Shear Strain Values Research Articles

Structural aspects of elasto-plastic deformation of a Zr-based bulk metallic glass under uniaxial compression

The structural rearrangements occurring during compressive deformation of a plastically deformable Zr52.5Ti5Cu18Ni14.5Al10 bulk metallic glass have been investigated in situ using high energy synchrotron X-rays. It was found that in the elastic regime, the atomic distances at both short and medium range order vary linearly with macroscopic stress where the atomic bonds in short range order appear significantly stiffer than medium range order. Upon elastic loading, a small fraction of bonds in the first shell is broken in the loading direction whereas some new bonds are formed in the transverse direction. Atomic strain–stress correlation at medium range order deviates from linearity at the onset of plastic deformation which was correlated to the activation of irreversible STZs. This was confirmed by quantifying the amount of atomic shear strain value during loading. The length scale of 12.5Å indicated the largest shear strain and is thought to be the most effective length scale in the formation of STZs. The typical fracture angle of this BMG was explained by the orientation of maximum atomic shear strain at the onset of major shear band formation.

Threshold Shear Strain for Dynamic Ramberg-Osgood Model in Soils Based on Thermomechanics

The threshold shear strain is a fundamental property of the soil behavior subjected to cyclic loading. Starting from the unloading and reloading hysteretic curves of dynamic Ramberg-Osgood model, construct small-strain dynamic dissipation function and explain small-strain dynamic characteristics by use of the skeleton curve back stress assumption. The plotting results of yield curves in true stress space indicate that there exist two threshold shear strains which are defined as the first threshold shear strain and the second threshold shear strain respectively which represent boundaries between fundamentally different dynamic characteristics of cyclic soil behavior. The yields of soil are controlled by the constant friction coefficient, the variable friction coefficient and dilatancy-related microstructural changes respectively. Both the first threshold shear strain and the second threshold shear strain do depend significantly on the maximum dynamic shear modulus coefficient and exponent. Comparison between the two threshold shear strain values and shear modulus reduction curves obtained on exactly the same soils confirms that the soil behavior is considerably at nonlinear at , the secant shear modulus, Gs, of the four soils studied is between 0.6 and 0.8 of its maximum value.

Finite Element Modeling of Shear Strain in Rolling with Velocity Asymmetry in Multi-Roll Calibers

Severe plastic deformation is now recognized the most efficient way of producing ultrafine grained metals and alloys. At the present time a lot of severe plastic deformation methods have been proposed and developed. They differ in the deformation schemes. Unlike such severe plastic deformation methods as high pressure torsion and equal-channel angular pressing, rolling with the velocity asymmetry is a continuous process. It helps to solve the problem of the limited length of manufactured bars with semi ultrafine structure. Rolling process with roll velocity asymmetry generates high shear strain necessary for obtaining ultrafine structures of the processed material. A new process of asymmetric rolling of profiles in multi-roll passes has been developed. This process can be used for production of high-strength profiles such as circles, hexagons, wire rods, etc. Compression of the bar in multi-roll passes can be done not only from two, as usual, but from three or four sides. In case of a multi-crimped bar, a uniform compression scheme with large hydrostatic pressure is created in the deformation zone. It enhances the ductility of the material and allows increasing the strain intensity. Simulation in DEFORM 3DTM proved that the process of asymmetric rolling in multi-roll calibers allows to obtain higher values of shear strain and strain effective.

Melt rheological properties of PBT/SEBS and reactively compatibilized PBT/SEBS/SEBS‐g‐MA polymer blends

ABSTRACTMelt rheological properties of PBT/SEBS and PBT/SEBS/SEBS‐g‐MA blends at SEBS volume fraction (Φd) = 0.00–0.38 were studied at 240°C, 250°C and 260°C using a capillary rheometer. The compatibilizer SEBS‐g‐MA addition resulted in significant reduction in the dynamic interfacial tension which in turn led to increased phase adhesion. The power law exponent n decreased with increasing Φd and increasing temperature for both the compatiblized and uncompatiblized blends. The consistency index of PBT/SEBS increased with increasing Φd but were smaller than those of PBT/SEBS/SEBS‐g‐MA blends. Melt elasticity such as die swell and first normal stress difference increased with Φd. Variations of first normal stress coefficient function (ψ1), recoverable shear strain (γR), relaxation time (λ), and shear compliance (Jc) values versus shear rate were analyzed. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 41402.

