs with faces parallel to (100) and dimensions of about 5 mm in diameter and 1.4 mm in thickness were cut from a single crystal rod purchased from Applied Physics Technologies Inc. using a low speed saw with a diamond wafering blade. The faces of the discs were polished to be parallel within ±1 μm. The orientation of all samples have been controlled by Laue backscattering and Bragg diffraction methods. The mass density, ρ, was measured by the buoyancy method on one of the raw crystals in pure water.The longitudinal and shear stiffnesses, c11 and c44, were determined from ultrasonic resonance frequencies using a plate mode technique It is well established that first principles studies based on density-functional theory (DFT) can be used to obtain reliable elastic properties of inorganic compounds In the present study, ab initio total-energy calculations of the elastic stiffness coefficients of TaC and of the lattice parameters of ZrC, NbC, VC, HfC and TiC were performed using a standard technique based on density functional theory as implemented in the CASTEP program The experimentally determined values of the mass density and the elastic stiffness coefficients c11 and c44 are presented in . It is well established that the lattice parameter of stoichiometric TaC is a0=4.4547 Å In addition to the experimentally determined values for a0 and ρ, we report in values obtained from the quantum mechanical model calculations. The agreement of results calculated with DFT-GGA in comparison to experiment is better than 2% for a0 and, consequently, better than 5% for the mass density. The slight overestimation of the lattice parameter is a feature consistently encountered in DFT-GGA calculations, the so-called ‘underbinding’, such as those presented here. On the other hand, results obtained from calculations performed with DFT-LDA show an a0 value smaller than 2% and a mass density larger than 4% when compared with TaC ideal values. The underestimation of lattice parameter with respect to the ideal value of 4.4547 Å, is due to the ‘overbinding’, which is a general feature of LDA-based DFT calculations.Our measured elastic stiffness coefficients at room temperature, along with the values obtained here in the athermal limit from theory and the results published earlier are also summarized in shows the large scatter (about a factor of 2 for c11 and c12) of the available data which cannot be explained by differences in the stoichiometry. While it is known that the mechanical properties of carbides, such as their hardness depend on the stoichiometry, variations in excess of a few ten GPa are very unlikely. As the data of Brown et al. From a similar analysis for c12, we believe that the values of Krajewski et al. Previous to this work, there had been only one value published for c44=79 GPa by Bartlett and Smith. In their study, the two other elastic stiffness coefficients are systematically too low compared to other results, and this is probably true for the value of c44 as well. Our experimental and theoretical values strongly suggest that c44 is significantly larger than previously thought, i.e. c44=160 GPa, and it will be discussed below that this is confirmed by a comparison with data for other carbides., further elastic properties, namely bulk and Young moduli and Poisson ratio are shown. Although Brown et al. A value of B=330 GPa is also in agreement with the results of the quantum mechanical calculations. As has been mentioned above, the bulk modulus has also been obtained from calculations of the P–V relation in the athermal limit. shows this pressure-volume relation. The dashed line is a fit for a Birch–Murnaghan third order equation of state (EOS) to the data points From a similar analysis of all results, we derive a Young's modulus for TaC, E=550 GPa, and the Poisson ratio, v≈0.22The elastic stiffness coefficients c11 and c44 were determined experimentally for a TaC single crystal sample using a plane-wave ultrasound method. The lattice parameter, the elastic stiffness coefficients c11, c12 and c44, bulk and Young moduli and Poisson ratio for TaC have been obtained from DFT calculations. All results have been compared to earlier published values and a preferred set of values has been obtained.These data can then be compared to data obtained for other cubic carbides crystallizing in the B1 (NaCl) structure type, namely VC, TiC, NbC, HfC, ZrC. The average lattice parameters of these have been obtained from the inorganic crystal structure database demonstrates the linear relation between the lattice parameters and the ionic radii of the metal ions. For the latter, we used the data published by Shannon clearly shows that due to the very large scatter in the data at the moment such an empirical correlation cannot be established. It is unlikely that small changes in the stoichiometry will change the bulk modulus by a factor of two, and hence part of the scatter may be due to the microstructures of the samples.The scatter in the bulk moduli data reflect the significant variations between individual data sets of elastic stiffness coefficients of other B1 TMC. For example, values for c44 for TiC range from 175–217 GPa Seismic evaluation of Bagan heritage site (Myanmar): The Loka-Hteik-Pan templeBagan site is one of the most remarkable heritage areas in Myanmar, belonging to the List of UNESCO World Heritage Sites. Besides its cultural importance, Bagan is located in an area with high seismic hazard and the evaluation of the seismic vulnerability is fundamental for the protection of the monuments. This work utilises Loka-Hteik-Pan temple, a typical Buddhist middle-size structure, to evaluate the seismic performance of this kind of monuments, which corresponds to more than 50 around Bagan area. Furthermore, the efficiency a strengthening proposal, composed by two kinds of steel ties, was evaluated, considering the past seismicity of the area and its current hazard defined by the Burmese code. The application of steel ties is recommended for the mitigation of the seismic vulnerability of this kind of Buddhist temple in Bagan, since it corresponds to a compatible and adequate strengthening technique.The significant increase of tourism, the growing interest of the international community and the seismicity of Burmese central regions recommends to perform structural analyses to understand the dynamic behaviour of the Buddhist temples of Bagan site Myanmar is located in an active tectonic zone, between the Indian and Eurasian plates, called Alpide Earthquake Belt, which starts from the northern Mediterranean Sea and extends eastwards, crossing Turkey and Iran, until reaching the Himalayas and Myanmar. Several types of motions are caused by the collision between these plates, such as subduction and strike-slip faulting, making Myanmar a country recurrently prone to strong earthquakes shows the earthquakes that occurred only in Bagan region and the events that caused damage in the temples of Bagan [USGS, 2018].One of the strongest events hit Bagan in 1975 with a magnitude of 6.5 (Richter scale), making the monuments disappear in one red huge cloud and leaving a dust of pulverized bricks After 1975, the 2016 seismic events are the most relevant. The first earthquake (Gwegyo earthquake) occurred at northeast of Chauk on March with a magnitude of 4.8, near Bagan site Although the Gwegyo and Mawlaik earthquakes did not directly affect Bagan site, the aftershocks caused more damage than expected Ground motion records of Chauk earthquake were measured by the Department of Meteorology and Hydrology (DMH) and by the Ministry of Transport and Communication. The data were recorded at the seismic station located in Nyaung U, about 48 km far from the epicentre and the Peak Ground Acceleration (PGA) was equal to 0.08 g along horizontal directions, and 0.12 g in the vertical direction According to Myanmar National Building Code ). It is noted that the Myanmar National Building Code does not provide design response spectrum for the vertical component of the seismic action. The horizontal PGA for Bagan is set at the value of 0.41 g Despite the low seismic input recorded in Bagan, the damage in the temples was widespread varying from light to severe, probably enlarged by the superposition of the effects of the three main shocks in 2016, without excluding the amplification of the ground motions ). Among the monuments of Bagan, 41 temples are catalogued as heavily damaged with the need of prompt intervention and 404 as moderately damaged. Damage seems to be mainly linked to the partial inefficiency of the works undertaken in many temples between 1975 and 1990’s ) and, in this paper, it is used as an example to understand the seismic response of a specific group Buddhist temples of Bagan, which represents about 50 temples according to Pichard’s catalogue Loka temple was selected and studied by the Department of Archaeology of Bagan (DoA) due to its religious importance, with the support of the Carleton University (Canada).), numbered as 1580 in the Pichard inventory Loka-Hteik-Pan temple is an isolated structure made of fired bricks and mud mortar, with linear plan and single-storey. Its 150 m2 plan can be divided into three main spaces (): the shrine, which hosts the Buddha’s statue, the vestibule and the porch Shapes are massive and articulated by a sequence of terraces, which mark the different levels of the structure from the height of 7.5 m, up to the level of the Śikhara (set at the height of 10.5 m). Heritage of Indian and Burmese styles, the Śikhara is, in this case, a sort of curvilinear high tower approximately 5 m tall, offering a slender appearance to the temple Three perforated brick windows let sun rays enter into the shrine and they are the only way to shed light in the interior. From the exterior, the windows are framed by ornamental portals containing characteristic details of Buddhist art. The North façade hosts the entrance and is marked by a portal and the tympanum.Most of the external surfaces were covered by stucco carvings, applied directly on the outer layer of the masonry, mouldings sculptures or reliefs. Nowadays, only partial remainings of these carvings are visible on the surfaces.Due to the past seismic events, Loka-Hteik-Pan temple, as well as many other Bagan’s temples, underwent several structural and non-structural interventions. After Bagan’s Earthquake, locals funded heavy strengthening interventions The Śikhara was restored several times and nowadays the majority of its bricks are not original. Bricks are more recent and set with a whitish mortar These aspects are the more relevant for structural performance. Beside they changed the appearance of the building, they have influence on the dynamic properties of the structure. Other non-structural interventions have been applied in this structure, in which the most relevant are linked to the safeguard of the original paintings located at the interior of the central shrine. summarises the main structural and non-structural carried out in the Loka-Hteik-Pan Temple.A new damage survey was carried out by the authors through visual inspection in May 2018 (), aiming at updating the past damage survey after the Chauk’s Earthquake. The temple presents a severe disconnection between the two orthogonal walls at the South-East corner, highlighted by two vertical cracks from both sides. In general, this part suffered more damage than the other portions of the monument. It is marked by a remarkable out of plane deformation and the generalized detachment of the corner along the entire height of the temple. It is important to underline that this damage, located at South-East corner, was already noticed by Pichard The tympanum in the North façade is visibly affected by out of plane deformations and some parts of it were reattached in the recent past, using cement-based mortar Sonic pulse velocity testing is a non-destructive test (NDT) used to estimate the elastic properties of materials, based on the propagation of waves inside the materials caused by an impulsive force. The velocity and the time spent to receive the signal, generated from the waves, can be read between the thickness of the internal and external surfaces of the walls (direct sonic tests) or along the same surface (indirect tests) at a specific distance The sonic tests were performed in situ in May 2018, using an impulse hammer of the PCB, a piezoelectric accelerometer of the PCB (±0.5 g) and an acquisition board NI USB 4431. The tests were repeated several times at the same location to obtain a statistical stability of the results. Indirect sonic tests were carried out along all the external surfaces of the walls, at different heights, testing both original and modern bricks. Direct sonic tests were performed only on the North façade of the temple, since the cross section of the walls at this location is visible and accessible.The results of the direct and indirect sonic tests allowed to estimate the average Younǵs modulus of the masonry walls of the temple (0.46 GPa), with a highest value of 1.10 GPa (recent masonry with cement-based mortar) and a lowest value of 0.25 GPa (deteriorated original masonry). summarizes the main results obtained, which will be adopted subsequently in the model updating.Dynamic identification tests allow to estimate the dynamic properties of the structure, namely natural frequencies, mode shapes and damping ratios. Four high sensitive piezoelectric accelerometers (sensitivity equal to 10 V/g, frequency range from 0.15 to 1000 Hz and dynamic range ± 0.5 g) were connected to an acquisition board (NI USB 4431, 24-bits resolution) by coaxial cables. The acquisition board was connected to a laptop with acquisition software developed by University of Minho. The use of high sensitive accelerometers allows to perform tests with low amplitude for the excitation source (ambient vibration) without causing damage to the building. In general, the highest modal components are located at the upper levels of the structure. Thus, it is recommended to measure the vibrations, using the accelerometers, at the upper levels of the building in order to obtain a good ratio between signal and noise, aiming at improving the signal processing of the results and the estimation of the modal properties ). Since the roof of the temple was accessible, it was possible to set the accelerometers at different heights, following the geometry of the terraces. The signals from the ambient vibrations were measured during 30 min with the sampling frequencies of 200 Hz, performing eight different setups. In total, 25 points at the terraces levels were measured, namely 12 in the transverse direction (Y) and 13 in the longitudinal direction (X). For each setup, four accelerometers were used, keeping one accelerometer as reference in the transverse direction (acc.1 ref, h7.5, see The data were processed in ARTeMIS software [2018], adopting the Enhanced Frequency Decomposition Domain Method (EFDD) method Five modes with frequency range from 3.67 Hz to 9.34 Hz were estimated (see ). The first and the second modes correspond to the first global ones in the transverse and longitudinal direction, respectively. Observing the second mode, the Śikhara is moving out of phase with respect with the other parts of the temple. Moreover, the south-eastern corner, which is the most damaged part of the structure, presents modal components significantly higher than the other corners of the main shrine. The third mode is a global torsional mode, mostly involving the main shrine. The last two modes present complex shapes: mode 4 is a local mode of the Śikhara, involving high modal displacements at the top, while mode 5 can be considered as a combined mode.The corners show different modal displacements, which can be mainly associated with the existing damage, detected in the results of the dynamic identification tests. The mass distribution of the structure, which is massive and non-uninform with a shrine, and the asymmetric geometry (stiffness) cause asymmetric mode shapes.The 3D Finite Element model (FEM) of the Loka-Hteik-Pan temple was prepared using Midas FX pre/post processor for DIANA FEA ). Some assumptions were made, such as the depth of the foundations, set at 1 m, the connections between the walls in the model, considered as perfect, and the geometry of the reinforced concrete beams, modelled taking into account the inspection made with rebar steel detector.The numerical model represents the current state of the structure in terms of geometry and materials. In addition, an unstrengthened model was also prepared in order to evaluate the performance of the temple without the reinforced concrete beams. The upper part of the Śikhara was also added to simulate a generic mid-size Bagan temple () and the condition before the 1975 Bagan earthquake.The calibration of the model was performed using eigenvalue analysis, by changing the masonry Young’s modulus and comparing the frequencies of the numerical model with the experimental frequencies obtained by the dynamic identification tests (The process aims at minimizing the difference between the experimental and numerical frequencies. The number of modes to be calibrated is an important aspect to take into account in this phase In the calibration of the numerical model, four principal trials were evaluated. For each calibration shown in In the first assumptions considered for the calibration, the MAC value of the first mode is about 0.94, but the average MAC value for the higher frequencies is very low (0.27). The total error between the calibrated frequencies was equal to 8% (not negligible).In the second calibration, the mode with the lowest MAC was neglected. The average of MAC for the higher frequencies was improved to 0.38, but still far from a good value. In this case, the total error between the calibrated frequencies was equal to 9%, still not negligible.The third calibration phase considered mainly the first two global modes (1st and 2nd). The MAC value of the 2nd mode increased from 0.54 to 0.55, but it is not enough to consider this trial as a good calibration. The total error between the calibrated frequencies was equal to 3%, acceptable but can be improved.Finally, in the last assumption of the calibration, the error was minimised giving more importance to the 1st mode, the updated Young’s modulus for the masonry of 0.57 GPa was obtained, which is comparable to the value obtained from the sonic tests (). MAC value corresponds to the highest values (0.97) and frequency error is equal to zero, as expected. Thus, and taking into account the importance of the first global mode for the dynamic behaviour of the structure, this calibration was considered as the most appropriated one, in order to obtain a calibrated numerical model with a MAC value equal to 0.97 for the first mode, which means perfect correlation between the first numerical and experimental mode shapes.After calibrating the model, the nonlinear properties of the materials were defined. The nonlinear behaviour of the masonry and the concrete elements was set considering the rotating Total Strain Based Crack Model (TSCR) The concrete is modelled according to a Total Strain Based Fixed Crack Model, considering a shear retention factor equal to 0.2. Regarding the properties of the steel of the concrete beams, and since there is no information on the characteristics of the steel bars, a steel of class S235 and the Von Mises behaviour were adopted. summaries the nonlinear material properties assumed.First, a linear static analysis for the action of the vertical loading of the self-weight was performed. In this analysis, the materials show linear elastic behaviour, which is useful and fast to depict inconsistencies between the model and the reality with low computational effort Nonlinear static (pushover) analysis was performed for both the unstrengthened model with the upper part of Śikhara (UM), and the strengthened one without the upper part (SM) in all the directions and orientations. In the pushover analysis, horizontal load pattern proportional to the mass of the structure was adopted. The unstrengthened model (UM) represents the configuration before Bagan earthquake (1975) without the insertion of the reinforced concrete beams, while the strengthened model (SM) represents the configuration after Chauk’s earthquake (2016) with the insertion of the reinforced concrete beams. The results obtained from pushover analyses can be used for a first evaluation of the performance of Loka-Hteik-Pan temple considering the current strengthening technique and the expected seismic load for Bagan, which is 0.41 g In general, the reinforced concrete beams improve the response of the temple, increasing the load capacity and the post peak behaviour is more ductile (). The most vulnerable direction of the structure is the negative transverse direction (, UM Y-), presenting a maximum load factor of 0.25 for the UM (load factor corresponds to the ration between the horizontal inertial forces and the self-weight of the structure). In the same direction, the reinforcements of the SM present an increase of the maximum load factor (0.42) of about 70%. For what concerns this study, the parameter to take into account the seismic action for Bagan was the PGA (0.41 g) defined in the Myanmar National Building Code , SM Y-), which is mainly associated to the improvement of the connections between orthogonal walls at the corners. present the results obtained from all the analyses. It is noted, that due to the staircase built in the west longitudinal wall (), the structure is not symmetric in the transverse direction. presents the tensile principal strains, which correspond to an indicator of the cracking.An alternative strengthening technique using steel ties was evaluating, aiming at improving the seismic performance of the Loka-Hteik-Pan temple, mainly in the most vulnerable direction, with low architectural impact for the temple. Pushover analyses were performed to evaluate the most proper and balanced configuration for the ties, which may be applied considering the minimum intervention criterion The application of ties in the Loka-Hteik-Pan temple took into account the damage pattern obtained from the previous analyses, its geometry and the aesthetic details. This technique aims at minimizing the damage in specific directions of the structure and counteract the high deformations caused by the seismic action, expected for the Bagan area In the iterative process towards a balanced and efficient strengthened configuration, the diameter of the cross-section of the ties (20 mm and 25 mm) and their disposition (six configurations) were considered as variables, in order to achieve the required seismic capacity for the temple. The six trials are summarised in , adopting Lean Duplex Stainless Steel (AISI 316), whose properties are presented in . In the preservation of historic buildings, durable solutions are recommended and AISI 316 is the least corrosion-prone stainless steel. show how the application of ties in Loka-Hteik-Pan temple improves the seismic load capacity of the structure for the most vulnerable direction. In the last configuration for the ties (6th trial), there is an increase of about 44% in the maximum load factor and about 70% in the displacement at the peak.), the damage pattern is spread along the structure and the out-of-plane of the eastern wall is less evident. It is also noted that, for a similar displacement of about 0.10 m at the same control point (the top of the spire), the load factor for the strengthened model is more than the double of the load factor of the unstrengthened model.This strengthening proposal showed its efficiency on the seismic response of the temple, but other aspects should also be considered, e.g. the cost of the strengthening and the effective use of the material. Thus, Austenitic Stainless AISI 316 steel was considered referring to the BSI Standards ). However, the diameter was enlarged up to 30 mm, aiming at assuring a similar seismic response. The main difference between the two types of steel is that the austenitic steel is a good compromise between cost, corrosion resistance and production, while the duplex steels have a very high resistance to wear and to stress corrosion at the expense of the production process. In terms of chemical composition, the austenitic steels contain 17–18% of chromium, 8–11% of nickel and the 0.07% of carbon, while the duplex steel has only the 0.03% of carbon, being therefore less prone to corrosion In the strengthening with Austenitic Stainless AISI 316, the 6th configuration for the ties was considered. The others trials were discarded, because the 6th one is the most efficient in terms of load factor, ductility and damage pattern. The capacity curves obtained by using the two types of Stainless steel are presented in the . The Duplex Stainless Steel allows to reach a slightly higher maximum load factor in comparison with the Austenitic Steel, but the behaviour is quite similar () and in both cases the peak load factor is higher than 0.41 g. The results show that the strengthened model with the ties made of Austenitic Stainless ASISI 316 and 30 mm of diameter presents also an appropriated seismic performance and can be an alternative to the ties made of Lean Duplex Stainless Steel AISI 316 with 25 mm of diameter.The seismic performance of Loka-Hteik-Pan temple was evaluated, by performing nonlinear static analyses and comparing the unstrengthened configuration with the strengthened one. A three dimensional finite element model was built and calibrated based on the dynamic properties estimated from dynamic identification tests. Pushover analysis was performed for all the directions and orientations to investigate the nonlinear behaviour of the structure, showing that the weakest scenario may occur in the transverse negative direction. Since several retrofitting techniques, such as FRP strips, TRM or grout injections, are not compatible with the presence of painted surfaces along the walls of the central shrine, and in order to improve the response in this direction, a strengthening proposal composed by steel ties, and with less architectural impact for the temple with respect to the exiting reinforced concrete beams, was evaluated. Two different stainless steel types were evaluated, considering its structural performance, chemical composition (resistance to the corrosion) and the cost. Even if the application of ties it can be considered an irreversible technique, at the same time it is one of the most compatible for historic buildings and their effect is usually beneficial. The choice of adopting ties in this structure is also supported by the fact that steel ties are able to avoid one of the most dangerous mechanism, namely out-of-plane failures of significant parts of the building. In addition, steel ties can also prevent diagonal cracks caused by in-plane shear.The results of the pushover analysis lead to the conclusion that the proposal strengthening technique with stainless steel ties improve significantly the seismic behaviour of the Loka-Hteik-Pan temple and can be adopted as an alternative to the existing strengthening with reinforced concrete beams. Thus, it can be adopted to reduce the seismic vulnerability of the existing unstrengthened middle-size temples of Bagan.As future works, the evaluation of the seismic performance of Loka-Hteik-Pan temple should be evaluated based on the Discrete Element Method The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.A technical issue in mercury spallation target development is pitting, which appears on the target vessel in conjunction with the pressure wave. Pitting has been found in off-beam line test by split Hopkinson pressure bar (SHPB) test as well as in the on-beam test of mercury target at WNR of LANSCE. In SHPB tests pressure in mercury was reduced from 80 to 40, 20 and 10 MPa. Specimens made of type 316 stainless steel were inspected before and after the impacting test at ×450 magnification. Results show that over 20 MPa pitting was generated. But at the lowest pressure in mercury, the number of pits was very limited and substantial damage was small. Substantial damage by pitting is characterized by holes where mass is removed from the wall. Depression itself may not be a substantial damage as long as it is not accompanied by holes.In R & D for high intensity spallation neutron sources, pitting has become a new technical issue for estimating the lifetime of mercury target vessels. A sub-μs short-pulsed proton beam is favored for a high intensity neutron source based on the spallation process. Currently liquid mercury is the choice of target material for a potential supply of several mega-watts of proton beam power because of the absence of damage from proton and neutron irradiations. A main technical concern for design of mercury target vessel was pressure wave effects. The ASTE collaboration Irradiation damage, corrosion and fatigue in the target shell have been researched for the mercury target development. It is possible to predict the intensity of pressure waves by computer simulation Pitting damage may significantly reduce the lifetime of mercury targets, therefore current R & D issues emphasize how to mitigate the pressure wave, what will be the damage to the vessel material after over a million cycles of short pulses, and material selection to resist pitting as well as irradiation. In this report the question of a threshold value for pitting will be discussed. If material is stressed within the elastic regime, deformation of material will be recoverable and material damage will not accumulate. shows the experimental apparatus used to generate on the mercury by applying the split Hopkinson pressure bar (SHPB) technique, which mainly consists of an impact bar of 300 mm length, an input bar of 1495 mm, an output bar of 1495 mm length, a collar and an air gun to shoot the impact bar. In this experiment the length of impacting bar is reduced to 300 mm from 500 mm in order to test at lower pressure regime.Specimens of stainless steel were connected with the end of the input and output bars on the mercury side by thread set; the bottom of the specimens is to be inspected. The impact bar is 16 mm in diameter and made of the maraging steel, which has 2 GPa in yield stress to remain elastic throughout the tests. The collar is made of type 316 stainless steel is 27 mm thick of the collar. A uniaxial strain condition will be generated in the mercury by using a thick collar. The clearance between the collar and the bars is 0.05 mm. O-rings were installed between the bars and collar to prevent leakage of the mercury and to allow the stress wave to travel smoothly through the bars.The axial length of the mercury was set to be 5 mm. The stress waves traveling in the input and output bars were measured by the strain gages set on the axial center of each bars. The gage length is 2 mm. The dynamic response of this strain measuring system is 500 kHz. Impact velocity of the impact bar, V, was measured by using two optical sensors.The mercury was carefully installed inside of the collar without any air bubbles, and the length of the mercury was adjusted to be 5 mm. After finishing the setup, the impact bar was shot by the air gun to collide with the input bar and the strains on both bars were measured and stored in a digital-storage-oscilloscope (DL708;YOKOGAWA).The incident strain is denoted by εi, the reflected strain by εr (both measured in the input bar), and the transmitted strain by εt (output bar).The axial stress and strain were calculated by using the Kolsky equations on the output bar side, respectively, where c0 is the sound velocity in the bars, E is the Young’s modulus, ρ is the mass density of the bar material and t is a time. t=0 indicates the time when the incident strain reaches the interface between input bar and mercury. The relative displacement of mercury between the interfaces in contact with the bars, ΔU, is given byThen the average strain of the specimen, ε(t), iswhere ls is the axial length of mercury. The loads Pi(t) (i=1,2) on the specimen ends are given byon the output bar side, respectively. Then the average stress in the specimen iswhere E is an elastic modulus of mercury, A is a cross section of the collar and As is a cross section of input or output bar. In the case of P1(t)=P2(t), the following relation is obtained from the Eqs. Therefore, the strain and stress in the specimen are given byWe measured εr(t) and εi(t) and estimated experimentally the relationship between the strain and the stress on the mercury by using the Eqs. . Assuming uniaxial strain condition in the mercury, the relationship between the pressure, P, and the stress components, σii (i=1,2 and 3) is given byand the relationship between the volumetric strain, ΔV/V, and strain components, εii (i=1, 2 and 3) is given byThen the strain of the mercury, ε(t), obtained by the Eq. are equal to the volumetric strain of the mercury, ΔV/V, and pressure, P, respectively. For a given test series the impact bar was shot at the same velocity. The mercury cavity length was carefully adjusted every shot. After 10 shots, the specimens were removed from the input and output bars to inspect by microscope. shows the planed mercury test pressures: they are 80, 40, 20 and 10 MPa.All specimens were made of type 316 austenitic stainless steel with the chemical composition 0.04C/0.47Si/1.64Mn/0.27P/0.25S/10.31Ni/16.52Cr/2.26Mo (wt%). shows the specimen geometry which were machined from 18 mm diameter round bar. Specimens were polished with a final step by 1 μm diamond paste after #4000 paper. Pre-test photos were taken by microscope at ×450, a Keyence 450-ZH with 1.2M pixel resolution. The observed area is a crossed band as shown in Sixty photos were taken and stored in the computer before test. The inspected area ratio is 9% of the total surface. After test another 60 photos were taken by the same microscope. SEM was used for auxiliary observation. Detailed comparison was done by using images taken from at exactly the same locations before and after the test.Simple rules were established for interpreting observed changes when comparing before and after images. A surface change is defined as pitting except for a similar form that was seen before the examination, a change that was added at the time of the attachment or detachment of a specimen, a change due to the removal of inclusion, or the addition of a foreign substance.We controlled the air pressure of the air gun in order to change the energy of the impact bar to create design test pressure. As shown in the realized average pressure was 84, 49, 26 and 17 MPa for cases 1, 2, 3 and 4. The actual values were larger than the scheduled ones. It must be noted that for case 4, we had one big shot: three times more than averaged value. 17 MPa is the averaged value except for the big one. shows the time dependent strain measured in the input/output bars in the case that the impact velocity, V, is 6.6 m/s. shows the pressure response in the mercury obtained by Eq. under the condition of V=6.6 and 3.5 m/s. In the case of V=6.6 m/s, pressure in mercury arises up to 80 MPa at 50 μs from start of pressure wave propagation in mercury. It becomes 40 MPa in the case of V=3.5 m/s. show the comparison of photos before and after the tests for the case of 84 MPa average pressure in mercury. This is the case of the highest pressure among the tests. There were scratches and dots in the images easily recognized in both before and after images. However, changes could be seen in the after test. There are marks or dots like bombardment craters. We defined those marks as pitting. The maximum size of dotted areas is tens of μm but not over hundred μm. Pits exist isolatedly and sometimes a couple of dots exist proximately. Ten shots were given to each specimen but the number of pits is more than 10. In other words, more than one pit is generated per shot. shows the comparison of before and after photos for the case of 49 MPa average pressure. Pitting was found after the test. The size appears to be smaller than for the case of 84 MPa at least within the area covered by the inspection photos. In fact, large pits with diameter of tens of μm were found for the case of lower pressure, 26 MPa, as shown in . Ten shots were given to the specimen and again the number of pits is over 10. show the before and after photos for the case of average pressure 17 MPa. As mentioned before, the first shot was so large that 52 MPa was applied in mercury. 