Development Of Shear Bands Research Articles

Self-organization of shear bands in titanium and Ti–6Al–4V alloy

The evolution of multiple adiabatic shear bands was investigated in commercially pure titanium and Ti–6Al–4V alloy through the radial collapse of a thick-walled cylinder under high-strain-rate deformation (∼10 4 s −1). The shear-band initiation, propagation, as well as spatial distribution were examined under different global strains. The shear bands nucleate at the internal boundary of the specimens and construct a periodical distribution at an early stage. The shear bands are the preferred sites for nucleation, growth, and coalescence of voids and are, as such, precursors to failure. The evolution of shear-band pattern during the deformation process reveals a self-organization character. The differences of mechanical response between the two alloys are responsible for significant differences in the evolution of the shear band patterns. The number of shear bands initiated in Ti (spacing of 0.18 mm) is considerably larger than in Ti–6Al–4V (spacing of 0.53 mm); on the other hand, the propagation velocity of the bands in Ti–6Al–4V (∼556 m/s) is approximately three times higher than in Ti (∼153 m/s). The experimental shear-band spacings are compared with theoretical predictions that use the perturbation analysis and momentum diffusion; the shortcomings of the latter are discussed. A new model is proposed for the initiation and propagation that incorporates some of the earlier ideas and expands them to a two-dimensional configuration. The initiation is treated as a probabilistic process with a Weibull dependence on strain; superimposed on this, a shielding factor is introduced to deal with the deactivation of embryos. A discontinuous growth mode for shear localization under periodic perturbation is proposed. The propagating shear bands compete and periodically create a new spatial distribution.

Development of shear bands in annular shear granular flows

ABSTRACTUsing hard-disk simulations of relatively dense packs of mono-sized system in an annular Couette geometry the formation of dilute regions inside the granular media, namely shear bands, are investigated. The results represent the influence of entire system characteristics such as solid area fraction and shear rate on the development of shear bands as well as the local properties of grains that cause them to participate in the formation of a shear band. Moreover, simulations have been performed for binary-sized system, which revealed that the formation of such diluted shear bands is unlikely.

The Deformation Microstructure and Recrystallization Behavior of Warm Rolled Steels.

The deformation microstructure of various warm (ferritic) rolled steels was characterized and its influence upon the subsequent annealing behavior determined. The materials investigated included three interstitialfree (IF) steels (stabilized with either titanium or niobium), an extra low carbon (ELC) steel, and four experimental low carbon chromium steels with varying levels of boron, nitrogen and phosphorus. Single pass rolling experiments were conducted in a pilot mill at temperatures between 440 and 850°C and the asrolled microstructures were examined using optical microscopy. Particular attention was paid to the nature and intensity of the in-grain shear bands produced. Partial annealing was conducted to examine the nucleation of recrystallization in the deformed microstructure. Shear bands of moderate intensity were usually formed in the IF steels, which tended to be insensitive to rolling temperature. For the ELC steel, intense shear bands were formed at low rolling temperatures, but at higher temperatures this intensity was found to be drastically reduced. The development of shear bands at the higher rolling temperatures was significantly enhanced by alloying with chromium. The differences in shear band frequency and intensity are explained in terms of the dynamic strain aging behaviors of the various materials. Recrystallized grains were found to nucleate preferentially on the shear bands during annealing, regardless of their morphology or intensity.

Thermo-plastic effects on structural behaviour during crush and impact

In this paper, the constitutive relation of plasticity with strain rate and temperature dependency was used to analyse the process of crushing and impacting of structures. Computer simulations of the localisation of plastic buckling patterns and the initiation and development of adiabatic shear band were performed. The thermoplastic effects were investigated and discussed.

Synergistic effects of plastic anisotropy and void coalescence on fracture mode in plane strain

The macroscopic fracture in plane strain is known to be shear-like in ductile materials.In most structural materials, fracture starts after diffuse necking,at the centre of the specimen, by micro-void coalescence giving rise afterwards tothe macroscopic shear fracture mode.In this paper, the effect of coalescence on shear band development and on associated fracture mode in plane strain is analysed numerically.The calculations are performed using a recent elastic-viscoplasticGurson-like model that accounts for void shape evolution, coalescenceand post-coalescence micromechanics along with isotropic hardeningand orthotropic plasticity for the matrix behaviour. The latter is introduced to represent the actualflow properties of hot-worked materials.No kinematic hardening or nucleation formulation is used in orderto focus attention on coalescence effects and to discuss, with respectto experiments, published results based on kinematic hardeningand nucleation effects.The most important finding is the synergistic effect of plasticanisotropy and post-coalescence yield surface curvatureupon the onset of a shear band after the fracture sets in at thecentre of the specimen.

