Occurrence Of Shear Bands Research Articles

Effect of grain size on the recrystallization kinetics and crystallographic texture of unidirectionally rolled Ti-15V-3Cr-3Al-3Sn alloy

In the present work, Ti-15V-3Cr-3Al-3Sn (Ti-15333) samples were solution annealed (SA) at two different temperatures (800 °C for 30 minutes and 1000 °C for 15 minutes) to investigate the effect of initial grain size (GS) on the cold rolling and recrystallization behavior. Average grain size (AGS) for samples SA at 800 °C and 1000 °C was 87±7.82 μm and 177±4.36 μm, respectively. Both the samples were cold rolled unidirectionally (UDR) upto 80 % thickness reduction, subsequently followed recrystallization at 780 °C. UDR samples showed elongated grain structure with a preferential formation of shear bands (SBs) in some grains. Formation of SBs was more prominent in coarse AGS sample and these bands were also found to be orientation sensitive. The frequency of occurrence of SBs was more in γ-fiber (ND//<111>) grains and Dillamore’s plastic instability criterion was used to explain their preferential occurrence in γ-fiber. Recrystallization was done at 780 °C, for various time periods ranging from 30 s to 30 minutes). 80 % UDR samples showed the formation of strong α- and γ-fibers in both the cases. Full recrystallization was attained within 10 minutes for the initial fine grained 80% UDR sample, and it exhibited a continuous γ-fiber texture. In contrast, initial coarse grained 80% UDR sample took 20 minutes to achieve complete recrystallization, and it showed a discontinuous γ-fiber texture. Notably, the {111}<112> texture component of the γ-fiber was prominently evident in both cases, while the α-fiber was entirely absent for both conditions.

Texture evolution and twinnability prediction of the most compliant orientation in GH3536 superalloy during cold rolling

In this study, GH3536 superalloy was subjected to the cold rolling processing up to 60% of thickness reductions for meticulously investigating the evolutions of both microstructure and texture. Crucial findings of deformation microstructures such as the twinning of the grain with Copper orientation and the occurrence of shear bands in matrix were captured by electron backscatter diffraction (EBSD). Twin trace analysis (TTA) was concomitant with resolved shear stress (RSS) analysis for identifying active twin variants. Higher strength and lower ductility were developed with increasing reduction ratios, which was evaluated in mechanical properties tests implemented by using nonstandard miniaturized specimens. The RSS ratio analysis was carried out to predict the twinnability of the most compliant orientation and disclose the orientation dependence of deformation twinning. Experimental and calculated results proved the discovery of the deformation twinning in a Copper orientation.

Rheology of Cohesive Granular Media: Shear Banding, Hysteresis, and Nonlocal Effects

Powders or cohesive granular materials are widely handled in industries. However, our understanding of the rheology of these materials is limited. Here, we provide a comprehensive analysis of the rheology of a cohesive granular medium, sheared in a normal-stress-imposed plane shear cell over a wide range of shear rate, employing numerical simulations. At high imposed shear rates, the flow is homogeneous, and the rheology is well described by the existing scaling laws, involving the inertial number and the effective cohesion number [S. Mandalet al., Insights into the Rheology of Cohesive Granular Media, Proc. Natl. Acad. Sci. U.S.A. 117, 8366 (2020)]. However, at low imposed shear rates, the flow is inhomogeneous, exhibiting the coexistence of flowing and nonflowing regions in the material, popularly known as shear banding. We thoroughly analyze the crucial features of this shear-banded flow regime and discuss striking similarities between the shear banding for granular media and other complex fluids. We reveal that the occurrence of shear banding is related to the existence of a nonmonotonic intrinsic rheological curve and that increasing adhesion increases the nonmonotonicity and the tendency toward shear localization. A simple theoretical model based on a nonlocal rheological model coupled with a nonmonotonic flow curve is proposed and is shown to successfully reproduce all the key features of the shear banding observed in the numerical simulations. The results have important implications for the handling of powders in industries.

Experimental investigation and micromechanical modeling of the brittle-ductile transition behaviors in low-porosity sandstone

This paper presents a unified experimental and numerical investigation on mechanical behaviors of a sandstone with brittle-ductile transition. A series of triaxial compression tests are performed at room temperature under a wide range of confining pressure, from which some critical states of damage are originally identified. It is shown that shear-induced dilation occurs in brittle faulting while macroscopic dilatant cataclastic flow takes place in the rock under elevated pressures without occurrence of shear bands by strain localization. There is a clear trend for peak strength to increase nonlinearly with confining pressure and that microcracking-related local friction is the dominant mechanism of inelastic deformation. In order to describe the nonlinear mechanical behaviors of the sandstone, a micromechanics-based isotropic plasticity-damage coupling model is formulated, in which two critical states of damage at rock failure are taken into account to establish the relations between the model’s parameters and experimental data. Theoretical predictions of the strength envelope and nonlinear mechanical responses of the sandstone show a quantitative agreement with the test results including the main features of stress-strain curves with different confining pressures.

