Stable Shear Bands Research Articles

A Comparison of Plasticity Regularization Approaches for Geodynamic Modeling

AbstractThe emergence, geometry and activation of faults are intrinsically linked to frictional rheology. The latter is thus a central element in geodynamic simulations which aim at modeling the generation and evolution of fault zones and plate boundaries. However, resolving frictional strain localization in geodynamic models is problematic. In simulations, equilibrium cannot always be attained and results can depend on mesh resolution. Spatial and temporal regularization techniques have been developed to alleviate these issues. Herein, we investigate three popular regularization techniques, namely viscoplasticity, gradient plasticity and the use of a Cosserat continuum. These techniques have been implemented in a single framework based on an accelerated pseudo‐transient solution strategy. The latter allows to explore the effects of regularization on shear banding using the same code and model configuration. We have used model configurations that involve three levels of complexity: from the emergence of a single isolated shear band to the visco‐elasto‐plastic stress buildup of a crust. All considered approaches allow to resolve shear banding, provide convergence upon mesh refinement and satisfaction of equilibrium. Viscoplastic regularization is straightforward to implement in geodynamic codes. Nevertheless, more stable shear banding patterns and strength estimates are achieved with computationally more expensive gradient and Cosserat‐type regularizations. We discuss the relative benefits of these techniques and their combinations for geodynamic modeling. Emphasis is put on the potential of Cosserat‐type media for geodynamic applications.

Achieving high strength and high electrical conductivity in Cu-Cr-Zr alloy by modifying shear banding during rolling

An economical and practical thermomechanical process that is able to achieve a good combination of strength and conductivity is highly desired for the copper alloys. Here, a new multi-stage thermomechanical treatment, characterized by a pre-rolling with small strain followed by a short-time aging before the secondary rolling and aging, is implemented in the Cu-Cr-Zr alloys. Its effect on the mechanical and electrical properties of the alloy is investigated, as well as the mechanism for improving the properties. Strength and ductility are improved at the expense of only a little electrical conductivity compared to those alloys that have undergone conventional single-stage thermomechanical treatment. The pre-rolling and pre-aging result in dense, dispersive and stable shear bands, which contain lots of dislocations and fine grains. Dislocation strengthening is the main reason for the increased yield strength, while heterostructure consisting of microstructures inside and outside the shear bands gives the processed alloys good tensile plasticity. Our studies shed some lights on development of a short and cost saving thermomechanical process for the Cu-Cr-Zr alloys.

Shear band stability and uniform elongation of gradient structured material: Role of lateral constraint

Here we report a shear bands-dominated deformation principle for the gradient material composed of two nanostructured gradient layers (NGLs) and a coarse-grained (CG) interior. Multiple shear bands form in the NGL to accommodate the applied strain. The magnitude of uniform elongation depends on shear band stability, and shear band stability is determined by the intensity of constraint between NGL and CG interior. Specifically, the stronger the constraint, the denser and more stable the shear bands dispersed in the NGL, thereby leading to larger uniform elongation. This finding sheds insight into the theoretical basis of harnessing dispersed stable shear bands in heterostructures by optimizing microstructure architecture.

Dense dispersed shear bands in gradient-structured Ni

During tensile deformation, nanostructured (NS) metals often fail soon after yielding by forming a localized shear band. Here we report the observation of high density of shear bands that are homogeneously dispersed in the NS layer of a gradient Ni sample. These shear bands were nucleated at early elastic/plastic strain stage, reached number saturation at ∼3% strain, and remained arrested by the central coarse-grained (CG) matrix during the entire plastic deformation, resulting in a uniform tensile plasticity comparable to that of CG matrix. The formation of dispersed shear bands was promoted by the elastic/plastic interaction between NS surface layer and CG matrix, and affected by the surface roughness and the hardness variation in the NS surface layer. The width of shear bands remained constant, but the intensity of strain accumulation increased almost linearly with applied tensile strain, suggesting a stable shear banding process. Microstructure examination revealed that the strain in shear bands was accommodated by mechanically driven grain boundary migration and grain coarsening. These results clarify the fundamental questions: why/how does the NS layer supported by CG matrix achieve large uniform elongation? Moreover, the findings demonstrate the possibility of activating dispersed stable shear bands by synthesizing gradient architecture for optimized mechanical performances, i.e., a new strategy for evading the strength-ductility tradeoff in NS metals.