Crack-tip plasticity in bulk metallic glasses

The fracture and plastic deformation mechanisms of a Zr–Ti–Ni–Cu–Be bulk metallic glass are reviewed. In particular, the effects of stress state and local heating on the development of shear bands are discussed. The temperature increase at the crack tip during fracture was measured and was found to be consistent with predictions of the dissipation of plastic work as heat. In order to examine the effect of stress state on failure, tensile bars with notches of varying severity were used to superimpose a tensile mean stress. A constant mean stress was found to provide an accurate correlation with the onset of strain localization and failure.

Study of the formation of adiabatic shear bands in steels

The formation and evolution of adiabatic shear bands at high strain rate deformation of AISI 4340 steel was investigated using a torsional split Hopkinson bar system. The process was also modeled by finite element methods. Factors affecting the occurrence of the adiabatic shear bands such as specimen geometry were also examined. Depending on these factors, it was found that the adiabatic shear bands occur more likely when there is differences in properties and microstructure than in the rest of the sample and that a specific specimen geometry and dimensions favor the occurrence of high strain rates and hence the formation of the adiabatic shear bands.

Shear band development predicted by a non-normality theory of plasticity and comparison to crystal plasticity predictions

A phenomenological plasticity model has recently been proposed, which combines a smooth yield surface for an anisotropic solid with a vertex-type plastic flow rule. Both polycrystal plasticity calculations and experiments have shown the type of non-normality of plastic flow, which is represented by this material model. The plasticity model is here implemented in a finite element programme and is used to analyze the plane strain tensile test, thus representing the formation of a neck and the subsequent evolution of shear bands in the neck region. To test the predictions of the phenomenological plasticity model the tensile test problem is also analyzed by polycrystal plasticity, based on the Taylor model for either b.c.c. or f.c.c. crystal structure. It is shown that the phenomenological plasticity model gives a good approximation of the crystal plasticity predictions.

Mechanics of extension and inversion in the hanging walls of listric normal faults

Fault shape, material properties and bedding anisotropy determine the style of deformation in the hanging walls of listric normal faults. We use numerical models to study this deformation in both extension and inversion during displacement on a variety of master fault shapes. Elastic‐plastic material properties in the models allow the development of shear bands, which simulate secondary faults within the hanging wall. If the master fault is composed of a planar ramp and planar flat separated by a sharp fault bend, a series of antithetic normal shear bands develops in the hanging wall, propagating up from the fault bend. Each shear band is progressively abandoned as displacement on the master fault moves it away from the fault bend. Displacements on the antithetic faults produce the limb of a hanging wall monocline and bound one side of a graben, the other side of which is bounded by the master fault. The antithetic shear bands are not rotated, and layering within the graben remains subhorizontal. On the other hand, if the fault bend is curved rather than sharp, symmetrical nested graben develop in the upper part of the hanging wall above the base of the ramp. Displacement on the master fault moves these shear bands away from the fault bend, after which they are abandoned in favor of new shear bands. Early formed synthetic shear bands become shallower and concave upward because of the folding and rotation of the hanging wall. With increasing radius of curvature of the master fault, localization into shear bands decreases and, with a large radius of curvature, shear bands do not develop. If weak bedding layers are included within the hanging wall, they become sites of bedding‐parallel shear bands that accommodate flexural slip folding and replace the synthetic shear bands that develop in homogeneous models. If extension is followed by shortening and inversion, normal shear bands that developed during extension are reactivated as reverse shear bands but are also crosscut by new reverse shear bands. The models produce results that are similar to both natural structures and analogue models and provide explanations for many observations of deformation in seismic profiles through extensional terranes.