Phase-resolving simulation of dense bubble clusters under periodic shear

The paper studies the response of a cluster of bubbles to osmotic pressure, and steady and oscillatory shearing by detailed numerical simulations. In contrast to other investigations, the movement of the interstitial fluid is fully resolved. To that end, an immersed-boundary method is employed, yielding the trajectory of each bubble and the flow and pressure field of the fluid. Additionally, a physically motivated collision model ensures realistic bubble interactions. Furthermore, a suitable numerical configuration is proposed which allows imposing osmotic pressure and shear in a way that integrates well into the simulation without generating artefacts. This method allows for the realistic investigation of the compression of bubbles across the jamming limit, demonstrating the influence of the inertia of the interstitial fluid. Applying oscillatory shearing with varying osmotic pressure, shear stress and frequency, the occurrence of shear bands is demonstrated and the influence on rheometric measurements is discussed.

Bedrock geology of DFDP-2B, central Alpine Fault, New Zealand

ABSTRACTDuring the second phase of the Alpine Fault, Deep Fault Drilling Project (DFDP) in the Whataroa River, South Westland, New Zealand, bedrock was encountered in the DFDP-2B borehole from 238.5–893.2 m Measured Depth (MD). Continuous sampling and meso- to microscale characterisation of whole rock cuttings established that, in sequence, the borehole sampled amphibolite facies, Torlesse Composite Terrane-derived schists, protomylonites and mylonites, terminating 200–400 m above an Alpine Fault Principal Slip Zone (PSZ) with a maximum dip of 62°. The most diagnostic structural features of increasing PSZ proximity were the occurrence of shear bands and reduction in mean quartz grain sizes. A change in composition to greater mica:quartz + feldspar, most markedly below c. 700 m MD, is inferred to result from either heterogeneous sampling or a change in lithology related to alteration. Major oxide variations suggest the fault-proximal Alpine Fault alteration zone, as previously defined in DFDP-1 core, was not sampled.

Theoretical derivation of basic mechanical property required for triggering mine-pillar rockburst

Rockburst is divided into two types, one is strain-type resulting from rock damage and another is sliding-type resulting from fault slip events. Triggering mine pillar rockburst mainly consists of two steps: the occurrence of shear-band and the application of disturbance. In this paper, mechanical model of mine pillar subjected to uniaxial compression is established. By simplifying the complete stress–strain curve and the crack propagation behaviour, based on the derived energy expressions corresponding to different crack propagation stages, the type of rockburst that the disturbance-induced pillar instability belongs to is defined. Next, by establishing the model of mine pillar with one inclined shear-band and by simplifying the stress evolution on the band, based on the necessary physical characteristics for triggering dynamic events, the basic mechanical property of mine pillar required for triggering instability is derived. It shows that the post-peak modulus greater than or equal to the pre-peak modulus is the basic mechanical property required for triggering mine pillar instability. Finally, by conducting laboratory experiments, the proposed model is verified. The requirement that the post-peak modulus is greater than or equal to the pre-peak modulus may be the reason why triggered mine pillar rockburst is not often observed.

Elucidating the flow-microstructure coupling in entangled polymer melts. Part II: Molecular mechanism of shear banding

