Orientation Of Shear Bands Research Articles

Three-Dimensional Noncoaxial Plasticity Modeling of Shear Band Formation in Geomaterials

Accurate prediction of shear band formation in geomaterials is crucial in the solution of various stability problems in geotechnical engineering. The initiation of shear band is strongly dependent on the constitutive description of the prelocalization homogeneous deformation. Conventional plasticity models assume that coaxiality exists between the directions of principal stresses and the directions of plastic strain increments. Accumulating evidence has however shown that this assumption is not appropriate. In this paper, a noncoaxial constitutive modeling platform is presented in a general three-dimensional stress space. It is shown that the classical vertex-like structure, which has been widely adopted to describe the noncoaxial constitutive response, only represents the two-dimensional condition. Examples are presented to demonstrate the capability of the modeling platform in capturing the initiation and orientation of shear band in a granular soil. The significance of the noncoaxiality effects is illustrated by comparisons of the predictions produced by coaxial and noncoaxial (both two-dimensional and three-dimensional) plasticity models.

Effects of Crystallographic Texture on Plastic Flow Localization

In this study, effects of typical texture components observed in rolled aluminum alloy sheets (i.e. Copper, Brass, S, Cube and Goss texture components) on plastic flow localization are studied. The material response is described by a generalized Taylor-type polycrystal model, in which each grain is characterized in terms of an elastic-viscoplastic continuum slip constitutive relation. First, forming limits of thin sheet set by sheet necking are predicted using a Marciniak–Kuczynski (M–K-) type approach. It is shown that only the Cube texture component yields forming limits higher than that for a random texture in the biaxial stretch range. Next, three-dimensional shear band analyses are performed, using a three-dimensional version of M–K-type model, but the overall deformation mode is restricted to a plane strain state. From this simple model analysis, two important quantities regarding shear band formation are obtained: i.e. the critical strain at the onset of shear banding and the corresponding orientation of shear band. It is concluded that the Cube texture component is said to be a shear band free texture, while some texture components exhibit significantly low resistance to shear band formation. Finally, shear band developments in plane strain pure bending of sheet specimens with the typical textures are studied.

Numerical studies of shear banding in interface shear tests using a new strain calculation method

AbstractStrain localization is closely associated with the stress–strain behaviour of an interphase system subject to quasi‐static direct interface shear, especially after peak stress state is reached. This behaviour is important because it is closely related to deformations experienced by geotechnical composite structures. This paper presents a study using two‐dimensional discrete element method (DEM) simulations on the strain localization of an idealized interphase system composed of densely packed spherical particles in contact with rough manufactured surfaces. The manufactured surface is made up of regular or irregular triangular asperities with varying slopes. A new simple method of strain calculation is used in this study to generate strain field inside a simulated direct interface shear box. This method accounts for particle rotation and captures strain localization features at high resolution. Results show that strain localization begins with the onset of non‐linear stress–strain behaviour. A distinct but discontinuous shear band emerges above the rough surface just before the peak stress state, which becomes more expansive and coherent with post‐peak strain softening. It is found that the shear bands developed by surfaces with smaller roughness are much thinner than those developed by surfaces with greater roughness. The maximum thickness of the intense shear zone is observed to be about 8–10 median particle diameters. The shear band orientations, which are mainly dominated by the rough boundary surface, are parallel with the zero extension direction, which are horizontally oriented. Published in 2007 by John Wiley & Sons, Ltd.

Coupled thermo-mechanical modelling of bulk-metallic glasses: Theory, finite-element simulations and experimental verification