Effect of sample disturbance on triaxial and oedometer behaviour of a stiff and heavily overconsolidated clay

The tests in this investigation were performed on a natural soft clay with plasticity index around 32%, which was K0consolidated to a vertical stress of 2942 kPa and then K0unloaded to a vertical stress of 74 kPa (i.e., to the “in situ” stress). The specimens so created were disturbed in various ways to study the effect of sample disturbance on the stress–strain relationships during undrained shearing and during drained K0loading (i.e., K0triaxial and oedometer tests). The results for two testing alternatives may be summarized as follows. Alternative 1: Allow the specimen to swell at the correct in situ effective stresses, but accept an initial water content that is higher than the in situ value. This alternative was found to give the best stress–strain relationships around the in situ effective stresses for undrained triaxial tests, but with undrained shear strength values up to about 20% too low, due to the swelling taking place during consolidation to the in situ effective stresses. Alternative 2: Prevent swelling by starting the test at effective stresses that are higher than the in situ stresses, but with a water content that is closer to the in situ value than if alternative 1 is chosen. Using only isotropic stresses prior to shearing, this alternative was found to give better undrained shear strength values (although up to about 14% too high) but strain values much too small around the in situ effective stresses. For oedometer tests, only alternative 2 was investigated. Also, for these tests, the strains around the in situ stress were too small, but preconsolidation stresses estimated from stress–strain curves were typically only around 60% of the true value.

Influence of a sedimentary basin infilling description on the 2-D P–SV wave propagation using linear and non-linear constitutive models

Numerical modelling is a useful tool to understand the role of different parameters (site geometry, impedance contrast, material properties, constitutive model, input motion) governing site effects. We focus here on the 2-D P-SV seismic wave propagation in a simple-shaped asymmetric model. We consider two ways of describing the sedimentary infilling properties: the basin is either composed of distinct homogeneous geological layers or is described through properties progressively changing as a function of depth (smooth model). In order to study the wave propagation in the two basins with similar soil properties, P and S velocities of the layered basin are deduced from the smooth basin ones, making both models compatible in a kinematic point of view. P and S velocities globally increase with depth. Following EPRI, non-linear properties are considered as constant in layers for the two basins. We assess the influence of the model choice on the wave propagation while taking into account linear and non-linear constitutive models. We test the influence of the input motion by propagating two different input motions, the first being a simple impulsive one and the second a real complex accelerogram. We find that transfer functions computed in each basin are quite similar irrespective of the soil constitutive behaviour and the input motion. Moreover, we show that the maximum shear strain spatial distribution depends on the input motion frequency content and maximum values depend on the input motion strength and complexity. Maximum shear strains are generally higher for superficial layers than for deeper ones. We show that the highest shear strain values are located above discontinuities, where velocities are lower and the soil is more non-linear than in the underlying layer, regardless of the input motion. Indeed, in a layered basin, the shear strain is higher above interfaces for all the soil constitutive models that were used. In the smooth visco-elastoplastic model, a kind of layering appears, absent in a viscoelastic model, due to the different non-linear properties in each layer. Moreover, no matter what the model structure and the input motion used, maximum shear strain levels are higher in the visco-elastoplastic soil than in the viscoelastic one. Such a numerical study helps to understand the non-linearity location and therefore the consequences of a model choice when performing a site-specific study.

Presentation of analytical solutions for seismically induced tunnel lining forces accounting for soil-structure interaction effects

