Magnitude Of Shear Strain Research Articles

Ice deformed in compression and simple shear: control of temperature and initial fabric

AbstractLayered and polycrystalline ice was experimentally deformed in general shear involving axial compression (strain magnitude 0.5-17%) and simple shear (strain magnitude γ = 0.1-1.4). As the temperature is increased from -20°C to -2°C, there is at least a twofold enhancement in octahedral shear strain rate, which coincides with the onset of extensive dynamic recrystallization and a change in grain-size distribution at -15°C. Between -150C and -10°C the c-axis preferred orientation rapidly evolves with the initiation of two-maxima fabrics in shear zones. From -10°C to -2°C there is progressive evolution of a final c-axis pattern that is asymmetric with respect to the direction of shortening, with a strong maximum at ~5° to the pole of the shear zone, a sense of asymmetry in the direction of the shear, and a secondary maximum inclined at ~45° to the plane of shearing. An initial c-axis preferred orientation plays a critical role in the initial mechanical evolution. In contrast to established ideas, a strong alignment of basal planes parallel to the plane of easy glide inhibited deformation and there was an increased component of strain hardening until recrystallization processes become dominant.

Experimental investigation of the dynamic behavior of frozen clay from the Beiluhe subgrade along the QTR

Abstract The dynamic behavior of frozen clay obtained from the Beiluhe permafrost subgrade along the Qinghai-Tibet Railway (QTR) was investigated through cryo-dynamic triaxial experiments. The effects of several key factors, including temperature, moisture content, frequency and confining pressure on the dynamic behavior, were analyzed. It was found that a hyperbolic model could describe the dynamic behavior of the frozen clay well. The maximum dynamic shear modulus of the frozen soil decreases as the temperature rises and as the confining pressure decreases; the reference shear strain magnitude decreases as the temperature and confining pressure increase and as the moisture content decreases; the maximum damping ratio increases as the temperature, frequency and confining pressure increase and as the moisture content decreases. There exists a critical moisture content (around 18%) that maximizes the dynamic shear modulus; at the critical frequency (about 6 Hz), the dynamic shear modulus is at its maximum, and the reference shear strain magnitude and the damping ratio attenuation exponent are at their respective minima. Moreover, functions were proposed to quantitatively describe the relationship between frozen clay dynamic parameters and various influencing factors.

The Effect of Height on Tibial Strain During Drop Landings

During landing, the human body is required to absorb impact forces throughout its tissues. Muscle and connective tissue dissipate much of this force. A portion of the impact is delivered to the bones. Repetitive forces acting on the tibia during landing can cause microfractures which may lead to stress fracture. It is difficult to quantify bone strain through invasive measure such as bone staple. PURPOSE: To calculate changes in bone strain during landing using a noninvasive approach by integrating a finite element tibia in a musculoskeletal model. METHODS: A musculoskeletal model representing a healthy male subject (22 years, 78.6 kg, 1.85 m) was created. A flexible tibia, created from a CT scan of the subject's right tibia, was included in the model. Motion capture data were collected while the subject performed drop landings from three separate heights (26, 39, and 52 cm) and served as inputs to perform dynamic simulations. Surface electromyography and joint angle data were compared to their simulation using a cross correlation. Maximum magnitudes of principal and maximum shear strain were computed. RESULTS: Strong cross-correlation coefficients (CCC > 0.87) were found between recorded and simulated lower extremity joint angles. Recorded activity in the vastus lateralis, vastus medialis, and the tibialis anterior agreed strongly with the model (CCC > 0.75). Weaker relationships existed in the gastrocnemius, hamstring, and soleus, which may be due to co-contraction. Maximum principal strain increased with height in 26cm (595 ± 136 μstrain), 39cm (879 ± 134 μstrain), and 52cm (1077 ± 108 μstrain). Minimum principal strain negatively increased with height in 26cm (-593 ± 86 μstrain), 39cm (-645 ± 35 μstrain), and 52cm (-769 ± 33 μstrain) landings. Maximum shear strain followed the same increasing trend in 26cm (592 ± 111 μstrain), 39cm (760 ± 83 μstrain), and 52cm (899 ± 98 μstrain) landings. CONCLUSION: The simulated results showed reasonable agreement with the recorded lower extremity joint angles and muscle activities. The calculated tibial strains were in reasonable agreement with the literature. This study demonstrates a valid non-invasive method of simulating landing movement and computing tibial strain produced during landing movements. Supported by DoD #W81XWH-08-1-0587 and BSU 2009 ASPiRE.