17 MPa is the value of nine shots and excludes the first shot. There was a very small number of pits observed and the size of it was less than 10 μm as shown in look like shallow depressions and differ from dot shapes.. Pitting defined as morphology change between before and after tests was observed in all cases. It should be noted that the number of pitting for the case of 17 MPa averaged pressure in mercury is very limited, even if the first large shot caused all damage observed on the specimen.The mechanism of pit formation is related to the pressure wave. A negative pressure in mercury generates bubbles, when pressure interferes with other waves or when the pressure expands a mercury filled target vessel. In spallation target the maximum power density is located near the target vessel. So bubbles favorite site may be near the target vessel because first the backward pressure wave changes the phase of pressure waves after inferring each other, and secondly the forward pressure wave changes the phase of pressure waves after interfering the target vessel. When bubbles collapse, a massive mercury jet flow will impinge on the target vessel and can cause pitting. The density is 13.6 g/cc in mercury and 7.8 g/cc in steel, respectively.However, if the mercury mass flow pressure is small enough to limit deformation to the elastic regime of the material, or the mass flow pressure will work as distributed compression, the material damage will be limited and controllable during spallation target operation.Throughout this SHPB test the test mercury pressure decreased from 84 to 17 MPa. The number of shots is only 10. There was an indication of a pressure threshold at the lowest test pressure which produced only a limited number of pits. This threshold must be proven by more than a million shots test.In current designs of mercury spallation targets pressure in mercury is roughly 40–50 MPa shows that there are two small holes close to each other in the center of the shallow depression with 5 μm diameter on the specimen surface taken at ×5000. The size of holes is less than 1 μm. shows the other small hole at a different place with . The size is also less than 1 μm but a large shallow depression is not seen in the surrounding area. Fragments are scattered in the bottom of small hole. These fragments may be a collapsed inclusion like carbide which is often seen in the material. Similar changes can be found in previous figures. For example, small holes with shallow depression can be seen in the circled area C in . The sizes of those areas are larger than the case in . Small hole only can be seen, for example, in circled area E of . Pitting did not occur in the rectangular area. Also there were crossed scratches in SHPB testing was done over a range of pressures relevant to current mercury spallation target designs. At 17 MPa average test pressure in mercury (the lowest pressure tested), the number of pits was small and damage was very limited. Although a threshold pressure must be proven by more than a million shots test, these results suggest a threshold less than 20 MPa for 316SS. Pitting was generated at pressures over 20 MPa.Substantial damage by pitting is characterized by holes where mass is removed from the wall. A depression alone may not be substantial damage as long as it is not accompanied with holes.Truss vs solid modeling of tendons in prestressed concrete structures: Consequences on mechanical capacity of a Representative Structural VolumeA comparative study is carried out on the mechanical behavior of a Representative Structural Volume of a prestressed concrete structure, using the state of the art of the numerical tools for engineers (and not the most recent developments of the academic research). The structural effect due to the presence of the tendons is carefully studied by comparing a classical truss finite element computation with a more sophisticated approach where the tendons are explicitly represented using a solid meshing. The classical approach based on truss elements appears to be poor to reliably represent the failure mode of concrete. Therefore, in some cases, it is essential to take into account both material (difference between steel and concrete stiffness) and geometrical heterogeneities through the effect of the inclusions. The well-known mesh dependency problem is also studied in this paper. For the truss simulations, contrary to the usual conclusions on bending beams for example, the mesh dependency does not only affect the position of the localized bands but also the global failure mode, questioning once again, for this particular application, the representativity of local simulations with truss elements. Finally, nonlocal calculations are carried out using the integral approach. Contrary to the well-documented simulations on bending beams, the value of the characteristic length does not only affect the width of the localized bands but also the global failure mode.The validity of the models (damage and/or plasticity, fracture, etc. Real structural applications are generally reinforced concrete structures containing reinforcement rebars but also in some cases prestressed cables. Concrete is generally considered as a 3D brittle material while steel is included as a 1D truss element with fictitious sections. This simplification eases the meshing process and decreases the computational cost. But it lacks the geometrical heterogeneity represented by the steel inclusions. The effect that this modeling choice has on the failure mode of concrete structures has rarely been investigated but experimental evidence seems to show that it may have an important role. For example, To evaluate this effect, a Representative Structural Volume (RSV) has been designed. First created to validate the models developed for the simulation of mechanical behavior of containment structures (Part 1) Computations using softening law also exhibit a mesh dependency effect. This is a well-known problem for softening model which is due to “strain localization” as mentioned in shows the results of local and nonlocal simulations of a three point bending beam. In this case, even if the local simulations are mesh dependent (as expected), the failure mode remains globally the same with several cracks located at the same place. The focus of the paper (Part 5) is to investigate the influence of cable modeling (1D and 3D) on the mesh dependency and to evaluate if the same failure mode is represented despite the mesh dependency (same conclusions that have been reached for beam bending). represents two nonlocal simulations on beam bending considering two values of the characteristic length using the integral approach developed by Pijaudier-Cabot and Bazant An application where the prediction of local damage is of great importance is the case of PCCV (Prestress Pressure Containment Vessels). For these structures the study of leakage tightness and local degradation of concrete is an essential ingredient since the increase of fluid flow is strongly related to the number of cracks and their openings that can be modeled in different ways (damage permeability relation, The model of the Representative Structural Volume (RSV) was initially designed to incorporate all components of real containment structures of nuclear power plants (NPP): concrete, vertical and horizontal reinforcement bars and tendons in horizontal and vertical directions. It was created to represent an experiment designed by EDF, to include only 9 horizontal and 11 vertical reinforcement bars (on both internal and external faces), 4 horizontal and 1 vertical tendons. Every steel component is modeled in this part using 1D elements. The geometry of the problem is given in provides information about the steel distribution and dimensions. The cables experimentally correspond to 37T15 cables with a steel cross section of 5550 mm2. It has thus been modeled with an equivalent circular steel cable of 84 mm diameter.The following boundary conditions are chosen for the simulation: face SB (bottom face) is blocked along the vertical direction and no rotations are allowed for faces SG and SD to keep the angular distance constant (). In order to model the effect of the horizontal prestress, truss elements are anchored to faces SG and SD, then prestressed using internal forces. They are restrained to surrounding concrete elements in order to represent the prestressing technology generally applied in French structures. It is to be noted that the vertical tendon is only cast, in this particular application, to maintain the global rigidity of the structure but will not be pretensioned in order to follow the conditions of the experiment that is going to be carried out on the same system. Finally, a compressive homogeneous pressure of 1 MPa is applied on SH (top face).The loading is represented by a radial pressure on the internal face SI. To simplify things, the effect of gravity is not represented. Boundary conditions and loading are summarized in . Different loadings are considered with a decrease in the initial pretension (from 100% to 60% of the initial value σref). illustrates the evolution of the prestress and of the internal pressure during the simulation. The last loading consists of an increasing internal pressure until the collapse of the Representative Structural Volume.The simulations are carried out using the elastic damage law developed in its initial form by Mazars where σij and εkl are respectively the stress and strain components, Cijkl is the fourth order elastic tensor and D is the damage variable.For the description of the damage growth, an equivalent strain is introduced from the local strain tensor: where 〈εi〉+ are the positive principal strains. where the damage variable D is also the history variable which takes the maximum value reached by d̃ during the history of loading, D=Max/t(d̃,0).d̃ is defined by an evolution law that distinguishes the mechanical responses of the material in tension and in compression by introducing two scalars Dt and Dc. d̃(ε)=αt(ε)Dt(εeq)+αc(ε)Dc(εeq)Dt,c=1−κ0(1−At,c)εeq−At,cexp[Bt,c(εeq−κ0)]αt,c=(∑i=13〈εit,c〉〈εi〉+εeq2)βκo is a parameter of the model and represents the initial threshold from which damage grows. Dt and Dc are the tensile and compressive parts of the damage. At,c, Bt,c are four parameters of the model. The weights αt and αc are computed from the strain tensor ε. They are defined as functions of the principal values of the strains εijt and εijc due to positive and negative stresses. In uniaxial tension, αt=1 and αc=0. In uniaxial compression, αc=1, αt=0. The exponent β reduces the effect of damage on the response of the material under shear compared to tension.The evolution of damage is determined by the Kuhn–Tucker conditions: For the simulations, the parameters have been chosen using the values given in . Values of 38 MPa and 3.5 MPa are obtained for the uniaxial compressive and tensile strengths respectively. To avoid the effect of the parameter “beta” in Mazars’ model, its value is kept equal to one.The reference solution (which means the state of the art of the engineering practice consisting in using models with truss elements to represent rebars and tendons) is presented in this part.From the simulation choices presented in Section provides the internal pressure applied on the inner surface (SI) of the RSV as a function of the radial displacement of a point located at the junction between surfaces SI–SB–SD. Due to symmetry conditions, only one fourth of the RSV is modeled using linear cubic elements (). The initial negative displacements are due to the hoop prestressing that contracts the structure to the center as a result of the boundary conditions (fixed orientation of SG and SD sides (see )). The lower the prestress, the lower the contraction. As the internal pressure increases, the contraction gets cancelled and the structure is stretched outwards. During the last inner pressure loading, we can see that the response curve can be divided in three sections. The initial state corresponds to the application of the prestress as already mentioned. A linear behavior follows where the contraction is reduced and the structure returns to its initial rest position and expands linearly outwards. Finally, a partial unloading appears, due to heavy cracking of the structure, for which the computation has been stopped.Very little damage appears during the application of the hoop prestressing (only in the area surrounding anchorages), and the following two sequences of pressure loading do not create any further nonlinearity. Through the last loading step, localized damage bands appear on the top face (SH). shows the concrete damage evolution during the last sequence of the load with a rise of internal pressure. By observing the evolution of the results, it appears that the damage, initiated on the top, propagates along the vertical tendon towards the bottom of the structure. An explanation of the damage initiation can be the pinching that occurs at the top surface of the wall (SH) where the vertical tendon is anchored. In fact, even though there was no vertical prestressing in the vertical tendon, hoop prestressing and pressure loading induce vertical displacements (contraction during prestressing and dilation during pressure application). The differences between steel and concrete stiffness produce a pinching that could account for the damage initiation (see ). Damage propagation then continues along the vertical tendon as the internal pressure is increased. This could be explained by the triaxial state of the stress in the concrete surrounding the vertical tendon that brings concrete to its threshold, sooner than in the rest of the model.As the tendon plays a key role in the initiation and propagation of damage, a new mesh is created where each tendon (horizontal and vertical directions) is geometrically represented using solid elements. The idea is to compare this approach with the one developed in Section in order to see if the geometrical heterogeneity, captured by this refined approach, has also an influence on the failure mode of the RSV.For the “truss” model (1d) presented in Section , tendons were modeled using truss elements located at the exact center of the cross section of each cable. The surrounding mesh that geometrically represents each cable’s shape was considered to be made of concrete. In the case of “solid” model (3d) it is considered to be made of steel. The steel tendons in both horizontal and vertical directions are thus explicitly meshed. Truss elements are still present in the horizontal direction to bring prestressing but their stiffness is null (see . In both cases, tendons and concrete are considered perfectly bonded. This is represented in the model with nodes in common between the two materials (concrete and tendons).It has to be noted that for classical industrial applications such as silos or NPP containment vessels, the usual approach corresponds to the “truss” modeling depicted in Section . The cost for a more refined model involving a solid representation of cables is not realistic with the current capacities of software and computers, and the skill necessary to create the mesh. In our study this was only possible because of the size of the RSV specimen.In order to evaluate the influence on the results of how tendons are modeled, compares the global response obtained from truss and solid analysis. shows the evolution of the pressure as a function of the radial displacement, as shown in No significant differences can be noticed on the global behavior (the two curves are almost the same) and the choice of the tendon modeling does not seem to have any impact on the evolution. The levels of initial radial displacements due to the prestressing are the same, as well as other characteristics of the curves, with the most important one concerning the maximum pressure of the RSV. illustrates the damage distribution for the solid model at different loading levels. Damage first develops along the vertical tendon and then propagates in the wall following two different patterns: localized bands on the top face and development of a heavy damaged zone on the internal surface near the vertical cable. Some interactions between the vertical and hoop tendons can also be noticed at the end of the loading. compares truss and solid damage distributions, where, contrary to the global behavior, clear differences can be noticed. If damage appears in both cases along the vertical cable (which plays the role of a rigid body in concrete) and propagates on the upper face along localized bands, their distribution at the end of the loading appears to be different. The damage is essentially concentrated around the vertical tendon in the truss case, whereas more complex effects appear in the other case, with damage localization on the inner surface of the wall. A certain degree of interaction with the damage developed around one of the hoop tendons is also noticed. It is important to recall that the most significant difference between these two models is the way tendons are meshed. In structural analysis where mechanical damage is important to be evaluated properly, it is essential to take into account the geometrical effect of tendons. The same conclusions were reached using an elastic plastic damage law for concrete The boundary conditions used in the previous sections could correspond to an RSV near the anchorage of vertical tendons where there is no constrain on the displacement over the top face. In order to try to study the behavior of a portion of the wall which is far from all boundaries, a uniform vertical displacement condition on the top face SH needs to be applied (see As previously shown, we can compare global and local results between a “truss” and a “solid” modeling. shows the pressure — displacement curve for both simulations. Contrary to the previous situation, a clear difference appears in the global behavior. While the result from the “solid” modeling shows more or less the same behavior, in the “truss” modeling the evolution looks more ductile with a progressive increase of the pressure up to its failure. This difference can be explained by the evolution of the mechanical degradation (damage) illustrated in With the “truss” modeling of the tendons, thanks to the uniform displacement condition, the pinching that appeared previously caused by the differences in the stiffness of the material is avoided (the vertical displacements of steel and concrete on the top face are the same). Damage thus appears to be quite homogeneously distributed on the model. On the other hand, with the “solid” modeling and the induced geometrical heterogeneity, even if the material heterogeneity is avoided (as for the “truss” approach), the distribution is variable in space and less affected by the change in boundary conditions.It is clear from this comparison, that depending on the boundary conditions, taking into account explicitly the cables by a 3D meshing can lead to significant differences in the simulated failure mode compared to classical truss simulations. From these results, it seems that the 3D approach enables us to capture more reliable effects on this particular structure.As presented previously in the introduction, mesh dependency is a common problem which is known to be caused by the use of a softening law that produces some localization in strains and damage. This problem was well documented on classical applications like bending beams or ties but its effect is less quantified for unusual structures.For beams, even if some regularization techniques are necessary to avoid the mesh dependency, the global failure remains qualitatively the same even if the mesh is reasonably changed (see for example). The idea here is to see if similar conclusions can be reached for the RSV. We decided to investigate this effect by using three different meshes with different degree of refinement (see ). This was made possible thanks to a Gibiane script First, we investigate the mesh effect on the classical “truss” approach. The results obtained from these three nonlinear analyses indicate that the global pressure–deflection response of the model remains unchanged (see ). Only very slight differences can be seen with a zoom on the very last loading step where models are quite damaged but the three curves are almost the same. Things are different if we consider local results such as the damage distributions (). A cross examination between the results indicate that in all cases damage initiates from the top surface and propagates downwards along the middle plane containing the vertical tendon. But the distributions vary more or less significantly with the mesh discretization: Coarse mesh: damage values are less intense but cover a wider area.Medium mesh: damage appears at the top surface, outer wall and along the vertical duct.Fine mesh: quite similar to medium, with a wider spreading close to the lower hoop tendon. The conclusion is that because of the well-known localization problem of softening material law there is a clear mesh dependency Nevertheless, and contrary to the behavior of beams on which the mesh dependency is generally studied, this effect also induces a difference in the global failure mode of the structure.If one considers that a solid meshing of tendons provides more reliable results, we can then carry out the same mesh sensitivity analysis. As in the case of “truss” modeling, the global mechanical behavior is not influenced by the mesh (same level of initial prestress and similar maximum value of the peak pressure). shows the damage distributions for the three meshes. The results indicate mesh dependency especially for the localized bands on the top face but contrary to the “truss” approach, we can notice that the failure mode remains quite the same regardless the mesh.Differences observed between medium and fine meshes (see ) are mainly due to the fact that results for such high nonlinear state do not exactly correspond to the same loading time step. Some mesh dependency is also observed, and can be explained by the softening feature of the concrete constitutive law.In conclusion, contrary to the “truss” modeling using solid elements for tendons allows us to avoid strong failure mode sensitivity to mesh discretization. In this way, the 3D modeling of tendons seams to provide more reliable results in predicting the failure mode.To further investigate the study about mesh dependency a nonlocal approach has been used since the mesh of the RSV is fine enough. The technique is based on the work proposed in Pijaudier-Cabot and Bazant . by its nonlocal counterpart εeqnl. This is classically defined by the following equations: εeqnl(x)=1Vr(x)∫ΩW(x−s)εeq(s)dsVr(x)=∫ΩW(x−s)dsW(x−s)=exp(−‖x−s‖2lc2) where lc is the characteristic length and corresponds schematically to the length on which the local equivalent strain is averaged.This technique can be used in this contribution because the mesh around the tendons is fine enough to allow three elements to be included in the characteristic length (lc is generally equal to a couple of centimeters). It is not the case for most classical industrial applications for which the mesh is too coarse to imagine using such an approach.The idea of these calculations is to see if the choice of the characteristic length only changes the length of the localized bands but does not affect the global failure mode, as observed for a bending beam. This point is significant as no standard method is used to determine the appropriate value of this variable. shows the damage distributions for different values of the internal length, considering the medium mesh with 3D elements for the tendons. A great influence of the value of lc can be noticed.As expected, if the internal length approaches small values the results correspond to the local computations. Higher values for the internal length will force the algorithm to spread the damage over a wider volume of concrete. As a result the damage is no more localized on the width of an element but on a zone whose size depends on the value of lc. If this technique is known to avoid mesh dependency, it is also responsible for a change in the failure mode. For example, for lc equal to 5 cm, which is quite an appropriate value for concrete, the damage is almost homogenized on the whole volume and a fast increase in the mechanical degradation is observed compared to the local calculations. Even for a value of 2.5 cm, damage develops in a very different way with a zone of heavy damage that propagates almost symmetrically between the two parts of the vertical tendons. It should be noticed that the change in the internal length also affects the value of the peak position in pressure: from 0 to 2.5 cm the result changes by 4.8% and from 0 to 5 cm the results changes by 6.7% The higher the internal length the more homogeneous is the spreading of damage.Contrary to the conclusions on bending beam or ties for example, the value of the internal length has a great impact on the failure mode of the structure. It seems thus that a characterization technique of the variable (or of its evolution, A comparative study was performed on a Representative Structural Volume in order to evaluate the influence of the 1D truss modeling of tendons on the failure mode of the structure. It showed that taking into account both material and geometrical heterogeneity through an explicit 3D modeling of the bars it’s essential in some cases if a representative failure mode wants to be captured, depending on the choice of the boundary conditions. The classical 1D “truss” approach may thus be insufficient and may lead to an incorrect distribution of the mechanical degradation. This point is clearly underlined when the effect of the difference in the material stiffness vanishes due to the choice of the boundary conditions (uniform vertical displacement on the top face for our case).The well-known problem of the mesh dependency was also investigated in the case of our RSV. Classical and well-documented conclusions on bending beams (mesh dependency of the width of the localization bands but no dependence of the global failure mode) were not reproduced in this study if the “truss” modeling is chosen: the global failure of the structure is also dependent on the mesh, questioning the representativity of the local calculations, even to qualitatively represent the failure mode of an unusual structure. Introducing the explicit meshing of the cables enables in our case to limit this effect and to reproduce a failure mode which globally remains the same independently from the mesh.The conclusions of the first part of this study show that a 3D modeling of the tendons leads to more reliable results. It focuses on the necessity of modeling the reinforcement and prestressed elements carefully if a misevaluation of the failure mode wants to be avoided. Nevertheless, as the 3D explicit modeling is not adapted with industrial applications (computational costs and meshing efforts), the use of “multi-scale” approaches should be investigated.Concerning the regularization techniques (integral method for this paper), and once again contrary to the classical conclusions reached on bending beams, the failure mode is heavily dependent on the value of the characteristic length, even in the range of values which is usually accepted (from 2 to 5 cm). lc does not only influence the width of the localization bands (as for bending beams for example) but also, in our case, changes the global failure mode. Once again, if a correct distribution of the mechanical degradation wants to be achieved, particular care must be given to the calibration of this parameter. It is a point of importance as, up to now, no standard method is used to choose the value of lc.Both points should be taken into account, especially in situations where the local degradation of concrete is an essential ingredient to evaluate the capacity of a structure. It is the case for PCCVs for example where the leakage could be directly influenced by the damage through a damage — permeability relation: a poor description of the damage variable could lead to a wrong evaluation of the weakest zones (The evolution of dynamic energy during drop hammer testing of Brazilian disk with non-persistent joints: An extensive experimental investigationRock mass is well known as a discontinuous, heterogeneous, and anisotropic material. The behavior and strength of rock mass is heavily controlled by the condition and orientation of discontinuities (faults, joints, bedding planes) and discontinuity sets. Under dynamic loading conditions, rock bridges along non-persistent discontinuity planes may crack, and a fully persistent discontinuity may form, potentially affecting the stability of a rock structure. The study of the dynamic behavior of rock discontinuities has critical implications for civil engineering, the mining industry, and any other areas where rock mass is utilized as a structural foundation in areas prone to dynamic loading conditions, such as those formed during earthquake events. In this paper, cement-mortar-based Brazilian disks containing open, non-persistent joints were constructed and subjected to impact loading to investigate their impact energy behavior. The effect of some parameters, such as joint continuity factor (the relationship between joint length and rock bridge length), bridge angle, joint spacing, joint orientation, and impact angle were investigated to estimate the required Dynamic Energy for Crack Initiation (DECI), Dynamic Energy for Crack Coalescence (DECC) and failure pattern of specimens. The results of the experiments revealed an increasingly continuous joint reduces the DECI and DECC, while larger joint spacings past the middle value of those experimented increase the DECI and DECC. The bridge angle and loading direction do not affect DECI, but by increasing bridge angle DECC decreases, and it increases by increasing loading direction angle. Finally, an optimization analysis was conducted which showed that joint spacing and joint continuity factors significantly affects DECI, and joint continuity factor and loading direction have significant effect on DECC.The role of discontinuities in the stability and failure of rock mass has been well explored by different scholars and practitioners in rock engineering The dynamic behavior of rock or rock-like materials have been investigated by many researchers In this paper, 68 Brazilian disks containing various configurations of non-persistent joints have been subjected to impact loading to investigate the effect of joint continuity k, joint spacing d, bridge angle γ, and loading direction β on the dynamic energy for crack initiation (DECI) and coalescence (DECC), through physical experiments (see Response Surface Methodology (RSM) was adopted to design the experiments and analyze the experiment results. The effect of each parameter, including k, d, γ, and β, as well as their interaction on DECI and DECC was investigated, and two statistical models are proposed.Artificial Brazilian disk samples with a diameter of 150 mm and a height of 75 mm were constructed using a mixture of cement, sand, and water by a weight ratio of 3.5: 5:3. The samples were cured at room temperature for 14 days A specific mold was designed and manufactured using Plexiglass and PVC tube. A grid of slots was created at the base of the model which acts as a host for the vertical blades. These blades are embedded in concert to create non-persistent joints with 10 mm length and 2 mm aperture. For this purpose, a pre-designed pattern was installed at the bottom of the model, and blades were fixed in the grid. All component of the mold and base grid is presented in After casting, the mold was shaken to condense the mortar and release any trapped air from the mixture. After four hours, the blades were removed from the mold, and non-persistent joints were created. A view of Brazilian discs containing non-persistent joints before and after test are presented in The drop hammer test was employed to measure the DECI and DECC of non-persistent jointed Brazilian Disks. For this purpose, a simple setup was designed in which the impact was applied to the sample based on free fall mass. A 3-kg cylindrical mass was released from a height of 90 cm above the specimen with an initial velocity of 0 mm/s. The mass is constrained from lateral movement via a tube which is positioned directly above the sample. The mass travels the 90 cm distance via free fall and the resulted impact energy on specimen can be calculated using following equations:where U is the impact energy per free fall of the mass, g is acceleration due to gravity, V is the velocity of the mass at impact and t is the time required for the mass to fall a height of 900 mm. W and m are the weight and mass of the impactor respectively, and H is the height of the fall.Substituting the relevant values in Eq. The impact energy per each free fall, U, of the mass can be obtained by substituting the values in Eq. A rigid foundation was constructed to hold the specimen in place using a non-contact clamping system to ensure the sample was free of confinement at the time of impact (see ). The joint properties, such as the orientation relative to the impact force, joint spacing, and joint continuity were varied according to the results of the response surface methodology (RSM) conducted in of this paper. The sample under test was carefully examined after each impact for the presence of macro-cracks, and non-persistent joint coalescence. When the first macro crack formed, the sum of the accumulated impacts was recorded as the DECI. The impact test was repeated until the sample failed or formed significant persistent joints, and then the sum of the accumulated impacts was recorded as the DECC.RSM is a powerful methodology for the design of experiments and post-data processing which is based on advanced mathematical and statistical analysisIn this study, the independent parameters are k, d, γ, β, and DECI and DECC are the dependent parameters, or the responses, which can be expressed using Eq. y=β0+∑i=13βiXi+∑i=13βiiXi2+∑i=13∑j=i+13βijXiXj+∑i=13βiiXi3+∑i=13∑j=i+13βijXi2Xj+∑i=13∑j=i+13βijXiXj2+∑i=13∑j=i+13∑k=j+13βijkXiXjXkwhere y is a response or a dependent variable (DECI and DECC)βijk, βij, βii, βi, and β0 are the regression coefficients, and Xi, Xj and Xk are the values of independent parameters (k, d, γ, β).In this research, Historical Data Design (HDD), which is a version of RSM and applied to historical data, was adopted and the experiments and their results are presented in The codes and the levels of independent parameters in this study are given in . For the four independent parameters, three levels were defined in which the focus of RSM is within the range of −1 to 1 for each independent parameter. The levels corresponding to each independent parameter were defined by trial and error as well as a pre-assessment of RSM to ensure success in the analysis. Moreover, based on the past experiencesThe histogram of the impact numbers for crack initiation and coalescence are presented in . It can be seen that the dominate impact numbers for crack initiation and coalescence are 4 and 6 respectively. The number of impacts can be calculated by dividing DECI or DECC by 26.49 kN·mm from , the polynomial models for the dependent parameters (DECI and DECC) were estimated as a function of the independent parameters (k, d, γ and β) through the best fits to Eq. log10DECI=1.73-0.1109k+0.0411d+0.0420kd+0.3257kγ+0.2103kβ-0.0566dγ+0.0477k2+0.1529d2-0.3132kdγ+0.4067kγβ+0.4535dγβ-0.3264k2γ+0.2752kγ2log10DECI=2.75237-4.05109k+0.109969d-0.892146kd+0.004214kγ-0.005193kβ-0.005069dγ+6.89852k2+0.124851d2+0.008882kdγ+0.000102kγβ-0.000012dγβ-0.043897k2γ+0.000095kγ21SqrtDECC=0.1374+0.0169K-0.0024D+0.0064γ-0.0059β-0.0350Kγ-0.0174Kβ+0.0071Dγ-0.0064γβ-0.0112K2-0.0295D2-0.0088γ2-0.0099β2+0.0357KDγ-0.0612Kγβ-0.0388Dγβ+0.0327K2γ-0.0071KD2-0.0396Kγ2-0.0065D2γ+0.0057D2β1SqrtDECC=1.58630-2.34526K-0.163016D-0.030190γ-0.011821β+0.059575Kγ+0.025917Kβ+0.002869Dγ+0.000130γβ-2.51884K2+0.052334D2+0.000133γ2-4.50621×10-6β2+0.003497KDγ-0.000246Kγβ-0.000016Dγβ+0.021019K2γ-0.096411KD2-0.000353Kγ2-0.000800D2γ+0.000437D2β, which are the coded and actual equations for DECI respectively. In the real equation the input variables are positive real numbers in their domain presented in and in coded equation the input of equation just could be −1, 0, and 1. It can be concluded that k2 has the maximum effect on the response, and d and k have positive and negative effects on DECI respectively. Moreover, based on Eqs. which are the coded and actual equations for DECC respectively, k and k2 affect DECC the most negatively.Analysis of variance (ANOVA) was adopted to estimate the contribution of each of the input parameters and their interaction in the variability of output responses for the results of the RSM designThe models’ components are chosen based on p-value, meaning that in a polynomial model each component which has a p-value < 0.05 is considered statistically significant, and will be selected for the models. The details of the models and also their F-value (the ratio of explained variance to unexplained variance) are presented in for both DECI and DECC models, respectively.The actual and predicted DECI and DECC are shown in (a and b), and the relationship between the probability of a normal percentage and the externally studentized residuals DECI and DECC explored are shown in (c and d). Response transformation is a crucial component of any data analysis. Transformation is necessary if the error (residuals) is a function of the value of the response (see c and d). The normality is usually checked by normal plot of the residuals. When there is a pattern in the plot of residuals versus predicted response values, response transformation is necessary. Unless the ratio of the maximum response to the minimum response is large, transforming the response will not make much difference . As it can be seen there is a linear pattern between studentized residuals versus predicted response values. Therefore, response transformation is vital. All of the above analyzes prove that the modified cubic response models are suitable for HDD testing and DECI and DECC prediction.The standard transformation will be recommended the current lambda falls closest to the best lambda value and is within the confidence interval. If there is no standard transformation within the confidence interval, then the Power transformation is recommended with the best lambda value. After implementing the best recommended transformation, the Box-Cox will can be check to be sure the transformation is satisfactory. The Box-Cox plot (See ) indicates that the transformation of data was effective.In order to investigate the impact of joint parameters on required DECI, the relationship between a dependent parameter and an independent variable when other variables are kept constant at their intermediate level is shown in . The effect of joint continuity factor, k on DECI shows that an increase in k from 0.17 to 0.67 causes a 39.97% decrease in DECI from 77.76 kN·mm to 46.68 kN·mm. The effect of joint spacing d on DECI revealed that an increase in d from 1.4 cm to 2.8 cm increases DECI by 9.51%. (From 69.81 kN·mm to 84.38 kN·mm). Finally, the variation of bridge angle γ and loading direction β has no effect on DECI value.As for interaction effects of joint parameters, (a and b) shows the effect of joint continuity factor k and joint spacing d on DECI. While d is constant, an increase in the k has a negative effect on the DECI, and when d = 1.4 cm, an increase in the k from 0.17 to 0.67 causes a 50.33% decrease in the DECI. When d = 2.8 cm, an increase in the k from 0.17 to 0.67 causes a 27.24% decrease in the DECI. On the other hand, when k is constant at 0.17, increasing d from 1.4 to 2.8 cm has no effect on DECI and when k is 0.67, the DECI increases by 46.47% (from 54.83 kN·mm to 80.31 kN·mm). (c and d) shows the effect of joint continuity factor k and bridge angle γ on the dynamic energy for crack initiation. (c and d) shows that while γ is constant at 90˚, an increase in the k from 0.17 to 0.67 causes a 52.56% decrease in the DECI, but when γ = 135˚, an increase in the k causes 858.13% increase in the DECI (9.17 kN·mm to 87.87 kN·mm). In addition, as shown in (c and d), when k = 0.17, an increase in the γ from 90˚ to 135˚ causes 95.05% decrease in the DECI, but when k is constant at 0.67, increasing γ from 90˚ to 135˚ has no effect on DECI. (e and f) shows the effect of joint continuity factor k and loading direction β on DECI. When β = 0˚, an increase in the k from 0.17 to 0.67 causes a 77.22% decrease in the DECI from 126.19 to 28.75 kN·mm, while at β = 90˚ an increase in the k causes 58.03% increase in the DECI. Moreover, while k is constant at 0.17, with rising β from 0˚ to 90˚, DECI increases 62.03% (From 126.19 kN·mm to 47.91 kN·mm). However, when k = 0.67, an increase in the β causes a 163.34% increase in the DECI (from 28.75 kN·mm to 75.71 kN·mm). (g and h) shows the influence of the joint spacing d and bridge angle γ on the DECI. When γ = 90˚ an increase in the d from 1.4 to 2.8 cm causes a 56.29% increase in the DECI, whilst at γ = 135˚ an increase in the d causes a 7.15% decrease in the DECI from 79.55 to 73.86 kN·mm. Furthermore, when d = 1.4 cm, an increase in the γ causes 29.81% increase in the DECI and at d = 2.8 cm with an increase γ from 90˚ to 135˚, DECI increases by 22.89%. Response surface and contour plots that represent the influence of two variables and their interaction on DECI of the non-persistent jointed Brazilian disk. (a) and (b) joint continuity factor and joint spacing (3D surface and interaction plot respectively); (c) and (d) joint continuity factor and bridge angle, (e) and (f) joint continuity factor and loading direction, (g) and (h) joint spacing and bridge angle.The effect of non-persistent joint parameters on DECC was also investigated, and the relationship between a dependent variable and an independent variable when other variables are kept constant at their intermediate level is shown in . An increase in k from 0.17 to 0.67 causes a 41.77% decrease in DECC from 84.19 kN·mm to 49.03 kN·mm. The effect of joint spacing d on DECC is also shown in this . By an increase in d from 1.4 cm to 2.8 cm, DECC increases 9.57%. (From 82.70 kN·mm to 90.61 kN·mm). Moreover, by an increase in γ from 90˚ to 135˚, DECC decreases 18.02% while an increase in β from 0˚ to 90˚ causes a 20.15% increase in DECC from 56.46 kN·mm to 67.84 kN·mm.As for interaction effects of joint parameters on response, (a) and (b) show the effect of joint continuity factor k and bridge angle γ on DECC. While γ is constant, an increase in the k has a negative effect on the DECC. It can be noted that when γ = 90˚, an increase in the k from 0.17 to 0.67 causes a 47.92% decrease in the DECC. Moreover, when γ = 135˚, an increase in the k from 0.17 to 0.67 causes a 373.09% increase in the DECC from 21.82 kN·mm to 103.21 kN·mm. On the other hand, when k is constant at 0.17, increasing γ from 90˚ to 135˚ causes a 90.61% decrease in the DECC as well as when k is in 0.67, the DECC decreases by 14.67% (from 120.95 kN·mm to 103.21 kN·mm). (c) and (d) show the effect of joint continuity factor k and loading direction β on the dynamic energy for failure DECC. While β is constant at 0˚, an increase in the k from 0.17 to 0.67 causes a 68.57% decrease in the DECC. However, when β = 90˚, an increase in the k causes a 1.72% increase in the DECC (81.7 kN·mm to 83.1 kN·mm). In addition, as shown in (c and d), when k = 0.17, an increase in the β from 0˚ to 90˚ causes a 37.45% decrease in the DECC, but when k is constant at 0.67, increasing β causes 102.47% increase in the DECC.