Accelerating heterogeneous nucleation to increase hardness and electrical conductivity by deformation prior to ageing for Cu-4 at.% Ti alloy

ABSTRACTDeformation bands, especially shear bands were intentionally formed in supersaturated Cu-4 at.% Ti alloy by groove-rolling with 75% area reduction. Cold deformation prior to the ageing process changed the precipitation behaviour of the alloy. The deformed structure with shear bands was maintained, without showing recovery and recrystallisation, even after prolonged ageing at 450°C for more than one day. The thermally stable shear bands act as nucleation initiation sites and prevent the expansion of discontinuous cellular precipitates. The hardness reached a value of 305 Hv and an electrical conductivity of 15% IACS (IACS = International Annealed Copper Standard. 100% IACS is defined as the conductivity corresponding to a volume resistivity at 20°C of 17.241 nΩ), compared to 283 Hv and 13% IACS for conventional solid-solutioned and peak-hardened alloy. In addition, the ageing time to reach the highest hardness was shortened from 720 to 180 min at 450°C.

Role of particle crushing on particle kinematics and shear banding in granular materials

The paper provides an in-depth exploration of the role of particle crushing on particle kinematics and shear banding in sheared granular materials. As a two-dimensional approximation, a crushable granular material may be represented by an assembly of irregularly shaped polygons to include shape diversity of realistic granular materials. Particle assemblies are subjected to biaxial shearing under flexible boundary conditions. With increasing percentage of crushed particles, mesoscale deformation becomes increasingly unstable. Fragmented deformation patterns within the granular assemblies are unable to form stable and distinct shear bands. This is confirmed by the sparsity of large fluctuating velocities in highly crushable assemblies. Without generating distinct shear bands, deformation patterns and failure modes of a highly crushable assembly are similar to those of loose particle assemblies, which are regarded as diffuse deformation. High degrees of spatial association amongst the kinematical quantities confirm the key role that non-affine deformation and particle rotation play in the generation of shear bands. Therefore, particle kinematical quantities can be used to predict the onset and subsequent development of shear zones, which are generally marked by increased particle kinematic activity, such as intense particle rotation and high granular temperature. Our results indicate that shear band thickness increases, and its speed of development slows down, with increasing percentage of crushed particles. As particles crush, spatial force correlation becomes weaker, indicating a more diffuse nature of force transmission across particle contacts.

Stability of shear banding process in bulk metallic glasses and composites

Abstract

Ideal shear banding in metallic glass

As the most fundamental deformation mechanism in metallic glasses (MGs), the shear banding has attracted a lot of attention and interest over the years. However, the intrinsic properties of the shear band are affected and even substantially changed by the influence of non-rigid testing machine that cannot be completely removed in real compression tests. In particular, the duration of the shear banding event is prolonged due to the recovery of the stressed compliant frame of testing machine and therefore the temperature rise at the operating shear band is, more or less, underestimated in previous literatures. In this study, we propose a model for the ‘ideal’ shear banding in metallic glass. The compliance of the testing machine is eliminated, and the intrinsic shear banding process is extracted and investigated. Two important physical parameters, the sliding speed and the temperature of shear band, are calculated and analysed on the basis of the thermo-mechanical coupling. Strain-rate hardening is proposed to compensate thermal softening and stabilise the shear band. The maximum value of the sliding speed is found to be on the order of 10 m/s at least, and the critical temperature at which strain-rate hardening begins to take effect should reach as high as 0.9Tg (Tg is the glass transition temperature) for a stable shear banding event in metallic glass according to the early experimental data. This model can help to understand and control the shear banding and therefore the deformation in MGs.