Recently, as the structural design has shifted to the performance design, seismic design of tunnel structures considering soil-structure interaction becomes more important. The effects of soil-structure interaction should not be overlooked for the reason that the interaction effects between a structure and surrounding ground may cause larger external forces to the structure. It has been highlighted that the relative rigidity between the soil and the structure is the predominant factor influencing the soil-structure interaction effects. With an aim to study the effects of tunnel-ground interaction, a number of analyses were carried out in this work, based on the most frequently used analytical expressions for evaluation of seismically induced stress increment in a tunnel lining accounting for the soil-structure interaction effects. These solutions are functions of the shear strain field which is the cause of the ovaling of the circular tunnel cross-section. A value of the average soil shear strain in the range of depths corresponding to the tunnel section, between the tunnel crown and the invert, has been computed through a free-field one-dimensional seismic site response analysis preformed by the code EERA. Various levels of analysis have been undertaken on different soil conditions, considering representative of two main soil classes - stiff soil of good conditions and soft saturated soil of poor conditions, as well as, two extreme cases of tunnel-ground interface - the full-slip and the no-slip conditions. Finally, the results for all the considered cases have been evaluated and compared, and the significant mutual differences with regard to a tunnel-ground interaction have been underlined.

Finite Element Modeling of Shear Strain in Asymmetric and Symmetric Rolling in Multi Roll Calibers

Methods of severe plastic deformation are used in the production of profiles for automobile, aircraft and chemical industry, medical implants, etc. However these methods have some shortcomings (low manufacturability, small size of produced bars, uneven distribution of deformations and mechanical stresses throughout cross sections and length of bars, significant heterogeneity of a deformable material structure, low ratio of material utilization, irregularity and anisotropy of deformed bars characteristics etc.). It significantly limits possibilities of their wide commercial use. New methods and apparatus of asymmetric rolling of metal profiles in multi roll passes are developed at Magnitogorsk State Technical University named after Nosov. Numerical comparison of values of shear strain in case of symmetric and asymmetric rolling is made in the paper. Adequacy of the developed models is demonstrated.

Design and validation of an in vitro loading system for the combined application of cyclic compression and shear to 3D chondrocytes-seeded agarose constructs

Physiological loading is essential for the maintenance of articular cartilage by regulating tissue remodelling, in the form of both catabolic and anabolic processes. To promote the development of tissue engineered cartilage which closely matches the long term functionality of native tissue, bioreactors have been developed to provide a combination of loading modalities, which reflect the nature of normal physiological loads. This study describes the design and validation of an in vitro mechanical system for the controlled application of bi-axial loading regimes to chondrocyte-seeded agarose constructs.The computer-controlled system incorporates a robust gripping system, which ensures the delivery of precise values of cyclic compressive and shear strain to 3D cell-seeded constructs. Sample prototypes were designed, optimised using finite element analysis and validated performing compressive and shear fatigue mechanical tests. The horizontal and vertical displacements within the bioreactor are precisely controlled by a dedicated programme that can be easily implemented. The synchronisation of the orthogonal displacements was shown to be accurate and reproducible.Constructs were successfully loaded with a combined compressive and shear loading regimen at 1Hz for up to 48h with no appreciable loss of cell viability or mechanical integrity. These features along with the demonstrated high consistency make the system ideally suitable for a systematic investigation of the response of chondrocytes to a complex physiologically relevant deformation profile.

Relationship between limiting shear strain and reduction of shear moduli due to liquefaction in large strain torsional shear tests

With the spread of performance-based design concepts in geotechnical earthquake engineering, conducting a practical and accurate analysis for estimating the liquefaction-induced ground deformation has become important. However, there is a difficulty in setting relevant parameters of liquefied soil that would be employed in the analysis because experimental investigations on large deformation behaviour of liquefied soil are still limited. Therefore, in order to investigate the liquefaction-induced ground deformation characteristics, a series of undrained cyclic torsional shear tests was performed by using a modified torsional shear apparatus that is capable of achieving double amplitude shear strain up to about 100%. The tested materials were saturated Toyoura sand, two kinds of in-situ frozen samples having different geological ages and their reconstituted samples. The in-situ samples were retrieved from Pleistocene deposits. In all the undrained cyclic torsional shear tests, cyclic mobility was observed and the double amplitude shear strain approached 100%, irrespective of the different initial conditions of the specimens. A limiting value of double amplitude shear strain to cause strain localization, which would be linked to the maximum possible liquefaction-induced ground deformation, was evaluated based on the change in the deviator stress during the undrained cyclic torsional loading. The limiting value was found to increase with decrease in initial values of small strain shear moduli which were evaluated by dynamic measurement. In addition, we measured tangent shear moduli at the limiting state as well as after strain localization, and evaluated a reduction ratio of shear moduli due to liquefaction, which would be employed in the ALID framework. These characteristics measured by such large strain liquefaction tests would be useful in estimating the maximum liquefaction-induced ground deformation.