A three-dimensional, finite-deformation-based constitutive model to describe the behavior of metallic glasses in the supercooled liquid region has been developed. By formulating the theory using the principles of thermodynamics and the concept of micro-force balance [Gurtin, M., 2000. On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids 48, 989–1036], a kinetic equation for the free volume concentration is derived by augmenting the Helmholtz free energy used for a conventional metallic alloy with a flow-defect free energy which depends on the free volume concentration and its spatial gradient. The developed constitutive model has also been implemented in the commercially available finite-element program ABAQUS/Explicit (2005) by writing a user-material subroutine. The constitutive parameters/functions in the model were calibrated by fitting the constitutive model to the experimental simple compression stress–strain curves conducted under a variety of strain-rates at a temperature in the supercooled liquid region [Lu, J., Ravichandran, G., Johnson, W., 2003. Deformation behavior of the Zr-Ti-Cu-Ni–Be bulk metallic glass over a wide range of strain-rates and temperatures. Acta Mater. 51, 3429–3443]. With the model calibrated, the constitutive model was able to reproduce the simple compression stress–strain curves for jump-in-strain-rate experiments to good accuracy. Furthermore stress–strain responses for simple compression experiments conducted at different ambient temperatures within the supercooled liquid region were also accurately reproduced by the constitutive model. Finally, shear localization studies also show that the constitutive model can reasonably well predict the orientation of shear bands for compression experiments conducted at temperatures within the supercooled liquid region [Wang, G., Shen, J., Sun, J., Lu, Z., Stachurski, Z., Zhou, B., 2005. Compressive fracture characteristics of a Zr-based bulk metallic glass at high test temperatures. Mater. Sci. Eng. A 398, 82–87].

Strain localization in geomaterials

Abstract The main purpose of this paper is a broad review of developments in observation and interpretation of localization in geomaterials in the laboratory, with an emphasis on low mean stress situations. Laboratory investigation of strain localization in granular soils and rocks has been pursued extensively and very accurate strain field evolution measurement techniques have been developed, including false relief stereophotogrammetry (FRS) and computed tomography (CT). These permit full characterization of strain localization, from onset to complete shear band formation. This paper reviews studies of sand, clay, sandstone, stiff marl and concrete, and observations of incipient and developed localization in initially ‘homogeneous’ laboratory tests are presented. Development of localization and peak strength, critical stress and strain, shear band orientation and thickness, and complex localization patterns are discussed. Deformation during triaxial compression of sand is shown to develop complex strain localization patterns. Consequently, the critical void ratio concept in granular materials is reconsidered. Void ratio evolution, global and local, monitored by CT, shows a limiting void ratio being rapidly attained in the strain localization zones. In cohesive materials (clays, rocks and concrete), crack development is also commonly observed. Displacement discontinuity measurement techniques are presented and the results for different cohesive geomaterials are discussed.

Effects of texture on shear band formation in plane strain tension/compression and bending

In this study, effects of typical texture components observed in rolled aluminum alloy sheets on shear band formation in plane strain tension/compression and bending are systematically studied. The material response is described by a generalized Taylor-type polycrystal model, in which each grain is characterized in terms of an elastic–viscoplastic continuum slip constitutive relation. First, a simple model analysis in which the shear band is assumed to occur in a weaker thin slice of material is performed. From this simple model analysis, two important quantities regarding shear band formation are obtained: i.e. the critical strain at the onset of shear banding and the corresponding orientation of shear band. Second, the shear band development in plane strain tension/compression is analyzed by the finite element method. Predictability of the finite element analysis is compared to that of the simple model analysis. Third, shear band developments in plane strain pure bending of a sheet specimen with the typical textures are studied. Regions near the surfaces in a bent sheet specimen are approximately subjected to plane strain tension or compression. From this viewpoint, the bendability of a sheet specimen may be evaluated, using the knowledge regarding shear band formation in plane strain tension/compression. To confirm this and to encompass overall deformation of a bent sheet specimen, including shear bands, finite element analyses of plane strain pure bending are carried out, and the predicted shear band formation in bent specimens is compared to that in the tension/compression problem. Finally, the present results are compared to previous related studies, and the efficiency of the present method for materials design in future is discussed.

Shear band formation in IF steel during cold rolling at medium reduction levels

The mechanisms of shear band formation in IF steel after cold rolling to ∼50% reductions have been investigated using transmission electron microscopy. The observations revealed that shear bands were always parallel to a second set of microbands, where these exist, and contained within individual crystals, indicating that shear banding is controlled by orientation. Crystallographic analysis revealed that shear banding involves two mechanisms, dislocation glide and rigid-body rotation. In the first step, dislocation glide causes a rotation about the ⟨211⟩ axis to produce the so called ‘S’ band, which gives the shear band its crystallographic character. In the second step, when the most heavily stressed slip plane parallel to the shear band is of the form {110}⟨111⟩, rigid-body rotation continues about the ⟨211⟩ axis in the sheared zone and, then, a rotation about the transverse direction (TD) is promoted by the geometry of the sample. Using rigid-body matrix theory, the calculated orientations of shear bands are shown to be in agreement with experimental observations. The process outlined is capable of explaining how slip processes in grains that contain microbands, using either {110} or {112} slip planes, can produce crystallographic shear bands.