(e) and (f) show the effect of joint spacing d and bridge angle γ on DECC. When γ = 90˚, an increase in the d from 1.4 to 2.8 cm causes a 47% increase in the DECC from 85.02 to 124.98 kN·mm; while at γ = 135˚ an increase in the d causes 17.37% decrease in the DECC. Moreover, while d is constant at 1.4 cm, by rising γ from 90˚ to 135˚, DECC increases 33.44% (from 85.02 kN·mm to 113.45 kN·mm), but when d = 2.8 cm, an increase in the γ causes 24.99% decrease. (g) and (h) show the influence of the bridge angle γ and loading direction β on the DECC. When β = 0˚ an increase in the γ from 90˚ to 135˚ causes a 33.93% decrease, whilst at β = 90˚ an increase in the γ causes a 0.26% increase in the DECC from 78.89 to 79.1 kN·mm. Furthermore, when γ = 90˚, an increase in the β causes 1.95% decrease in the DECC and at γ = 135˚ with the increase of β from 0˚ to 90˚, it increases by 48.79%. Response surface and contour plots that represent the impact of two variables and their interaction on DECC of the non-persistent jointed Brazilian disk. (a) and (b) joint continuity factor and bridge angle; (c) and (d) joint continuity factor and loading direction, (e) and (f) joint spacing and bridge angle, (g) and (h) bridge angle and loading direction (3D surface and interaction plot respectively).DECI is one of the critical parameters for crack initiation in rock structures. Materials with a low DECI value will fragment easily when exposed to dynamic loads, such as those encountered during drilling and blasting operations. In this case, minimum joint spacing and maximum joint continuity factor contribute to this reduction (see Conversely, materials in which non-persistent joint configuration results in high DECI values are better suited to resist deformation due to dynamic loading. They should be selected for the construction of underground and surface rock structures which are exposed to dynamic loads. Minimum joint continuity factor and maximum joint spacing contribute to maximizing the DECI (see Bridge angle and loading direction were found to have no impact on DECI, which is demonstrated as these parameters have the same values in both the minimum and maximum DECI parameter combinations.DECC is also one of the important parameters for crack coalescence in rock structures. A low DECC value indicates that material will fragment easily when exposed to dynamic loads, such as those encountered during drilling and blasting operations. In this case, maximum joint continuity factor and loading direction contribute to this reduction while minimum bridge angle and average joint spacing may result in minimum DECC (see Geomaterials which require a high DECC may resist deformation due to dynamic loading, and represent optimal materials for use in the construction of rock structures which may be subjected to such loading conditions. Minimum joint continuity factor, loading direction and bridge angle, and maximum joint spacing contribute to maximizing the DECC (see The cracking process of specimens is categorized into three categories which will be presented following, and in each group, the effect of two non-persistent joint parameters is explored. Since the experiments were conducted based on the design of experiment technique, the variation of parameters is not in order. The effect of k in conjunction with β on the cracking behavior of specimens is shown in . By increasing k from 0.17 to 0.67 when β = 0° the failure pattern moves from the edge of the sample toward its center (see a and d). When k = 0.17, the distance between joints is 5 cm and this may result in the failure of the left side of the specimen, but when k = 0.67 the distance between joints is 0.5 cm and this could lead the failure at the center of the specimen. The crack development process as a function of successive impacts is illustrated through colored crack traces (). Specimen S19 (k = 0.17, β = 0°), required five impacts for crack initiation (green lines, a) and a total of 6 impacts for complete crack coalescence (red lines a). When k = 0.42 and β = 45° the tip-to-tip distance of joints is 1.4 cm, and a step-pass failure happens in the center of the specimen (see c). In this case, the initiation and propagation of cracks happened at second impacts (blue color in c). However, at β = 90° by increasing k from 0.17 to 0.67, failure surface moves from the center of the specimen to the left side (see b and e). In both specimen’s tip-to-tip failure happens on the left side of the pre-existing joints. In specimen S20, crack initiation happens at second impact and the coalescence occurred in third impact while in S47 both of them happened at third impact (see b and e). Moreover, the impact of joint inclination on failure pattern is shown in . At k = 0.17, by increasing β from 0° to 90°, failure surface moves from the edge of specimen to its center (see a and b), but at k = 0.67 this happens vice versa, meaning that when k = 0.17, failure occurs at the center of specimen and by increasing k to 0.67 it moves to the left side (see The effect of γ in conjunction with β on the failure pattern is shown in . At β = 0°, by increasing γ from 90° to 135°, failure surface does not change and it develops at the center of specimen in both cases (see a and d). Moreover, in specimen S11, the cracks initiated at second impact (blue color in a) and it failed at third impact (red color in a) but in specimen S27 both of them happened at the same time at second impact (blue color in d). However, at β = 90° and at both levels of γ failure surface starts at second impact on the top of specimen (blue color) and develops at third impact (pink color) toward the left side of the specimens (see b and e). Moreover, when γ is 90° and 135°, at β = 0° the failure happens at the center of the specimen (see a and d), but at β = 90° the failure surface moves toward the left side of specimen (see The effect of joint spacing d on failure patter in conjunction with β is shown in . When β = 0°, by increasing d from 1.4 cm to 2.8 cm the failure pattern does not change and it occurs at the center of the specimen. On the other hand, when β = 90°, this failure happens toward the left side of the specimen regardless of the joint spacing d. Moreover, when d = 1.4 cm step-pass failure forms due to the function of pre-existing joints, but at d = 2.8 cm, some central pre-existing joints do not contribute to the failure surface, and the failure surface forms in the intact part of the specimen. Moreover, when d is 1.4 cm and 2.8 cm, at β = 0° the failure happens at the center of the specimen (see a and d), but at β = 90° the failure surface moves toward the left side of the specimen (see b and e). When k = 0.42 and β = 45° the tip-to-tip a step-pass failure happens in the center of the specimen (see c). Moreover, in specimens S17, S21, S24 and S30 the first crack initiated at third impact and it failed at fourth impact (see a, b, d and e). The crack initiation and coalescence of specimen S6 happened at the same time (see In this study, a number of cement-mortar-based Brazilian disk specimens containing a set of open non-persistent joints were subjected to the drop hammer impact test to investigate the effect of joint continuity factor (k), joint spacing (d), bridge angle γ), and loading direction (β) on the dynamic energy required for crack initiation (DECI) of non-persistent joints, and energy required for crack coalescence (DECC) of non-persistent joints. Several conclusions can be drawn from the experimental results:Both DECI and DECC are heavily influenced by k and d.Through laboratory testing it has been observed that while γ and β are insignificant for the initiation of cracks (DECI), they are critical parameters for the subsequent coalescence of cracks (DECC) into a single persistent discontinuity.Interaction effects between two or more of the studied parameters have been shown to greatly affect the DECC, while the effect on DECI when considering these interactions is less pronounced.The non-dependance of DECI on bridge angle and loading direction, when considering the heavy dependance of DECC on these parameters, could suggest that crack initiation is more a function of the intact material or the mechanical properties of the rock bridges, while crack coalescence is more a dependent upon the discontinuity surface itself, and its orientation with respect to the loading direction. While the presented study focuses upon samples with multiple joint sets, in most samples, especially those with low joint spacing and higher discontinuity trace frequency; only single fully persistent fracture surfaces were formed during the experimental phase. These results may indicate that under dynamic loading conditions, cracks will coalesce around the most prominently formed initial cracks, concentrating stress about those points rather than distributing across multiple discontinuities within a set. We suggest doing a research using a lower weight hammer to monitor microcracking process during the test. However, future work for this research involves extensive numerical investigations and conducting an experimental test using Split Hopkinson Pressure Bar (SHPB) to measure impact force and recorded cracking process using high-speed camera and techniques such as digital image correlation and acoustic emission.Mostafa Asadizadeh: Conceptualization, Methodology, Supervision,Funding acquisition, Writing – original draft. Jamshid Shakeri: Investigation, Data curation, Software, Writing – original draft. Nima Babanouri: Investigation, Project administration. Samuel Nowak: Validation, Visualization, Writing – review & editing. Taghi Sherizadeh: Resources, Writing – review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Sensitivity of femoral strain calculations to anatomical scaling errors in musculoskeletal models of movementThe determination of femoral strain in post-menopausal women is important for studying bone fragility. Femoral strain can be calculated using a reference musculoskeletal model scaled to participant anatomies (referred to as scaled-generic) combined with finite-element models. However, anthropometric errors committed while scaling affect the calculation of femoral strains. We assessed the sensitivity of femoral strain calculations to scaled-generic anthropometric errors. We obtained CT images of the pelves and femora of 10 healthy post-menopausal women and collected gait data from each participant during six weight-bearing tasks. Scaled-generic musculoskeletal models were generated using skin-mounted marker distances. Image-based models were created by modifying the scaled-generic models using muscle and joint parameters obtained from the CT data. Scaled-generic and image-based muscle and hip joint forces were determined by optimisation. A finite-element model of each femur was generated from the CT images, and both image-based and scaled-generic principal strains were computed in 32 regions throughout the femur. The intra-participant regional RMS error increased from 380 με (R2=0.92, p<0.001) to 4064 με (R2=0.48, p<0.001), representing 5.2% and 55.6% of the tensile yield strain in bone, respectively. The peak strain difference increased from 2821 με in the proximal region to 34,166 με at the distal end of the femur. The inter-participant RMS error throughout the 32 femoral regions was 430 με (R2=0.95, p<0.001), representing 5.9% of bone tensile yield strain. We conclude that scaled-generic models can be used for determining cohort-based averages of femoral strain whereas image-based models are better suited for calculating participant-specific strains throughout the femur.The quantification of femoral strain during daily activities is important for understanding the biomechanical implications of osteoporosis (), for which post-menopausal women are most at risk. For example, intra-participant femoral strains can provide information about fracture risk () while inter-participant averages can provide insights into understanding the bone response to exercise treatments (). In vivo femoral strains can be estimated non-invasively using a scaled-generic musculoskeletal model scaled to participant anatomies (herein referred to as ‘scaled-generic models’) combined with a finite-element model of the femur (). However, errors in the definition of the model anthropometry affect calculation of muscle forces (), which likely propagate to bone strain calculation. Several studies have investigated the sensitivity of muscle and joint force calculations to uncertainties in anatomical and muscle parameters () while others have examined the sensitivity of femoral strain calculations to uncertainties in measurements of the geometry and material properties of the femur (). To date, no study has investigated the sensitivity of femoral strain calculations to anthropometric errors arising from uncertainties in, for example, body-segmental masses and lengths.Magnetic-resonance (MR) and computed-tomography (CT) images can provide detailed anthropometric information about the human musculoskeletal system. While MR imaging is the preferred method for acquiring muscle–tendon attachment sites and paths, joint centre positions, and the orientations of joint rotation axes (), this approach is not suitable for extracting bone mineral density (BMD), which is needed to model the elastic properties of bone (). Alternatively, bone surfaces, joint centres and orientations can be determined by segmenting CT images (), and the images' Housfield unit data can be used to describe the BMD and elastic property distributions (). Although the low contrast of CT images complicates extracting soft-tissue anatomical structures such as muscles, CT images can serve as a reference for registering a muscular system atlas to a participant's anatomy (). Therefore, CT images can provide all information necessary to generate both musculoskeletal and finite-element models of a specific participant (herein referred to as ‘image-based models’).Scaling procedures have been used to generate musculoskeletal models of participants by applying a limited number of anthropometric parameters to a scaling algorithm (). Typically, the body mass and segment lengths in a generic-reference model are scaled to an individual participant using information from the skin-mounted marker positions and ground reaction forces acquired during a static pose, thereby creating a ‘scaled-generic’ model. Scaled-generic models have been successfully used to study general patterns of human motion (). However, scaling causes unavoidable anthropometric errors, which in turn may compromise the assessment of individual features in muscle and joint force patterns (Previous studies addressing the sensitivity of scaled-generic models investigated different model outputs and reached different conclusions. concluded that scaled-generic models are as accurate as image-based models when evaluating the potential (per-unit-force) contributions of individual muscles to joint and centre-of-mass accelerations during walking. concluded that participant-specific hip geometry is important in the calculation of hip contact forces while walking; they reported average differences between scaled-generic and image-based models of 0.52 times body weight (BW). No study has reported the sensitivity of femoral strain calculations to anthropometric errors committed while scaling a scaled-generic model to participants' anatomies. However, this information is essential for understanding the limits of applicability of the model results (The aim of this study was to investigate how anthropometric errors introduced when scaling a scaled-generic musculoskeletal model to a participant's anatomy propagate to femoral strain calculations. Femoral strains were computed using scaled-generic and image-based models of 10 participants for six weight-bearing tasks. The influence of scaled-generic anthropometric errors was assessed by analysing (a) participant-specific (intra-participant) femoral strains, and (b) average (inter-participant) femoral strains within a cohort.Ten healthy post-menopausal women (age, 66.7±7.0 years; height, 159±6.6 cm; weight, 66.3±22.5 kg) were recruited to this study (). All participants could walk unassisted and had no reported history of musculoskeletal disease. Ethics approval for the study was obtained from the Human Research Ethics Committee at the University of Melbourne.CT images of the pelvic and thigh regions of each participant were obtained using a clinical whole-body scanner (Aquilon CT, Toshiba Corporation, Tokyo) and an axial scanning protocol (tube voltage: 120 kV; tube current: 200 mA). For each scan, two datasets of monochromatic, 16-bit, 512×512 pixel images with slice thickness of 0.5 mm and spacing of 0.5 mm were obtained. The femur dataset was reconstructed using an in-plane transverse resolution of 0.5×0.5 mm2 whereas the pelvis dataset was reconstructed using an adjusted in-plane transverse resolution to accommodate the entire pelvis. A five-sample (hydroxyapatite density range: 0–200 mg/cm3) calibration phantom (Mindways Software, Inc., Austin, TX) was placed below the participant's dominant leg while scanning.Gait analysis experiments were performed at the Biomotion Laboratory, University of Melbourne. Forty-six skin-mounted reflective markers were attached to anatomical locations as described by , including the pelvis (3), thigh (6), shank (5) and foot (6). The remaining markers were placed along the upper extremities and torso. Marker trajectories were recorded with a 10-camera motion capture system (VICON, Oxford Metrics Group, Oxford) sampling at 120 Hz. Each participant was instructed to (a) walk at a self-selected speed; (b) walk at a faster self-selected speed; (c) ascend and descend a flight of 3 steps (step height=16.5 cm) at self-selected speeds while engaging with the first step of the staircase using the dominant foot; (d) rise from and sit on a chair (chair height=47 cm); and (e) jump as high as possible from a comfortable standing position with each foot placed on a separate force platform. Five repetitions of each task were executed. Ground reaction forces and moments were recorded using three strain-gauged force plates (AMTI, Watertown, MA) sampling at 2000 Hz. The ground force data were low-pass filtered using a fourth-order, recursive, zero-lag, Butterworth filter with a cut-off frequency of 40 Hz. A static trial was recorded to measure the inter-marker distances. Marker trajectories were low-pass filtered using a second-order recursive, zero-lag, Butterworth filter with a cut-off frequency of 6 Hz.The scaled-generic and image-based musculoskeletal models were based on the generic model developed by . The generic model was comprised of 12 segments with 31 independent degrees-of-freedom actuated by 92 Hill-type muscle–tendon units (A). A ball-and-socket joint represented the lumbar joint, each shoulder, and each hip; a translating hinge joint represented each knee; and a universal joint represented each ankle. The shoulder and elbow joints were actuated by 10 ideal torque motors, while all other joints were actuated by Hill-type muscle–tendon units.Scaled-generic models were obtained by scaling the generic model to match each participant's body anthropometry and mass using OpenSim (). Inter-marker distances recorded during the static trial (B) were used to scale bone geometries, joint centres, joint rotation axes, muscle paths, fibre lengths, and tendon slack lengths. The mass of the generic model was scaled to match that of each participant by preserving the mass ratio between segments in the generic model. Image-based models were created using anthropometric measurements obtained from the CT images for the pelvis and femur segments, skin-marker locations for the torso, and scaled-generic parameters for the remaining segments. The geometries of the pelves and femora were segmented from the CT data using Amira (Visage Imaging GmbH, Burlington, MA). The hip joint centre was defined as the centre of the sphere used to best-fit the femoral head surface. The knee axis was assumed to be the axis connecting the femoral epicondyles, and the lumbar joint was assumed to be located at the antero-posterior level of the vertebral foramen and at the mid-point of the L5-S1 inter-vertebral space as identified in the sagittal plane. The torso was adjusted to match the vertical distance between the sacrum and the seventh cervical spine calculated from the skin-mounted markers (). Muscle paths in the scaled-generic model were registered on the skeletal surfaces by superimposing the muscle lines-of-action onto the CT data (C). The values of optimum muscle-fibre length and tendon slack length reported by were uniformly scaled so that each muscle develop its peak isometric force at the same joint angle in both the scaled-generic and image-based models.Scaled-generic and image-based muscle and joint forces were calculated for the dominant leg of a selected trial. Joint angles were computed by performing an inverse kinematics analysis according to methods described by . The joint angles and the measured ground reaction forces were used to calculate the net moment developed about each joint. Static optimisation was then used to decompose the net joint moments into muscle forces by minimising the weighted sum of the squares of muscle activations (). The hip joint force was calculated by solving for static equilibrium at the femur.Bone tissue was modelled using 10-node tetrahedral elements. A linear regression equation relating the grey levels in the CT data to the hydroxyapatite density contained in the five-sample calibration phantom was used to convert the images' grey levels into apparent bone density levels. The apparent bone density distribution was converted into an isotropic Young's modulus for each voxel using the relationships derived in . The Young's modulus values were integrated over each mesh element using Bonemat© (Super Computing Solutions, Bologna). The femur was partitioned into eight different levels: four diaphyseal, one pertrochanteric, and three femoral neck levels. Each level was further subdivided into four regions: anterior, posterior, medial and lateral aspects, giving 32 sub-regions altogether (). Each femur finite-element model was kinematically constrained at the femoral epicondyles, a condition that is statically equivalent to applying forces acting on the most distal femur (). Five element layers surrounding the muscle attachment points were excluded to avoid boundary condition artefacts.Scaled-generic and image-based muscle and hip joint forces were applied to the finite-element model using custom code developed in Matlab (MathWorks Inc., Natick, MA). The pelvic, femoral and tibial anatomical coordinate systems were calculated according to International Society of Biomechanics standards (). The unit vector describing the line-of-action of each muscle force was assumed to originate at the muscle's attachment point on the femur and was oriented along the line-of-action of the muscle force. The muscle force components were obtained by multiplying the magnitude of the muscle force calculated from static optimisation by the unit force vector. The muscle force components were then applied at the node closest to the muscle attachment point in the finite-element model.The hip joint force was applied to the node on the surface of the femoral head closest to the intersection between the hip contact force vector passing through the hip centre and the femoral head surface. Linear static simulations were performed in Abaqus© (Dassault Systemes, Vélizy-Villacoublay) using the implicit direct solver. The 90th percentile of the scaled-generic and image-based principal tensile and compressive strain values were calculated for each femoral sub-region over the course of 20 time steps during the load-bearing phase of each activity.Image-based joint angles, joint moments, hip-joint contact forces, muscle activation patterns and femoral strains were compared with corresponding published values (Anthropometric errors were defined as the difference between the scaled-generic and image-based joint-to-joint distances, femoral anteversion angles, caput-collum-diaphyseal (CCD) angles, femoral neck lengths, and muscle moment arms. Scaled-generic and image-based muscle and joint forces were compared using linear regressions. The moment generated by the image-based and scaled-generic force systems about six locations uniformly distributed between the mean constrained node at the distal femur and the hip joint centre was calculated. The distribution of the scaled-generic and image-based moment differences was assessed at each location.The effect of scaled-generic anthropometric errors on regional femoral strain calculations was assessed using linear regressions and Root Mean Square (RMS) errors. Calculations were performed for each region along the length of the femur. The normality of the strain difference distributions was assessed using Kolmogorov–Smirnov test () were used to compare normal and non-normal differences in strain distributions over the different activities.The effect of sample size on inter-participant strain averages was assessed by calculating the regional average tensile and compressive strains using a sample size increasing from 2 to 10 participants. The linear regression and the RMS error between the inter-participant (sample size: 10) scaled-generic and image-based averages of regional femoral strains were also calculated.The joint angles, net joint moments, hip-joint contact forces, and muscle activation patterns calculated for walking using the image-based models were consistent with earlier findings (see in Supplementary material). The peak femoral strains in the proximal-lateral femoral shaft calculated for walking and stair ascent were consistent with corresponding strain measurements reported by ; mean peak tensile and compressive strains calculated for the 10 participants ranged from 1351 to 1647 με and 971 to 988 με, respectively, compared to corresponding strains of 1198–1454 με and 393–948 με measured from two hip syndrome patients.Scaled-generic and image-based anthropometric differences for the hip-to-hip and hip-to-knee distances were within ±1.04 cm (±6.1% of the hip-to-hip image-based distance) and ±1.88 cm (±5.5% of the hip-to-knee image-based distance), while the femoral anteversion and CCD angles were within ±8.9 and ±2.8 degrees, respectively, and femoral neck length was within ±0.4 cm (). The average absolute and percent differences in the moment arms of the hip- and knee-spanning muscles calculated for all six activities were −1.7 cm and −0.85% whereas the peak absolute and percent differences were 15.6 cm and +38.9% (). The linear regression between the scaled-generic and image-based muscle and hip contact forces yielded a coefficient of determination of R2=0.78 for muscle forces and R2=0.74–0.91 for the hip contact force components. The average Root Mean Squared Error (RMSE) ranged from 0.2 to 0.7 BW for the hip contact force components and was 0.1 BW for the muscle forces. The slope of the regression line ranged from 0.77 to 0.85 (0.76–0.86 95% confidence interval) for the hip contact force components and was 0.89 (0.88–0.89 95% confidence interval) for the muscle forces (). The median difference between scaled-generic and image-based moments was −8.6 Nm at the distal constraint and −1.1 Nm at the hip joint centre, while the 80th percentile of scaled-generic and image-based moment differences was −155.8 Nm at the distal constraint and −25.4 Nm at the hip centre (The coefficient of determination relating scaled-generic and image-based femoral strains decreased in the proximal-to-distal direction along the femur from level A to level H. The coefficient of determination varied from R2=0.92 (level A, anterior) to R2=0.48 (level H, medial). The average strain error (RMSE) varied from 380 με (level A, anterior) to 4064 με (level H, medial). The peak strain error varied from 2821 με (level A, anterior) to 34,166 με (level H, medial) (). The strain error distribution was not normally distributed (Kolmogorov–Smirnov, Lilliefors, p<0.001) and was activity-independent (Wilcoxon test, α=0.05) (). Scaled-generic and image-based strain maps were different both in terms of the spatial distribution of strain and in magnitude. The differences in spatial distribution reached a peak at the most distal level H, at which point the location of the peak strain differed by as much as an anatomical quadrant compared to the image-based models (). The peak tensile and compressive strain differences per femoral level (A–H) increased linearly (R2=0.77–0.82) from the proximal to distal femur, reaching 1051 με and −570 με, respectively, in the femoral neck (levels A–C), and 12,307 με and −3668 με in the remainder of the femur (levels D–H) (The inter-participant average for regional bone strain was a monotonic function of sample size that converged asymptotically (). The inter-participant averages for the scaled-generic and image-based bone strains showed similar patterns (); the coefficient of determination was R2=0.95, the RMSE was 430 με, and the slope of the regression line was 0.96 (95% confidence interval: 0.96–0.97) (We examined the sensitivity of femoral strain calculations to the anthropometric errors committed while scaling a generic musculoskeletal model to an individual participant's anatomy. Our results indicate that anthropometric errors cause a region-dependant strain error, which may lead to unrealistic participant-specific strain calculations in every femoral sub-region. In accordance with the central limit theorem, however, averaging the calculated bone strains over a cohort of participants can reduce strain errors, making scaled-generic models a viable tool for studying average patterns of femoral strains within a cohort of participants.The anthropometric errors caused a region-dependant participant-specific strain error that increased from 2821–5500 με in the very proximal neck to 22,620–34,166 με in the distal diaphysis (). These region-dependant strain differences are attributable to scaled-generic and image-based differences in terms of hip contact force () and moments exerted on the femur by scaled-generic and image-based force systems (). Calculated strain values ranged from 39% to 468% of the bone yield strain threshold (i.e. 7300 με in tension and 10,400 με in compression) reported by . Therefore, anthropometric errors in scaled-generic models may lead to unrealistic estimates of participant-specific regional femoral strains. Specifically, image-based and scaled-generic strain maps over level-by-level femoral cross-sections differed either in terms of orientation or magnitude: orientation differences could cause the peak strain location to rotate about the femoral axis by up to a quadrant (), whereas peak strain differences over level-by-level cross-sections in the femoral neck (levels A–C) were −570 με in compression and 1051 με in tension (), overall less than the 14.4% of the yield strain reported by . Therefore, scaled-generic models may be used to calculate the participant-specific peak strain in the femoral neck when the peak strain, but not its location, is of interest.The comparison of inter-participant averages of image-based and scaled-generic regional femoral strains showed good agreement for every femoral sub-region (). The average error was 430 με and the coefficient of determination was R2=0.95. Therefore, scaled-generic models are a viable tool for determining average femoral strains within a cohort of participants. The minimum size of the cohort is a function of the femoral region of interest and the admissible error for the intended application, and can be determined using convergence plots (The reliability of the present results can be better understood by comparing intermediate results with previous findings. Image-based models yielded joint kinematics, net joint moments, hip joint forces, muscle activation patterns and bone strains in the proximal-lateral femoral shaft in agreement with earlier studies (). We found errors in the hip-joint-centre location of up to 2.01 cm for the scaled-generic model, which is similar to the 2.09 proximal shift of the hip-joint-centre location reported by . Errors in the flexion–extension moment arms of the hip-spanning muscles over the investigated activities were as high as 38.9% (), which agrees with the 36.3% error reported by for gait. The 0.52 BW difference between scaled-generic and image-based hip joint forces reported by for walking compares well with the 0.2–0.7 BW average difference over a broader range of tasks found in the present study. Image-based models yielded a tensile strain of 1912 με () in the femoral neck during walking, in line with the 2004 με reported earlier using a model entirely generated from dissection