Numerical study on stability analysis of geocell reinforced slopes by considering the bending effect

Geocell reinforced soil may be used in many areas of geotechnical engineering, however, there is little information on analysis of the behavior of geocell reinforced slopes. Due to the height of the geocell, the geocell-reinforced mattress more likely provides a beam or plate effect than a planar membrane effect. The purpose of this paper is to use beam model to simulate the geocell behavior as a flexible slab foundation which can carry both bending and membrane stresses for stability analysis of geocell reinforced slopes. In addition, the interface resistance between the geocell–soil was considered. The Young's modulus of geocell encased soil was obtained from the elastic modulus of the unreinforced soil and the tensile modulus of the geocell reinforcement using an empirical equation. Parametric studies of geocell reinforced slope are carried out by varying placement depth of the geocell layer, number of geocell layers, vertical spacing between reinforcement layers, length, thickness and Young's modulus of the geocell reinforcement. The influence of slope geometry, shear strength properties and soil compaction on the behavior of geocell reinforced slope is also discussed. The obtained results show that geocell reinforcement acts as a wide slab and thus it can restrain the failure surface from developing and redistribute the loads over a wider area. Therefore, under the geocell placement, the lateral deformation and shear strain values of the slope considerably decrease. Furthermore, the effective placement of geocell reinforcements is found to be between the middle of the slope and the middle of critical failure surface of the unreinforced slope.

Depth-dependent strain fields of articular cartilage under rolling load by the optimized digital image correlation technique

It is significant to investigate the depth-dependent mechanical behaviors of articular cartilage under rolling load since considerable rolling occurs for cartilage joint in activities of daily living. In this study, the rolling experiments of articular cartilage were conducted by applying an optimized digital image correlation (DIC) technique for the first time and the depth-dependent normal strain and shear strain of cartilage were analyzed. It is found that the normal strain and shear strain values of different layers increase firstly and then decrease with rolling time, and they increase with increasing compressive strains. The normal strain and shear strain values decrease along cartilage depth with constant compressive strain. The normal strain values of different normalized depth decrease with increasing rolling rates. The shear strain values of superficial layer and middle layer decrease; however there are no major changes for the shear strain values of deep layer with increasing rolling rates. The normal strain values with different rolling time increase with increasing rolling numbers and the 30.6% increase in initial normal strain is observed from 1st to 99th cycle. The fitting relationship of the normal strain and normalized depth was obtained considering the effects of compressive strain and rolling rate and the fitting curves agree with the experimental results for cartilage very well.

Strain localization characteristics of loose saturated Toyoura sand in undrained cyclic torsional shear tests with initial static shear

Strain localization, or the formation of shear bands, is a key aspect in understanding soil failure mechanisms. While efforts have been made in terms of measuring the shear band properties and the stress–strain behavior within shear bands, there are still uncertainties regarding when shear bands initiate and their influence on the development of large ground deformation. In this paper, the limiting value of shear strain, at which strain localization appears during undrained cyclic torsional shear tests with initial static shear, performed on loose Toyoura sand specimens (Dr=44–48%) up to a single amplitude of shear strain exceeding 50%, was evaluated. Non-uniform specimen deformation was observed at strain levels larger than 20%. However, the onset of strain localization could not be defined on the basis of visual observations. Therefore, the limiting values for half of the double amplitude (γDA/2) and single amplitude (γSA) shear strain, to initiate strain localization, were determined from test results based on changes in the deviator stress response and strain accumulation properties as well as changes in the strain-softening behavior during cyclic shear. It was found that γSA is a more appropriate parameter than γDA/2. Irrespective of the static shear stress level, the limiting strain value for γSA was evaluated to be in the range of 23–28% for liquefied loose Toyoura sand specimens (i.e., stress reversal and intermediate tests). Alternatively, the limiting strain value could not be properly defined when liquefaction did not occur (i.e., non-reversal stress tests), although various methods were employed.