The modelling of anchors using the material point method

AbstractThe ultimate capacity of anchors is determined using the material point method (MPM). MPM is a so‐called meshless method capable of modelling large displacements, deformations and contact between different bodies. A short introduction to MPM is given and the derivation of the discrete governing equations. The analysis of a vertically loaded anchor and one loaded at 45° is presented. The load–displacement curves are compared to that obtained from experiments and the effect of soil stiffness and anchor roughness is investigated. The results of the vertically loaded anchor are also compared to an analytical solution. The displacement of the soil surface above the anchor was measured and compared to the numerical predictions. Convergence with mesh refinement is demonstrated and the effect of mesh size and dilatancy angle on the shear band width and orientation is indicated.The results show that MPM can model anchor pull out successfully. No special interface elements are needed to model the anchor–soil interface and the predicted ultimate capacities were within 10% of the measured values. Copyright © 2005 John Wiley & Sons, Ltd.

Investigations of shear banding in an anisotropic hypoplastic material

This paper focuses on the analysis of shear band formation in a cohesionless and initially transversely isotropic granular material based on a hypoplastic continuum approach. The constitutive equation for the evolution of the stress is formulated with a non-linear tensor-valued function depending on the current void ratio, the Cauchy stress, the rate of deformation and a structure tensor for anisotropy effects. The possibility of shear band formation in biaxial, plane strain compression is analyzed and the sensitivity of the shear band orientation to the slenderness of the specimen is discussed.

Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry

AbstractExperimental results are presented from the extensive program of drained plane strain compression tests on sand carried out in Grenoble over the last two decades. Systematic analysis of photographs of the deforming specimen allowed for measuring deformations and determining strain fields throughout the test, that is: prior to, at, and after the onset of strain localization. The principles, details and accuracy of the procedure are described, as well as its suitability to properly depict the patterns of deformation. Findings concerning the occurrence and progression of strain localization are discussed. The issues of shear band orientation and thickness are addressed, as well as temporary and persistent complex localization patterns, and the volumetric behaviour inside a band after its formation. The influence of such variables as initial state of the sand (effective stress and relative density), specimen size and slenderness, as well as grain size, is discussed. Copyright © 2004 John Wiley & Sons, Ltd

Experimental characterisation of the localisation phenomenon inside a Vosges sandstone in a triaxial cell

Abstract The behaviour of a Vosges sandstone is studied, including quasi-homogeneous deformation, incipient strain localisation and localised rupture. The homogeneous behaviour is first presented from about 60 experiments in triaxial compression with two slenderness ratios ( H / D =1 and 2), in triaxial extension, and in isotropic compression. A large range of confining pressures (0–60 MPa) is investigated, showing a significant evolution of material response. A strong positive dilatancy is observed at lower pressure, decreasing to become negative (contractancy) at higher pressure. Simultaneously, the strength decreases with increasing confining pressure. The localisation is described in terms of onset of localisation, shear band orientation and patterning. The volumetric strain is analysed inside the band with computed X-ray tomography and electron microscopy. We observed the formation of a gouge layer, and around it, a dilating shear band at lower confining pressure and a compacting shear band at higher pressure. This compacting shear band seems to be the transition mechanism between the brittle and semi-brittle regime.