Erosional control of the kinematics and geometry of fold‐and‐thrust belts imaged in a physical and numerical sandbox

We investigate the effect of systematically varying erosion intensity (K) on the geometry and kinematics of fold‐and‐thrust belts modeled using equivalent conditions in physical and numerical experiments. Similar material properties and boundary conditions were used to compare numerical experiments to those modeled in the sandbox using an erosion rule that removes mass from the scaled sand wedges according to rates expected from bedrock fluvial incision. The geometry of both modeling approaches is quantitatively compared with that expected from analytical theory. The fold‐and‐thrust belt growth rate is inversely proportional to K and is well predicted by theory, except for the high erosion case, in which both the numerical and the experimental sandbox grows supercritically. A direct relationship exists between the erosion intensity and the number of fore‐shear bands and shear strain magnitude. The number of fore‐shear bands decreases, and their strain increases with erosion intensity. The results indicate that realistic and mechanistic erosion rules can be applied to physical experiments to model mass removal, and this approach opens up the possibility of calibrating strain history to erosion intensities for predictions in natural settings. Quantitative comparisons between the physical and numerical sandbox experiments indicate that deformation style and geometry of the thrust‐and‐fold belts are similar when identical rheologies and boundary conditions are used. This benchmarking suggests that numerical experiments realistically model conditions observed in the simple, cohesionless rheologies commonly employed in sandbox experiments. This suggests that numerical simulation may reliably model experimental deformation in geological situations that are difficult to represent in scaled experiments because of the different scales and rheologies of natural orogenic wedges.

Adiabatic shearing behaviour of unweldable Al–Sc alloy under extremely high shear loading

The present study applies a compressive type split Hopkinson pressure bar to investigate the adiabatic shear behaviour of unweldable Al–Sc alloy under high strain rates ranging from 3·0 × 105 to 6·3 × 105 s–1. The effects of the strain rate on the shear stress, adiabatic shear band characteristics, and fracture features of the unweldable Al–Sc alloy are systematically examined. The results show that both the shear stress and the strain rate sensitivity increase with increasing the strain rate. In addition, it is shown that an adiabatic shear band is formed within the deformed specimens for all values of the strain rate. As the strain rate is increased, the width of the shear band decreases, but the microhardness increases. Moreover, the distortion angle and the magnitude of the local shear strain near the shear band both increase with increasing the strain rate. At a strain rate of 3·0 × 105 s–1, the fracture surface is characterised by multiple transgranular clearage fractures. However, for strain rates greater than 4·5 × 105 s–1, the fracture surface has a transgranular dimple-like characteristic, and thus it is inferred that the ductility of the unweldable Al–Sc alloy improves with increasing the strain rate.

Through-thickness shear strain control in cold rolled silicon steel by the coupling effect of roll gap geometry and friction

Through-thickness shear strain distribution in cold rolled non-oriented silicon steel under different roll gap geometries and friction coefficients was analyzed by finite element method (FEM). Cold rolling textures were also investigated quantitatively to validate the calculated shear strain distribution. The results showed that both direction and magnitude of shear strain through thickness depend sensitively on the two rolling parameters. The coupling effect of roll gap geometry and friction was satisfactorily explained based on their contributions to shear strain and the involved mechanisms. A shear strain distribution diagram (SSDD), which can clearly characterize the shear strain state with roll gap geometry, friction and through-thickness position as variables, was proposed to serve as a convenient tool for through-thickness shear strain control.

Numerical and experimental studies of the plastic strains distribution using subsequent direct extrusion after three twist extrusion passes

In this investigation, simulation of three consecutive clockwise twist extrusion for commercially pure aluminum samples at ambient temperature with and without subsequent direct extrusion is presented. The influences of 50% reduction on strains distribution are analyzed on the specimen middle transverse cross-section. The results show that performing subsequent direct extrusion after twist extrusion increases the shear strain magnitude in the center of the specimen. High shear strain results in more grain refinement in the center regions in contrast to the corner ones. Few experiments were also carried out to validate the numerical findings. Furthermore, examination of microstructure evolutions and mechanical properties for the commercially pure aluminum samples were conducted using SEM, microhardness and tensile tests. The study shows that adding direct extrusion to the twist extrusion process alleviates the mechanical heterogeneity due to producing more intensified strains in the center regions than in the corner ones.