data (There are limitations associated with the analyses presented. The imaging protocol was designed to focus only on the femur and pelvis to minimise the X-ray radiation dose given to participants. Extending the image-based anthropometric information to the remaining body segments may have increased further scaled-generic and image-based femoral strain differences. The reported average strain values might not be representative for larger cohorts due to the high strain errors () and the limited sample size of 10 participants. Additional sources of error that can affect femoral strain calculations include the definition of the constraint of the femur (). Functional methods have been found to improve the estimation of the hip joint centre () over landmark-based scaling procedures and have been used to determine musculoskeletal forces at the knee (). Therefore, functional methods may help reduce anthropometric errors in scaled-generic models and their effect on femoral strain calculation. Regarding the effect of aging on muscle function, concluded that age-related changes in muscle function may be important when simulating movements with substantial power requirement while showed that muscle function is invariant to age when walking speed is controlled. Therefore, we do not expect femoral strains during daily activities to be significantly affected by age-related changes in muscle function. Last, the absence of in vivo bone deformation measurements makes it impossible to assess the accuracy of scaled-generic and image-based models. However, the present results provide information about the sensitivity of model outputs to anthropometric errors in scaled-generic musculoskeletal models.Despite the above limitations, this study provides a better understanding of the sensitivity of femoral strain calculations to anthropometric errors committed while scaling a reference model to a participant's anatomy. Our analyses showed that the calculation of participant-specific bone strain from scaled-generic models should be considered with caution because it may yield unrealistic strain estimates, particularly in the most distal region. In accordance with the central limit theorem, however, the effect of anthropometric errors is reduced significantly by averaging strain calculations over multiple participants, making the use of scaled-generic models a viable solution with which to assess cohort-based averages of femoral strain during different activities.None of the authors have a conflict of interest in relation to this study.Supplementary data associated with this article can be found in the online version at Microstructural evolution and strengthening mechanisms operating during cryogenic rolling of solutionized Al-Cu-Mg alloyIn this work, microstructural evolution of a solutionized Al-Cu-Mg alloy during rolling at liquid-nitrogen temperature was studied and concomitant strengthening effect was elucidated. It was found that a prior solid-solution treatment as well as a lowering of deformation temperature to the cryogenic range essentially suppressed dislocation mobility. This promoted an abrupt increase of dislocation density but considerably retarded microstructural processes, particularly texture evolution and development of deformation-induced boundaries, thus suppressing grain refinement. Hence, the strengthening effect of the cryogenic rolling was mainly contributed by the work hardening mechanism.Due to attractive combination of properties including relatively low density, high strength, good ductility and fracture toughness along with satisfactory corrosion resistance, wrought heat-treatable aluminum alloys are widely used in various industries including aerospace, transportation and military. The optimal balance of service characteristics in such materials is typically achieved through a complex thermo-mechanical processing involving solution heat treatment followed by cold rolling and final artificial aging Recently, it has been demonstrated that efficiency of the ageing treatment may be further improved by lowering of the rolling temperature to cryogenic range Bearing in mind the promising potential of cryogenic rolling, substantial research efforts have been devoted to elucidate its effect on microstructure and properties of heat-treatable aluminum alloys Although the above works have provided a valuable insight into the studied phenomenon, the underlying physical mechanisms remain poorly understood. Considering the pronounced pinning effect of solutes as well as the essential retardation of thermal-assisted deformation processes expected at cryogenic temperatures, the widespread grain subdivision model The present work attempted to provide a deeper insight into microstructural evolution with the final aim to provide a deeper insight into the microstructure-strength relationship. To this end, advanced capabilities of electron backscatter diffraction (EBSD) technique were employed for thorough characterization of microstructural changes. The obtained results were used to figure out the contributions of various hardening mechanisms to overall material strength.The program material comprised commercial 2519 aluminum alloy with nominal chemical composition of Al-5.64Cu-0.33Mn-0.23Mg-0.15Zr-0.11Ti-0.09V-0.08Fe-0.08Zn-0.04Sn-0.01Si (all in wt%). This is a typical aluminum heat-treatable alloy with relatively high copper content. The latter solute is believed to be exceptionally effective for dislocation pinning The material was manufactured by semi-continuous casting followed by a homogenization annealing at 510 °C for 24 h with subsequent furnace cooling. The produced ingots were swaged at 400 °C to an accumulated true (logarithmic) strain of ~0.9 and then rolled at 425 °C to a total thickness reduction of 75 pct. Finally, the material was given a solution annealing at 525 °C for 1 h followed by immediate water quenching. The produced microstructure was dominated by fully-recrystallized grains with mean equivalent diameter of ~ 30 µm, nearly random misorientation distribution and a weak texture. In greater detail, the material processing technique as well as the evolved microstructure has been reported elsewhere Microstructural characterizations were focused at the mid-thickness portion of the longitudinal (i.e., the RD×ND) section of the rolling sheets and were performed by EBSD, transmission electron microscopy (TEM) and X-Ray techniques. In all cases, the final surface finish was achieved by electro-polishing in a solution of 25 pct. nitric acid in ethanol with an applied potential of 20 V by using a Struers Tenupol-5 twin-jet electro-polishing machine. In greater details, the sample preparation procedure has been described elsewhere EBSD analysis was conducted with a FEI Nova NanoSEM 450 field-emission gun, scanning electron microscope equipped with TSL OIM™ EBSD system. The total statistics of EBSD measurements is summarized in . For each diffraction pattern, five Kikuchi bands were used for indexing, thus minimizing mis-indexing errors. To improve reliability of EBSD data, the small grains comprising three or fewer pixels were automatically removed from the maps using the standard grain-dilation option of the TSL software. Furthermore, to eliminate spurious boundaries caused by orientation noise, a lower-limit boundary misorientation cut-off of 2° was used. A 15° criterion was applied to differentiate low-angle boundaries (LABs) and high-angle boundaries (HABs). Grain size measurements were made by the linear-intercept method.TEM examinations were performed using JEOL JEM-2100 and a Technai G2F20 field-emission gun, transmission electron microscopes both equipped with double-tilt stage and operated at 200 kV.Dislocation density was evaluated by X-ray technique. The measurements were carried out with the Smart LAB Rigaku X-Ray diffractometer using Cu Kα radiation source. The θ - 2θ scans were conducted from 2θ = 35° to 125° with a step size of 0.02°. The coherent domain size and the crystal-lattice microstrains were estimated based on the modified Williamson-Hall approach To examine the effect of cryogenic rolling on mechanical behavior, uniaxial tension tests were performed at ambient temperature. To this end, dog-bone tension specimens were machined along the RD of the rolled sheets by using a Sodick AQ300 wire-electrical-discharge machine. According to ASTM E-8 standard, the specimen cross-section dimensions were kept 3 × 7 mm2 whereas the gauge length was 25 mm. The tension tests to failure were conducted at a constant crosshead velocity corresponding to a nominal strain rate of 1.3 × 10−3 s−1 using a screw-driven Instron 5882 universal testing machine equipped with automatic high-resolution contacting extensometer MFX 500. Three tensile specimens were tested for each material condition.EBSD orientation maps illustrating grain structure development during cryogenic rolling are summarized in . In the maps, the grains are colored according to their crystallographic directions relative to the RD (color code triangle is given in the bottom right corner of a) whereas LABs and HABs are depicted as white and black lines, respectively. To quantify microstructural changes, the mean HAB intercept was derived from EBSD data and shown as a function of true rolling strain in a. For comparison purposes, the theoretically predicted geometrical reduction of the grain thickness due to the imposed rolling strain was also shown in this figure by a broken line.After rolling to a true strain of 0.36, original grains were found to be compressed along the ND (a) presumably due to geometrical effect of strain. Moreover, a developed LAB structure was observed in grain interior (a). Considering the fully-recrystallized character of original grain structure, the revealed LABs were obviously produced during rolling and therefore they could be referred to as deformation-induced boundaries a). In some cases, LAB segments accumulated misorientation over 15° thus transforming into deformation-induced HABs (several examples are arrowed in a). The sub-boundary development gave rise to noticeable orientation spread within original grains seen as local variation of orientation contrast in TEM observations confirmed the formation of the closely-spaced banded structure after rolling to relatively low reduction (a). From TEM micrographs, the mean LAB spacing was estimated to be ~ 0.2 µm thus being essentially lower that detected by EBSD (compare a). This perhaps evidenced that significant portion of the deformation-induced LABs had misorientation below EBSD resolution limit, i.e., 2°. As expected, an abrupt increase of dislocation density was revealed (A further increase of the true rolling strain to 0.92 and 1.61 resulted in a development of ribbon-shaped grains which contained dense LAB substructure (b & c). The measured mean HAB spacing was substantially lower than that predicted from geometrical effect of strain (a). This perhaps evidenced that notable portion of HABs originated from LAB-to-HAB transformation. Nevertheless, the evolved microstructure was obviously dominated by LABs (b & c). Therefore, cryogenic rolling did not result in a formation of an ultrafine-grained structure, in contrast to some reports in scientific literature a & b). This may indicate that the LAB formation had stagnated at relatively low strains. Dislocation density was also tended to saturate at ~ 1015 m−2 (It is also worth noting that no clear evidence of macro-scale shear banding was found for the entire investigated range of strains.To provide a deeper insight into microstructure evolution, orientation data were extracted from EBSD maps and arranged as orientation distribution functions (ODFs). The representative sections of the ODFs (φ2 = 0°, φ2 = 45°, or φ2 = 65°) showing texture development during cryogenic rolling were summarized in a to c. Pertinent details of the ODFs calculations as well as ODF reference frame are shown in the bottom right corner of the figure. For comparative purposes, several ideal rolling orientations were indicated in Despite the texture in the initial material was relatively weak, some crystallographic preference of Goss {011}<100> and Cube {001}<100> orientations was found (a). Surprisingly, the rolling to low reductions resulted in some strengthening of Cube component (b). With this exception, however, the resulting texture was essentially irregular and weak (b). The development of a distinct rolling texture was found only after 80 pct. reduction (c), i.e., the texture evolved relatively slowly. The produced texture was dominated by {110}<uvw> α-fiber; additionally, a relatively-weak β fiber was also observed (To quantify the texture evolution, volume fractions of principal textural components (within 10-degree tolerance) were derived from EBSD data and summarized in a as function of rolling strain. To assist interpretation of this process, these components were highlighted in EBSD maps, as shown in The textural measurements confirmed the strengthening of the Cube component at relatively low strains (a). Moreover, it has been also found that this effect was associated with a development of deformation bands within grains (b). Though this phenomenon is known for many years With further increase in rolling strain, the Cube texture tended to disappear (a). On the other hand, a significant intensification of S and Brass components was detected (a). Additionally, a less-pronounced strengthening of Copper and Goss orientations was also observed (c & d, it is interesting to note that the formation of rolling texture at relatively large strains was not associated with a development of deformation bands within grains, as normally expected for the grain subdivision model Attempting to provide a closer inspection into the texture development, orientation intensity along the α- and β fibers was measured and shown as a function of rolling strain in . It is seen that more or less clear α-fiber had evolved only after a true strain of ~ 1.61 (a), i.e., the texture evolution was relatively sluggish. Despite the texture intensity was not uniform along the α-fiber, no distinct Goss or Brass components were found (a). This additionally evidenced a relatively slow character of the texture evolution. The β fiber also contained no clear peaks near the Copper or S orientations whereas the orientation density was skewed towards the Brass component (b). From this observation, it may be suggested that S orientation had a transient character and its accumulation during rolling was associated with a relatively slow motion of orientations along the β fiber towards the Brass. This perhaps explains the interspersed distribution of the S and Brass orientations in EBSD maps mentioned above.To examine the evolution of misorientation distribution, misorientation-angle and misorientation-axis distributions were derived from EBSD data and summarized in , respectively. Attempting to obtain a deeper insight into microstructural changes, misorientation-angle distributions in a were expressed in terms of grain-boundary density, i.e., the measured grain-boundary length for a given misorientation angle divided by the area of the EBSD map. From prior experience, this metrics provides a direct comparison of grain-boundary characteristics, thus enabling more reliable interpretation of underlying physical mechanisms [e.g. ]. To provide a closer inspection of misorientation changes, a magnified image of high-angle portion of misorientation-angle distributions was given as an insert in the top right corner of a. The effect of rolling strain on HAB fraction was shown in The initial material was characterized by relatively low LAB fraction (a) and nearly-random HAB distribution (insert in a). Rolling to a true strain of 0.36 resulted in an abrupt increase of LAB content (a & b). Moreover, a nearly-homogeneous enlargement of HAB area was observed in the entire misorientation range from 15° to 62.8° (insert in a). The latter effect was presumably associated with geometrical compression of original grains during rolling (a) and the concomitant increase of their grain-boundary area. On the other hand, the evolved misorientation-axis distribution had no distinct features (The increment of the rolling strain to 0.91 and 1.61 provided further increase of LAB area (a), thus mirroring the extensive formation of deformation-induced boundaries within grains (b & c). Of particular interest was a skewing of the LAB distribution towards higher misorientations (a) and significant increase of density of ~ 15o–25° boundaries (insert in a). These observations obviously reflected a gradual increase of LAB misorientation and the subsequent LAB-to-HAB transformation, thereby being in the line with the measured enlargement of HAB fraction (b). It is worth noting in this regard that considerable portion of LABs was presumably missed during EBSD mapping, as discussed in . It is quite likely therefore that the measured HAB fraction was overestimated.In the misorientation range above ~25°, the boundary density first increased more or less homogeneously (insert in b & c). After a true strain of ~ 1.61, however, a broad misorientation peak in the range of ~ 40–60° was observed (insert in a). Furthermore, a pronounced clustering of misorientation axes of these boundaries near <101> was also detected (b & c). It is interesting to note in this context that a formation of {110}<uvw> α-fiber texture was found at this strain level (a). To examine a possible relationship between misorientation changes and texture development, the so-called “uncorrelated” (or texture-derived) misorientation distribution was calculated by using a standard option of EBSD software and shown in c. In contrast to the real misorientation distribution displaying the misorientation data between neighboring pixels in an EBSD map, the texture-derived distribution was calculated assuming no spatial correlation between the pixels, i.e., all possible misorientations between the pixels (including non-contiguous ones) were calculated. The relatively good matching between the uncorrelated- and the measured distributions in c suggested that the broad maximum near ~ 55° was perhaps attributable to the development of the α-fiber texture.To investigate the strengthening effect of rolling, axial tension tests were conducted at ambient temperature and the obtained results were summarized in . As expected, the rolling resulted in a considerable material hardening (a & b) as well as in substantial reduction in ductility (). Moreover, a smoothing of the deformation diagrams, i.e., the suppression of the Portevin-Le Chatelier effect inherent to the initial material, was also worthy of remark (Remarkably, the strengthening effect rapidly saturated with strain (b). To quantify this process, the hardening rate δσ/δe (in which δσ denotes the increase in yield strength for an increment of the true rolling strains δe) was calculated, as shown in c. As normally observed during cold working, the hardening rate rapidly stagnated with strain.On the basis of detailed microstructural characterization given above, the various contributions to the strength of the cryo-rolled material were evaluated within the context of yield strength measurements. The obtained results were summarized below.Assuming that the strengthening mechanisms act independently (and thus are additive in nature) and considering a solutionized (i.e., a precipitation-free) character of the examined material conditions, the yield strength can be expressed as σ=σ0+σd+σgb, where σ0, σd and σgb are threshold strength, dislocation strengthening and grain-boundary strengthening, respectively.For solutionized material conditions used in the present study, the threshold stress has been reported to be ≈ 110 MPa The dislocation strengthening is usually described by the classic Taylor relation σd=αMGbρ, where α is a constant, M denotes the Taylor factor, G is the shear modulus (= 25.4 GPa), b is the magnitude of Burgers vector (= 0.286 nm), and ρ is dislocation density. Considering a relatively homogeneous distribution of dislocations (b), the calculated hardening effect was found to vary from 214 MPa to 271 MPa (, misorientation distributions evolved during cryogenic rolling were dominated by LABs. Accordingly, the grain-boundary strengthening was also assumed to be dictated by the sub-boundaries and thereby it may be quantified as ). Importantly, significant proportion of LABs in the cryo-rolled material was below EBSD detectable limit and therefore the mean LAB misorientation could not be simply derived from EBSD data. In this regard, the LAB hardening was estimated by a subtraction of the threshold stress as well as the dislocation strengthening from the measured yield strength. The obtained results were summarized in . From these estimations, the mean LAB misorientation was calculated. It was found to vary from ≈ 0.3° at the rolling reduction of 40 pct. to ≈ 0.6° at the rolling reduction of 80 pct., thus being relatively low. For comparison, the mean LAB misorientation in heavily-cold-rolled aluminum alloys is often reported to be ~2–3° , the deformation-induced microstructures produced during cryo-rolling were characterized by (i) a formation of regular arrays of extended LABs, (ii) their alignment with {111} slip-plane traces as well as (iii) the gradual LAB-to-HAB transformation (). From these morphological characteristics, it seems that microstructure evolution was governed by the grain-subdivision mechanism An important characteristic of the cryo-rolled material was a dominance of α-fiber texture (c). It is worth noting in this regard that aluminum alloys normally exhibit a development of Copper-type {112}<111> texture during cold rolling and this effect is typically attributed to a relatively high stacking fault energy in such materials. For instance, the prevalence of the Copper orientation has been found in commercial 2519 aluminum alloy (studied in the present work) which has been rolled at ambient conditions Another important effect revealed in the present study was a relatively slow texture evolution. Specifically, a formation of distinct rolling texture was observed only after 80-pct. reduction (c). It should be noted that the rolling textures are known to typically develop at substantially lower strains. For example, a development of clear rolling texture in the cold-rolled 2519 aluminum alloy (used in the present work) has been found after 40-pct. reduction ) as well as with the relatively slow evolution of the LAB misorientation, as discussed in the previous section.Thus, an application of prior solution-heat-treatment as well as the lowering of deformation temperature to a cryogenic range employed in the current study had efficiently suppressed dislocation mobility and thus hindered dynamic recovery and dynamic recrystallization, in accordance with our expectations. On the other hand, this also essentially retarded LAB evolution and thus inhibited a grain refinement.In this work, microstructure evolution and strengthening mechanisms operating during cryogenic rolling of solutionized 2519 aluminum alloy were investigated. The main conclusions derived from this study are as follows.The cryo-rolled material was characterized by relatively slow microstructure evolution. Specifically, a distinct rolling texture was established only after a true strain of 1.61 and the mean LAB misorientation was found to be essentially lower than that usually measured after rolling at ambient temperature. Moreover, the evolved texture was dominated by {110}<uvw> α fiber instead of the normally-expected {112}<111> Copper orientation.Based on the experimental observations, it was deduced that the prior solution-heat treatment as well as the lowering of deformation temperature to the cryogenic range had efficiently suppressed dislocation mobility. This promoted an abrupt increase of dislocation density but retarded a LAB development and thus inhibited a grain refinement.Accordingly, the strengthening effect of the cryogenic rolling was mainly contributed by the substructure mechanisms, i.e., the dislocation- and the LAB hardening.Stress-induced martensite transformationMicrostructures and mechanical properties of Ti–Mo alloys cold-rolled and heat treatedIn this study, the microstructures and mechanical properties of Ti–10Mo and Ti–20Mo alloys (mass%) are investigated to assess the potential use in biomedical applications. The microstructures are examined by X-ray diffraction analysis (XRD) and scanning electron microscopy (SEM). The mechanical properties are determined from uniaxial tensile tests. The experimental results indicate that the microstructures and mechanical properties of Ti–Mo alloys are dependent upon the cold rolling, solution heat treatment, and Mo content. The Ti–10Mo alloy exhibits (α″ + β) and (β + ω) phases under the cold rolling (CR) and solution treatment (ST), respectively. By contrast, the Ti–20Mo alloy comprises only β phase under such conditions. The quenched Ti–20Mo alloy has the lowest elastic modulus and CR Ti–20Mo alloy has the highest tensile strength. The quenched Ti–10Mo alloy exhibits the excellent ductility and two-stage yielding from stress-strain curves due to the stress-induced martensite transformation from β to α″ during tensile deformation. These Ti–Mo alloys exhibit low yield strength and good ductility, and they are more suitable for biomedical applications than the conventional metallic biomaterials from the viewpoint of better mechanical compatibility. The quenched Ti–10Mo alloy has some advantages over the other β binary Ti–Mo alloys for biomedical applications. β type Ti–Mo–Sn alloys are expected to be promising candidates for novel metallic biomaterials.► The microstructures and mechanical properties of Ti–Mo alloys are dependent upon the cold rolling, solution heat treatment, and Mo content. ► The quenched Ti–10Mo alloy exhibits the excellent ductility and two-stage yielding due to stress-induced martensite transformation from beta to alpha double prime during tensile deformation. ► The Ti–Mo alloys are more suitable for biomedical applications than the conventional metallic biomaterials from the viewpoint of better mechanical compatibility. ► The quenched Ti–10Mo alloy has more advantages over the other beta binary Ti–Mo alloys for biomedical applications.Stress-induced martensite transformationThe Ti–6Al–4V alloy has become one of the most frequently used implant materials, particularly for orthopedic applications, due to its higher corrosion resistance, better biocompatibility, and significantly lower elastic modulus as compared to more conventional metallic biomaterials such as stainless steel and Co–Cr alloys To overcome the above drawbacks, Nb, Ta, Zr, Hf, Mo, and Sn, which have been judged to be non-toxic and non-allergic, have been selected as safe alloying elements to develop low elastic modulus Ti alloys having high strength for bone implant applications Nb, Mo, and Ta among the above safe alloying elements are considered as the excellent β phase stabilizers The concentrations of alloying elements, Mo, Nb, and Ta above which β is retained after quenching from β field are 8, 22, and 52 mass% (hereafter, ‘mass%’ will be omitted), respectively for binary Ti–Mo The designed Ti–10Mo and Ti–20Mo alloys were synthesized by the following procedure. Appropriate amounts of high-purity sponge Ti (99.5%) and Mo powder (99.8%) were mixed. The mixtures were melted by non-consumable arc melting for three times in order to ensure chemical homogeneity. The obtained ingots were homogenized in a vacuum at 1273 K for 21.6 ks in order to eliminate the as-cast microscopic segregation and were then cold rolled (CR) into 3-mm-thick plates. The blank samples with a size of 3 × 12 × 60 mm3 were cut from the rolled plates along the rolling direction and some of the samples were subjected to a solution treatment (ST) in a vacuum above the β-transus temperature of the alloys Microstructures of the Ti–Mo alloys were observed by scanning electron microscopy operated at 20 kV. The samples for the microstructural observation were ground, polished, and etched in a solution composed of 5 vol.% HF, 10 vol.% HNO3, and 85 vol.% H2O. The phase constitutions of Ti–Mo alloys were analyzed by X-ray diffraction analysis using Cu-Kα radiation in the typical 2θ range of 30–80° with an accelerating voltage of 40 kV, current of 250 mA, and a scanning speed of 1°/min.Tensile specimens with a gage length of 12 mm and a cross section of 3 mm (width) × 2 mm (thickness) were machined from the blank ST and CR samples after removal of surface oxides on their surfaces. Uniaxial tensile tests were carried out at a crosshead speed of 8.33 × 10− 6 |
m/s at room temperature. A strain gage was attached to the gage section of each specimen to measure the strain change during each test. The ultimate tensile strength (UTS), the 0.2% offset yield strength (YS), and the elongation at fracture (El) were accordingly determined. The tensile elastic modulus (EM) is determined according to ASTM E111-97 The chemical compositions of the Ti–10Mo and Ti–20Mo alloys are determined by wet chemical and gas analysis. The results are shown in , which reveal that the chemical compositions of two Ti–Mo alloys are closely related to their nominal compositions. Thus, the Ti–Mo alloys were synthesized successfully.The XRD patterns of the Ti–Mo alloys are shown in . The XRD peaks reveal that the CR Ti–10Mo alloy is composed of β + α″ two phases and the CR Ti–20Mo alloy comprises only single β phase. The CR Ti–Mo alloys exhibit obvious texture because their strongest peaks are (200) rather than (110) or (211) which is normally the strong peak of β phase , it can be observed that the intensity of β phase in the ST Ti–10Mo alloy is much stronger than that of the ω phase, indicating that the volume fraction of ω phase is very smaller than that of the β phase.The SEM microstructures of the Ti–Mo alloys are shown in . It can be observed that the CR Ti–Mo alloys exhibit microstructures with obvious fibrous stripe, which correspond well with the rolling texture detected by the above XRD analysis. By contrast, the ST Ti–Mo alloys exhibit similar microstructures with equiaxed β grains. No other significant difference exists in their microstructures except larger β grains in the ST Ti–10Mo alloy than in the ST Ti–20Mo alloy. The ω phase is invisible in the SEM microstructure of Ti–10Mo alloy, which may be related to its very small size and limited SEM resolution.The mechanical properties and nominal stress-strain curves of the Ti–Mo alloys are shown in , respectively. It can be noticed that the ST Ti–20Mo alloy has the lowest elastic modulus of 75 GPa and the ST Ti–10Mo alloy has the highest modulus of 93 GPa. It is well known that the elastic modulus, one of the intrinsic natures of materials, is determined by the bonding force among atoms It also can be observed that the CR Ti–Mo alloy has higher UTS and lower elongation at fracture than the corresponding ST Ti–Mo alloy despite the same chemical composition, which is related to the work-hardening caused by cold rolling. It is considered that an increase of solid strengthening with addition of Mo content from 10 to 20% leads to higher UTS values of the CR and ST Ti–20Mo alloy than those of the corresponding Ti–10Mo alloy, respectively. These alloys exhibit low yield strength and good ductility, which is related to the presence of β phase since this phase with the bcc structure under most conditions exhibits more ductile than the other less symmetric structures in Ti alloys (b). By contrast, the CR Ti–10Mo and Ti–20Mo alloys exhibit rapid work hardening after yielding.In order to understand the above striking observation, the near fracture surface of ST Ti–10Mo alloy was examined by the XRD analysis and the result is shown in . The XRD peaks detect the existence of three phases of (α″ + β + ω) after the tensile test. As compared to , it is considered that α″ phase is formed during tensile deformation since the constituent phases before tensile test are two phases of (β + ω). Therefore, the metastable beta phase in this alloy undergoes a strain-induced martensite α″ transformation (SIMT) during tensile deformation, which is responsible for the double yielding observed on the stress strain curve in . The first yielding occurs at around 465 MPa during tensile test, which is caused by SIMT, is followed by a repaid work hardening resulting from an increasing difficulty to produce additional α″ phase. The second yielding would be associated with the initiation of slip deformation. No double yield phenomenon is observed for the Ti–20Mo alloy, indicating that no SIMT occurs and the β phase in this alloy is more stable than that in the ST Ti–10Mo alloy. The stress-strain curve of the Ti–20Mo alloy suggests that its deformation is accommodated solely by slip. Hence, the above results show that the tensile deformation behavior of the Ti–Mo alloys is related to Mo content.Such a deformation mechanism in β Ti alloys, which includes dislocation glide, twinning, stress-induced martensite, or a combination of these account for that the ST Ti–10Mo alloy undergoes SIMT during tensile test and the ST Ti–20Mo alloy does not in this study. According to Refs.Two kinds of ω phases have been reported in Ti alloys ), we understand that the volume fraction of ω phase is very limited in the ST Ti–10Mo alloy and its size is very small. These two reasons help to understand the reason why the ST Ti–10Mo alloy in this study exhibit the excellent ductility in spite of the presence of ω phase just like the ST Ti–14Mo alloy , the low modulus of a metallic biomaterial ensures more favorable conditions for bone healing and remodeling. The (elastic) admissible strain, defined as the ratio of (yield) strength to modulus (RSM), is a useful parameter in orthopedic applications. The higher the admissible strain, the more suitable the material is for such applications . It can be observed that the Ti–Mo alloys have much higher yield strength than the human bone As compared to the newly-developed β type Ti–35Nb–5Ta–7Zr and Ti–29Nb–13Ta–5Zr alloys In this study, we investigated the microstructures and mechanical properties of Ti–Mo alloys cold rolled and solution heat treated for potential use in biomedical applications. The conclusions of this study are summarized as follows.The microstructures and mechanical properties of Ti–Mo alloys are dependent upon the cold rolling, solution heat treatment, and Mo content. The Ti–10Mo alloy exhibits (α″ + β) and (β + ω) phases under the cold rolling and solution treatment, respectively. By contrast, the Ti–20Mo alloy comprises only β phase under such conditions. The quenched Ti–20Mo alloy has the lowest elastic modulus and CR Ti–20Mo alloy has the highest tensile strength. The quenched Ti–10Mo alloy exhibits the excellent ductility and two-stage yielding from stress-strain curves due to the stress-induced martensite transformation from β to α″ during tensile deformation. These Ti–Mo alloys exhibit low yield strength and good ductility, and they are more suitable for biomedical applications than the conventional metallic biomaterials from the viewpoint of better mechanical compatibility. The quenched Ti–10Mo alloy has some advantages over the other β binary Ti–Mo alloys for biomedical applications. β type Ti–Mo–Sn alloys are expected to be promising candidates for novel metallic biomaterials.A systematic procedure for the design of a cold rolling millThis paper presents a systematic design procedure for the design of a laboratory cold rolling mill. In order to arrive at proper decisions at various stages of the design, the concepts of fuzzy sets and priority decision tables were employed. The design process starts from deciding specifications and gradually reaches the detailed design phase. Specifications were fixed by trading-off various conflicting goals using the fuzzy set-based methodology. The various factors to be considered for deciding the roll diameter are presented. The roll diameter and motor power are chosen using the fuzzy set-based technique. Three possible arrangements for transmitting the power to rolls were conceived. The best among these three design alternatives was chosen by preparing a priority decision table. After the conceptual and embodiment stages of the design, the detailed design was carried out in a conventional way. The present paper gives more emphasis to a systematic design procedure for the conceptual and embodiment stages in the design process.Design of a rolling mill is a complex task requiring thorough understanding of the process as well as good decision-making capability for satisfying various conflicting goals. Numerous investigations have been carried out for the analysis of the rolling process. For a brief review of representative papers, one can refer to the paper by Dixit and Dixit The design process starts from deciding the specification of the product. In the beginning, the specifications are allowed to have a certain amount of flexibility and they gradually crystallize to crisp form as the design progresses. Three important stages of the design are: conceptual design, embodiment design and detailed design. Conceptual design takes the problem statement and generates broad solutions for it in the form of design concepts. In the context of a rolling mill, it is the stage where the designer decides about the type of roll arrangements, suitable roll-drive mechanism, motor type, etc. At the embodiment stage, the concepts are converted into bodily form. This is also called preliminary design. This stage will require decisions regarding critical rolling parameters, layout of the mill with several sets of general drawings and