Coupled computations for an elastic-perfectly plastic soil using adaptive mesh refinement

An adaptive mesh refinement algorithm has been developed for non-linear computations in geomechanics, based on a smoothed stress–strain finite element formulation. This uses estimates of error in the incremental shear strain invariant to guide the regeneration of unstructured meshes at regular intervals during loading. Following each mesh-update, no re-analysis of previous increments with the new mesh is necessary. Algorithm performance has been investigated by analysing a passive earth pressure problem using a linear elastic-perfectly plastic Mohr–Coulomb soil model. Perfectly drained behaviour has been considered, as have partially drained situations using hydromechanical coupling, while undrained behaviour has been approximated using time steps close to zero. In all cases, mesh adaptivity has been successful in capturing regions of high strain gradient. The results have been compared with analytical solutions. Accurate computations of limit load and shear band orientation have been obtained for a wide range of material dilation angles. Copyright © 2000 John Wiley & Sons, Ltd.

Sand Shear Band Thickness Measurements by Digital Imaging Techniques

Digital imaging analysis was used to study localized deformations in granular materials tested under plane strain condition. Two independent techniques were applied and compared. In the first technique, the digitized optical images of a grid printed on the latex membrane were used to measure the shear band orientation angle and thickness, and were found to be 54.5° and 3.01 mm, respectively. The second technique involved introducing an ultra-low viscosity resin into the specimen in preparation for thin-sectioning and microscopic study of the internal fabric. A total of 24 microscopic images obtained from four thin sections were analyzed and void ratio variation was measured. The shear band thickness measurements from images located along the shear band axis (at two locations) were equal to 3.19 and 3.29 mm, which are very close to the average value obtained from surface analysis. The study was then extended to investigate the effects of sand grain-size, specimen density, and confining pressure on shear band thickness. It was found that the normalized shear band thickness decreases as grain-size increases and as density decreases. Finally, shear band thickness is dependent on the specimen dilatancy angle.

Perturbation analysis of high strain-rate shear localization in B.C.C. crystalline materials

A perturbation analysis has been used to obtain a detailed and fundamental understanding of the high strain-rate material mechanisms associated with material instabilities and adiabatic shear-band formation in single body-centered cubic (b.c.c.) crystals. The interrelated effects of wave number, shear-band orientation, strain hardening, strain-rate sensitivity, and thermal and geometrical softening on material instability and shear-strain localization have been investigated in terms of the competition between the softening and hardening mechanisms for nominal strain-rates from 100/s to 5000/s. A perturbed system of equations has been obtained, accounting for arbitrary crystal orientations, and since no approximations have been made for the magnitude of the strain-rate sensitivity parameter, all the roots associated with the stability of the perturbed equations can be obtained for physically representative deformations. Hence, a comprehensive characterization of material instabilities can be obtained beyond the initial instability point, and the strength of material instabilities can be then monitored throughout the deformation history to distinguish between material instabilities and shear-strain localization.

Test environments and mechanical properties of Zr-base bulk amorphous alloys

The mechanical properties of two Zr-base bulk amorphous alloys (BAA), Zr-10Al-30Cu-5Ni (BAA-10) and Zr-10Al-5Ti-17.9Cu-14.6Ni (BAA-11), were studied by both tensile and compressive tests at room temperature in various test environments. The BAA ingots up to 7 mm in diameter were successfully produced by both arc melting and drop casting and induction melting and injection casting. The BAA specimens deformed mainly elastically, followed by catastrophic failure along shear bands. Examination of the fracture region revealed ductile fracture features resulting from a substantial increase in temperature, which was attributable to the conversion of the stored elastic strain energy to heat. Surprisingly, “liquid droplets” located at major shear-band cracks adjacent to the fracture section were observed, indicating the occurrence of local melting during fracture. The angle orientation of shear bands, shear-band cracks, and fracture surfaces relative to the stress axis is quite different for BAA specimens tested in tension and compression. This suggests that both shear stress and normal stress may play a role in developing shear bands during plastic deformation. The tensile properties of BAAs were found to be insensitive to the test environment at room temperature. However, the reaction of BAAs with distilled water and heavy water was detected by laser desorption mass spectrometry (LDMS). These results suggest that moisture-induced hydrogen embrittlement in BAAs may be masked by catastrophic fracture following shear bands.

