Nucleation Of Shear Bands Research Articles

Programmable heterogeneous lamellar lattice architecture for dual mechanical protection

Shear bands frequently appear in lattice architectures subjected to compression, leading to an unstable stress-strain curve and global deformation. This deformation mechanism reduces their energy absorption and loading-bearing capacity and causes the architectures to prioritize mechanical protection of external components at the expense of the entire structure. Here, we leverage the design freedom offered by additive manufacturing and the geometrical relation of dual-phase nanolamellar crystals to fabricate heterogeneous lamellar lattice architectures consisting of body-centered cubic (BCC) and face-centered cubic (FCC) unit cells in alternating lamella. The lamellar lattice demonstrates more than 10 and 9 times higher specific energy absorption and energy absorption efficiency, respectively, compared to the BCC lattice. The drastic improvement arises as the nucleation of shear bands is inhibited by the discrete energy threshold for plastic buckling of adjacent heterogeneous lattice lamella during loading. Despite its lower density than the FCC lattice, the lamellar lattice exhibits significant enhancement in plateau stress and crushing force efficiency, attributed to the strengthening effect induced by simultaneous deformation of unit cells in the BCC lattice lamella and the resulting cushion shielding effect. The design improves the global mechanical properties, making lamellar lattices compare favorably against numerous materials proposed for mechanical protection. Additionally, it provides opportunities to program the local mechanical response, achieving programmable internal protection alongside overall external protection. This work provides a different route to design lattice architecture by combining internal and external dual mechanical protection, enabling a generation of multiple mechanical protectors in aerospace, automotive, and transportation fields.

A failure model for bulk metallic glass based on strain rate-correlated softening mechanism

Due to the amorphous nature of the bulk metallic glasses (BMGs), catastrophic fractures occur once the nucleation and propagation of shear bands occur, which is quite different from crystal materials. So far, the underlying mechanism of BMG failure behavior and its strain rate effect are still controversial. In this work, the quasi-static and dynamic compression experiments of Vit-1 BMG were carried out in a wide range of strain rates from 0.001 s−1 to 5000 s−1. The results show that the variation tendency of failure stress with strain rate can be divided into three stages. The quasi-static failure stress is insensitive to the change of strain rate with only almost constant free volume softening effect inside the material during the failure process. When entering dynamic loading stage, the failure stress decreases significantly, which is caused by a combination of increasing thermal softening and free volume softening effects. When the strain rate increases to the third stage, that is, over 2000 s−1, the failure stress and the softening effects basically remain unchanged. The transformation of failure mechanism is well confirmed by the micromorphology of fracture surfaces. Based on the experimental results, a concise empirical failure model is established, in which the failure stress is decomposed into softening and non-softening parts. The verification experiments show that the model can effectively predict the compression failure stress of BMG under different strain rates.

Two-stage work-hardening of a transformable B2-enhanced metallic glass composite by molecular dynamics simulation

The crystalline-amorphous interfaces play vital roles in affecting martensitic transformation, shear band nucleation and interface stability. Though both quasi-static and dynamic mechanical behaviors of shape memory enhanced bulk metallic glass composites have been studied via experiments, the atomic-level interactions among martensitic transformation, localized shear softening and interfacial strain concentration imposed by strain rate remain elusive. We employ molecular dynamics simulations to study strain rate effect on uniaxial compression behavior of transformable B2–CuZr enhanced bulk metallic glass composite. As strain rate increases, the proportion of martensitic transformation accelerates. During the competition among martensitic transformation induced-hardening, shear induced-softening and interface debonding, a two-stage work-hardening is observed, which is in agreement with experimental findings.

Nucleation mechanisms of shear bands in amorphous alumina

The origin of the plastic deformation in amorphous solids is a challenging issue unlike that of the plasticity in crystals. Plasticity in amorphous systems can occur by the nucleation and propagation of shear bands (SBs). In this work, we investigate the mechanical response of an amorphous alumina sample subjected to shear deformation via extensive molecular dynamics simulations. We find SBs form only within a certain range of parameter values, e.g., low quenching rates, low temperatures and high strain rates. In our proposed atomic-scale model shear transformation zones (STZs) first nucleate and act as precursors of SBs due to their high stress concentration. The results showed that STZs generate an anti-symmetric stress that is responsible for the vortex-like motion of atoms that facilitate the percolation of STZs, finally forming an SB. These results provide insight into the mechanisms of plastic deformation of similar amorphous solids.