In this study, we have elucidated the molecular origin of shear banding in the entangled polymeric melts. Specifically, it is shown that the inflection point corresponding to the stress-overshoot indicates the possibility of inhomogeneity and this combined with slow orientation relaxation in step-strain start-up experiments will lead to formation of local inhomogeneity along the velocity gradient direction. Once the aforementioned inhomogeneities are created, a localized jump in entanglement density and a commensurate jump in normal stress and viscosity will lead to formation of the incipient shear banded flow structure. To this end, number of step-strain and start-up simulations with different deformation rate ramp times in the planar Couette flow with entanglement densities ⟨Zk⟩ ≥ 17 were performed to demonstrate the effect of deformation rate ramp time on the formation of local inhomogeneities and occurrence of shear banding. It has been demonstrated that if the time scale for the deformation rate to reach its steady value is larger or on the order of the orientation relaxation time of the chain, local inhomogeneities in the velocity gradient direction will not form and the linear velocity profile will prevail. Overall, the molecular mechanism of incipient shear banding as well as its evolution to steady shear banding or to a linear velocity profile (transient shear banding) is described for the first time. Moreover, our findings are in agreement with a host of prior step-strain and start-up experiments with synthetic and natural Deoxyribonucleic acid (DNA) entangled polymeric fluids.In this study, we have elucidated the molecular origin of shear banding in the entangled polymeric melts. Specifically, it is shown that the inflection point corresponding to the stress-overshoot indicates the possibility of inhomogeneity and this combined with slow orientation relaxation in step-strain start-up experiments will lead to formation of local inhomogeneity along the velocity gradient direction. Once the aforementioned inhomogeneities are created, a localized jump in entanglement density and a commensurate jump in normal stress and viscosity will lead to formation of the incipient shear banded flow structure. To this end, number of step-strain and start-up simulations with different deformation rate ramp times in the planar Couette flow with entanglement densities ⟨Zk⟩ ≥ 17 were performed to demonstrate the effect of deformation rate ramp time on the formation of local inhomogeneities and occurrence of shear banding. It has been demonstrated that if the time scale for the deformation rate to r...

Shear banding in nematogenic fluids with oscillating orientational dynamics.

We investigate the occurrence of shear banding in nematogenic fluids under planar Couette flow, based on mesoscopic dynamical equations for the orientational order parameter and the shear stress. We focus on parameter values where the sheared homogeneous system exhibits regular oscillatory orientational dynamics, whereas the equilibrium system is either isotropic (albeit close to the isotropic-nematic transition) or deep in its nematic phase. The numerical calculations are restricted to spatial variations in shear gradient direction. We find several new types of shear-banded states characterized by regions with regular oscillatory orientational dynamics. In all cases shear banding is accompanied by a non-monotonicity of the flow curve of the homogeneous system; however, only in the case of the initially isotropic system this curve has the typical S-like shape. We also analyze the influence of different orientational boundary conditions and of the spatial correlation length.

DEM-aided study of shear band formation in dip-slip faulting through granular soils

A GPU-based two-dimensional discrete element methodology allowing for grain rolling resistance is adopted to study the engineering and fundamental aspects of shear band formation in normal and reverse faulting through an initially dense sand; of course, the paper emphasizes on fundamental aspects. The employed DEM modeling methodology is verified with the experimental results and FEM prediction of the pattern of shear bands developed through a trap-door centrifuge model test. Regarding the engineering aspects, a parametric study is carried out and the obtained results from the DEM simulations are compared with the experimental results. Concerning the fundamental aspects, various micro and macro aspects of shear banding, such as void ratio and coordination number, the evolution of particle-scale energies and second order work within the localized areas along the shear bands are studied. Moreover, a link is established between the micro and macro events occurring inside the shear bands. Regarding the engineering results, the analyses show that the reverse fault ruptures may deviate toward the hanging wall or footing wall, depending on the faulting angle; however, the primary and secondary normal fault ruptures refract at the soil–bedrock interface, deviating toward the hanging wall. Regarding the fundamental results, the analyses show that the pre-failure disintegration of strong contacts whose directions are aligned between the minimum principal strain and zero-extension line directions within the localized areas plays a fundamental role in the development of shear bands at micro scale. This leads to the local rotation (buckling) of columnar chains within shear bands at failure, being associated with a softening behavior, development of large voids, generation of high particle rotation gradients, rapid decrease of internal energy and rapid increase of dissipated energy within the shear bands at macro scale. In addition, the rolling mechanism plays a significant role in energy dissipation within the shear bands even though the sliding mechanism has a dominant role. Furthermore, the second order work becomes negative within the localized areas by the occurrence of shear banding.

Texture evolution of AZ31 magnesium alloy sheets during warm rolling

The purpose of this study was to examine the microstructure and texture evolution of a twin roll cast AZ31 magnesium alloy after multi-pass warm rolling in a temperature range from 233 to 248°C. Reduction per pass was kept constant at about 10% and the total reduction was 98.2% after 33 pass steps with a change of sheet thickness from initially 2.85mm down to 50μm. The rolled sheets exhibited a fairly strong basal texture with an intensity of 17–21 multiples of random distribution (MRD) in the initial stages (with a thickness above 0.47mm) due to the lower rolling temperatures. The basal texture intensity decreased to 13–15 MRD in the later stages (with a thickness below 0.3mm) due to the occurrence of dynamic recrystallization at slightly higher rolling temperatures to balance out the demand of rolling force. The basal pole in the thicker sheets spread slightly along ±TD with an ellipse shape mainly due to the activation of 〈a〉 prismatic slip and the occurrence of shear bands, while the splitting of basal pole in the thinner sheets was observed to be along the RD with a tilting angle of about ±10°. This was attributed to the activation of 〈a+c〉 pyramidal slip. The average grain size in the thinner sheets in the later stages during the multi-pass rolling decreased almost linearly with increasing number of rolling steps. This could be explained via a change in the Zener–Hollomon parameter which was associated with the strain rate affected by the sheet thickness during rolling at a constant percent reduction.