specifications. At this stage, a final check is made on function, spatial compatibility, design aesthetics and economics. Finally, detailed design is carried out. The outcome of this stage is a set of drawings obtained as a result of rigorous design calculations.Although the detailed design is carried out in a systematic manner, most of the time, the earlier stages of the design are based on intuition, experience and judgment of the designer and rarely do they follow a formal procedure. Various researchers of the design methodology have suggested systematic decision-making procedures for early stages of the design. A review of these methodologies has been nicely carried out in During the last three decades, fuzzy set theory has been finding wide applications in various fields of engineering including decision-making in design. It was introduced by Zadeh Considering that the material parameters and friction coefficient in the rolling process are uncertain, Dixit and Dixit The aim of the present paper is to describe a systematic methodology for the design of a cold rolling mill, giving more emphasis to the preliminary phases of the design, i.e. the conceptual and embodiment phases. A vast amount of literature is available on the detailed design aspects of rolling mills Arriving at the design specification is the first task in the design process. After that the conceptual, embodiment and detailed design stages follow. Quite often the decisions taken at one stage are revised after getting more information about the design in subsequent stages. The following subsections describe the salient features of the design methodology adopted for the cold rolling mill.In arriving at a decision regarding the design specifications, the following are the minimum required parameters:Yield strength and hardening coefficient of material.Inlet thickness and outlet thickness of the strip.In a systematic procedure, first the range of inlet thickness is decided, depending on the requirement. Here, a range of 2–10 mm was chosen. It is known that if the width is about 10 times the thickness, the process can be considered as plane strain. Since the objective of the laboratory rolling mill might be to study the plane strain rolling of large thickness strip, a strip of width 100 mm was chosen.The outlet thickness decides the percentage reduction. This is a very important parameter influencing roll power and roll separating force. A designer would like to see the capability of maximum reduction and high rolling speed, but would be constrained by motor power and roll separating force. The motor power and roll separating force directly influence the cost of the rolling mill. A rough estimate of the rolling power P is giving by where σ0 is the average flow stress, b the width of the strip, h1 the inlet thickness of the strip, h2 the outlet thickness of the strip, r the reduction and v the roll velocity.The average flow stress of the material was taken as 550 MPa, so that a wide variety of steel materials may be rolled. As already discussed, the maximum strip width (b) is 100 mm and minimum inlet thickness (h1) is 2 mm. Considering these values of b and h1 as crisp, the parameters v, r and P were treated as fuzzy. To construct the membership function for these parameters, the following procedure was adopted. The combination of rolling speed equal to 1 m/s, reduction equal to 40% and power less than 10 kW was considered ideal design at a brainstorming session of three designers. In other words, a best design will allow a 100 mm wide and 2 mm thick strip to be rolled up to 40% reduction in one pass, at rolling speed of 1 m/s in less than 10 kW power. Thus, a membership grade of 1 is assigned to v≥1 m/s, r≥40% and P≤10 kW. It was expected that these goals could not be met simultaneously. So, it was decided that, in proportion to deviation from the ideal values, membership grades be reduced. Thus, a membership grade (μv) of 0 is taken for v=0, and between v=0 and 1 m/s, the membership function varies in a linear fashion, as shown in (a). Similarly for 0% reduction the membership grade (μr) of 0 is taken, and between 0 and 40% reduction, the membership grade varies as shown in (b). Since 10 kW is the ideal power, 20 kW power (100% more) is assigned a zero membership grade (μp). Between 10 and 20 kW, the membership grade varies in a straight-line manner, as shown in (c). For each particular combination of v and r, a particular power value P is obtained using . Its membership grade may be found from (c). This figure basically represents a fuzzy set of low power. Since the cost of the overall mill is directly dependent on power, which was of prime concern in the design, the membership function for very low power was used in the decision-making process, which was obtained by squaring the membership function of low power. This is a widely used practice for obtaining a fuzzy set with linguistic hedge very low from a fuzzy set of low.A particular design may obtain different membership grades in different aspects of the design. However, the goal is to maximize overall preference of the designer/customer. In the fuzzy set-based optimization procedure, the overall preference is expressed in the form of overall membership grade. For obtaining the overall membership grade μ0, two types of strategies are commonly employed, a compensating trade-off and a non-compensating trade-off. In a compensating trade-off strategy, the aspects that perform well can compensate for aspects that perform poorly. For example, low cost of the mill may compensate for less maximum possible reduction, because a customer may be ready to have a low cost mill, even if the maximum possible reduction is lowered to some extent. A non-compensating strategy will produce an overall measure of a design alternative that is limited by the most poorly performing aspect. For example, designing one shaft stronger in the power transmission system cannot compensate for the weakest shaft in the transmission line. Relevant to the present problem, a suitable compensating trade-off function is μ0=(μvμrμp2)1/3 and a non-compensating trade-off function is μ0=min[μr,μv,μp2] that reduces to pure compensating strategy for α=1 and pure non-compensating strategy for α=0. In this work, α=0 was chosen, based on the discussions of designers. Computations provided the overall membership grade of 0.539, which gives r=21.56%, . Based on this, it was decided to have nominal values of velocity as 0.5 m/s and reduction as 20%. The corresponding power is 10.9 kW. For this power, the estimated reduction possible in a 10 mm thick and 100 mm wide strip is approximately 4%, which was acceptable to the design team.After the specifications have been finalized, various possible options were conceived. The most crucial design decision was regarding the arrangement for power transmission from the gear box to the rolls. In the rolling mill, the lower roll position was fixed and the upper roll has to move up and down for proper roll gap adjustment. At a meeting of the designers at the concept phase of design, three possible arrangements were conceived.First arrangement (bevel gear drive arrangement) consists of three pairs of bevel gears. First pair of bevel gears transmits the power from a horizontal shaft of the main motor to a vertical shaft. Second pair of bevel gears transmits power from the vertical shaft to the fixed lower roll. The last pair of bevel gears transmits power from the vertical shaft to the upper roll. This pair is connected to the vertical shaft through a key and key-way arrangement so that it can slide vertically along the shaft as the upper roll is displaced for adjusting the roll gap.The second arrangement (spur gear arrangement) consists of four spur gears for transmitting power from the main shaft to the rolls. The first spur gear transmits power directly to the fixed lower roll. The same spur gear also transmits power to the fourth gear attached to the upper roll. In between the first and fourth gears, there are two spur gears whose centres can be moved along circular paths. This way, the upper roll can easily be moved up and down for roll gap adjustment.The third arrangement (universal joint drive arrangement) consists of transmitting power to two working rolls by means of universal joints and telescopic shafts. The telescopic shaft consists of two parts. One part of the telescopic shaft consists of internal splines through which the other part of the shaft containing external splines can slide. This arrangement takes care of the increase in the shaft length as the upper roll moves during roll gap adjustment.. First, various design criteria were chosen and their importance was decided on a scale of 0–10, 0 indicating low and 10 indicating high. For each criterion, the three design alternatives were assigned a rating on the same scale as was used in assigning importance. This was done in a brainstorming session of the designers. For each alternative, its criteria rating was multiplied by the respective importance factors, and all the resulting parts were added. shows the maximum score is achieved by the universal joints drive arrangement. Hence, it was decided to design using a universal joint drive.At the embodiment stage, the design is given a bodily form. At this stage, most of the decisions regarding roll diameter, motor power and overall approximate dimensions of the mill are taken. The output of the embodiment stage of the design is a set of general layout drawings, which will be the input to the detailed design stage. The design methodology for deciding roll diameter and motor power is described in The selection of roll diameter is an important decision for rolling mill design. It is generally selected on the basis of strip thickness, the type of material to be rolled, maximum reduction to be given to the strip, the coefficient of friction, mill speed, etc. Large diameter rolls provide better rigidity and better cooling. On the other hand, small diameter rolls require small rolling force and are less sensitive to the effects of changes in the rolling lubricant. For the same reduction in the pass, the larger is the diameter of the work rolls, the greater is the spread, i.e. increase in the width of the strip Large initial thickness of the sheet or strip;Tensile traction on either the front or the back of the strip.where R is the roll radius. Avitzur et al. . The above equation provides different values of roll radius depending on the inlet strip thickness and reduction. This mill is expected to have a minimum reduction of 2%. If the inlet strip thickness is 10 mm, the minimum roll radius will come out to be 271 mm. However, this is based on the extreme conditions to which mill may be subjected once in a while. At other conditions, the roll radius will not be required to be so high. Hence, it was decided to make a membership function of the desired roll radius. This has been achieved in the following way. Assume, that the low reduction cases are from 2 to 5%, and inlet thickness is from 2 to 10 mm. The membership grade for a roll radius is equal to the fraction of times in which the process is safe from alligatoring to the total number of possible conditions. The membership grade of roll diameter, from the point of view of a defect free process, is depicted in Another simple equation for obtaining minimum roll radius is , the rolls will skid over the strip surface and the strip will not be drawn. This provides,Taking h1=2 mm, r=0.2 and the minimum coefficient of friction equal to 0.04 based on Table 6.10 in Heat transfer consideration also provides an expression for roll radius. If it is assumed that the entire rolling power is dissipated as convective heat, a simple equation can be written, as follows:where l is the length of the roll, h the convective heat transfer coefficient, and tR and t0 are the temperatures of roll surface and surroundings, respectively. Since the laboratory mill would not be required to work continuously and sufficient time would be available for cooling, this equation was not used in the present design. However, if the maximum allowed roll surface temperature is known as a fuzzy number, the desired roll radius from the effective heat transfer consideration can be obtained as a fuzzy number using A simplified analysis of the rolling process shows that rolling power is approximately proportional to the square root of roll radius , in order to avoid skidding, the minimum roll radius should be at least 30 mm approximately. Hence, the roll radius of 30 mm may be assigned a membership grade of 1 and for roll radius values greater than 30 mm, the membership grade may be taken as inversely proportional to the square root of the roll radius. Hence, the membership grade, from the point of view of low power, is given by depicts the membership grade. Using non-compensating trade-off between the twin objectives of low power and a defect-free process, the roll radius is obtained at the intersection of the two membership functions in . This basically maximizes the minimum of the membership grades of the two objectives. If there are more than two objectives (e.g., if were to be considered), the procedures remains same, i.e. one would have to select a roll radius for which the minimum of the membership grades from different objectives gets maximized. This radius is 98 mm and the overall membership grade is 0.55. A nominal roll radius of 100 mm is very close to 98 mm. Hence, the roll radius was fixed at 100 mm. The barrel length of the mill rolls is usually established by the maximum width of the strip to be rolled, the mill width usually being a few inches greater than maximum strip width. Here, the barrel length was taken as 300 mm. With 200 mm diameter and 300 mm length, the estimated maximum deflection is of the order of 10−2 |
mm.In view of cost and availability, it was decided to use an AC induction motor. The motor was the costliest item in the present design. Hence, its power had to be decided judiciously. By now, most of the parameters had been decided and hence, it became possible to compute power more accurately, using finite element analysis with fuzzy parameters, following the method presented in are the flow stress, uni-axial yield stress, hardening coefficient, hardening exponent and equivalent strain, respectively. In the present work, (σy)0, b, n and coefficient of friction f were considered as four fuzzy parameters. A triangular membership function was considered to represent each fuzzy parameter, based on the most likely (m), low (l) and high (h) estimates of the parameter. A typical triangular membership function is shown in . Note that the value of μ is 0.5 at x=l (low estimate) as well as at x=h (high estimate) and 1 at x=m (most likely estimate). The values of the lower and upper bounds of the parameter at membership grade 0 can be called extreme low and extreme high values, respectively. In case the extreme low value becomes negative as a result of constructing the membership grade in this fashion, the extreme low value can be taken as 0 and a modified straight-line can be drawn by joining this point to the vertex of the triangle. However, in the present case, that situation did not arise. The low, most likely and high estimates of these parameters were taken as follows:The finite element analysis using the fuzzy parameters provides the roll torque as a fuzzy number as shown in . As roll velocity is specified, the power requirement at different membership grades may also be found. Selecting a higher power motor will give more reliability to design, but will increase the mill cost. The reliability value associated with each power can be calculated using the method in Having obtained the roll torque as a fuzzy number, we have to give some measure of “trustworthiness” to different design torques. In a probabilistic approach, a measure to compare different designs is “reliability” that is defined as the probability of not failing the element. Here, a measure called “fuzzy reliability” is proposed. The method is based on the concept of entropy. The term entropy is normally used to describe the degree of uncertainty about an event. For an event consisting of q discrete random variables, the Shannon entropy, H, is defined as where pi is the probability of an event. Analogous to the definition of Shannon entropy, the entropy associated with a particular membership grade may be defined as In this form, the value of entropy is maximum (and=1) at μ=0.5, when the uncertainty is maximum. It is to be noted that De Luca and Termini Suppose TR(μ) and TL(μ) are the right and left limits of the roll torque at the membership grade μ, respectively (see ), then the possibility index, PI, is defined asIn the above equation T∗ is the torque for which the reliability is needed. The reliability index is defined asThus, for each particular μ, a different reliability index β is obtained. To make the definition of reliability independent of μ, the area under the β–μ graph is taken as the measure of reliability. The maximum value of the area corresponds to the case when PI=1 for all μ. So it is taken as 100% reliability. Thus, the reliability is defined as shows the reliability for different torques. It is seen that 100% reliability is achieved at a torque value of 3.28 kN m, which will be a worst-case design. At a torque value of 2.8 kN m, 99% reliability is achieved, which was considered sufficient for the present design. The corresponding motor power came to 14 kW. The worst-case design would have selected a torque value of 3.33 kN m, resulting in approximately 19% higher power. Considering the frictional losses during power transmission and the availability of standard motor power, it was decided to procure a 15 kW capacity motor.The detailed design was carried out using conventional machine design practice. The finite element code provided an accurate estimation of roll separating force and roll torque. Appropriate safety factors were chosen for the design of various elements and structure. The detailed assembly and component designs were prepared using standard CAD packages.The present paper describes a systematic design procedure for a rolling mill designed by the authors. A formal method of design was used even at the conceptual and embodiment phases of the design. The fuzzy set-based methodology could easily consider many attributes concurrently, while deciding the specifications of the rolling mill. An optimum roll radius was arrived at by considering two conflicting objectives. The methodology can be easily extended to a situation involving diverse conflicting objectives. The priority decision table provided an objective and crisp method to choose among three possible designs, whereas the conventional design methodology would have chosen any one of them in an intuitive and subjective manner. The motor power was decided considering the uncertainties and imprecision present in the process parameters.The rolling mill has been fabricated and is functioning in the Manufacturing Laboratory of the institute. The performance of the mill is quite satisfactory. Since the design procedure is formal and well recorded, all the decisions can be examined and appropriately modified to give a revised design in a different situation. It is expected that the guidelines presented here can form a basis for industrial design of metal forming equipment in general and rolling mills in particular.Versatile tool for characterising long-term stability and reliability of micromechanical structuresMicromechanical devices have a wide range of applications in the near future. Therefore it is important to study their long-term behaviour under various conditions and environments. We introduce atomic force microscopy as a comprehensive tool in reliability study of MEMS devices. Mechanical properties of micromechanical structures can be characterised with high accuracy. Real-time monitoring of these properties during accelerated ageing tests gives information about the long-term stability of the structures. The AFM is a versatile instrument for predicting long-term operating of micromachined devices in a convenient way without building complicated experimental set-ups.The first MEMS devices already appeared on the market decades ago, but their failure mechanisms are not yet completely understood. In case of simple micromachined sensors and actuators, oversized dimensions can reduce the failure probability. However, designing robust structures is not an adequate solution for the problem, and cannot be applied for more sophisticated constructions. Development of highly sensitive, small size MEMS devices involve accelerated ageing tests, failure analysis and optimization. Reliability is the key for practical application and commercialisation of today's micromachined devices. Their failure can have serious and expensive consequences, just like in case of the GE-3 communications satellite and the US$2 billion Hubble Space Telescope, where gyro sensors caused problems recently.Material properties and degradation processes on the size scale of MEMS can essentially differ from that in bulk materials. For instance, the bulk silicon nitride is a sintered ceramic material with grain structure. On the contrary, the thin film is mostly formed by low-pressure or plasma induced chemical vapour deposition (LPCVD, PECVD), and usually amorphous. Depending on the different process conditions, such as gas ratio, flow rate, or temperature a wide variety of chemical composition, structure, residual stress, strain, Young's modulus, refraction index, and etch rate can be obtained The first step is to characterise mechanical properties such as Young's modulus, spring constant, and fracture toughness with high accuracy. This data is indispensable for realistic finite element simulations and analytical calculations in order to design advanced micromechanical structures. The long-term stability of the realised device can be monitored through the change of mechanical properties. Hence, the structures are subjected to various accelerated ageing tests, and the mechanical properties are measured frequently. The tests can be basically grouped as follows: (a) fatigue test: the device is working in the normal operating range. This test helps to determine the long-term behaviour and the average lifetime of the device. (b) overstress test: operation in short or long-term harsh conditions, generating high stress in the structure. This overload usually results in unstable operation and short lifetime.Several studies can be found in the literature on fatigue failure of micromechanical structures In the current work atomic force microscopy (AFM) is implemented to characterize micromachined cantilever beams. Material and mechanical properties like Young's modulus, quality factor, and spring constant can be calculated from the measurement results. The elastic properties of the material can be described with the Young's modulus (E). The Young's modulus in first approach can be calculated from the resonance frequency of a cantilever beam as follows where f is the resonance frequency, A is a coefficient (A=3.52 for the first natural mode of a clamped-free cantilever), I is the area moment of inertia of beam cross-section, L is the beam length, and ρL is the mass per unit length of the beam. The resonance frequency of the sample cantilever is measured with the ‘resonant method’ described later.The quality factor describes the efficiency of the resonator structure, and can be calculated aswhere f is the peak value (resonance frequency), and Δf is the full width at half amplitude, both read from the measured resonance curve of the cantilever.The spring constant or bending stiffness is another characteristic value of the mechanical behaviour of micromachined structures. The spring constant of the sample can be determined from the following equation:where k is the sample-, measured-, and AFM-cantilever spring constant respectively, L is the cantilever length, and x is the lateral position of the AFM cantilever on the sample cantilever along the length. The measured spring constant is the combination of the other two, measured with the ‘bending method’ described later.The atomic force microscope is basically an imaging tool, which gives high-resolution information of the surface topography. Hereby, the AFM is utilised in the field of reliability. The relevant measurements and tests can be realised conveniently with the AFM, so there is no need to build complicated testing instruments. The experiments in the present work were conducted with a NanoScope MultiMode SPM-Digital Instruments, and an AutoProbe M5 SPM-Park Scientific Instruments. In one set of the experiments the sample cantilever is loaded in the sample holder stage in the conventional way. In other experiments the sample cantilever is mounted in the AFM head replacing the AFM cantilever.The reliability tests are demonstrated in this study on silicon and silicon nitride samples with different shape and size, see . The highly sensitive, silicon rich, low-stress, LPCVD silicon nitride cantilever beams were deposited at 850°C. The process results in an amorphous film with a silicon to nitride ratio close to 1. The more robust, crystalline, n-type silicon beams and paddle-beams were fabricated by topside etching. The applied contactless galvanic electrochemical etching technique is described in There is one additional aspect which needs to be considered while designing test structures for the AFM reliability method. The shape and size of the test structure substrate should be such as to fit in the AFM head.The chip with the beam samples is mounted in the AFM head. The cantilever is excited mechanically with a sweep, while the deflection of the free end is measured continuously with a laser beam (see ). The measured peak gives the resonant frequency of the cantilever beam (see ). This optical read-out technique provides very high accuracy and measurement reproducibility of 10 Hz.The resonant method can be applied as a fatigue-ageing test, where the beam is driven in resonance for an arbitrarily long time. The excitation amplitude can be set in the AFM. The resonance curve is measured frequently during the ageing, and the driving frequency is set to the peak of the resonance curve.The sample cantilever is mounted conventionally on the AFM sample stage. The AFM tip is positioned on top of the sample cantilever to deflect it (see ). The deflection and the displacement of the AFM cantilever are measured. The lateral position and the spring constant of the AFM cantilever are known as well. From these data the deflection and the spring constant of the sample cantilever beam can be calculated using . The spring constant of the sample should be close to that of the AFM cantilever to achieve higher measurement accuracy Cyclic bending deflection of the sample cantilever serves as a reliability test. This is similar to the resonant method, but here the frequency and the amplitude of the deflection are arbitrary, and precisely maintained.In a large number of applications the micromechanical structures do not operate in vacuum. The interaction between the structure and the environment can lead to different effects initiating degradation process. The AFM equipped with vacuum facilities or environmental chamber is a perfect choice to study these effects by comparing the measurements in different environments. Oxidation of the silicon surface stiffens the structure, which can be detected by resonance frequency measurements. Reactive surfaces can be studied as well by the resonant method, absorption of molecules from the environment lowers the resonance frequency of a resonating structure. Corrosion fatigue takes place in humid environment, moisture can catalyse the degradation processes of micromechanical structures The basic operational mode of the atomic force microscopy is imaging the surface topography. The AFM is an excellent tool to image and analyse morphological properties such as surface roughness, or for instance to visualise surface cracks.The Young's modulus of micromechanical structures can be calculated from the resonance frequency, see for simple case. The inaccuracy of the resonant method is rather determined by the measurement accuracy of the length, thickness and mass density of the sample. Compared to the measurement uncertainty of these values, the effect of air damping can be neglected. Finite element method (FEM) simulations and analytical calculations proved this assumption. In the case of the LPCVD SiNx beams, Young's modulus of 230±11 GPa was calculated from the measurements. Note that values from 95 to 320 GPa were presented in the literature for low-stress LPCVD SiN. The quality factor of the resonating SiNx cantilevers is 50±10 in air, calculated with During resonant ageing on air at low excitation amplitudes, a positive shift of the resonant frequency was measured on the LPCVD SiNx cantilevers (see ). This corresponds to a slight stiffening effect, which is not yet understood completely at the moment The crystalline silicon beams and paddle-beams showed a reversed behaviour. The resonant frequency decreased due to cyclic resonant ageing. This is in accordance with the literature High amplitude bending tests and shock loads result in a few hundred hertz abrupt drop of the resonance frequency on silicon nitride samples. The resonance frequency of the tested SiNx beam is presented on . The positive shift in resonance frequency is the stiffening effect due to moderate resonant ageing, while the negative drop is the result of shock load applied to the sample. The fast recovery behaviour after the shock is in accordance with the stiffening effect theory. The Si clusters on the SiNx surface are oxidized in air To verify the theory of oxidation of SiN, resonant tests were conducted in an environmental chamber with nitrogen over-pressure. The results were compared to the tests on air, and seem to prove the theory. Oxide film formation on the SiNx surface leads to stiffening of SiNx beams on air. The oxide film cracks under shock. The cracks heal slower in nitrogen rich atmosphere, than in air. The results are compared in air and in nitrogen in . The resonance frequency following the mechanical shock never reaches the initial value in nitrogene atmosphere.Cracks appear in the surface oxide layer of silicon nitride samples during aging. The 0.5 μm long microcrack on was imaged with the AFM in the conventional imaging mode.Characterisation of MEMS materials and their long-term stability does not require building complicated experimental setup. All the significant components of mechanical reliability study can be realised in a convenient way, if there is an atomic force microscope available. The capabilities of AFM as a reliability tool have been demonstrated in the present work. Low-stress LPCVD silicon nitride and crystalline silicon cantilever beams have been used as samples. The measurement methods can be grouped as follows: resonant measurements, static bending, dynamic bending, and imaging. Extending the measurements to various environments gives information of the interaction between the surface and the environment. The measured properties are Young's modulus, spring constant, and surface morphology. Fracture toughness and creep behaviour can be characterized as well. Accelerated ageing tests like resonant fatigue test, low-and high-amplitude dynamic bending test were demonstrated. The observed characteristic behaviours are stiffening effect and crack generation in case of the silicon nitride samples. A crack related fatigue effect was found on the crystalline silicon samples.Robert Kazinczi was born in 1973 in Hungary. He received his MSc degree in Physics Engineering at the Technical University of Budapest, Hungary in 1997. His specialisation was material science, and he worked in the field of scanning tunnelling microscopy (STM), and electrochemical STM. He developed a fast EC STM tip preparation method. In 1996–1997, he worked in part-time on scanning electron microscopy and X-ray microanalysator systems at the Central Research Institute for Chemistry of the Hungarian Academy of Science. From 1997 he is working as a PhD student at Delft University of Technology, The Netherlands. His topic is reliability of micromechanical structures. Currently he is engaged in mechanical studies of structural films in microelectromechanical systems (MEMS).Andre Bossche was born in Rotterdam, The Netherlands, in 1956. He received the MSc degree in Electrical Engineering with honours in 1983, and the PhD degree in Electrical Engineering in 1988, both from Delft University of Technology, The Netherlands. His project group is engaged in research work on the subjects of measurement theory, the reliability of instrumentation systems, sensors devices and sensor packaging at the Laboratory of Electronic Instrumentation from the Delft University's Faculty of Electrical Engineering.Jeff Mollinger is a research assistant of the Electronic Instrumentation Laboratory at the Electrical Engineering Department of the Delft University of Technology. He was born in Djakarta, Indonesia on September 9, 1951. In 1975, he received his diploma in Electrical Engineering, after which he joined T.N.O. in Delft, Department of Groundwater Survey. From 1980 to 1981, he joined the Volker Stevin Dredging . In 1981 he started working for the Department of Mechanical Engineering of the Delft University of Technology where he switched to the Department of Electrical Engineering, laboratory of Electronic Instrumentation, in 1986. He supports the scientific research on the subjects of reliability and electronic measurement systems.Electrochemical and biocompatibility response of newly developed TiZr-based metallic glassesThis paper presents systematical investigations, including electrochemical activity, MTT cell assay and in vivo test, on the biocompatibility of three metallic glasses. The electrochemical behaviors and the cell toxicity of two newly developed TiZr-based metallic glasses (MGs), Ti42Zr40Si15Ta3 and Ti40Zr40Si15Cu5, with lower or without unfavorable elements are systematically investigated. Results show that the MGs with low Cu content exhibit a low electrochemical response. Cytotoxicity tests for the MGs and the mediums after the potential state test are evaluated with in vitro MTT assays. The solid specimens and the mediums after the potential state test for the pure Ti, Ti42Zr40Si15Ta3 and Ti40Zr40Si15Cu5 exhibit no significant cytotoxicity in the MTT test, while the tested medium for Ti45Cu35Zr20 MG shows lower cell viability. The inductively coupled plasma-mass spectrometry (ICP-MS) results also indicate that the Cu-rich sample released a significant amount of ions which may be the major factor causing the low viability in the MTT test. The good healing condition and the low C-reactive protein (CRP) index for the implanted New Zealand rabbits in a one-month in vivo test also show the satisfactory short-term biocompatibility of the TiZr-based MGs. The electrochemical measurements, in vitro, and in vivo experiments confirm that the developed TiZr-based MGs with lower Cu content (≦ 5%) are promising for biomedical purposes.Metallic materials have been used in a number of artificial parts in the human body, such as substitutes for hard tissue replacement, fracture healing aids and the fixation devices, due to their excellent mechanical properties Recently, another category in metal alloys for biomaterial applications, called metallic glass, has attracted a number of researchers working in this field. Metallic glasses are amorphous since there are no crystal structural deficiencies in the metallic glasses such as dislocation, twinning, vacancy, or grain boundary. Metallic glasses have a homogenate composition, providing higher strength, hardness and elastic limit compared to typical alloys Ti-based metallic alloys are excellent candidates for biomedical applications due to their good biocompatibility and corrosion resistance This study develops two new Ti–Zr–Si amorphous systems with lower Ta and Cu contents. The newly developed MG systems will reduce the cost and the process temperature for producing the bio-implantable MGs. The TiZr-based amorphous ribbons with low Ta and Cu contents of Ti42Zr40Si15Ta3 and Ti40Zr40Si15Cu5 are first produced. It is known that the additive minor elements might affect GFA or corrosion behavior for the new MG systems. Because of this, it is necessary to evaluate their electrochemical behaviors and biocompatibility. One positive control and one negative control, utilizing pure Ti and another MG composed of higher Cu content, Ti45Cu35Zr20, are also prepared for a biocompatibility comparison with the currently developed TiZr-based MGs. The corrosion behaviors of the samples were conducted using the standard electrochemical test scheme in the Hank's simulation body fluid (SBF). Cyclic voltammetry, potential state and Tafel curve measurements are used to investigate the corrosion properties. The MTT assays are used to test the cell toxicity of the solid MG samples and the mediums after electrochemical corrosion testing. The biocompatibility of these MGs is then in vivo evaluated by implanting small pieces of the MG samples into New Zealand rabbits. The results presented in this study strongly confirm the electrochemical stability and the biocompatibility of the two newly developed MGs of Ti42Zr40Si15Ta3 and Ti40Zr40Si15Cu5.In this study, the TiZr-based and Ti-based metallic glasses with nominal composition of Ti42Zr40Si15Ta3, Ti40Zr40Si15Cu5, and Ti45Cu30Zr20 were produced with the melt spinning method in a vacuum chamber. The pure metals of Ti (99.99 wt.%), Cu (99.999 wt.%), Zr (99.9 wt.%), Si (99.99 wt.%) and Ta (99.99 wt.%) were mixed with the designed atomic ratios and then heated to liquid state. The molten metal was then rapidly quenched to the solid state via single roller melt-spinning under argon atmosphere to produce MG ribbons measuring 1 mm in width, 10 mm in length and 0.1 mm in thickness. X-ray diffraction (XRD) analyses of the melt spun MG ribbons were carried out using a Bruker D8 Advance diffractometer with a mono-chromatic Cu-Kα radiation (λ = 0.15406 nm) and operated at 40 kV and 40 mA. The thermal properties of the MG ribbons were characterized by a differential scanning calorimeter (DSC, Mettler Toledo DSC 1) at a constant heating rate of 0.67 °C/s. The liquidus temperature of the MG ribbons was characterized by a high temperature differential scanning calorimeter (HTDSC, Netzsch STA449F3) at a constant heating rate of 0.33 °C/s. The Young's modulus and hardness of the produced MG samples were measured by a MTS nanoindentation XP system equipped with a Berkovich tip.The electrochemical properties of the MGs in the SBF and the culture medium were first evaluated using a commercial electrochemical analyzer (CHI 614 D, CH Instruments Inc., USA). The electrochemical measurement was conducted in a three-electrode scheme. The MG ribbons were cut into small pieces with dimensions of around 4 × 4 mm2. The MG specimen served as the working electrode for the EC measurement where sputtered platinum film with the area of around 5 × 5 mm2 was used as the counter electrode and the reference electrode was standard Ag/AgCl. The MG ribbon was immersed into a 40 ml Hank's solution (pH: 6.5) at 310 K for cyclic voltammetry (CV), potential state and potentiodynamic polarization measurements. The typical composition of SBF, the Hank's solution, is 0.137 M NaCl, 5.4 mM KCl, 0.25 mM Na2HPO4, 0.44 mM KH2PO4, 1.3 mM CaCl2, 1.0 mM MgSO4, and 4.2 mM NaHCO3. In comparison with other SBFs, the Hank's solution is a chlorine-ion-rich buffer which may induce electrochemical corrosion for the MG, especially for ones containing copper content. The CV measurement was carried out with scanning potential from − 1.0 V to + 1.0 V and scan rate of 0.1 V/s. In addition, materials used in medical applications may contact living cells and be exposed to a membrane potential of 75–80 mV. A potential state measurement with a small applied voltage of 80 mV for 30 min was used to mimic the possible electrochemical reaction between the MG ribbons and cell tissues. Before the potentiodynamic polarization measurements, the specimens were stabilized in SBF for 12,000 s with the criterion of the variation for the open circuit potential (OCP) less than 2.0 mV in 5 min. The potential scans were started from − 0.5 V to 2.0 V with a 0.33 mV/s scanning rate. The important electrochemical parameters including corrosion potential (Ecorr) and corrosion current (Icorr) were determined by the Tafel extrapolation method.The standard MTT (3-(4,5-cimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) assay (50 μg MTT in 100 μl in PBS buffer, pH: 7.35 to 7.40) was used to observe cell viability experiment of the metallic glasses. The in vitro cell culture test of the specimen was investigated using pluripotent mesenchymal cells. Balb/c mouse bone marrow stem cells, D1 cells (ATCC), were incubated in a low glucose Dulbecco's modified Eagle's medium (DMEM). The DMEM is composed of 10.0% fetal bovine serum (FBS), 1.5 g/l sodium bicarbonate, 1.0% NEAA, 1.0% vitamin C and 1.0% penicillin and streptomycin For the in vivo tests, 6 male New Zealand white rabbits with weights of about 2.5 to 3.5 kg were purchased from the Taiwan Livestock Research Institute (Tainan, Taiwan), following Taiwan's required ethical procedures. The rabbits were kept on a 12:12 light–dark cycle (light on at 06:00) and housed in a temperature-controlled room (25 ± 1 °C). One hour before the operation, the rabbits were IM injected with Cefazolin (1 g/kg, Yung Shin, Taiwan) for anti-bacterial effect and atropin (0.3 mg/kg, TTY Biopharm, Taiwan) for analgesic properties. Animals were anesthetized by a mix of ketamine (40 mg/kg, Ketalar, Parke-Davis, Taiwan) and xylazine (10 mg/kg, Rompun, Bayer HealthCare, Germany). All the MG ribbons were sliced into small pieces of around 3 mm × 3 mm. The surgical sites were located below the epiphyseal growth plate of each right leg. The 3 mm × 3 mm × 0.5 mm fractures were made by medical saw for implantation and the wounds were then stitched by surgical sutures. X-ray images of the rabbits' legs were then taken at 4.2 kV and exposure time of 3.5 s (HP 9178 A and HP 9816S; Hewlett-Packard, Fort Collins, CO, USA). The rabbits recovered under careful attention and were finally sacrificed one month after treatment. The legs with implantation were soaked in 10% formalin prior to the micro-computed tomography (μ-CT) observation. All proximal tibiae were assessed by μ-CT (Skyscan 1076: Skyscan, Antwerp, Belgium) after tissues were removed. Data were collected at every 0.5° rotation step through 180°. The scanning width was 34 mm, and the height was 17 mm. The voxel size was isotropic and fixed at 8.7 μm The Ti-based and Zr-based MGs typically have lower Young's modulus but higher yield strength and hardness compared to pure Ti shows that all the XRD patterns of MG ribbons reveal a diffuse hump, with no obvious crystalline peak, implying their dominant amorphous structure nature. The glass transition behavior for the produced MGs was inspected with a thermal DSC scan, as shown in b. The calculated supercooled temperatures, defined as ΔTx (= Tx |