Flaw tolerance of metallic glasses

The flaw tolerance of bulk metallic glasses (BMGs) is evaluated using a thermoplastic synthesis approach. We found that flaw tolerance quantified by the notch toughness decreases apparently with decreasing radius until a critical value. Below this critical value, measured notch toughness is independent of its radius, revealing a flaw tolerance behavior of BMGs. We explain such flaw tolerance by a critical plastic zone originating from the BMGs' inherent crack tip blunting capability. This zone defines a characteristic distance over which stable shear banding plastic process develops prior to fracture instability. The specific characteristic distance and crack blunting capability vary widely among BMGs, which rationalizes the vast variety in their fracture behavior and suggest specific flaw tolerance. Our finding is encouraging for BMGs' structural applications since flaws smaller than the critical value are increasingly difficult to avoid but are “indistinguishable” in their influence to fracture toughness.

The material-dependence of plasticity in metallic glasses: An origin from shear band thermology

The material origin of plasticity in metallic glasses is a puzzled question for decades. In this work, we tackled this question from a perspective of excessive heating. With a simultaneous heat generation and dissipation model to describe the spatial and temporal distribution of temperature-rise in shear bands, an upper bound of temperature-rise of about tens of Kelvins was noticed for the reported stable shear banding. These results implied the fracture of metallic glasses being triggered at some critical temperature-rise. Based on the thermal property data of a series of bulk metallic glasses (BMGs) with different plasticity, a trend of low temperature-rise in large plasticity BMGs was revealed. A new material-dependent parameter based on thermal properties was then suggested to estimate or predict the plasticity in metallic glasses. This study provides a reasonable physical picture to understand the origin of BMGs' fracture and their different plasticity, which sheds a light to the understanding of the complex mechanical properties of these materials.

Strength softening at shear bands in metallic glasses

The plasticity of metallic glasses (MGs) is mediated by localized shearing in thin bands, degrading the mechanical properties at shear bands (SBs), which can cause shear localization and poor deformability. Quantifying the strength loss at SBs in MGs is important for both further material improvement and failure prediction. By applying a combination of microscale bending with in situ tensile tests, we successfully determine the strength loss at SBs in two typical MGs, namely Zr41Ti14Cu12.5Ni10Be22.5 and (Cu50Zr50)95Al5, that are about 20% lower than those of their intact counterparts. We further notice, based on fractographic examinations, that stable SBs may induce only a negligible heat, but unstable SBs give rise to a high temperature increase in SBs. This observation sheds light on the controversy about whether SBs in MGs must be hot.

Plasticity in Cu(111)/Cu46Zr54 glass nanolaminates under uniaxial compression

We perform large-scale molecular dynamics simulations to investigate plasticity in Cu/Cu46Zr54 glass nanolaminates under uniaxial compression. Partial and full dislocations are observed in the Cu layers, and screw dislocations are seen near the amorphous-crystalline interfaces (ACIs). Nucleation of shear bands in a glass layer is directly induced by the dislocations in the neighboring crystalline Cu layer through ACIs, and they grow from the ACIs into the glass layer and absorb ambient shear transformation zones. Plasticity in the glass layers is realized via pronounced, stable shear banding.

Dual character of stable shear banding in bulk metallic glasses

In this work, a systematical study of the stable shear banding behavior is performed across a wide range of alloy compositions of bulk metallic glasses (BMGs). Through microcompression, it can be demonstrated that the stable shear banding behavior could exhibit a dual character of stochastic and deterministic propagations. Different from the stochastic character, which is found insensitive to sample sizes, the deterministic character displays a clear trend of a sample size effect, which can be captured by the energy balance principle. Based on the theoretical framework laid out in this work, a correlation between the plastic energy dissipation and the sample size effect is established, which can be then utilized to explore the influence of the alloy’s chemical compositions on the behavior of shear-induced material softening. Finally, the energy-based formalisms aimed to quantify the shear banding size effect in MGs are discussed.

Steady-state shear banding in entangled polymers?