Shear banding and its contribution to texture evolution in rotated Goss orientations of BCC structured materials

Due to progressive deformation, the dislocation densities in crystals are accumulated and the resistance of grains to further deformation increases. Homogeneous deformation becomes energetically less favorable, which may result for some orientations in strain localization. In-grain shear banding, a typical kind of localized deformation in metals with BCC crystal structure, has been accounted for by the geometric softening of crystals. In this study, the occurrence of shear bands in rotated Goss ({110}<110>) orientations of Fe-Si steel is predicted by crystal plasticity simulations and validated by EBSD measurements. It was observed and confirmed by crystal plasticity modeling that such shear bands exhibit stable cube orientations The orientation evolution of crystals in shear bands and its impact on annealing texture of materials are also described.

Effect of stacking fault energy and strain rate on the mechanical properties of Cu and Cu alloys

The effect of stacking fault energy (SFE) and strain rate on the mechanical properties of Cu, Cu–10wt%Zn and Cu–20wt%Zn alloys prepared by rolling and Split Hopkinson Pressure Bar (SHPB) impact has been investigated. Using tensile tests, we demonstrated that the Cu and Cu alloys exhibited a combination of significantly enhanced strength and ductility with decreasing SFE when the samples were deformed at the same quasi-static strain rate of rolling. Meanwhile, the Cu and Cu alloys exhibited slightly higher strength and remarkably better ductility when the materials were deformed by rolling at a quasi-static strain rate (10−4–10−2s−1), compared to the materials deformed by SHPB at a dynamic strain rate (104s−1) with the same SFE. The Cu and Cu alloys processed at the high strain rate resulted in the occurrence of shear bands and fractures, which led to a decrease in both the strength and ductility of the materials.

A micromechanics-based model for estimating localized failure with effects of fabric anisotropy

This paper presents a micromechanics-based approach to investigate the effects of fabric anisotropy on the behavior of localized failure in granular materials. Based on a micromechanical analysis, the origin of deviatoric stress is decomposed into two components: contact force anisotropy and fabric anisotropy. Using a micro–macro approach, the back stress is interpreted as an contribution to the change of the fabric’s principal direction. The evolution of the back stress is deduced from the stress–fabric relationship and determined with reference to the deviation of the principal directions between the rate of the reduced stress tensor and the actual reduced stress tensor. With this micro–macro framework, a mixed (isotropic–kinematic) hardening model is developed based on the classical isotropic hardening theory. A laboratory simple shear test is first analyzed to validate the proposed model and illustrate the kinematic-hardening mechanism which is usually displayed under non-proportional loading. The analysis further focuses on the anisotropic aspect of localized failure. It has been discovered that the fabric anisotropy can play an important role in the occurrence of shear banding. An increasing degree of fabric anisotropy tends to delay the initiation of the strain localization and result in higher failure strength. The effects of fabric anisotropy have also been illustrated by comparing the theoretical predictions and measured results on the shear band inclination angle, shear strain level and dilatancy at bifurcation.

Occurrence of shear bands in rotated Goss ({1 1 0}〈1 1 0〉) orientations of metals with bcc crystal structure

The occurrence of shear bands in the rotated Goss ({1 1 0}〈1 1 0〉) orientation of Fe–1.2 wt.% Si alloy was investigated by the hypothesis of the geometric softening mechanism. The reduction of Taylor factor and the orientation evolution of in-band crystals were calculated by applying the full-constraints Taylor crystal plasticity model. The presence of in-grain shear bands and particularly the Cube-oriented crystal volumes in shear bands was predicted by the models and confirmed by experimental electron backscattered diffraction observation.