Study of mechanical deformation in bulk metallic glass through instrumented indentation

Instrumented sharp indentation experiments at the nano- and micro-length scales were carried out in an attempt to quantify the deformation characteristics of Vitreloy 1™ bulk metallic glass. The experiments were accompanied by detailed three-dimensional finite element simulations of instrumented indentation to formulate an overall constitutive response. By matching the experimentally observed continuous indentation results with the finite element predictions, a general Mohr–Coulomb type constitutive description was extracted to capture the dependence of multiaxial deformation on both shear stresses and normal stresses. This constitutive response is able to provide accurate predictions of the evolution of shear bands seen in uniaxial compression tests. Constrained deformation of the material around the indenter results in incomplete circular patterns of shear bands whose location, shape and size are also captured well by the numerical simulations. The analysis is also able to predict the extent of material pile-up observed around the indenter. The surface deformation features are also consistent with mechanisms such as localized shear flow, serrated yielding and adiabatic heating, which are observed during macroscopic mechanical tests.

Heterogeneous 40Ar* distributions in naturally deformed muscovite: in situ UV-laser ablation evidence for microstructurally controlled intragrain diffusion

Micas are commonly used in 40Ar/ 39Ar thermochronological studies of variably deformed rocks yet the physical basis by which deformation may affect radiogenic argon retention in mica is poorly constrained. This study examines the relationship between deformation and deformation-induced microstructures on radiogenic argon retention in muscovite. A combination of furnace step-heating and high-spatial resolution in situ UV-laser ablation 40Ar/ 39Ar analyses are reported for deformed muscovites sampled from a granitic pegmatite vein within the Siviez–Mischabel Nappe, western Swiss Alps (Penninic domain, Briançonnais unit). The pegmatite forms part of the Variscan (∼350 Ma) Alpine basement and exhibits a prominent Alpine S–C fabric including numerous mica ‘fish’ that developed under greenschist facies metamorphic conditions, during the dominant Tertiary Alpine tectonic phase of nappe emplacement. Furnace step-heating of milligram quantities of separated muscovite grains yields an 40Ar/ 39Ar age spectrum with two distinct staircase segments but without any statistical plateau, consistent with a previous study from the same area. A single (3×5 mm) muscovite porphyroclast (fish) was investigated by in situ UV-laser ablation. A histogram plot of 170 individual 40Ar/ 39Ar UV-laser ablation ages exhibit a range from 115 to 387 Ma with modes at approximately 340 and 260 Ma. A variogram statistical treatment of the 40Ar/ 39Ar results reveals ages correlated with two directions; a highly correlated direction at 310° and a lesser correlation at 0° relative to the sense of shearing. Using the highly correlated direction a statistically generated (Kriging method) age contour map of the 40Ar/ 39Ar data reveals a series of elongated contours subparallel to the C-surfaces which where formed during Tertiary nappe emplacement. Similar data distributions and slightly younger apparent ages are recognized in a smaller mica fish. The observed intragrain age variations are interpreted to reflect the partial loss of radiogenic argon during Alpine (∼35 Ma) greenschist facies metamorphism. One-dimensional diffusion modelling results are consistent with the idea that the zones of youngest apparent age represent incipient shear band development within the mica porphyroclasts, thus providing a network of fast diffusion pathways. During Alpine greenschist facies metamorphism the incipient shear bands enhanced the intragrain loss of radiogenic argon. The structurally controlled intragrain age variations observed in this investigation imply that deformation has a direct control on the effective length scale for argon diffusion, which is consistent with the heterogeneous nature of deformation.

Comparative study of cataclastic rocks from a drill core and outcrops of the Nojima Fault zone on Awaji Island, Japan