Reexamination of fault angles predicted by shear localization theory

This paper reexamines orientations of shear bands (fault angles) predicted by a theory of shear localization as a bifurcation from homogeneous deformation. In contrast to the Coulomb prediction, which does not depend on deviatoric stress state, the angle between the band normal and the least (most compressive) principal stress increases as the deviatoric stress state varies from axisymmetric compression to axisymmetric extension. This variation is consistent with the data of Mogi (1967) on Dunham dolomite for axisymmetric compression, extension and biaxial compression, but the predicted angles are generally less than observed. This discrepancy may be due to anisotropy that develops due to crack growth in preferred orientations. Results from specialized constitutive relations for axisymmetric compression and plane strain that include this anisotropy indicate that it tends to increase the predicted angles. Measurements for a weak, porous sandstone (Castlegate) indicate that the band angle decreases with increasing inelastic compaction that accompanies increasing mean stress. This trend is consistent with the predictions of the theory but, for this rock, the observed angles are less than predicted.

The Use of Digital Image Processing in Monitoring Shear Band Development

Abstract A new technique involving sample preparation, video imaging, and image analysis has been developed to observe the kinematics of shear bands when geomaterials are subjected to a general state of combined stress. The technique provides an effective, low-cost, and non-invasive way to monitor the development and measure the deformations inside and outside the shear bands. Its capabilities are demonstrated through a series of drained tests in which thin hollow cylinders of sand are subjected to combinations of hydrostatic, axial, and torsional stresses. It is shown that the deformation within the shear band is different from the global one and the one in its vicinity. For sand specimens with the same configuration, density, and confining pressure, the initiation, orientation, and thickness of shear bands depend on the loading path.

On the failure of pressure-sensitive plastic materials part II: Comparisons with experiments on ultra fine grained Fe-10% Cu alloys

In Part 1 of this article the authors presented theoretical results pertaining to the yield behavior of pressure-sensitive plastic materials with emphasis on shear band width and orientation. These results are applied here to model the experimental data obtained for compression and tension tests of ultra fine grained Fe-10% Cu alloys. As will be reported in detail elsewhere these alloys exhibit almost perfectly plastic behavior and deform by intense shear banding as the only mode of plastic deformation. Due to the fine grain structure, it may be speculated that grain rotation and void formation can contribute significantly to the aforementioned shear band mechanism for plastic flow, in addition to the traditional dislocation motion. It follows that the pressure-sensitive plastic models elaborated upon in Part 1 may be suitable candidates for the description of the shear band behavior for these alloys. In fact, it is shown in Part 2 that the mechanical property data obtained for the strengths in tension and compression, the shear band angles and the shear band widths verify the theoretical expressions derived in Part 1 for the yield condition, the shear band orientation, and the shear band width.

On the failure of pressure-sensitive plastic materials part I. Models of yield & shear band behavior

The purpose of this two-part article is to theoretically establish and experimentally support a simple method for calculating shear band angles and shear band widths in tension or compression samples commonly used to investigate mechanical properties. The method is illustrated in conjunction with experimental results on the yielding behavior and shear band formation in tension and compression of an ultra fine grained Fe-10% Cu alloy, properly milled and consolidated. The experimental techniques for preparing the samples, their microstructural characteristics and the details of the performed mechanical tests will be reported elsewhere, but a brief summary is contained in Part 2 of the present article. In Part 2 comparisons are made between theoretical predictions for pressure-sensitive plastic materials established in Part 1 and experiments on the yield behavior of an ultra fine grained Fe-10% Cu alloy along with observations on shear band orientations and widths.

Qualitative analysis of strain localization. Part II: Transversely isotropic elasticity and plasticity

We consider first materials whose elastic and plastic properties display rotational symmetry about a common axis. Loading is restricted to uniaxial tractions. We obtain the anisotropic materials through a perturbation, by a finite number of parameters, of an isotropic reference. For the anisotropic materials, there is, to within some particular cases, a finite number of critical planes along which the onset of strain localization may occur simultaneously. In contrast, for the isotropic reference, there exists a cone of critical planes. We analyze the localization characteristics as the isotropic reference is approached. The direction of approach in the space of anisotropic parameters plays a crucial role on the orientation of the critical planes of localization. In a second step, the analysis is repeated assuming the elastic and plastic symmetry axes to be distinct. The influence of each of the three directions involved, namely loading, elastic and plastic symmetry axes, on the shear band orientation is shown to be weighted by the absolute and relative amounts of elastic and plastic anisotropies.