Non-linear oscillatory rheological properties of a generic continuum foam model: Comparison with experiments and shear-banding predictions

The occurrence of shear bands in a complex fluid is generally understood as resulting from a structural evolution of the material under shear, which leads (from a theoretical perspective) to a non-monotonic stationary flow curve related to the coexistence of different states of the material under shear. In this paper we present a scenario for shear-banding in a particular class of complex fluids, namely foams and concentrated emulsions, which differs from other scenarios in two important ways. First, the appearance of shear bands is shown to be possible both without any intrinsic physical evolution of the material (e.g. via a parameter coupled to the flow such as concentration or entanglements) and without any finite critical shear rate below which the flow does not remain stationary and homogeneous. Secondly, the appearance of shear bands depends on the initial conditions, i.e. the preparation of the material. In other words, it is history dependent. This behaviour relies on the tensorial character of the underlying model (2D or 3D) and is triggered by an initially inhomogeneous strain distribution in the material. The shear rate displays a discontinuity at the band boundary whose amplitude is history dependent and thus depends on the sample preparation.

Atomistic free-volume zones and inelastic deformation of metallic glasses

The amorphous nature of metallic glasses and their mechanical properties make them interesting for structural applications. However, the interplay between the nature of atomic structures in metallic glasses and mechanical properties remains poorly understood. In this study, high-frequency dynamic micropillar tests have been used to probe both atomic clusters and flow defects in metallic glasses. We show that loosely bonded atomistic free-volume zones that are enveloped elastically by tightly bonded atomic clusters show a deformation character similar to supercooled liquids. At room temperature, the effective viscosity of these free-volume zones is of the order of 1 x 10(8) Pa s before the occurrence of shear banding. The confined liquid-like deformation of free-volume zones leads to significant mechanical hysteresis in micropillars under dynamic loading, providing important insight into how atomistic structural features affect the deformation behaviours in metallic glasses in the apparent elastic regime. The inelastic behaviour also serves as the basis for the superior damping resistance of metallic glasses.

Microstructural and Textural Aspects of Shear Banding in Plane Strain Deformed Fcc Metals

Periodic crystal lattice rotations within compact clusters of shear bands, developed in copper, have been characterized over a range of scales by optical microscopy, high resolution FEG-SEM-EBSD and TEM orientation mapping, to examine the role of local lattice re-orientation on slip propagation across pre-existing barriers to dislocation motion. Two different cases were analysed in detail. The single crystal analysis addresses the relation between the crystallographic microtexture and microstructure development due to the crystal anisotropy after a strain path change. All the changes in strain path directly lead to crystallite subdivisions and strain localization in the form of macroscopically visible bands of different morphology at the micro scale. The elongated cell substructure formed during primary straining was the source of anisotropy after changing deformation path. It is thought that the presence of this structure (here subcells) as barriers to dislocation motion is crucial for the occurrence of shear banding. The analysis of pure polycrystalline copper has been focused on the influence of local lattice re-orientations within particular grains on slip propagation across grain boundaries. The crystal lattice rotated in such a way that one of the {111} slip planes became nearly parallel to the direction of maximum shear (due to the actual state of anisotropy). A natural consequence of this rotation was the formation of a specific microtexture which facilitated slip propagation across grain boundaries.

Strain localization analysis using a large deformation anisotropic elastic–plastic model coupled with damage

Sheet metal forming processes generally involve large deformations together with complex loading sequences. In order to improve numerical simulation predictions of sheet part forming, physically-based constitutive models are often required. The main objective of this paper is to analyze the strain localization phenomenon during the plastic deformation of sheet metals in the context of such advanced constitutive models. Most often, an accurate prediction of localization requires damage to be considered in the finite element simulation. For this purpose, an advanced, anisotropic elastic–plastic model, formulated within the large strain framework and taking strain-path changes into account, has been coupled with an isotropic damage model. This coupling is carried out within the framework of continuum damage mechanics. In order to detect the strain localization during sheet metal forming, Rice’s localization criterion has been considered, thus predicting the limit strains at the occurrence of shear bands as well as their orientation. The coupled elastic–plastic-damage model has been implemented in Abaqus/implicit. The application of the model to the prediction of Forming Limit Diagrams (FLDs) provided results that are consistent with the literature and emphasized the impact of the hardening model on the strain-path dependency of the FLD. The fully three-dimensional formulation adopted in the numerical development allowed for some new results – e.g. the out-of-plane orientation of the normal to the localization band, as well as more realistic values for its in-plane orientation.

Identification of Simple Shear in Plane Strain Deformation

A theoretical analysis of plane strain incompressible velocity fields is first carried out. Two types of local fields are distinguished according to the sign of det(L), where L is the velocity gradient tensor, whereas det(L)=0 is associated with simple shear. A geometrical interpretation is used to illustrate the various decompositions of L. Finally, it is suggested that the condition det(L)=0 can be used to predict the occurrence of shear bands during metal forming processes.