Abstract Cataclastic rocks found in the Disaster Prevention Research Institute, Kyoto University (DPRI) 500 m drill core and outcrops along the Nojima Fault zone on Awaji Island, southwest Japan, were examined at mesoscopic and microscopic scales. The damaged zone of this fault in granitic rocks, observed on the southeast side of the fault, is 50–60 m wide and is composed of fractured host rocks and cataclastic rocks including cataclasite, fault breccia, and fault gouge. The fault breccia and gouge of small scales are scattered in the damaged zone. Fault core (zone of extremely concentrated shearing deformation along a fault) consists of fault gouge measuring several tens to approximately 150 mm in width, as recognized both in the drill core and at outcrops of the Nojima Fault along which surface ruptures formed during the 1995 Kobe earthquake. Fault breccia, measuring a few meters wide, has developed pervasively in the damaged zone, just next to the fault core. Pseudotachylyte has been found interlayered with fault gouge within the fault core only at outcrops at Hirabarashi, not in the DPRI 500 m core. Petrological studies and powder X‐ray diffraction analysis show that the pseudotachylyte and fault gouge are composed mainly of fine‐grained angular clasts of the host granitic rocks, suggesting the pseudotachylyte is of ‘crush origin’. Foliated cataclasite is characterized by the preferred orientation of elongated biotite clasts and granular aggregates of quartz and feldspar clasts, and by the development of cataclastic shear bands. Unlike cataclastically deformed quartz and feldspar in the cataclasite, biotite in the foliated cataclasite shows combinations of brittle and plastic deformation, such as biotite ‘fish’, cleavage steps, bending and kinking. These textures suggest that the foliated cataclasite formed at a deeper level than the cataclasite, fault breccia and gouge, possibly before the Quaternary period during which the Nojima Fault has moved as a dextral strike–slip fault with some reverse movement resulting in the uplifting of Awaji Island. Examination of fault rocks from surface outcrops can yield similar results to those obtained from drill cores with regard to the internal structures of a fault zone.

Shear band instabilities in compacted metal powder with or without interparticle cohesion

A simple model for analysis of shear band development in uniformly strained solids is used to study the possibility of flow localization during metal powder compaction. Earlier analyses for a metal powder with full interparticle cohesion have predicted no localization. Here, a material model is used, in which the value of a cohesion factor is used to represent either cohesionless powder or powder with a certain amount of cohesion. It is found that localization under compaction depends strongly on the cohesion factor, the stress state, and the magnitude of an initial imperfection.

Microstructural evolution in adiabatic shear bands in Ta and Ta–W alloys

Microstructural evolution of adiabatic shear bands originated due to high strain, high strain rate deformation in Ta and Ta–W alloys has been examined. Tests were performed using a specially designed stepped specimen in a Hopkinson bar. Upon completion of the deformation, the region is cooled to below one half of the temperature achieved during adiabatic heating in less than one millisecond. Microstructural characterization of the shear bands was performed using optical microscopy as well as scanning and transmission electron microscopy. No evidence of recrystallization within the shear bands could be found. This is in contradiction with several recent reports, which claim that recrystallization may take place at these stringent time and temperature conditions. These studies, however, do not take into account the kinetics of boundary refinement processes, which are a distinctive characteristic of a recrystallized microstructure. It will be shown that the absence of recrystallization in Ta and Ta–W adiabatic shear bands can be predicted by a progressive subgrain misorientation (PriSM) recrystallization model, applied successfully in previous studies to predict the microstructure evolution in copper adiabatic shear bands.

Formation of Shear Bands in Model Ground Composed of Aluminum Rods Beneath a Footing

Abstract In this study, a series of bearing capacity tests were carried out on a model ground composed of aluminum rods in order to investigate the initiation and development of shear bands during loading. This paper describes the test apparatus, the methods of testing and data treatment, and some of the test results. Two types of model grounds were prepared depending upon whether the aluminum rods used were single-diameter or two different diameters. During the loading test, by utilizing both front and back of the test apparatus, detailed observations were made on the global deformation of the model ground, on the translational and rotational movements of selected aluminum rods, and on the change of void ratio. It is shown that, in the case of the single-diameter aluminum rods, the slip surface was observed and that dilatancy behavior was noted at the boundary. In the case of the aluminum rods with two different diameters, discontinuous shear bands defining a so-called plastic flow zone were observed, which were initiated at the bottom corners of the footing and extended diagonally downwards. The rotational behavior of the rods differed inside and outside the plastic flow zone, particularly near the boundaries.