The mechanical consequences of load bearing in the equine third metacarpal across speed and gait: the nonuniform distributions of normal strain, shear strain, and strain energy density

Distributions of normal strain, shear strain, and strain energy density (SED) were determined across the midshaft of the third metacarpal (MCIII, or cannon bone) of 3 adult thoroughbred horses as a function of speed and gait. A complete characterization of the mechanical demands of the bone made through the stride and from mild through the extremes of locomotion was possible by using three 3-element rosette strain gauges bonded at the diaphyseal midshaft of the MCIII and evaluating the strain output with beam theory and finite element analysis. Mean ± sd values of normal strain, shear strain, and SED increased with speed and peaked during a canter (-3560±380 microstrain, 1760±470 microstrain, and 119±23 kPa, respectively). While the location of these peaks was similar across animals and gaits, the resulting strain distributions across the cortex were consistently nonuniform, establishing between a 73-fold (slow trot) to a 330-fold (canter) disparity between the sites of maximum and minimum SED for each gait cycle. Using strain power density as an estimate of strain history across the bone revealed a 154-fold disparity between peak and minimum at the walk but fell to ~32-fold at the canter. The nonuniform, minimally varying, strain environment suggests either that bone homeostasis is mediated by magnitude-independent mechanical signals or that the duration of stimuli necessary to establish and maintain tissue integrity is relatively brief, and thus the vast majority of strain information is disregarded.

Microstructure and Mechanical Properties of a Copper Alloy Sheet Processed by a Differential Speed Rolling

The microstructure and mechanical properties of a copper alloy sheet processed by differential speed rolling (DSR) were investigated in detail. A copper alloy with thickness of 3 mm was rolled to a 50% reduction at ambient temperature without lubrication and with a differential speed ratio of 2.0:1. For comparison, conventional rolling (CR), in which the rolling speeds of the upper and lower rolls is 2.0 m/min, was also performed under the same rolling conditions. The shear strain of the sample processed by CR showed positive values at the positions of the upper roll side and negative values at the positions of the lower roll side. On the other hand, the sample processed by the DSR showed zero or positive shear strain values at all positions. However, the microstructure and mechanical properties of the as-rolled copper alloys did not show such significant differences between the CR and the DSR. The samples rolled by the CR and the DSR exhibited a typical deformation structure. In addition, the DSR processed samples showed a typical rolling texture in which {112}<111>, {011}<211> and {123}<634> components were developed at all positions. Therefore, it is concluded that the DSR was very effective for the introduction of a uniform microstructure throughout the thickness of the copper alloy.

Evaluation of local deformation behavior accompanying fatigue damage in F82H welded joint specimens by using digital image correlation

By using digital image correlation, the deformation behaviors of local domains of F82H joint specimens welded using tungsten inert gas (TIG) and electron beam (EB) welding were evaluated during tensile and fatigue testing. In the tensile test specimens, the tensile strength decreased in the TIG-welded joints, and ductility decreased in both the EB- and TIG-welded joints. Because axial strain increased in the tempered heat-affected zone (HAZ) and led to the fracture of the TIG-welded joint, the strength was considered to have decreased because of welding. In fatigue testing, the number of cycles to fracture for the welded joint decreased to less than 40–60% of that for the base metal. For both fracture specimens, the largest value of shear strain was observed in the region approximately between the fine-grained HAZ and tempered HAZ; this shear strain ultimately led to fracture. Cavities and macrocracks were observed in the fine-grained HAZ and tempered HAZ in the cross sections of the fracture specimens, and geometrical damage possibly resulted in the reduction of fatigue lifetime.

Analysis of superposed strain: A case study from Barr Conglomerate in the South Delhi Fold Belt, Rajasthan, India