Diffraction theory of nanotwin superlattices with low symmetry phase: Adaptive diffraction of imperfect nanotwin superlattices

The diffraction behaviors of imperfect nanotwin superlattices were considered and the effects of random variations in nanotwin layer thicknesses and variant volume fractions on the diffraction peak intensity profiles investigated. Imperfect nanotwin superlattices exhibit a pronounced adaptive diffraction phenomenon when the Brillouin zone-dependent condition, , is met, where T is twin-related bilayer thickness, γ is twinning shear strain magnitude, s is twinning shear direction unit vector, and K is the reciprocal lattice vector of the constituent crystal denoting the fundamental reflection spots and Brillouin zones in reciprocal space. Nanotwin layer thickness variations produce little effect on the diffraction intensity distributions of adaptive Bragg reflection peaks, whereas variant volume fraction variations significantly reduce the height and broaden the width of adaptive peaks, but only affect their integrated intensities slightly and do not change their positions. In spite of imperfections, an extraordinary peak still appears at position k along twin peak splitting vector ΔK, as determined by a lever rule according to the average twin variant volume fraction : . Imperfect nanotwin superlattices exhibit a certain degree of diffuse reflection around the adaptive peaks with strong Lorentzian shape characteristics; adaptive peaks exhibit anisotropic broadening, i.e. peak is broader in the direction perpendicular to twin plane, and sharper parallel to the twin plane. The width of the adaptive peak does not provide direct information of nanodomain size, but the Brillouin zone-dependent diffraction behavior can be used to determine the nanodomain sizes.

Adiabatic Shearing Localisation in High Strain Rate Deformation of Al-Sc Alloy

Aluminium-scandium (Al-Sc) alloy is subjected to shear deformation at high strain rates ranging from 3.0×105 s−1 to 6.2×105 s−1 using a compressive-type split-Hopkinson pressure bar (SHPB). The effects of the strain rate on the shear stress, adiabatic shear band characteristics, and fracture features of the Al-Sc alloy are systematically examined. The results show that both the shear stress and the strain rate sensitivity increase with an increasing strain rate. In addition, it is shown that an adiabatic shear band is formed within the deformed specimens for all values of the strain rate. As the strain rate is increased, the width of the shear band decreases, but the microhardness increases. Moreover, the distortion angle and the magnitude of the local shear strain near the shear band both increase with an increasing strain rate. At a strain rate of 3.0×105 s−1, the fracture surface is characterised by multiple transgranular clearage fractures. However, for strain rates greater than 4.4×105 s−1, the fracture surface has a transgranular dimple-like characteristic, and thus it is inferred that the ductility of the Al-Sc alloy improves with an increasing strain rate.

Formation of nanostructured metal particles using negative rake angle cutting tools

The results of initial chip formation demonstrate a very complex interaction between metal chip and rake face of the cutting tool. These complex interactions can impart a sophisticated internal microstructure where grains are strained with nanometer dimensions. Plastic shear strains between two and ten result in the creation of nanostructured grains that are between 45 nm and 150 nm in diameter depending upon the material strained and the magnitude of shear strain. This paper describes how the contact conditions between chip and a negative rake angle cutting tool can control the internal microstructure of the metal chip in order to produce a nanostructured metal. Metal chips produced can act as feedstock for secondary manufacturing processes that produce engineering components that have superior mechanical and physical properties compared to cast and wrought materials.

Deformation Geometry and Through-Thickness Strain Gradients in Asymmetric Rolling

Experiments and simulations focusing on cold rolling under conditions where the work roll velocities are different (asymmetric rolling) have been performed to provide a basic framework for understanding the effects of the roll velocity ratio and deformation geometry on through thickness shear strain development. It is shown that deformation geometry, controlled by varying the reduction per pass, has a significant impact on the through thickness shear strain gradients at a given level of asymmetry. Large reductions per pass lead to more uniform through thickness shear strains, but lower overall shear strain magnitudes compared to rolling conditions involving small reductions per pass. Moreover, the results show that a critical value of the roll velocity ratio exists, for a fixed set of rolling conditions, above which the shear strains induced by asymmetric rolling remain unchanged. This is interpreted based on the relative importance of geometrically induced shear strains and those arising from frictional effects. In this context, the position of the neutral points plays a vital role.