− Tg), for Ti42Zr40Si15Ta3, Ti40Zr40Si15Cu5, and Ti45Cu35Zr20 were 80 °C, 76 °C and 99 °C, respectively. Results showed that Ti42Zr40Si15Ta3 with the thermally stable Ta element exhibits the highest Tg and Tx in the DSC test. The XRD and DSC results confirmed that the three melt spun MGs were all in the metallic glass form. The glass forming ability for these three MGs was characterized by the two representative indexes, γ [= Tx |
/ (Tg |
+ Tl)] (Tl: liquid temperature) The Young's modulus E and hardness H data measured by nanoindentation are also complied in . The modulus and hardness of the Ta-containing Ti42Zr40Si15Ta3 both exhibit high values of 90 GPa and 7.2 GPa, respectively, followed by Ti40Zr40Si15Cu5 and Ti45Cu35Zr20. For these three MGs, the specimen with the highest Tg temperature exhibits the largest E and H, which is consistent with the measurements of many previous BMGs Cyclic voltammetry (CV) is one of the most effective ways to determine the electrochemical properties of samples. presents the CV curves of pure Ti, two TiZr-based MGs and the Cu-rich Ti-based MG in the Hank's solution. Results showed that the electrochemical activity of the two MGs of Ti42Zr40Si15Ta3 and Ti40Zr40Si15Cu5 exhibited stable electrochemical properties since there were no significant redox peaks in the CV scans. The measured current responses of these two MGs were in the same scale as those of the reference pure Ti. On the contrary, there was an obvious electrochemical response of the Cu-rich MG of Ti45Cu35Zr20 at the positive applied potential, indicating the occurrence of oxidation reaction. The Cu-rich ribbon was not able to sustain the rapid corrosion response and was decomposed after 3 CV scan cycles. Results confirmed that the high Cu content could lower corrosion resistance. This could be caused by the strong polarization of Cu in the MG, especially when immersing the MG in an environment with high concentrations of chloride ions presents the magnified current response of the three CV curves with low current response. It is clear that the current levels of the Ti42Zr40Si15Ta3 and Ti40Zr40Si15Cu5 MGs are even lower than those of the reference pure Ti, indicating the excellent electrochemical stability of the two produced MGs.Alternatively, the implantable biomaterials may suffer from electrochemical corrosion due to the potential difference across the cell membrane (membrane potential). The values of membrane potential typically range from 40 mV to 80 mV, depending on the concentration of the sodium and potassium ions of a cell. In order to mimic the real biological environment, the specimens were immersed in Hank's solution with an applied potential of 80 mV. displays enlarged amperometric i–t curves showing the close-up current density responses of the pure Ti and the two TiZr-based metallic glasses. The measured current response of the MG of Ti45Cu35Zr20 was too high and not in the same scale, such that it was excluded from . The measured current values of the two TiZr-based metallic glasses were monitored for 30 min, illustrating the low electrochemical response in a biological environment for the Cu-free and low-Cu TiZr-based specimens. In short, the potential state tests also revealed superior electrochemical stability of Ti42Zr40Ta3Si15 and Ti40Zr40Si15Cu5 metallic glasses, consistent with the CV tests above.Although the CV measurement is a straight-forward way for evaluating the electrochemical properties of the developed MGs, the rapid electrochemical tests are not able to analyze the corrosion mechanisms and the polarization dynamics. Therefore, a more accurate electrochemical method with a lower scanning rate at the positive applied potential region to examine the polarization peak that appears at a positive range of CV curves is essential for understanding the corrosion behavior of these MG materials. There are three important electrochemical parameters which can be obtained for analyzing TiZr-based and Ti-based metallic glasses via the potentiodynamic polarization measurement. The measured current response at a slow scan rate of 0.33 mV/s is shown in . The corrosion potential (Ecorr) and the corrosion current density (Icorr) are the parameters for evaluating the driving force and activity of corrosion reaction, respectively. presents the average Ecorr for measuring the MGs and the pure Ti reference.The Ecorr readings of Ti42Zr40Si15Ta3 and Ti40Zr40Si15Cu5 were slightly lower than those of Ti45Cu30Zr20 and pure Ti, but the difference is only less than 0.2 V (about − 0.4 V versus − 0.26 V). The slightly lower Ecorr indicates that the MGs with low Cu-content are slightly easier to become polarized or oxidized than the Cu-rich MG of Ti45Cu30Zr20 and pure Ti. Although Ecorr is an important parameter for examining the material corrosion property, this value is not entirely indicative of the material's corrosion resistance that the Cu-free and low Cu-content TiZr-based MGs, Ti42Zr40Si15Ta3 and Ti40Zr40Si15Cu5, exhibit lower Icorr than the Ti45Cu30Zr20 and pure Ti. The more critical issue that influences the electrochemical property is the pitting corrosion. Pitting corrosion could happen particularly under a high concentration of chloride ions which are likely to react with the Cu atoms in the MGs. The sudden current increases in the Tafel curves indicate that there were significant electrochemical reactions for the MGs in the SBF Hank's solution. The pitting potential (Epit) was a significant index to determine the occurrence of the pitting corrosion via observing the sudden signal rise in The Ti45Cu35Zr20 exhibited a negative Epit at − 0.078 V, indicating the spontaneous pitting corrosion of this material in SBF. In contrast, the Ti42Zr40Si15Ta3 and Ti40Zr40Si15Cu5 MGs have a positive Epit at + 1.2 and + 0.7 V, respectively (), indicating a non-spontaneous corrosion reaction of these two MGs in SBF. The pitting potential of these two MGs is much higher than the membrane potential of 80 mV which confirms the satisfactory stability and corrosion resistance for these two MGs in SBF. Moreover, the low passivation current density, Ipass, of pure Ti () also indicated that there was a dense passivation layer formed on the Ti surface, preventing the inner Ti from further oxidation. The lower Ipass readings for the Ti42Zr40Si15Ta3 and Ti40Zr40Si15Cu5 MGs (compared to pure Ti) also revealed that these two MGs possessed good corrosion resistance in SBF since the protective passivation layer was formed on the MG surface Cytotoxicity testing is used to evaluate the occurrence of the death of cells in the designed environment. shows the results for the MTT assays of a 72-h D1 cell culture with the solid metal species and a 24-h cell culture with the DMEM medium after the potential state test. The pure Ti was used as the standard in the cell viability test. The ions released into the culture medium are known to be the major factor causing the death of the cells. The blue bars show the cell viability for culturing D1 cells with the solid metal specimens for 72 h. The cell viability for each group was higher than 85%, indicating only a minor ion release for all metal specimens in a short period of time. Although there was bigger variation for the viability in the Ti45Cu35Zr20 group, the variation of different groups was not significant. The red bars show the cell viability for a 24-h cell culture using the medium (DMEM) after the potential state test, which applies a low voltage of 80 mV that induces significant electrochemical corrosion for Ti45Cu35Zr20 and causes ion release into the medium. Results show that the viability of the Ti45Cu35Zr20 group was significantly lower (< 70%) than that of the other groups, indicating a noticeable cytotoxicity for this group.In order to further validate if there was an ion release for the Ti45Cu35Zr20 group, ICP-MS was used to measure concentration variation (ppm) for the target ions in the medium prior to and after the potential state tests, as shown in . The large variation in the concentration for Ti45Cu35Zr20 group indicates that a significant number of ions were released into the medium during the potential state test, especially for the Ti, Zr and Cu ions. The toxic Cu concentration of Ti45Cu35Zr20 was up to 30 times higher than that of Ti40Zr40Si15Cu5. This could be the primary issue causing the low cell viability of Ti45Cu35Zr20. In addition, there were also noticeable concentration variations for the Si ion in both MGs with good electrochemical stability. Nevertheless, the Si ion was considered as bio-inner such that the viability of these two MGs showed no difference in comparison with the pure Ti control group. presents photos showing the surgical implantation of the MGs into the rabbits' right tibias, and corresponding X-ray images after the surgical operations. The implantations were carried out without infection in the rabbits. The rabbits recovered well and were fed with great care. shows the 2D and 3D micro-CT images of the three metallic glasses one month after implantation. It is clear that the physical structure of the three Ti42Zr40Si15Ta3, Ti40Zr40Si15Cu5 and Ti45Cu35Zr20 MGs was still complete, and the symptoms of the rabbits recovered well after 1 month of implantation, as presented in In addition, 3D μ-CT was used to further evaluate the bone ingrowth/ongrowth property for the implanted MGs. In general, the higher density region will appear lighter in the μ-CT images. The cortical bone (compact bone) showed a dark-green color while the cancellous bone (sponge bone) appears reddish purple in color in Modelling the correlation between processing parameters and properties in titanium alloys using artificial neural networkA model is developed for the analysis and prediction of the correlation between processing (heat treatment) parameters and mechanical properties in titanium alloys by applying artificial neural network (ANN). The input parameters of the neural network (NN) are alloy composition, heat treatment parameters and work (test) temperature. The outputs of the NN model are nine most important mechanical properties namely ultimate tensile strength, tensile yield strength, elongation, reduction of area, impact strength, hardness, modulus of elasticity, fatigue strength and fracture toughness. The model is based on multilayer feedforward neural network. The NN is trained with comprehensive dataset collected from both the Western and Russian literature. A very good performance of the neural network is achieved. Some explanation of the predicted results from the metallurgical point of view is given. The model can be used for the prediction of properties of titanium alloys at different temperatures as functions of processing parameters and heat treatment cycle. It can also be used for the optimization of processing and heat treatment parameters. Graphical user interface (GUI) is developed for use of the model.A generic class of titanium-based materials has been developed over the past years. Titanium and its alloys are currently finding widespread applications in many industries due to their desirable and versatile combination of properties. The advantages of titanium alloys include: (i) low densities, which give very attractive strength to weight ratios allowing lighter and stronger structures; (ii) superior corrosion and erosion resistance in many environments; (iii) high temperature capability. Although the titanium materials are still considered as expensive materials, for many applications the cost of titanium alloys can be justified on the basis of their desirable properties.The mechanical properties and the application of titanium alloys depend essentially on the characteristics of the microstructure Artificial neural networks (ANN), on the other hand, are currently one of the most powerful modelling techniques based on a statistical approach. There has been only limited work on the application of neural networks (NNs) in the field of titanium alloys In the present work we aim to design an artificial neural network for the prediction of the mechanical properties of titanium alloys as functions of the processing parameters and alloy composition. The work was motivated by the desire to create a tool for optimization of the processing parameters and the alloy composition.Following the main aim of this work a most general scheme of the model is given in . The input parameters of the neural network are alloy composition, heat treatment parameters and work (test) temperature. The composition includes the most commonly used alloying elements in titanium alloys, namely Al, Mo, Sn, Zr, V, Cr, Fe, Cu, Bi, Si, Nb, Ta, Mn and O. Typical heat treatments of titanium alloys are taken into account: (i) annealing in and β regions; (ii) solution treatment in β and α+β regions followed by ageing at different temperatures; (iii) duplex annealing. Since the titanium alloys are considered as desirable and sometimes essential for many structural applications in high temperatures the test/work temperature is included as another input in the model. In this way the model is extended to trace the correlation “processing parameters–working conditions (temperature)–mechanical properties”.The outputs of the neural network model are the nine most important mechanical properties namely ultimate tensile strength, tensile yield strength, elongation, reduction of area, impact strength, hardness, modulus of elasticity, fatigue strength and fracture toughness.Artificial neural network modelling is a relatively new technique. It is essentially a “black box” operation linking input data to output data using a particular set of nonlinear basis functions. Since artificial neural network modelling is a nonlinear statistical technique, it can be used to solve problems that are not amenable to conventional statistical methods. In the past few years there has been a constantly increasing interest in neural network modelling in different fields of materials science Artificial neural networks consist of simple synchronous processing elements, which are inspired by biological nervous systems . In the present work feedforward hierarchical artificial neural networks are used. The model is shown schematically in . In feedforward neural networks the information is processed in one direction – from input to output – and the neurons are ordered in layers. The numbers of neurons in the input layer and the output layer are determined by the numbers of input and output parameters, respectively.Commonly, neural network modelling follows these steps: database collection; analysis and pre-processing of the data; training of the neural network. The latter includes the choice of architecture, training functions, training algorithms and parameters of the network; testing of the trained network; and using the trained neural network for simulation and prediction. The model developed here has adopted these steps.A network is usually trained using a large number of input with corresponding output data (input/output pairs). That means that for reliable training and performance of any neural network we need an appropriate database. Using such a database we can train neural network to perform complex functions.The database was constructed by collecting available data on mechanical properties for titanium alloys at different heat treatment conditions and working temperatures The selection of the input parameters is a very important aspect of neural network modelling. Usually this choice is based on the physical background of a process. All relevant input parameters must be represented as the input data of the neural network. It is known that the training of an artificial neural network requires a large number of input/output pairs, and this can lead to lengthy training times. Therefore, before training the number of actual input parameters should be restricted by ignoring the linearly dependent input parameters.In the present work the following were used as input parameters:After preprocessing analysis the 14 alloying elements initially chosen (see above) were reduced to 11, namely Al, Mo, Sn, Zr, Cr, Fe, V, Si, Nb, Mn and O. Cu, Bi and Ta were contained in only one alloy, Ti–2.5Cu(IMI230), Ti–6Al–2Sn–1.5Zr–1Mo–0.35Bi–0.1Si and Ti–6Al–2Nb–1Ta–0.8Mo, respectively, at different conditions and temperatures. The data pairs containing Cu and Bi were excluded from the training database while Ta, where present, was converted to Nb equivalent. When oxygen level of the alloy was unknown an amount of 0.15 wt% was attributed. Modelling of the oxygen influence on the mechanical properties was based on 61 data pairs with oxygen content above 0.2 wt% or below 0.1 wt% (ELI alloys). For the remaining part of the database the oxygen content was in the range 0.1–0.2 wt%. When Fe was not an alloying element in the titanium alloy an amount of 0.15 wt% was attributed. Analysis of the database in terms of the alloy elements present is given in Nine classical heat treatment types for titanium alloys for which data in the literature exist were taken into account in the neural network model. Since neural networks operate with digits the heat treatments were digitized by means of attributing different digits to the different heat treatments. The heat treatment used and the corresponding digits are given in . The distribution of the inputs within the corresponding range is another very important characteristic of the data set since it gives information about intervals where we can achieve higher or lower accuracy of training and prediction. The distribution in terms of the heat treatments is presented in showing the number of the data pairs corresponding to each type of heat treatment. The large amount of data is available for the two most popular heat treatments of titanium alloys, namely annealing in the α+β field and solution treatment in the α+β field followed by ageing.Most of the data on the different mechanical properties were at room temperature (see ). However, there were a lot of data at temperatures −193°C, −70°C, −62°C, 20°C, 100°C, 200°C, 300°C, 316°C, 350°C, 400°C, 427°C, 450°C, 480°C, 500°C, 538°C, 550°C and 600°C. Some data for mechanical properties at very low (−253°C) as well as at very high (800°C) temperatures were collected. The analysis of the database distribution in terms of the test/work temperature is present in in a form of histogram showing the number of the data pairs in each temperature interval. This analysis gives us a confidence that our model can work with sufficient accuracy within a temperature interval of −100°C to +600°C.Different numbers of data pairs for the different mechanical properties were collected. Analysis of the database regarding the outputs is presented in . Most of the data collected were for tensile test properties but there were also data for the other mechanical properties. The ranges of varying of the properties as well as the conditions at which data with respect to the alloy composition, heat treatment and temperature existed are shown in The process of fitting the network to the experimental data is called training. It consists of adjusting the weight associated with each connection (synapse) between neurons. The weight of a synapse, multiplied by the strength of the signal on that synapse, defines the contribution of that synapse to the activation of the neuron for which it is an input. The total activation of a neuron is then the sum of the activations of all its inputs, and this defines the value of the output signal for that neuron, via a transfer function. Transfer functions are generally s-shaped (sigmoid) curves, with the output value confined within limits such as (0,1) or (−1/2,1/2). The choice of transfer function is one of the decisions which must be made by the user, although it is not usually a very critical factor. The most popular functions are: Hard limit (hardlimBy adjusting the values of synaptic weights throughout the network, the outputs of the artificial neural network for any given set of inputs can be altered. Training consists of adjusting the weights until the outputs for each set of data inputs are as close as possible to the data outputs; i.e., until the network correctly simulates the known behaviour of the system to be modelled. The simulation will rarely be exact; training is usually aimed at minimizing the sum of the squares of the differences between predicted and measured values of the outputs.It became standard for some years to train artificial neural networks by a method called Backpropagation. This consisted of assigning a random initial set of weights to the artificial neural network, then presenting the data inputs, one set at a time, and adjusting the weights so as to reduce the corresponding output error. This was repeated for each set of data, and then the complete cycle was iterated until an acceptably low value of the sum of squares of errors was achieved. The method suffers from the drawback that the adjustments which reduce the errors on a given set of data, may increase the errors on the other sets of data, so the process is constantly undoing the improvements made so far. The result is a method which is both inefficient and unreliable, requiring many iterations to converge if it converges at all.A much better approach has turned out to be to use one of the many methods of numerical optimization which have been developed for solving nonlinear sums-of-squares problems In this work the neural network models were designed and trained using the MATLAB 5.3® package. Standard multilayer feedforward networks (see ) were created. The general model of the neural network () consisted of separate networks for each mechanical property.Before the training of the network both input and output variables were normalized within the range −1 to 1 as follows:where xN is the normalized value of a certain parameter, x is the measured value for this parameter, xmin and xmax are the minimum and the maximum values in the database for this parameter, respectively.For all created neural networks the general structure of input, one hidden and one output layer was used. In order to determine the optimal architecture, several neural networks were trained with different number of neurons in the hidden layer and different transfer functions (see ). The results from the artificial neural network with the best result for each case are shown here. In the general case these models include 13 neurons in the input layer, 13 neurons in the hidden layer and 1 neuron in the output layer. For all cases a linear transfer function (purelin) was used in the output layers. In the hidden layers “tangent sigmoid transfer function (tansig)” and “log sigmoid transfer function (logsig)” were attempted (see ). When the logsig was applied, the inputs and the outputs were normalized to within the range 0–1 using an equation similar to The most accurate predictions of the neural networks were obtained with hyperbolic tangent sigmoid transfer functionfor the neurons in the hidden layer and with linear transfer function for the neurons in the output layer.The networks were automatically initialized with the default parameters. In order to achieve the best result, different training options have been attempted including training on variations of mean square error for better generalization, training against a validation set, and training until the gradient of the error reaches a minimum. Improving of the generalization has been attempted by means of “regularization” and “early stopping with validation”. Finally, automated regularization based on the Bayesian regularization in combination with the Levenberg–Marquardt training was chosen.Before training the data set was randomly divided into two groups. Two-thirds of the data were used for training and one-third for test. When the training was performed against a validation set, the groups were as follows: one-half – training set, one-quarter – validation set and one-quarter – test set. The training program was written in a way that each time when the program is run a new random distribution of the whole data set into the above subdatasets is executed. By varying all the parameters described above trained neural networks with the best performance were achieved.After the training the neural network performance was checked. The results from the trained neural networks with the best result for each mechanical property are shown here. The performance of the neural network for prediction of tensile strength of titanium alloys is demonstrated in . The diagrams show an analysis of the network response in a form of linear regression analysis between the network outputs (predictions) and the corresponding targets (experimental data) for the different datasets. It is obvious that the predicted values from the trained neural network outputs track the targets very well. Acceptable performances were achieved in the neural networks for the other mechanical properties (see ). The correlation coefficient (R) values for all cases of training/test datasets and different training techniques used are shown in . A good performance of the neural network has been achieved and the network can be used for further simulations and predictions.Additionally we reproved the performance accuracy by statistical analysis of the error of neural network predictions (). For the test dataset neural network predictions were calculated. These were compared with the corresponding experimental values. Thereafter the relative errors were calculated usingwhere RmEXP is the experimental (measured) tensile strength and RmNN is the predicted value from the neural network.The results were presented in a typical plot “frequency versus error”. The error had a classical Gaussian distribution around the zero value. For more than 95% of the test dataset the error of prediction was within ±10%. These results gave us a confidence that our model can predict with sufficient accuracy for the practice.On the basis of artificial neural networks a model for simulation of the mechanical properties for titanium alloys was created. This model can be used to predict mechanical properties with sufficient accuracy within the range of the data set used in the training (see ). It should be reiterated here that the designed models are “statistical” models, i.e., they are not based on any physical theory. Because of this, some explanation of the results from the metallurgical point of view will be given.In the following, mechanical properties for different titanium alloys and different heat treatment and temperature conditions are predicted by this model and thereafter analysed. Some of the results are compared with experimental data from the literature. All comparisons between neural network predictions and experimental data are for data pairs which have not been involved in the training process.The tensile strengths for some of the most popular commercial titanium alloys were calculated (see ) using the model. The predictions are performed for different heat treatment conditions and working temperatures. The neural network predictions are in good agreement with the experimental data. Similar correspondences were observed for the other mechanical properties. In fact, the accuracy of the neural network predictions was higher for the tensile test properties. This is due to the fact that the number of training data pairs was larger for the tensile properties as compared to the other mechanical properties (see ). However, the accuracy of the neural network predictions was within acceptable error range for all other properties. Some uncertainty existed only regarding the prediction of the fracture toughness.Since most of the data pairs used were for mechanical properties at room temperature the highest accuracy of the neural network is expected for the prediction of room temperature properties. Using the trained neural network, the mechanical properties for different titanium alloys at room temperature were predicted. The results are compared with experimental data published in different sources The very good agreement between the predicted values from the neural network and the experimental data for the different properties is obvious (). The difference between the neural network predictions and the experimental data is comparable with the difference between experimental data published in different sources. This gives us a confidence in the predictions from the model.Since operating temperature is another very important parameter in the application of titanium alloys, its influence was also studied by using the above model. The well-known high-temperature commercial alloys Ti–6Al–2Sn–4Zr–2Mo (Western) and VT-8 (Russian) were chosen. Their mechanical properties were calculated from the neural network model in the temperature range from −200°C to 800°C (The predicted tensile and yield strength were not affected much when the temperature was increased from room temperature to ∼500°C for both alloys (see (a) and (b)). When the temperature was increased to above 600°C a significant decrease of tensile and yield strength was observed. From the results it can be concluded that the maximum operating temperature at which the strength properties are still kept stable is around 550°C which is in agreement with the recommendations in the literature for the temperature range of use for these alloys.On the other hand, an increase in temperature results in significant increasing of the elongation (especially above 600°C, see At sub-zero temperatures naturally the influence was opposite. The strength properties were increased ((a), (b) and (f)) while the plasticity of the alloys was significantly decreased ((c), (d) and (e)). The effect of the temperature estimated from the trained neural network on the mechanical properties is consistent with what is expected from metallurgical point of view. it is also obvious that the predicted temperature dependencies of the different mechanical properties match well with the experimental data.The method of heat treatment is a significant process parameter. The optimization of the heat treatment in order to achieve desirable mechanical properties has major importance in titanium alloys practice. In the following the neural network predictions for the influence of heat treatment on mechanical properties will be discussed.The effects of the most commonly used heat treatments for titanium alloys were studied. The influence of heat treatment was modelled for Ti–8Al–1Mo–1V alloy (). A very good agreement between predicted and experimental tensile strength after different heat treatments was found. From the results it can be concluded that the neural network has been trained to “understand” the influence of the heat treatment on the microstructure and therefore on the properties of titanium alloys. It must be admitted, however, that the approach used is not purely quantitative regarding the heat treatment. The heat treatment processes are considered only qualitatively. The particular heat treatment parameters such as temperature of heating, time, heating/cooling rates are not taken into account in the model. This implies the assumption that all data are at optimal heat treatment conditions for the corresponding heat treatment procedure (α+β annealing, solution treatment + ageing, etc.) and alloy.The model would be more accurate and precise if the particular characteristics of the microstructure (type of phases present, grain size and grain shape, morphology and distribution of the fine microstructure, e.g., α+β colonies, texture, etc.) were involved as input parameter instead of simply the type of heat treatment. However, at present in the literature there are not enough data for training of such neural network.Additionally we tried to model the influence of the ageing temperature on the mechanical properties. The tendency towards decreasing tensile strength was simulated when the ageing temperature was raised but the accuracy of prediction was not acceptable. Apparently more data for mechanical properties after ageing at different temperatures are needed to train the neural network to cope with this effect.(b) and (d)) on the mechanical properties for one of the most popular titanium systems (Ti–Al–V) was modelled. Attention was paid to this system since it is well known that Ti–6Al–4V alloy is the most widely used titanium alloy. The mechanical properties were computed assuming increased and decreased content of aluminium and vanadium from the Ti–6Al–4V composition in α+β annealing condition.From the simulations it can be concluded that with increasing aluminium content both tensile strength and yield strength are increased appreciably ((a)). Simultaneously a very high influence of aluminium on the elongation (especially when the aluminium exceeds 8 wt%) was found. A very small increase of the aluminium content causes a significant decrease of the elongation (see (c)), approaching a value of zero when the aluminum content was as high as 11 wt%. The predicted effect of significant decrease of the ductility properties can be explained from the metallurgical point of view with the formation of the Ti3Al phase.The influence of vanadium on the mechanical properties shows a similar tendency. With increasing vanadium content tensile strength and yield strength are increased ((b)) while the plasticity properties (elongation and reduction of area) are decreased ((d)). The vanadium influence on the tensile strength is much weaker as compared to the influence of aluminium.The predicted dependencies on aluminium and vanadium are in accordance with the well-established influence of the above elements over the mechanical properties. From the metallurgical point of view, it is also not surprising that in general substitutional elements increase the strength properties in titanium alloys. The simulated results are therefore consistent with what is expected from the theory and practice of the titanium alloys.The influence of other alloying elements like Mo, Sn, Zr, Fe and oxygen was also studied. Different tendencies for the influence of the different alloying elements on the mechanical properties were found. Hence, the trained neural network can be used for optimization of the alloy composition in order to obtain the desired combination of properties.Based on the trained neural network a computer program for optimization of the alloy composition and processing parameters was designed (), using a simple grid search. The input parameters of the program are the optimization criteria such as desired property (or combination of properties) at any conditions. The trained neural network is incorporated in the body of the program. Loops are organized for alloy composition, heat treatments and temperature. For each combination of inputs (alloy composition, heat treatments and temperature), the output values are predicted from the neural network and compared with the input criteria. As a result of these computations the “best” solution in respect to alloy composition and/or heat treatment corresponding to the desired properties is obtained at the output. In the following one example simulated from the program is demonstrated:Find: Alloy composition with maximal tensile strength (Rm) at 420°C.Fix: Heat treatment – α+β annealing; T=420°C; zero amount of Sn, Cr, Fe, Si, Nb, Mn; O=0.12Solution: The optimal composition is Al=5.8 wt%, Mo=7.3 wt%, Zr=5.2 wt%, V=0 wt%; This composition gives tensile strength at 420°C – . The other mechanical properties at 420°C are: The above program can be used to find a solution for “best” alloy composition and processing parameters for arbitrarily optimization criteria or combination of optimization criteria. In future, more efficient optimization methods can be incorporated On the base of the designed model of artificial neural network a graphical user interface (GUI) was created () for easy further use of the model. On input of the chemical composition of the titanium alloys, temperature interval and the heat treatment the chosen mechanical property is simulated and plotted. In this way, the user can very easily obtain the temperature dependence of any from the nine mechanical properties involved in the model for any heat treatment conditions and arbitrarily alloy composition. Furthermore, the GUI provides opportunity for easy comparison of mechanical properties corresponding to different conditions by plotting them together. An option is incorporated where the mechanical properties can be calculated and plotted versus the amount of a chosen alloying element at any fixed temperature. The GUI also allows easy switch between the different heat treatments and mechanical properties. In this way, the user can analyse the influence of the different factors (heat treatments and alloy composition) on the different mechanical properties at different operating temperatures. It should be noted here that the program will work with appropriate accuracy within the range of the data set used for training of the neural network.An artificial neural network model has been created for the prediction of the mechanical properties of titanium alloys as functions of the alloy composition, heat treatment conditions and working temperature. The model has been used to study the influence of different factors on the mechanical properties in titanium alloys.A GUI for use of the model has been created. The program and the model can be used for:prediction of mechanical properties for titanium alloys as functions of their chemical composition, heat treatment conditions and working temperature,investigation of the influence of different factors on the mechanical properties in titanium alloys,optimization of the alloy composition and processing parameters. |