補強砂地盤の支持力破壊の数値解析

The load-settlement behaviour and bearing capacity of a strip footing on reinforced sand was simulated by a nonlinear elasto-visco-plastic FEM analysis incorporating an elasto-viscoplastic constitutive model for sand that was developed to have a stress path-independent work-hardening parameter based on the modified plastic strain energy concept. The constitutive model has been modified to take into account the nonlinear viscous property of sand based on a three-component model consisting of a hypo-elastic component connected in series to a combination of a non-linear inviscid and viscous components connected to each other in parallel. The model ground was made of air-dried dense Toyoura sand, which was either unreinforced or reinforced with different lengths, numbers of layers and vertical spacings of layers of linear, tensile reinforcing members placed horizontal beneath a strip footing. Load-settlement relationships obtained by the FEM analysis were well comparable with those from the physical experiment. Although the peak footing load obtained by the FEM analyses was slightly larger than the measured value, the effects of reinforcing patterns and progressive failure of model ground with a development of shear bands observed in the tests were simulated very well.

Finite-element analysis of localization of deformation and fluid pressure in an elastoplastic porous medium

The paper concerns the issue of progressive development of shear bands in the problem of coupled deformation and fluid diffusion in porous media. The governing continuum equations are based on porous media theory applied to an elastic–plastic solid skeleton at small deformations. In the localization analysis, the concept of regularized discontinuity is extensively used at the application to the conservation laws of momentum and mass. As a result, we obtain a coupled localization condition that is preserved also in the numerical formulation. Attention is also given to the design of an overall numerical algorithm to solve the coupled set of non-linear finite-element equations that arise from the element-embedded band approach. In order to arrive at the proper design of the algorithm, we resort to a staggering between the continuous (global) problem and the discontinuous (element) problems. In the numerical examples, the algorithm is shown to be able to capture onset of localization as well as the progressive development of shear bands. In the examples, we study the influence of local and global (boundary) drainage conditions, and the internal friction angle to the failure mechanisms.

Signatures of granular microstructure in dense shear flows

Granular materials and ordinary fluids react differently to shear stresses. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands--narrow zones of large relative particle motion, with essentially rigid adjacent regions. Because shear bands mark areas of flow, material failure and energy dissipation, they are important in many industrial, civil engineering and geophysical processes. They are also relevant to lubricating fluids confined to ultrathin molecular layers. However, detailed three-dimensional information on motion within a shear band, including the degree of particle rotation and interparticle slip, is lacking. Similarly, very little is known about how the microstructure of individual grains affects movement in densely packed material. Here we combine magnetic resonance imaging, X-ray tomography and high-speed-video particle tracking to obtain the local steady-state particle velocity, rotation and packing density for shear flow in a three-dimensional Couette geometry. We find that key characteristics of the granular microstructure determine the shape of the velocity profile.

Study on couple stress and shear band development in granular media based on numerical simulation analyses

From the reasonable accordance between the simulation and laboratory tests, it is concluded that the simulation test using the distinct element method can provide a powerful tool to simulate the micro- as well as macro-behavior of granular media. This is true, in particular, when the rotational resistance is introduced into the conventional one. Based on both the simulation and laboratory tests, we reached the following conclusions: One of the most important changes in microstructure, which takes place during a strain hardening process, is the formation of column-like structure growing parallel to the major principal stress direction. After failure, the column-like structure is reconstructed during a strain softening process by means of rolling, not sliding, at contact points so that a high gradient of particle rotation is generated, changing from negative to positive in a relatively narrow shear zone. Large voids appear in the shear band, and the resulting local void ratio can exceed the corresponding maximum one determined by a standard method. This fact strongly suggests that unique stress condition, which leads to such special microstructure, may develop in the shear band. In fact, couple stresses exist in a shear band in a manner consistent with the change of the particle rotation gradient from negative to positive. In spite of the presence of the couple stress, the stress tensor is nearly symmetric, indicating that the couple stress is very small in magnitude. The presence of the small couple stress still plays an important role in the development of microstructure in shear bands.

Self-Organization, Localization of Shear Bands, and Aging in Loose Granular Materials

We introduce a mesoscopic model for the formation and evolution of shear bands in loose granular media. Numerical simulations reveal that the system undergoes a nontrivial self-organization process which is governed by the motion of the shear band and the consequent restructuring of the material along it. High density regions are built up, progressively confining the shear bands in localized regions. This results in an inhomogeneous aging of the material with a very slow increase in the mean density, displaying an unusual glassylike system-size dependence.