Melt-filled hybrid fractures in the oceanic mantle: Melt enhanced deformation during along-axis flow beneath a propagating spreading ridge axis

Mid-ocean ridges represent important locations for understanding the interactions between deformation and melt production, transport, and emplacement. Melt transport through the mantle beneath mid-ocean ridges is closely associated with deformation. Currently recognized transport and emplacement processes at ridges include: 1) dikes and sills filling stress-controlled fractures, 2) porous flow in a divergent flow field, 3) self-organizing porous dunite channels, and 4) shear zones. Our recent observations from the sub-oceanic mantle beneath a propagating ridge axis in the Oman ophiolite show that gabbronorite and olivine gabbro dikes fill hybrid fractures that show both shear and extensional components of strain. The magnitudes of shear strain recorded by the dikes are significant and comparable to the longitudinal extensions across the dikes. We suggest that the hybrid dikes form from the interactions between shear deformation and pressurized melt in regions of along-axis flow at mid-ocean ridges. The displacement across the dikes is kinematically compatible with high temperature flow recorded by plastic fabrics in host peridotites. Field observations and mechanical considerations indicate that the dikes record conditions of higher stress and lower temperature than those recorded by the plastic flow fabrics. The features of hybrid dikes suggest formation during progressive deformation as conditions changed from penetrative plastic flow to strain localization along melt-filled fractures. The combined dataset indicates that the dikes are formed during along-axis flow away from regions of diapiric upwelling at propagating ridge segments. Hybrid dikes provide a potentially powerful kinematic indicator and strain recorder and define a previously unrecognized mechanism of melt migration. Our calculations show that hybrid dikes require less melt pressure to form than purely tensile dikes and thus may provide a mechanism to tap melt reservoirs that are under-pressurized with respect to lithostatic pressure.

Buckling of thick cylindrical shells under external pressure: A new analytical expression for the critical load and comparison with elasticity solutions

In this paper a set of stability equations for thick cylindrical shells is derived and solved analytically. The set is obtained by integration of the differential stability equations across the thickness of the shell. The effects of transverse shear and the non-linear variation of the stresses and displacements are accounted for with the aid of the higher order shell theory proposed by [Voyiadjis, G.Z. and Shi, G., 1991, A refined two-dimensional theory for thick cylindrical shells, International Journal of Solids and Structures, 27(3), 261–282.]. For a thick shell under external hydrostatic pressure, the stability equations are solved analytically and yield an improved expression for the buckling load. Reference solutions are also obtained by solving numerically the differential stability equations. Both the full set that contains strains and rotations as well as the simplified set that contains rotations only were solved numerically. The relative magnitude of shear strain and rotation was examined and the effect of thickness was quantified. Differences between the benchmark solutions and the analytic expressions based on the refined theory and the classical shell theory are analysed and discussed. It is shown that the new analytic expression provides significantly improved predictions compared to the formula based on thin shell theory.

The Influence of ECAP Die Channel Geometry on Shear Strain and Deformation Uniformity

The present work was performed in order to analyze the influence of the outer corner radius (R) of ECAP die channels on the strain field of billets subjected to ECAP deformation in a Φ = 120o die, employing three different methods: (i) physical simulation, consisting of the direct measurement of deformations of a grid inscribed in longitudinally cut mid-planes of ECAPed billets; (ii) numerical simulation employing an explicit finite element code for large displacements and large plastic deformations, and (iii) calculation by the Iwahashi formula. Materials employed were Al-4%Cu and an eutectic Pb-62Sn alloy, and the dependence of shear strain with R was satisfactorily described using the three methods. The experimental method showed a small deviation from the other two, which was explained making use of the corner die formation concept. Similarly, this concept helped to understand the increase of strain heterogeneity with R. Also, it was shown that large corner radii decrease ECAP pressing loads, facilitating deformation of high strength materials. Finally, the data show that the deformation characteristics of the materials here studied do not exert a measurable influence on the shear strain magnitude and distribution.

Study of Impact-Induced Mechanical Effects in Cell Direct Writing Using Smooth Particle Hydrodynamic Method

Biomaterial direct-write technologies have been receiving more and more attention as rapid prototyping innovations in the area of tissue engineering, regenerative medicine, and biosensor∕actuator fabrication based on computer-aided designs. However, cell damage due to the mechanical impact during cell direct writing has been observed and is a possible hurdle for broad applications of fragile cell direct writing. The objective of this study is to investigate the impact-induced cell mechanical loading profile in cell landing in terms of stress, acceleration, and maximum shear strain component during cell direct writing using a mesh-free smooth particle hydrodynamic method. Such cell mechanical loading profile information can be used to understand and predict possible impact-induced cell damage. It is found that the cell membrane usually undergoes a relatively severe deformation and the cell mechanical loading profile is dependent on the cell droplet initial velocity and the substrate coating thickness. Two important impact processes may occur during cell direct writing: the first impact between the cell droplet and the substrate coating and the second impact between the cell and the substrate. It is concluded that the impact-induced cell damage depends not only on the magnitudes of stress, acceleration, and∕or shear strain but also the loading history that a cell experiences.