The structural geometry in the Barr conglomerate and the neighboring rocks in the western flank of the Meso- to Neoproterozoic South Delhi Fold Belt indicate superposed deformation, with structures developed by horizontal dextral simple shear deformation superimposed on earlier structures formed during approximately ESE-WNW compression and subvertical maximum elongation. The first deformation produced NNE-SSW trending subvertical schistosity, and associated steeply plunging isoclinal folds, mineral lineation and pebble elongation lineation having almost downdip alignment on the schistosity surface. The second deformation produced dextral folds both on bedding and schistosity surfaces and modified the shape of the pebbles already deformed by the first deformation. On vertical sections perpendicular to the schistosity trace the pebbles show sub-ellipsoidal shape with their mean elongation direction parallel to the schistosity trace. On the horizontal section the pebbles often show asymmetrical shape and asymmetrical deflection of the schistosity surface around the pebbles. The mean elongation direction makes a small angle (2°–8°) in the counter-clockwise sense with the schistosity surface. This obliquity is due to modification of post-first-deformation sub-ellipsoidal shape by later horizontal simple shear using the schistosity surface as the movement plane. Analytical expressions are derived for the modification of an original ellipse by simple shear parallel to the long axis of the ellipse. A family of curves has been generated to depict the change in axial ratio and orientation of long axis for different initial axial ratios, and for different values of shear strain ( γ). Using these curves it has been possible to factorize the total strain into two components representing the earlier compression and the later simple shear. It is noted that the computed earlier shortening strain ellipsoids are consistently in the flattening field close to the line of pure oblate ellipsoids in the Flinn plot. There is no systematic spatial control on the variation in the values of shear strain ( γ), strain ellipsoid shape parameter ( k), and intensity of distortion ( d) as one proceeds south to north along the strike of the conglomerate.

Sand Deformation around an Uplift Plate Anchor

AbstractThis paper presents an experimental investigation on soil deformation around uplift plate anchors in sand by using digital image correlation (DIC). The experimental setup consists of a camera, loading frame, plexiglass mold, and computer, which is developed to capture soil deformation during anchor uplifting. A series of model tests are performed to investigate the influence of particle size, soil density, and anchor embedment depth on soil deformation. A set of images captured during anchor uplifting are used to calculate soil displacement fields by DIC. The failure surface is studied by tracking the points with maximum shear strain values. On the basis of this study, it is found that soil deformation and the pullout resistance of plate anchors are substantially influenced by soil density and anchor embedment depth, whereas particle size within the studied range has limited influence. In dense sand, the shape of the failure surface changes from a truncated cone above a shallow anchor to a combine...

Dynamic Shear Modulus and Damping Ratio for Threshold Strain in Cohesionless Soils

Based on modern ideas of thermomechanics, small strain dynamic dissipation function of Hardin-Drnevich model for soils is formulated using the assumptions of the beeline and the skeleton curve shift laws. Fundamentally, for cohesionless soils, two types of cyclic strain thresholds are identified: first threshold strain and second threshold strain represent boundaries between fundamentally different dynamic characteristics of cyclic soil behavior. Comparison between the two threshold shear strain values and dynamic degradation curves obtained on exactly the same soils, the results showed that the ratio of secant modulus and maximum dynamic shear modulus for the first threshold strain are almost 1.0, and the damping ratio is almost constant. When dynamic strain level exceeds the second threshold strain, the soil behavior is considerably at nonlinear, and the primary deformation mechanism is related to fabric changes during cyclic loading. The first and the second threshold strains are therefore essential for the understanding and solving soil dynamic problems.

Digital image correlation analysis of the load transfer by implant-supported restorations

This study compared splinted and non-splinted implant-supported prosthesis with and without a distal proximal contact using a digital image correlation method. An epoxy resin model was made with acrylic resin replicas of a mandibular first premolar and second molar and with threaded implants replacing the second premolar and first molar. Splinted and non-splinted metal–ceramic screw-retained crowns were fabricated and loaded with and without the presence of the second molar. A single-camera measuring system was used to record the in-plane deformation on the model surface at a frequency of 1.0Hz under a load from 0 to 250N. The images were then analyzed with specialist software to determine the direct (horizontal) and shear strains along the model. Not splinting the crowns resulted in higher stress transfer to the supporting implants when the second molar replica was absent. The presence of a second molar and an effective interproximal contact contributed to lower stress transfer to the supporting structures even for non-splinted restorations. Shear strains were higher in the region between the molars when the second molar was absent, regardless of splinting. The opposite was found for the region between the implants, which had higher shear strain values when the second molar was present. When an effective distal contact is absent, non-splinted implant-supported restorations introduce higher direct strains to the supporting structures under loading. Shear strains appear to be dependent also on the region within the model, with different regions showing different trends in strain changes in the absence of an effective distal contact.