The authors believe that the proposed model is convenient and powerful tool for practical optimization of the alloy composition and processing parameters of titanium alloys in order to obtain the desired combination of properties at different working temperatures. The model is open for constant upgrade and improvement.List of the alloys used for training and test of artificial neural network for prediction of mechanical properties of titanium alloysTi–6Al–2Sn–1.5Zr–1Mo–0.35Bi–0.1Si, Ti–6Al–2Nb–1Ta–0.8Mo, Ti–6Al–2Nb–1Ta–1Mo, Ti–6Al–1Mo–2Nb–1Ta, Ti–3Al–2.5V, Ti–5Al–2.5Sn, Ti–5Al–2Zr–2Mo–0.25Si, Ti–6Al–2Sn–4Zr–2Mo, Ti–6Al–2Sn–4Zr–2Mo–0.1Si, Ti–1Sn–5Zr–2.25Al–1Mo–0.25Si, Ti–8Al–1Mo–1V, IMI 834, IMI 417, Titanium 1100, Ti–10V–2Fe–3Al, Ti–11.5Mo–Zr–4.5Sn, Ti–3Al–8V–6Cr–4Mo–4Zr, Ti–12V–2.5Al–2Sn–6Zr, Ti–15Mo–5Zr, β-21S, Ti–11.5V–2Al–2Sn–11Zr, Ti–13V–11Cr–3Al, Ti–13V–2.7Al–7Sn–2Zr, Ti–15V–3Cr–3Al–3Sn, Ti–15Mo–5Zr–3Al, Ti–8Mo–8V–2Fe–3Al, β-CEZ, Ti–4.5Al–5Mo–1.5Cr (Corona 5), Ti–8Mn, Ti–5Al–2Sn–2Zr–4Mo–4Cr (Ti–17), Ti–6Al–2Sn–2Zr–2Mo–2Cr–0.25Si, Ti–4Al–4Mo–2Sn–0.5Si (IMI550), Ti–6Al–2Sn–4Zr–6Mo, Ti–6Al–4V, Ti–6Al–6V–2Sn, Ti–7Al–4Mo, Ti–5Al–5Sn–2Zr–2Mo–0.25Si, Ti–5Al–3.5Sn–3Zr–1Nb–0.3Si, Ti–5Al–6Sn–2Zr–1Mo–0.25Si, Ti–6Al–1.7Fe–0.1Si, Ti–4.5Al–3V–2Mo–2Fe, Ti–6Al–7Nb, Ti–4Al–4Mo–4Sn–0.5Si, Ti–4Al–3Mo–1V, Ti–5Al–1.5Fe–1.4Cr–1.2Mo, Ti–5Al–2.5Fe, Ti–6.4Al–1.2Fe, Ti–2Fe–2Cr–2Mo, Ti–8V–5Fe–1Al, Ti–16V–2.5Al, Ti–3Al–1.5Cr–1.5Fe, Ti–6Al–2Fe, Ti–6Al–2Fe–0.1Si, Ti–6Al–1Fe–1Cr, Ti–8Al–2Fe, VT14, VT15, VT16, VT18, VT20, VT22, OT4, VT1-00, VT3-1, VT5, VT5-1, VT-6, VT-6C, VT-8, VT-9.Predicted mechanical properties from the neural network (A) versus experimental values (T) for the training and test data sets are presented in Enhanced band-gap properties of an acoustic metamaterial beam with periodically variable cross-sectionsIn order to enhance the vibration reduction capacity in a wide frequency range, a novel acoustic metamaterial beam with periodically variable cross-sections is designed by combining the mechanisms of the Bragg scattering and the locally resonant band-gaps. The spectral element method (SEM) is extended to investigate the band-gap properties of the novel acoustic metamaterial beam. Based on the exact frequency responses obtained by solving the spectral equations in the frequency domain, it is found that the interaction of the Bragg scattering and the locally resonant band-gaps can enlarge the band-gap widths. More band-gaps can be achieved if the material periodicity is harmonized with the cross-section periodicity. When these two kinds of band-gaps exist simultaneously, the locations of the locally resonant band-gaps do not strictly correspond to the resonator's natural frequencies. The width and the attenuation ability of the Bragg scattering band-gaps become wider and stronger with the increase of the ratio of the cross-sectional sizes of the two sub-cells. The experimentally measured band-gap positions and widths agree very well with the SEM results, which guarantees the correctness of the numerical results.The mechanisms of the Bragg-scattering and locally resonant band-gaps are combined by designing an acoustic metamaterial beam with periodically variable cross-sections to enhance the vibration isolation capacity in wide frequency ranges. The interaction of the Bragg-scattering and locally resonant band-gaps can enlarge the band-gap widths. More band-gaps can be achieved if the material periodicity is harmonized with the geometrical or cross-sectional periodicity. The experimentally measured band-gap positions and widths agree very well with the SEM results, which guarantees the correctness of the parametric analyses. Acoustic metamaterial is one kind of phononic crystals and it can generate band-gaps in very low frequency regions, which has attracted much attention in view of its great potential for sound and vibration reduction The studies on the elastic wave band-gaps began with the phononic crystals of the Bragg scattering mechanism. The advantages of the Bragg scattering band-gaps include the large band-gap width and the strong attenuation ability The concept of acoustic metamaterials was proposed by Li and Chan ]. Nevertheless, the locally resonant band-gaps in acoustic metamaterials are rather narrow There are several methods proposed to study the band-gap properties, including the boundary element method In contrast to the FEM, the spectral element method (SEM) proposed by Doyle [] is based on the discrete Fourier-transform theory and the exact solutions of the wave equations in the frequency-domain, which means that the corresponding spectral stiffness matrix is exact. Thus, each uniform structural part can be modeled as one spectral element The uniform acoustic metamaterials have long been the main object of numerous researches. Nateghi et al. Recently, researchers showed a great interest to the non-uniform periodic structures. Xu et al. Based on the above analyses, it can be concluded that there exist already numerous investigations on the wave propagation in various acoustic metamaterial structures. However, to the best of our knowledge, the band-gap properties of the acoustic metamaterial beams with periodically variable cross-sections have not been studied so far. Motivated by the above facts, in this paper, a novel acoustic metamaterial beam with periodically variable cross-sections is proposed and the band-gap enhancement characteristics are explored by effectively combining the mechanisms of the Bragg scattering and the locally resonant band-gaps. The local resonator is designed as a two-degree-of-freedom (T-DOF) sub-system. The effects of several key parameters on the band-gap characteristics of the acoustic metamaterial beam are studied. Furthermore, a prototype of the proposed acoustic metamaterial beam is designed for the vibration experiments to validate the correctness of the dynamic modeling by the SEM. The key emphasis of this paper is to combine the mechanisms of the Bragg scattering and the locally resonant band-gaps of the periodic beam with the T-DOF local resonators so as to enhance the band-gap properties. The findings of the present study can be utilized as a guide in the design and optimization of the acoustic metamaterials with much more band-gaps not only in low-frequency regions but also in medium and high-frequency ranges.An acoustic metamaterial beam with periodically variable cross-sections as shown in is considered, where the local resonator in each unit-cell is a T-DOF sub-system. In (a), Fex is the external excitation force, D is the excitation point, and E is the receiving or observation point. In (b), k2, k3, m2 and m3 are the corresponding spring stiffnesses and masses, L1 and L are the lengths of the left part of the unit-cell and the whole unit-cell. The left and right parts of the unit-cell are denoted as sub-cell 1 and sub-cell 2. The cross-sections of the sub-cells 1 and 2 are all rectangular.The acoustic metamaterial beam is modeled as the Euler-Bernoulli beam. The equation of motion of the beam can be written aswhere v(x, t) is the transverse displacement in the time-domain, E is the Young's modulus, I is the cross-sectional moment of inertia, ρ is the mass density, and A is the cross-sectional area.Based on the discrete Fourier-transform theory, v(x, t) can be expressed as where V(x, ωn) is the spectral displacement of v(x, t), N is the sample number in the time-domain, and ωn is the frequency of the nth harmonic wave. For convenience, the subscript n of ωn will be omitted hereinafter.where C1, C2, C3 and C4 are the coefficients which are functions of ω, andin which Lb is the length of the beam, and kb is the wavenumber of the elastic wave, which is defined as, the nodal displacement vector Vb (ω) in the frequency domain is obtained asVb(ω)={Vb1Θb1Vb2Θb2}={V|x=0V′|x=0V|x=LbV′|x=Lb}=Rb2{C1C2C3C4},where Vb1, Θb1, Vb2 and Θb2 are the transverse displacements and the rotational angles of the two nodes as shown in , the prime (…)′ denotes the derivative with respect to the coordinate x, and Rb2 is given byRb2=[11e−ikbLbe−kbLb−ikb−kbikbe−ikbLbkbe−kbLbe−ikbLbe−kbLb11−ikbe−ikbLb−kbe−kbLbikbkb].where Nb=Rb1Rb2−1 is the dynamic shape function matrix of the spectral beam element.By means of the weighted-residual approach, where δV is the virtual variation of V, and V IV represents ∂4V/∂x4.The bending moment and the transverse (shear) force are determined bywhere Mf (x, ω) and Qf (x, ω) are the spectral components of the bending moment Mt (x, t) and the transverse (shear) force Qt (x, t) in the time-domain.in which Ffb is the nodal force vector of the beam element, and it is defined aswhere Qf1 = −Qf (0, ω), Mf1 = −Mf (0, ω), Qf2 = Qf (Lb, ω) and Mf2 = Mf (Lb, ω) are the transverse (shear) forces and the bending moments of the two nodes as shown in δVbT[(∫0LbEINb″TNb″dx−∫0LbρAω2NbTNbdx)Vb−Ffb]=0,where Sb(ω) is the spectral stiffness matrix of the beam element, which can be written as, the specific expression of Sb(ω) can be obtained The resonator is a spring-mass sub-system. The spectral element of a resonator with one-degree-of-freedom will be established, which is called the spectral resonator element. For a resonator with multiple degrees of freedom, one can obtain the spectral stiffness matrix by assembling the corresponding spectral resonator elements.The internal forces and displacements of a one-degree-of-freedom resonator can be transformed to the spectral forms as shown in , in which the positive directions of the related physical quantities are also defined. From the equilibrium equations of the spring, the following relations can be obtained:where fT, fM, VT and VM are the magnitudes of the internal forces and displacements on points T and M, and kTM is the stiffness of the spring. can be transformed to the following forms:Based on the Newton's second law and the continuity of displacement, the equations of motion for the mass m in where fB and VB are the magnitudes of the internal force and displacement on point B. , the equation of motion of a resonator with one degree of freedom in the frequency-domain can be written aswhere Ure = [VT VB]T and f¯re=[f¯Tf¯B]T are the nodal displacement and the nodal force vectors of the spectral resonator element, in which f¯T = −fT and f¯B = fB, and Sre (ω) is the spectral stiffness matrix of the resonator, which is expressed asAccording to the spectral beam and resonator elements, the spectral stiffness matrices of the unit-cell in (b) and the whole acoustic metamaterial beam can be assembled, which is similar to the process in the FEM. The spectral equation of motion of the whole metamaterial beam can be obtained aswhere Sw (ω) is the spectral stiffness matrix of the whole metamaterial beam, and Uw and Fw are the nodal displacement and force vectors in the frequency-domain.The frequency responses are calculated by and then the band-gap characteristics of the acoustic metamaterial beam can be analyzed.The frequency responses and band-gap properties of the metamaterial beam with periodically variable cross-sections will be investigated. The material and structural parameters are listed in An external force Fex = 10e iωt is applied on the excitation point D along the y-direction as shown in (a). Aluminum is used for the two beam segments of the unit-cell. The resonator is located on the point A, which is the midpoint of the sub-cell 1. The cross-sections of the sub-cells 1 and 2 are all rectangular. Here, hl and bl are the thickness and width of the sub-cell 1. The ratio of the cross-sectional sizes of the sub-cells 1 and 2 is rsd = br /bl = hr /hl, in which hr and br are the thickness and width of the sub-cell 2. The length ratio is defined by rL = L1/L, and m1 is the mass of the beam part in the unit-cell without the resonator. The mass ratio of the resonator is defined by rm = m3/m2. The spring stiffness ratio of the resonator is rss = k3/k2. The stiffness-mass ratio rsm of the resonator follows the relation rsm2= k2/m2 = k3/m3.Six spectral elements are used to model each unit-cell as shown in , in which the beam is divided into four parts for different resonator locations. The frequency responses of point E, i.e. the right edge of the acoustic metamaterial beam, are calculated by the SEM and the commercial FEM software ANSYS, for the validation purpose as shown in . The FEM results are obtained with the coarse meshes (each beam part is divided into 1 element) and the finer meshes (each beam part of the unit-cell is divided into 2 elements). It can be observed that the conventional FEM results converge to the SEM results with the mesh refinement, which validates the correctness of the SEM results and the effectiveness of the SEM for the frequency response calculations of the acoustic metamaterial beam. Moreover, the SEM is more efficient because each beam part of the unit-cell is modeled by only one spectral element, which minimizes the total degrees of freedom of the acoustic metamaterial beam. Compared with the FEM, the advantages of the SEM will become much more obvious for the calculation of the high-frequency responses. Furthermore, based on the smoothly varying attenuation property of the Bragg scattering band-gaps and the sharply changing attenuation behavior of the locally resonant band-gaps Furthermore, a comparison between the band-gap results of the reference consisting of 32 cells, and resonator 2 in . It can be observed that there are a locally resonant band-gap (673–946 Hz, the green shaded part) and a Bragg scattering band-gap (1083–1200 Hz, the gray shaded part) in the considered frequency range, which agrees well with the band-gap positions and widths of the results in The frequency responses of the acoustic metamaterial beam with different resonator locations on points A, B and C as shown in (b) are calculated by the SEM and displayed in . Compared with the other two situations, the widths of the two kinds of band-gaps are broader and the attenuation ability is stronger when the resonator is located on point A, i.e. the middle point of the thinner sub-cell (sub-cell 1). The width of the locally resonant band-gap is narrowest when the resonator is located on point B, i.e. the connecting point of the two sub-cells.The frequency responses of the acoustic metamaterial beams with 10, 15 and 20 unit-cells are calculated by the SEM and shown in , in which the curves C10, C15 and C20 correspond to the metamaterial beams with 10, 15 and 20 unit-cells. It can be seen that the band-gaps become more obvious by increasing the unit-cell number. This property can be used as an effective method to identify band-gaps. Thus, in what follows, the frequency responses of the acoustic metamaterial beams with different unit-cell numbers can be calculated in order to identify less apparent band-gaps if it is necessary.The influence of the unit-cell length on the band-gap property is investigated and illustrated in . For the identification purposes, the frequency responses of each metamaterial beam with a specific unit-cell length are calculated. From (a), it can be observed that there are two locally resonant band-gaps (the green shaded parts, i.e. 351–407 Hz and 426–617 Hz) and two Bragg scattering band-gaps (the gray shaded parts, i.e. 212–258 Hz and 1159–1357 Hz) in the given frequency range.With the unit-cell length decreasing from 0.35 m to 0.265 m, the first Bragg scattering band-gap moves to higher frequency, and it syncretizes with the first locally resonant band-gap, which leads to a coupled Bragg-local resonance band-gap (the yellow shaded parts, i.e. 349–424 Hz). This coupled band-gap is wider than each of the first two individual band-gaps in Besides, when the first Bragg scattering band-gap moves towards the right direction, the second locally resonant band-gap becomes wide significantly as observed in (b) (the green shaded part, i.e. 462–821 Hz), which is nearly two times as the width of the corresponding locally resonant band-gap in (a). It indicates that the approach of the Bragg scattering band-gaps to the locally resonant ones from the low-frequency has a great broadening effect on the band-gap width.Furthermore, when the length of the unit-cell is decreased to 0.257 m, the locations of the first locally resonant band-gap (the green shaded part, i.e. 359–380 Hz) and the first Bragg scattering band-gap (the gray shaded part, i.e. 396–425 Hz) in (c) are reversed compared with those in (a). The broadening effect on the second locally resonant band-gap (the second green part, i.e. 465–859 Hz) in (c) reserves. However, the first locally resonant band-gap is much narrower than that in (a). Generally speaking, the second Bragg scattering band-gap moves to the high-frequency with the decrease of the length of the unit-cell.Additionally, the natural frequencies of the resonator remain the same (355.88 and 444.85 Hz) for all the cases of . The locally resonant band-gaps contain the two natural frequencies separately in (a). However, both of the two natural frequencies are not covered by the locally resonant band-gaps due to the influence of the Bragg scattering band-gaps in (c). Thus, it can be concluded that there is no strict one-to-one correspondence between the locations of the locally resonant band-gaps and the natural frequencies of the resonators on the condition that the two kinds of the band-gaps exist at the same time.The influence of the ratio of the cross-sectional sizes of the two sub-cells rsd is investigated and illustrated in . Here, rsd = 1 means that the cross-section of the acoustic metamaterial beam is uniform. In this situation, it can be seen that there are two locally resonant band-gaps and no Bragg scattering band-gaps. Moreover, the widths and the attenuation ability of the Bragg scattering band-gaps become larger and stronger with the increase of rsd, which is beneficial to the occurrence of the coupled Bragg-local resonance band-gaps.Next, the effects of the material combinations on the band-gap characteristics are studied. Four combinations of the sub-cells 1 and 2 are examined, i.e. aluminum-aluminum (Al–Al), aluminum-steel (Al–St), epoxy-aluminum (Ep–Al) and epoxy–steel (Ep–St) as displayed in (a). For this case, the material densities and the Young's moduli of the sub-cell 1 are not larger than those of the sub-cell 2. It can be observed that the greater the difference between the two materials, the wider the Bragg scattering band-gaps, and the attenuation ability becomes stronger at the same time. Besides, the broadening effect can be found obviously from the results for the combinations of Ep–Al and Ep–St due to the approaches of the Bragg scattering band-gaps to the locally resonant band-gaps from the low-frequency direction.The frequency responses of the reverse material combinations are calculated as seen in (b). It can be found that the band-gaps cannot be broadened even the material combination is quite different in this situation. The number and the widths of the Bragg scattering band-gaps decrease in this case compared to the material combination in (a) are completely opposite to those from (b). This is mainly due to the fact that the material properties are harmonized with the cross-sectional properties of the corresponding sub-cells in (a), i.e., when ‘light’ and ‘soft’ materials are used in the sub-cells with small cross-sectional sizes and ‘heavy’ and ‘hard’ materials are used in the sub-cells with big cross-sectional sizes, the periodicity of the metamaterial beam can be strengthened to the utmost extent by harmonizing the material periodicity and the cross-sectional periodicity. So (a) contains more band-gaps. However, the cross-sectional periodicity is counteracted by the material periodicity significantly in (b), which is a main obstacle for the generation of the Bragg scattering band-gaps.The frequency responses of the uniform metamaterial beam with the same material combinations as (c). The influence of the material contrast is similar to that in (a) it can be observed apparently that the acoustic metamaterial beam with variable cross-sections can generate much more and wider band-gaps than the beam with a uniform cross-section as seen in (c). It implies that the variable cross-sectional design of acoustic metamaterial beams is an effective strategy to obtain more and broader band-gaps. shows the effects of the length ratio of the unit-cell rL on the band-gap properties. It can be found that the widths of the Bragg scattering band-gaps increase with the decrease of rL, and the Bragg scattering band-gaps move to higher frequency regions. However, rL has no obvious influence on the locally resonant band-gaps. Thus, the length ratio of the unit-cell can be used to tune the widths and locations of the Bragg scattering band-gaps in order to obtain wider band-gaps by means of the coupling and broadening effects between the Bragg scattering and the locally resonant mechanisms.The influences of the resonator and the material damping on the band-gap characteristics are investigated by introducing the complex stiffness k (1 + i ηr) of the resonators and the complex Young's modulus E(1 + i η) of the beam material, in which ηr is the loss factor of the resonators and η is the loss factor of the beam material. The frequency responses are shown in . Generally speaking, the damping cannot change the locations and the widths of the band-gaps. It mainly reduces the amplitudes in the pass-bands. Specifically, the damping of the resonators can reduce the amplitudes of the pass-bands around the locally resonant band-gaps effectively as shown in (a). The material damping can reduce all the amplitudes of the pass-bands, which is more obvious in the high-frequency ranges as shown in (b). Combining the resonator and the material damping, the amplitudes of all the pass-bands can be reduced significantly as shown in The influence of the mass ratio rm of the resonators on the band-gap properties is examined and shown in . It can be observed that the two locally resonant band-gaps move to the opposite directions with the increase of rm. The first moves to lower frequencies while the second moves to higher frequencies with the increase of rm. Furthermore, the first locally resonant band-gap widens and the second becomes narrower with rm increasing. Additionally, a larger mass ratio rm can enhance the attenuation ability of the first Bragg scattering band-gaps in the lower frequency range, while it has no obvious influences on the second Bragg scattering band-gaps. illustrates the frequency responses of the acoustic metamaterial beams with different spring stiffness ratios rss of the resonators. It can be observed that both of the two locally resonant band-gaps move to lower frequencies when rss decreases, and the first band-gap moves faster than the second one. Additionally, the increase of rss can broaden the first locally resonant band-gap but narrow the second one. So one can design the locations and widths of the locally resonant band-gaps by tuning the spring stiffness ratio of the resonators.The frequency responses of the acoustic metamaterial beams with different stiffness-mass ratios rsm of the resonators are displayed in . Both of the two locally resonant band-gaps move to higher frequencies with the increase of rsm. And the widths of the band-gaps are nearly unchanged. In other words, rsm can only change the locations of the locally resonant band-gaps, and it has almost no influence on the Bragg scattering band-gaps.The main purpose of this experiment is to validate the correctness of the dynamic modeling by using the SEM, which can ensure that the above parametric analyses are correct. A prototype of the acoustic metamaterial beam with T-DOF local resonators is designed for the vibration experiment. Free boundary conditions are simulated by suspending the prototype with two rubber bands. An excitation is applied on the excitation point using the hammer, and the response is measured at the other end of the beam using an acceleration sensor. The prototype of the acoustic metamaterial beam and the experimental setups are shown in . The springs and masses in the resonators are simulated by cylindrical rubber rods and steel cylinders. The beam is made of aluminum alloy. The material and the structural parameters of the prototype obtained from the manufacturer and the actual measurement are listed in The stiffness of the cylindrical rubber rod kru is calculated by the following formula where Eru is the Young's modulus of the rubber, Aru and Hru are the cross-sectional area and the height of the cylindrical rubber rod, and nru = Dru/(4Hru) is a shape factor, in which Dru is the diameter of the rubber rod.The displacement response calculated by the SEM and the acceleration response measured by the sensor are displayed in . It can be seen from the SEM results that there are one locally resonant band-gap (the green shaded parts, i.e. 92–132 Hz), one coupled Bragg-local resonance band-gap (the yellow shaded parts, i.e. 167–267 Hz) and one Bragg scattering band-gap (the gray shaded parts, i.e. 686–1364 Hz) in the considered frequency range. By comparison, it can be found that the experimentally measured band-gap positions and widths agree very well with the SEM results. Due to the influence of the damping, the locally resonant band-gaps in the experimental results are not so obvious as in the SEM results. However, this does not affect the experimental verification, thus it can be stated that the dynamic modeling by the SEM is correct, which guarantees the correctness of our numerical results.Based on the coupling mechanisms of the Bragg scattering and locally resonant band-gaps, a novel acoustic metamaterial beam with periodically variable cross-sections is designed to enhance the vibration reduction capacity in wide frequency ranges. The band-gap characteristics of the acoustic metamaterial beam are analyzed by using the SEM. The experimentally measured band-gap positions and widths agree very well with the SEM results. The main findings of the present study can be summarized as follows:The frequency-domain SEM based on the discrete Fourier-transform theory is an exact and efficient tool for the band-gap analysis of the acoustic metamaterial beams.The periodic variable cross-section design for the acoustic metamaterial beam is an effective measure to obtain more and broader band-gaps. The acoustic metamaterial beam with the resonators located on the thinner sub-cell can generate wider band-gaps with stronger vibration attenuation ability.The movement of the Bragg scattering band-gap to the locally resonant band-gap from the low-frequency has a great broadening effect on the widths of the locally resonant band-gaps. The coupled Bragg scattering and local resonance band-gap is wider than each of the individual band-gaps.The widths and the vibration attenuation ability of the Bragg scattering band-gaps become wider and stronger with the increase of the ratio of the cross-sectional sizes of the two sub-cells in each unit-cell. More band-gaps and the broadening effect can be achieved if the material periodicity is harmonized with the geometrical or cross-sectional periodicity.We have no conflicts of interest to declare.Beam rotation actuator based on dove prism in the optical storage mediaA beam rotation actuator, which can be utilized to improve the data transfer rate for optical disk systems, has been developed. The newly developed beam rotation actuator with high-resolution and fast response was assembled for micro positioning of an optical storage media. The beam rotation actuator is utilized to put multi-beam spots on more than one track on an optical disk simultaneously in addition to tracing multi-beam spots on tracks in a radial direction. Multi-beam spots turn on an optical axis by rotating dove prism in the optical path at the end of a cantilever arm. The beam rotation actuator is made of bimorph peizoelectric material. The dove prism is responsible for both high-resolution movement as well as multi-beam spot rotation. The dynamic equation of the beam rotation actuator is derived theoretically. The actuator is designed on the grounds of an analytical equation. It is shown that the beam rotation actuator has a natural frequency of 54 Hz or more, and the actuator has high-resolution. The application performance of the beam rotation actuator is verified as the feedback control is applied.An optical disk system has been utilized many times as a storage system. The technology of fast data transfer rate is important because a high-speed optical disk system is required for many applications, such as digital video files and code data files Several methods have been researched to improve the data transfer rate in an optical disk system. A multi-beam optical disk system has been suggested as one method for the enhancement of the data transfer rate, by increasing the number of beam spots as a reading source in an optical disk In this paper the beam rotation actuator is proposed as one actuator of an important part of a multi-beam optical system. The beam rotation actuator, made of the dove prism and piezoelectric bimorph, is needed to make up for the track pitch variation in appearance caused by the eccentricity of a disk.The beam rotation actuator in a previous study, which had two moving coil parts attached to each side of the dove prism along with two magnet segments, had the dove prism made in the manner of a cantilever arm Our newly developed beam rotation actuator in this paper, is proposed in the manner of a cantilever arm in application to a multi-beam optical disk. The dove prism is used as the main part of a beam rotation optical device. This beam rotation actuator must have high-resolution and high enough response to adapt to the environment of a multi-beam optical system. For this reason, the actuating system based on piezoelectric material is suggested. Piezoelectric actuators with high-resolution and fast frequency response are widely assembled in micro-positioning applications It is verified experimentally that the beam rotation actuator has enough performance in applying well to a multi-beam optical system, because of its high-speed and high-resolution characteristics in piezoelectric materials. This beam rotation actuator is above the ±0.5° range with high-resolution, overcoming beam spots track-off along with optical parts misalignments. To overcome beam spot track-off due to the eccentricity of a disk and other disturbances, the actuator has 50 Hz or more bandwidth, enough to rotate beam spots with ±0.005° or less resolution. We derived our dynamic model of a newly designed beam rotation actuator on the basis of this proposed model. We compare the experimental with the theoretical results in this dynamic model. The system’s performance is experimentally investigated through both a step response and track following characteristics of the multi-beam.In order to trace individual beam spots in a multi-beam optical system simultaneously on more than one track, the conventional tracking method, which moves the beam spots laterally across a track with only one tracking actuator, is insufficient. The reason is that the track pitch varies in appearance due to any eccentricity in the disk along with the possibility of the carriage’s inaccurate movement when the objective lens moves between the inner and outer tracks of the disk. In order to make up for these variations in track, apparently it is necessary that beam spots be also rotated at the optical axis in addition to tracing beam spots on tracks in the radial direction. For this reason, a dove prism inserted in an optical path is used to rotate beam spots on a disk for simultaneous multi-beam spot tracing.The optical path in this study is constructed more simply than the previous multi-beam system, because of a focusing/tracking error signal detection method using the one beam. That is, the astigmatism method for focusing on detecting an error, and the differential phase tracking method for detecting errors on one beam spot are used. in which the bundles of rays arrive parallel to the hypotenuse face of the prism. After being refracted downward at the entrance face, the rays are then