Velocity profiles of highly entangled polymer solutions under shear have been measured using particle tracking velocimetry to ascertain whether steady-state shear banding occurs in these samples. Under controlled torque flow, the velocity profile becomes nonlinear and the shear rate starts to rise when the true shear strain reaches about 2.5, suggesting that the shear rate rise is initiated by chain alignment and/or disentanglement. At long times, the velocity profile can become either smoothly curved or sharply banded for the same sample in the same geometry, implying that shear banding is not a deterministic behavior as expected from a non-monotonic constitutive relation. It is suggested that the stable shear banding observed in the measured entangled polymer solution is not true steady-state shear banding but may be “trapped” transient banding.

Force and Flow Transition in Plowed Granular Media

We use plate drag to study the response of granular media to localized forcing as a function of volume fraction ϕ. A bifurcation in the force and flow occurs at the onset of dilatancy ϕc. Below ϕc rapid fluctuations in the drag force F(D) are observed. Above ϕc fluctuations in F(D) are periodic and increase in magnitude with ϕ. Velocity field measurements indicate that the bifurcation in F(D) results from the formation of stable shear bands above ϕc which are created and destroyed periodically during drag. A friction-based wedge flow model captures the dynamics for ϕ>ϕc.

Flow Velocity Profiles and Shear Banding Onset in a Semidilute Wormlike Micellar System under Couette Flow

Velocity profiles in Couette flow are measured in a wormlike micellar solution made of cetyltrimethylammonium bromide (CTAB), sodium salicylate (NaSal), and water, at R (= [NaSal]/[CTAB]) = 2 and at R = 4; [CTAB] = 100 mM. Velocity profiles were obtained by using a two-incident beam laser Doppler technique. Profiles reveal that one of the micellar solutions (R = 2) becomes heterogeneous a long time after flow inception, even at very low imposed shear rates. However, profiles do not correspond to what is expected for gradient shear banding, because the fluid splits in one section close to the moving cylinder where the local mean velocity depends linearly on the gap position and in a second section presenting important velocity fluctuations. Close to the static cylinder, there is a third section where the fluid does not flow; it behaves like a slipping block. On the other hand, at high imposed shear rates, the former slipping block flows and presents a linear profile. Here, velocity profiles are consistent with gradient shear banding. The onset of shear banding was observed. The picture of two stable shear bands separated by a thin steady interface is not always valid. Inhomogeneous flow could be observed, although it cannot be classified as shear banding. In addition, conditions can be found where, as shear rate is increased and before shear banding appears, instead of a thin interface, a fluctuating intermediate band can be observed. On the contrary, for the R = 4 solution, the flow never becomes heterogeneous even at high shear rates. Flow curves were measured in a Couette cell under shear rate control in two cases, when stress is sensed with the moving cylinder and when it is sensed with the static cylinder of the cell. Differences between the flow curves can be explained by using the velocity profiles for both solutions.

Stabilization of nonlinear velocity profiles in athermal systems undergoing planar shear flow

We perform molecular dynamics simulations of model frictionless granular systems undergoing boundary-driven planar shear flow in two spatial dimensions with the goal of developing a more complete understanding of how dense particulate systems respond to applied shear. In particular, we are interested in determining when these systems will possess linear velocity profiles and when they will develop highly localized velocity profiles in response to shear. In previous work on similar systems we showed that nonlinear velocity profiles form when the speed of the shearing boundary exceeds the speed of shear waves in the material. However, we find that nonlinear velocity profiles in these systems are unstable at very long times. The degree of nonlinearity slowly decreases in time; the velocity profiles become linear when the granular temperature and density profiles are uniform across the system at long times. We measure the time t(l) required for the velocity profiles to become linear and find that t(l) increases as a power law with the speed of the shearing boundary and increases rapidly as the packing fraction approaches random close packing. We also performed simulations in which differences in the granular temperature across the system were maintained by vertically vibrating one of the boundaries during shear flow. We find that nonlinear velocity profiles form and are stable at long times if the difference in the granular temperature across the system exceeds a threshold value that is comparable to the glass transition temperature in an equilibrium system at the same average density. Finally, the sheared and vibrated systems form stable shear bands, or highly localized velocity profiles, when the applied shear stress is lowered below the yield stress of the static part of the system.