Reliability Estimation of Solder Joint by Using the Failure Probability Models

The differences in the coefficient of thermal expansion (CTE) between the chip and the FR-4 board generate the shear strains and the bending moment in the solder joint. It seems to be a main cause of failure in the solder joint when the chip and the FR-4 board are heated repeatedly. Thus, the fatigue loading induced by thermal cycling is a major concern in the reliability of the solder joint. The magnitude of shear strain and the final failure are known to be influenced by varying boundary conditions such as the difference of CTE, the height of solder, the distance of the solder joint from the neutral point (DNP) and the temperature variation. In this paper, the effects of boundary conditions on the failure probability of the solder joint are studied by using the failure probability models such as the First Order Reliability Method (FORM) and the Monte Carlo Simulation (MCS). Furthermore, the stiffness of the solder joint is considered to investigate the influence at the failure probability.

Twinning modes of Nd 2Si 2O 7

Theory of deformation twinning by Bilby and Crocker [B.A. Bilby, A.G. Crocker, Proc. R. Soc. 288 (1965) 241] is applied to calculate the twinning elements for all possible low index twinning modes in tetragonal, orthorhombic and monoclinic Nd 2Si 2O 7 . The magnitude of shear strain was also calculated for each twinning mode. The criteria of small shear strain and minimum shuffling is applied to predict the operative twinning modes for tetragonal, orthorhombic and monoclinic Nd 2Si 2O 7. These predictions of the theory are compared with the available experimental information for analogue oxides and may act as guideline for future experimental work.

The estimation of elasticity and viscosity of soft tissues in vitro using the data of remote acoustic palpation

The presented study revealed the significant dependence of displacement magnitude and strain relaxation on phantom elasticity and viscosity. It has been shown that simultaneous analysis of temporal behavior and magnitude of shear strain induced by the radiation force of focused ultrasonic beam gives the necessary data for quantitative estimation of tissue shear modulus because of the known functional dependencies of displacement on local viscosity and elasticity. As a result, the simplest calibration procedure of acoustic radiation force-based methods is performed and algorithm for separate reconstruction of tissue elasticity and viscosity is proposed. These findings were tested, in particular, using the data obtained for specially prepared phantoms containing calf liver and muscle tissue in vitro. The observed complex character of shear strain relaxation and noise in some tissue phantoms and tissues in vitro reduces the preciseness of viscoelastic properties estimation. (E-mail: barannik@niiri.kharkov.com)

Ontogeny of bone strain: the zygomatic arch in pigs

At the time of weaning, infant animals have little experience with hard food, and thus their skulls are not likely to be epigenetically adapted for the loads imposed by mastication. We examined bone strain in the zygomatic arch of 4-week-old weanling piglets. Functional strains in piglets differed from those previously reported for older pigs in that the squamosal bone was not bent in the horizontal plane and the principal tensile strain on the zygomatic bone did not correspond to the direction of masseter muscle pull. Strain patterns were more variable in piglets than in older pigs. In older pigs, masticatory strains can be reproduced by stimulating the masseter muscles. When the piglet masseter was stimulated, strain patterns were more similar to those of older pigs, but shear strain magnitudes were the largest yet recorded from mammalian skull bones, up to 4000 muepsilon. To put these findings in the context of skeletal adaptation, 45 dry skulls, including some animals from the strain study, were measured. Reduced major axis regressions indicated that the infant arch was rounder in cross section and straighter than that of older animals. With growth, the arch became dorsoventrally higher, while mediolateral thickness decreased in the squamosal bone. Overall, these changes should make strain more predictable, explaining the lower variability in older animals. Other factors likely to be important in causing unique strain regimes in piglets include (1) unfamiliarity with hard food, (2) greater importance of muscles other than the same-side masseter and (3) greater proximity of molariform teeth to the arch. Collectively, these data indicate that the skeleton is not pre-adapted for specific functional loads.

Twinning modes of Er2Si2O7

Theory of deformation twinning by Bilby and Crocker is applied to calculate the twinning elements for all possible twinning modes in monoclinic Er 2 Si 2 O 7 TYPE C and TYPE D. The magnitude of shear strain was also calculated for each twinning mode. The criteria of small shear strain and minimum shuffling is applied to predict the operative twinning mode for monoclinic Er 2 Si 2 O 7 TYPE C and TYPE D. These predications of the theory are compared with the available experimental information and may act as guideline for future experimental work.