reflected upward from the hypotenuse, and finally emerge after a second refraction at the exit face. If this prism is used in a convergent light beam, it will introduce a substantial amount of astigmatism. For this reason, the dove prism is also used almost exclusively in parallel light. The dove prism has a very interesting effect on the orientation of the image, that is, the image is rotated twice as fast as the prism.The principle of beam rotation is shown schematically in . The size of the dove prism is determined by the diameter of the parallel beam section. Consequently, the geometrical properties of the dove prism are represented in The overall system, which will be applied to a multi-beam optical system, is shown in . The rotating angle generated at the end of a cantilever beam causes the rotation of the beam’s array. A lateral direction shift exists in the cantilever type. However, the problem of track miss due to this lateral shift of the cantilever beam is minimized, as this shift is set in a tangential direction from the track on the disk., and its material properties are further tabled in . Bimorph material is composed of two thin layers of lead zirconate titanate (PZT), with their opposite poling directions bonded together with a thin brass film medium. The upper piezoelectric layer is poled so that it expands longitudinally, while the lower layer contracts with an applied electric field. When voltage is applied to both the upper as well as the lower piezoelectric materials, the device bends. A bimorph material bends in the opposite direction in the case of reverse voltage. The bimorph material used in this paper was fabricated by NGK SPARK PLUG. The product name of the piezoelectric material is EB-300-80MSH2-3.Consider a bimorph composed of two strips of piezoelectric materials and brass film of length l, width W, thickness of piezoelectric material t1, thickness of brass t2, as shown in . This bimorph material device is modeling as a cantilever beam.For a small upper layer element in the upper piezo material, the relative extension can be found as follows:The longitudinal force ΔF, and momentum ΔM, generated by the small element in the Therefore, the total bending moment generated by the bimorph piezoelectric material is as followsA composed bimorph beam, which consists of both brass film and piezoelectric material, is shown in . The flexural rigidity of a composed beam is:Let’s derive the dynamic model of the beam rotation actuator in a cantilever arm with the above . Suppose that the input applied voltage is linear to deflection at the end of the cantilever beam, and the deflection is also small in the elastic range. The dove prism is attached to the end of the bimorph material as shown in . The beam rotation actuator is shown schematically in , and can also be replaced with the equivalent spring-mass system, as shown in . The dynamic equation of the beam rotation actuator is analyzed on the grounds of an equivalent spring mass system. Point C is shown in , located in the middle of the undeflected bimorph beam, is the virtual rotational center for the dove prism in the view of its rigid motion. The dynamic equation iswhere Isys is the equivalent moment of inertia, and is the angular acceleration. Assuming a small angle and from where Kb is the stiffness of the composed piezo beam, and δy is the vertical deflection at the end of the beam.For the servo system of this actuator, the transfer function of the actuator can be obatined from where Kb is the linear spring constant. The transfer equation was utilized to simulate the servo system of the beam rotation actuator.The equivalent moment of inertia of the beam rotataing actuator can be written aswhere Idove, Ibeam, and Ietc are the moment of inertia for dove prism, for the beam and for the acryl.The equivalent mass of the bimorph beam can be derived by the Rayleigh–Ritz method where ρp is the density of the PZT in the piezo bimorph and ρs is the density of the brass in the piezoelectric bimorph; and le is the effective length of the piezoelectric bimorph.where mdove is the mass of the dove prism.For two acryl supports with which dove prism and bimorph material connectwhere metc is mass of two acryl supports.The natural frequency of the beam’s rotator is derived from , the static rotating angle can be found from The natural frequency and the static rotating angle caused by applied voltage can be found approximatedly from In order to design the beam rotation actuator, we should first determine the design specifications such as the beam rotation range, rotating resolution, and the frequency characteristics in the beam rotation actuator. Then the beam rotation actuator is designed appropriately, according to these design specification.Firstly, let us set the rotating range of the dove prism. The rotating angle for a spot array on a disk is calculated as follows:where Ec, rd, e, and pd are the eccentricity of a disk, the effective data area radius of a disk, the tracking error level, the beam spot interval on a disk, respectively. The first term is the most important factor in the servo system of the beam rotation actuator. The second term is relatively small. α is an angle caused by the radial difference between the inner and outer tracks. However, it can be negligible if the pickup does not move a long distance. β is an angle variation, owing to either an unpredictable external disturbance or other internal vibrations. It can also be negligible in an anti-vibration experimental condition, and is also small in a real system since the external disturbance is also rejected through the anti-vibration support system. ϵ is an optical alignment angle, and has a large value when an optical disk is initially loaded. Therefore, the initially applied voltage to the beam rotation actuator can compensate sufficiently for ϵ. The eccentricity amplitude of a disk is about 100 μm. The effective data area radius of a disk is 25–58 mm. The interval of the beam spot on a disk is 20 μm or less.With the above considerations, the rotating range of beam spot on a disk from requires above ±1°. Accordingly, the multibeam disk system is set above ±0.5° rotating range of a dove prism, because the spot array on a disk is rotated twice as fast as the dove prism. However, a rotating angle has to have as large a value as possible. This is because of the optical misalignment problem, that increases, increasing the rotating range of the dove prism. As calculated from , a static rotating angle is 0.5° or more at the effective length above 22 mm, when the maximum applied voltage is 45 V.Secondly, the rotating angle’s resolution must be determined enough in order to trace individual beam spots simultaneously on more than one track. As a general rule of an optical disk, it is acceptable that the tracking error Te of a beam spot is below ±0.03 μm in the radial direction of a disk in a tracking servo. Therefore, a tracking error of a side beam spot in a multi-beam optical system can be set as follows:where te and Δx are the tracking error level of a side spot undertaken by the tracking actuator, and the rotating tracking error level of a side spot undertaken by a beam rotation actuator, respectively.Let us investigate the rotating mechanism of the beam array on a disk in . The second beam spot is the center beam in this muti-beam system, as seen in . The ideal center of a disk does not coincide with the rotating center of a disk in a real system. Therefore, eccentricity always exists according to the way a disk is rotated by a spindle motor. The eccentricity has the same frequency as that of rotating a disk. shows the rotating effect of a beam array due to eccentricity, which must be controlled in the rotating beam servo system. In more detail, it can be seen in that the track-off of a side spot is caused by the sinusoidal eccentricity of a disk.The initial tilt angle of a beam array is calculated as follows:where p is the pitch of a disk, 1.6 μm. The rotating of side spot Δθ, due to the eccentricity, is calculated as follows:The rotating tracking error Δx is the track-off deviation of a side spot, owing to the eccentricity, and can be calculated as follows:where θ0+Δθ is a small angle. It is difficult to reduce the value of te in to below some limit value, because of a sensor problem and the control stability issue. However, as the tracking error te that is undertaken by the tracking servo system increases, the rotating tracking error Δx due to the eccentricity of a disk, also decreases. For that reason, te is in inverse proportion to the rotating angle error Δθ. There must be a trade-off between a tracking error undertaken by a tracking actuator, and a rotating tracking error owing to the dove prism rotation. With the above considerations, we set te as around ±0.026 μm or more in this study. The error level of the rotating angle on a disk must be below ±0.012°, as calculated from . The minimum rotating angle resolution of the beam rotation acautor can reduce ±0.005° or less, because the sensitivity is 0.012°/VFinally, the natural frequency value of the beam rotation actuator must be as large as possible in the cases where the rotating resolution exists below allowable limits and the rotating range of the dove prism is enough to cover above 0.5° in the range of the applied 45 V input. The natural frequency is decided to be 50 Hz or more, because the rotating speed of a disk is set below 3000 rpm. For these reasons, an effective length of piezoelectric bimorph material is determined to be 22 mm, as seen from . Consequently, a beam rotation actuator is constructed, as seen in the picture of . Both a bonding material and a supporting plate fix one end of a piezoelectric bimorph. The other end is attached to the dove prism with a dove holder. The dove holder, which is made of acryl, is then utilized in order to easily attach piezoelectric material to a dove prism.The rotating angle generated at one end of a composed piezoelectric beam was then measured in static experiments. Its rotating range and the resolution were verified by these experiments. The rotating angle is measured quantitatively when the driving input voltage is applied to a piezoelectric material. shows our experimental method in measuring the rotating angle. A He–Ne laser source is reflected on the side of the dove prism. After that, the rotating angle of a piezoelectric material is calculated by measuring the displacement of the reflected laser beam on the round measuring ruler. The distance between the He–Ne laser source and the dove prism is 6 m. As shown in , the rotating angle is calculated as follows:where L, d and θ are the length between the He–Ne laser beam and the dove prism, the moving displacement of the reflected laser beam at the ruler, and the rotating angle at the end of bimorph piezoelectric beam, respectively. The rotating angle value of static experiments is similar to that of , which was obtained from the theoretical analysis. represents the rotating range of the beam rotation actuator throughout three measurements. As seen from static experimental results, the piezoelectric material shows an inherently hysteresis phenomenon.As piezoelectric material has hysteresis characteristics, the rotating angle is not linear to the applied input voltage, as seen in . However, when input voltage is low, the rotating angle is approximately similar to that obtained from . But, this nonlinear problem can be solved easily by using the photo diode sense signal of a optical disk, or other external sensing mechanisms such as a laser measuring instrument and strain gage.The dynamic response of a beam rotation actuator is obtained experimentally by the dynamic analyzer HP 35670A. As a position sensor, an OFV-3000 laser vibrometer from Polytec was used. A rotating angle is calculated by unit conversion with the deflection, the length of the piezoelectric beam and sensor gain. A frequency response is measured by the swept sine method. The experimental results of the frequency test are shown in . The results show that a natural frequency of the beam rotation actuator is around 54 Hz.The transfer Function throughout curve fitting is as follows:where θL and Vi are the rotating angle (°) and a input driving voltage (V), respectively.Assuming that the relation between the input driving voltage and the output rotating angle is linear and a rotating angle is small, obtained theoretically. So, it is shown that the theoretical results agree with the experimental results in the view of the natural frequency and DC sensitivity. The percentage difference between the analytical natural frequency (52 Hz) and the experimental natural frequency (54 Hz) is within 2%. It is also shown that the rotating angle value in DC sensitivity from The beam rotation actuator must follow the sinusoidal rotating value, due to the main sinusoidal eccentricity of a disk, as can be seen in . The input frequency of the main sinusoidal eccentricity of a disk is below 50 Hz when the disk is rotated less than 3000 rpm. Therefore, the closed loop servo bandwidth can be let above 50 Hz. The beam rotation actuator must follow the rotational angle reference input caused by the main sinusoidal eccentricity of a disk, which is always below 50 Hz frequency. represents the Simulink block diagram. A piezo amplifier made of PA88 from Apex was used. The gain of the amplifier is 10. In the servo system, Kps, Kd, and Pg are the sensor gain (1.099E3), the feedback velocity gain (3.7E−4), and the proportional gain (9.4), respectively. The state feedback control like PD control is applied to the actuator, where the velocity is obtained from the derivation of position.. The difference in value between the input and output is error displayed on the center of a scope. The reference input is half of the value calculated from . It is shown experimentally that the minimum error level of the beam rotation actuator is below ±0.005° when the reference-input angle is 0.13°. It is demonstrated that the beam rotation actuator has enough performance to apply to the multi-beam optical system on the grounds of this control scheme. shows the step response when the corresponding input is 0.1°. The settling time is about 13 ms when the servo system is established. Experiments show that the servo system has fast response characteristics to any eccentricity disturbance of a disk below a 50 Hz frequency.A conventional tracking actuator is not sufficient to trace beam spots on more than one track simultaneously in a multi-beam optical system, because the rotation of the beam spots apparently varies in accordance with the movement in the radial direction. Therefore, the beam rotation actuator is newly developed for one of the actuators in the multi-beam optical system, in order to rotate the beam array and put beam spots properly on all tracks of a disk. The beam rotation actuator helps multi-beam spots trace tracks on a disk simultaneously in optical circuits. Because multi-tracks on a disk can be read, the data transfer rate of an optical disk can be enhanced without advancing the performance of another actuator, such as the focusing/tracking actuator and spindle actuator.In order to develop the beam rotation actuator, the mathematical model of the beam rotation actuator was derived using an equivalent spring-mass system on the basis of the virtual rotational center. The design specifications of the beam rotation actuator are determined on the grounds of its multi-beam system characteristics and mathematical analysis results.The rotating angle range, the angle resolution, and the bandwidth obtained from this theoretical analysis was demonstrated through static and dynamic experiments. The natural frequency of the beam rotation actuator was investigated at above 50 Hz, theoretically as well as experimentally. It is shown that the beam rotation actuator is sufficient to overcome rotating disturbances due to disk eccentricity, as this is the only simple feedback servo-system construct. It is found that the rotating angle resolution of the beam rotation actuator is 0.005° or less. It is shown experimentally that the total rotating angle range is ±0.5° or more when the input driving voltage is 45 V.A fibre optic corrosion fuse sensor using stressed metal-coated optical fibresA novel optical fibre-based corrosion sensor based on the mechanical failure of stressed metal-coated optical fibres when exposed to a corrosive environment is presented. The current work discusses proof-of-principle tests carried out using commercially available aluminium-coated optical fibres. Tests have been undertaken in a non-corrosive environment, in aqua regia and in sea water. The failure times of stressed aluminium-coated fibres were found to correlate with the corrosivity of the test environment. The results are discussed in relation to microscopic investigations of the metal coatings in the aforementioned corrosive environments as a function of immersion time.Studies of a number of countries have estimated the cost of corrosion to be between approximately 2 and 5% of the gross national product In recent years there has been increased interest in using optical fibres in the development of corrosion sensors due in part to their small size and the potential to provide a means of remote detection. Thus optical fibre-based sensors have advantages in areas where traditional sensing technologies have difficulty in accessing. One of the most often discussed applications of such sensors is in the detection of corrosion in aircraft, where the benefits of light weight and small size are of considerable importance.Previous work on optical fibre-based corrosion sensors has focussed on the use of either:changes in the transmitted optical power of metal-coated fibres using the evanescent field the use of an optical fibre to monitor the failure of a bulk material due to corrosion While fibre Bragg grating and spectroscopic-based techniques show promise, they typically require non-trivial and sometimes costly equipment to monitor. The use of changes in the transmitted power of metal-coated fibres, while potentially offering a low-cost sensor, is susceptible to variations in transmitted power caused by non-measureand effects (e.g. bends and light source fluctuations). The technique proposed here does not require a complex optical system, therefore is relatively low in cost, and should be less susceptible to non-measureand-based fluctuations in optical power.The proposed corrosion sensing technique is based on the mechanical failure of a stressed metal-coated fibre. The strength and failure mechanisms of optical fibres have been studied extensively due to their widespread use in telecommunications, where interest lies in determining how long fibres will survive in the environments in which they are used The static fatigue life of an optical fibre can be extended by excluding the detrimental effects of moisture from the surface of the fibre. This is most commonly achieved using a jacket material that provides a hermetic seal and typically metal coatings are used for this purpose. In some cases metal-coated optical fibres have shown significant improvements in fibre strength from ∼5 GPa To date the most common approach in determining the strength of metal-coated fibre has involved dynamic testing. Investigations on the static fatigue strength of metal-coated fibres have been carried out by Pinnow et al. The basic sensing principle of the stressed metal-coated optical fibre corrosion sensor is illustrated in . The sensor uses a stressed metal-coated optical fibre which transmits light to indicate that no corrosion is present (a). When the fibre is exposed to a corrosive solution the metal coating of the fibre corrodes away (b). After a certain amount of time the metal jacket corrodes to the extent that the glass cladding of the optical fibre is exposed. Once the glass is exposed the fibre will fracture at a rate dependant upon a variety of factors including the level of stress and the amount of moisture present. After the fibre has broken it will no longer transmit light, and the loss of signal can be used to indicate the presence of corrosion (c). In this work tests were conducted on the static fatigue of aluminium-coated optical fibres in a range of environments with the aim of developing a corrosion sensor based on this principle.In the present investigation a bend was applied to induce stress on optical fibres and the subsequent failure times were measured. For consistency the optical fibre samples were bent inside glass tubes of known internal diameter. This test method has several advantages over other approaches illustrates several optical fibres bent inside a glass tube. The section of fibre on the inside of the bend is subject to a compressive stress, while the portion of the fibre on the outside of the bend is in tension. One of the most common expressions for the maximum tensile stress on a fibre due to bending is where σ is the stress, E is the Young's modulus, d is the faceplate separation and df and dc are the diameters of the glass fibre (excluding the coating) and of the overall fibre (including the coating). Eq. , however, does not consider the strain dependence of the Young's modulus of silica glass at high stress levels and therefore tends to underestimate the stress in these situations.In this work we use the equations developed by Muraoka The a and b parameters represent the non-linearity of the stress–strain relationship and are equal to 3.2 and 8.48, respectively. The strain is given byκ≈2.396df2(d−dc)1+0.5825(a2−b)df2(d−dc)2The aluminium-coated fibres used in this work were purchased from Fiberguide Industries and Polymicro Technologies. In addition to the aluminium-coated fibres, samples of standard telecommunication and polyimide-coated fibres were also tested, the details of which are also shown in The corrosive solutions investigated in this work were aqua regia and natural sea water. Aqua regia is a highly corrosive acid solution consisting of a mixture of hydrochloric acid and nitric acid in a 3:1 ratio. The sea water used in these experiments was obtained at the Middle Park Pier (Port Phillip Bay, Victoria) and was aerated using a simple air pump with a diffuser. All results presented herein were taken at ambient temperature.The applied stress measurements were made by bending the optical fibre samples inside glass tubes with known inner diameters. Failure of the samples were determined visually with either continuous or periodic inspection depending upon the failure times of the samples. The surface of aluminium-coated fibre samples immersed in sea water and aqua regia were recorded after various immersion times using an Olympus BH2-UMA microscope with a variety of magnifications from 5 to 100 times.In this section the results of static fatigue tests on both metal-coated and non-metal-coated optical fibres in corrosive and non-corrosive environments are presented and discussed. The tests on the non-metal-coated optical fibres are important as they provide an understanding of the expected failure times of the stressed fibres once the metallic jacket has corroded sufficiently to expose the glass fibre.The failure times of samples of acrylate-coated F-SMF-28 and polyimide-coated fibres were measured for various bend diameters in ambient atmosphere. The results are shown in , where the bend diameters have been converted to applied stresses using Eq. The static fatigue behaviour of optical fibres is commonly modelled using the power law where B is a constant, Si is the inert strength and n is the stress corrosion constant. The constants of Eq. were determined from a linear fit to a log–log graph of the failure time versus applied stress and are listed in together with the coefficient of determination (r2) of the fits.The values of the stress corrosion constant, n, for silica fibres with standard coatings typically reported in the literature are close to 20 Samples of a range of aluminium-coated fibre types have been subjected to applied stresses and monitored for failures in ambient atmosphere, used to represent a non-corrosive environment. Details of the maximum stresses which the glass component of the fibres were subjected to, calculated using the known bend diameter, are shown in are the number of samples tested and the number of samples which have survived for the total length of the test to date. out of the 119 fibres tested only 1 sample has failed for test times between 585 and 742 days (5.05–6.41 × 107 |
s). The only sample which did fail did so ∼12 days after insertion and was possibly caused by damage to the fibre during insertion. These results show that the fibres with an aluminium coating survive without breaking for time scales at least 4 orders of magnitude longer than acrylate-coated fibres when subjected to similar stresses. Acrylate-coated fibres for example were found to break in time scales of 1 × 101 to 1 × 104 |
s in ambient atmosphere when subjected to similar stress ranges. This suggests that:the aluminium coating provides an additional fatigue resistance mechanism, and,sensors should survive in a non-corrosive environment for long time scales.The effect of a highly corrosive environment on the failure times of stressed aluminium-coated optical fibres was measured by immersing the test samples in aqua regia. shows the failure times of ASI9/125/175A fibres in aqua regia as a function of applied stress. indicate that the failure times of the fibre follow the trend observed for the non-metal-coated fibres where faster failures are observed as the applied stress increases. Static fatigue constants of n |
= 1.0 ± 0.2 and BSin−2=3.17±0.07 were obtained for a fit with an r2 value of 0.946. The average failure times of the aluminium-coated fibres in aqua regia are at least 4–5 orders of magnitude smaller than the same fibre types subjected to similar stress levels in ambient atmospheres.It is interesting to compare the failure times of aluminium-coated fibres in aqua regia with the values obtained by non-metal-coated fibres. The range of applied stresses tested on the metal-coated fibres in aqua regia was approximately 1–5.9 GPa. Using the fits obtained for non-metal-coated fibres in Section this corresponds to failure times of approximately 1018 to 101 |
s. The failure times of metal-coated fibres in aqua regia are reasonably close for the high stress regime but differ significantly for the lower stress levels. A possible explanation of the faster than expected failure times of the aluminium-coated fibres in the low stress regime may lie in changes to the glass surface resulting from the metal coating process. Previous work In another example of a corrosive environment stressed aluminium-coated optical fibres were immersed in sea water and periodically inspected for failures. Details of the fibres that have been tested, the stresses on the fibres, the number of samples which have failed and the test times are given in show that only 16 out of the 124 samples (13%) of Fiberguide fibres have failed during immersion times of ∼1.5–1.75 years. Conversely, nearly all (93%) of the Polymicro fibre samples have failed within 1.3 years of immersion. The time dependence of the failure of the Polymicro fibre samples immersed in sea water is shown in Using the data obtained for the FIL100110150 aluminium-coated fibre a plot of the average failure times versus the applied stress is shown in . Static fatigue constants of n |
= 1.4 ± 0.4 and BSin−2=7.6±0.2 were obtained for a fit with an r2 value of 0.931.The failure times of the FIL100110150 fibres were significantly longer than measured for the non-metal-coated fibres for the high stress regime, but lower than predicted by the fit for the non-metal-coated fibre for the lower stresses tested. The increase in failure times for the highest applied stress tested can be explained by the time taken for the aluminium coating to corrode through to expose the glass. The failure times were faster than expected for the optical fibres with lower applied stresses which follows the trend observed for the aluminium-coated fibres immersed in aqua regia.A comparison between the ranges of failure times observed in the environments tested is shown in . Also shown for the sake of comparison is the range of failure times of a non-metal-coated fibre in ambient atmosphere when subjected to similar stress levels. indicate that the failure times of the stressed aluminium-coated fibres tested are related to the corrosivity of the environment, i.e. the samples in aqua regia fail relatively fast while the samples in ambient atmosphere have survived for significantly long times without failing.An improved understanding of the failure of the aluminium-coated fibres tested has been achieved by examining samples of the fibres under an optical microscope as a function of immersion times in the corrosive solutions investigated. These tests provide an alternative means to monitor the corrosion on the surface of the optical fibre and determine the time taken for corrosion to expose the glass to the environment. They also help to explain differences observed between the failures of stressed Polymicro and Fiberguide fibres in sea water.Measurements for aluminium-coated fibres immersed in aqua regia found complete removal of the aluminium coating in approximately 30–60 min, with some dependence on the age of the solution. Significant degradation of the coating, however, was observed for times less than 30 min. This observation agrees with the relatively fast failure times of the stressed aluminium-coated fibres tested in aqua regia. The form of corrosion appeared to be crystalline in nature as shown in Significant differences in the rate of corrosion were observed between the Polymicro and Fiberguide aluminium-coated fibres tested in sea water. The majority of the fibres supplied by Fiberguide were found to survive for significant times (approximately 1 year) without any exposure of glass. b shows an example of the surface condition of an ASI9/125/175A Fiberguide fibre after 37 weeks immersion in sea water. The Polymicro fibres tested however showed that glass was exposed in time scales of approximately 70 days, as shown in c. These results correlate well with the failure data observed for stressed aluminium-coated fibres immersed in sea water where very few failures were observed for the Fiberguide fibres, which would be expected if the glass had not been exposed. The relative large numbers of failures of the Polymicro fibre samples however would be expected as glass is exposed in short-time frames.The time to failure of stressed aluminium-coated fibres have been tested in a range of environments including a non-corrosive environment, in aqua regia and in sea water. Aluminium-coated fibre failure times of 102 to 103 |
s were observed for immersion in aqua regia and 106 to 107 |
s in sea water (for one of the fibre types tested), while in a non-corrosive environment ∼99% of samples have survived without failing for periods up to 2 years (>6 × 107 |
s). These results indicate that failure time of the aluminium-coated fibres is related to the corrosivity of the environment indicating that the proposed method could be used as a corrosion sensing mechanism. Optical microscope studies of aluminium-coated fibres immersed in the corrosive environments have helped to explain the observed failure rates, and differences between fibres purchased from different manufacturers.S.A. Wade graduated in 1994 from Victoria University of Technology with a BSc (Hons.) in applied physics. He was subsequently awarded a PhD from Victoria University of Technology in 2001 for work on the development of optical fibre-based temperature sensors. He has been working in the Mechanical Engineering Department at Monash University since 2003. His current research interests include the development of both optical- and electrical-based corrosion sensors for industrial applications.C.D. Wallbrink graduated in 2001 from Monash University with a BE (Hons.) in mechanical engineering and a BSc in physics and applied mathematics. After receiving an Australian postgraduate award he graduated in 2005 from Monash University having completed a PhD studying the remnant fatigue life of complex structures. Presently he is working as a research fellow at Monash University and his current research interests include, optical corrosion sensors, infrared NDT, and small fatigue crack growth.G. McAdam graduated from the University of New South Wales in 1990 with a PhD in high temperature corrosion. Since graduating he has worked for the Defence Science and Technology Organisation. His current research interests include: optical fibre corrosion sensors, rare earth-based corrosion inhibitors and characterisation of the operating environment for aircraft.S. Galea received his Doctor of Philosophy from the University of Southampton in 1989. He is currently a principal research scientist and functional head of the Smart Structures and Advanced Diagnostics Group at the Defence Science and Technology Organisation. His current interests include the development and application of smart materials and structures technologies to aircraft structures, including in situ structural health monitoring and self-powering techniques.B.R.W. Hinton graduated from the Department of Mining and Metallurgical Engineering at the University of Queensland in 1968. He joined Aeronautical Research Laboratories at Fishermans Bend in Melbourne in 1969. In 1977 he was awarded an Australian Public Service Scholarship to study for a PhD in the Corrosion and Protection Centre, University of Manchester Institute of Science and Technology, England. He is currently a principal research scientist and head of the Aircraft Corrosion Control Group at the Defence Science and Technology Organisation in Melbourne.R. Jones graduated with a doctor of philosophy from the University of Adelaide. He is currently a professor in the Mechanical Engineering Department at Monash University. His current research interests include composite materials, fatigue, fracture, infrared thermography, smart structures and materials.Lattice strains and load partitioning in bovine trabecular boneMicrodamage and failure mechanisms have been well characterized in bovine trabecular bone. However, little is known about how elastic strains develop in the apatite crystals of the trabecular struts and their relationship with different deformation mechanisms. In this study, wide-angle high-energy synchrotron X-ray diffraction has been used to determine bulk elastic strains under in situ compression. Dehydrated bone is compared to hydrated bone in terms of their response to load. During compression, load is initially borne by trabeculae aligned parallel to loading direction with non-parallel trabeculae deforming by bending. Ineffective load partitioning is noted in dehydrated bone whereas hydrated bone behaves like a plastically yielding foam.Trabecular bone microdamage is a function of the trabecular bone material properties as well as load transfer through the trabecular network We have recently shown that high-energy wide-angle synchrotron X-ray diffraction (WAXS) can be used to experimentally determine bulk elastic strains in apatite crystals of trabecular bone The bovine trabecular bone used in this study was obtained from a bovine femoral head. The femur was obtained from a local abattoir and was kept frozen until use. The bone was sectioned using a Struers Accutom-50 precision cut-off machine (Struers Ltd., Rotherham, UK) with a diamond cutting wheel under constant water irrigation. The bone was tested parallel to the long axis of the femur and therefore aligned approximately to the natural loading direction.Transmission X-ray diffraction was conducted at station 1-ID of the Advanced Photon Source (APS) at the Argonne National Laboratory, USA. The experimental setup and data analysis approach utilized has been reported previously . The samples were irradiated for 60 s for a single data acquisition (diffraction pattern) with a monochromatic 80.5 keV beam (λ |
= 0.0154 nm), of beam size 100 × 100 μm, travelling through the centre of the sample in transmission. PTFE tape was applied to the upper and lower platens of the loading rig to reduce end-effects. The diffraction patterns were recorded with the use of a MAR 345 image plate detector, which was situated 1000 mm away from the sample. The detector allowed data to be collected in the loading (axial) and perpendicular (transverse) directions simultaneously. The sample was loaded at a constant cross-head displacement rate of 200 nm s−1 and was compressed to densification, with data accumulated constantly. Forty-three two-dimensional (2-D) diffraction patterns (180 s per pattern) were collected during the experiment for the dehydrated sample, and 31 were collected for the hydrated sample.The method used to convert the 2-D diffraction patterns from polar to Cartesian coordinates has already been published Data from the two bins in the loading direction (90° and 270°) and the two bins perpendicular to the loading direction (0° and 180°) were averaged to obtain axial and transverse lattice strain data, respectively. Lattice strains in the mineral phase were determined using εa |
= (ai–a0)/a0 where a0 is the initial lattice parameter and ai is the lattice parameter when loaded. Lattice strains are expressed in units of microstrain (με), which correspond to a strain of 10−6.The initial lattice parameters, extracted from the Rietveld refinement and averaged from all four bins, were: a |
= 0.94801 ± 0.00075 nm and c |
= 0.6902 ± 0.00049 nm (dehydrated), and a |
= 0.95126 ± 0.0011 nm and c |
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