High pressure suppression of plasticity due to an overabundance of shear embryo formation

High pressure shear band formation is a critical phenomenon in energetic materials due to its influence on both mechanical strength and mechanochemical activation. While shear banding is known to occur in a variety of these materials, the governing dynamics of the mechanisms are not well defined for molecular crystals. We conduct molecular dynamics simulations of shock wave induced shear band formation in the energetic material 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) to assess shear band nucleation processes. We find, that at high pressures, the initial formation sites for shear bands, “embryos”, form in excess and rapidly lower deviatoric stresses prior to shear band formation and growth. This results in the suppression of plastic deformation. A local cluster analysis is used to quantify and contrast this mechanism with a more typical shear banding seen at lower pressures. These results demonstrate a mechanism that is reversible in nature and that supersedes shear band formation at increased pressures. We anticipate that these results will have a broad impact on the modeling and development of high-strain rate application materials such as those for high explosives and hypersonic systems.

Effect of initial grain size on the recrystallization behavior and recrystallization texture of a Mg–3Gd alloy

The effect of initial grain size on the recrystallization and recrystallization texture of a rolled Mg–3Gd (wt.%) alloy is studied in detail. The results show that the deformation microstructure of an initially coarse-grained (CG) sample has a larger twinned area and a higher density of twin boundaries than a fine-grained (FG) sample. After annealing, the CG sample recrystallizes preferentially in the twinned area, whereas the FG sample adopts the higher density grain boundaries as the nucleation sites. Furthermore, weak recrystallization texture components appear from the grain nucleation stage, regardless of the initial grain size, and are preserved after complete recrystallization due to uniform grain growth. The majority of recrystallization texture is deviated 20°–45° away from normal direction (ND), accounting for more than 50 %. Especially, the recrystallization texture of the FG sample is a “Rare Earth texture”, in contrast to the widely reported texture modification unrelated to grain boundary nucleation. Only a scattered basal texture is observed in the CG sample, which also differs from the reported “Rare Earth texture” originating from shear band nucleation in dilute Mg–Gd alloys. Finally, based on the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model, the recrystallization kinetics are calculated, and it is found that the initial grain size mainly affects the nucleation rate, and has limited effect on the grain growth rate.

Distinct avalanche dynamics detected in metallic glasses with high energy state revealing the crack-like shear banding mechanism

When a sufficiently high stress is applied to a metallic glass, causing plastic deformation, the material undergoes structural reconfiguration through dissipative slip avalanche events that release local stresses. By utilizing isothermal annealing and cold rolling techniques to tune the energy levels of metallic glasses, it has been observed that structural rejuvenation is accompanied by structural relaxation, as evidenced by distinct changes in avalanche dynamics. We present detailed statistics of the avalanche dynamics during shear band formation in energy-tuned metallic glasses, ranging from structurally relaxed to rejuvenated states. By analyzing shear band characteristics and examining scaling exponents, avalanche durations, and stress relaxation rates, we can establish a connection between the local activation of shear transformation zones and the formation of macroscopic shear bands. The statistics of avalanche duration indicate that an increase in soft zones within metallic glasses can alleviate stress release and stabilize plastic flow, as evidenced by the characteristics of shear bands. We attribute the significant transition of serrated flow, observed at different energy levels (i.e., as-cast, relaxed, and rejuvenated states) to the variations in nucleation and multiplication of shear bands that originate from local weak spots. Analysis of the distinct avalanche dynamics suggests that in lower energy level metallic glasses, the nucleation and propagation of shear bands exhibit localized crack-like behavior, while in higher energy level metallic glasses, they display diffused crack-like characteristics. Indeed, our results strongly support that the decreased avalanches observed in the high energy level metallic glasses originate from the nucleation of numerous small shear bands, which directly compete with the propagation of the main local shear band. These findings deepen our fundamental understanding of the relationship between the microscopic mechanism of slip avalanche dynamics and shear banding, providing a pathway to control the plasticity of metallic glasses.

Potential regulation of strength-ductility by nucleation and growth mechanisms of shear bands in heterogeneous laminates

Shear bands (SBs) expand rapidly in hard domains and are suppressed in soft domains, effectively improving the tensile plasticity of the material. Significant evolution of SBs during elastoplastic deformation exists in heterogeneous laminates (HLs). Molecular dynamics (MD) simulation results indicate that the activities of grain boundary (GB) and dislocation jointly mediate the nucleation and growth of SBs. SBs tend to nucleate near the interface, and then grow rapidly under the promotion of GB activities and dislocation slips, resulting in a rapid increase in plastic strain gradient. Ultimately, the density and morphology of SBs determine the magnitude of the plastic strain gradient. In structures with lower layer thickness, the band-like SBs are densely distributed, which achieves higher strain gradient strengthening capability. However, the interface serves as an accumulation site for geometrically necessary dislocations (GNDs), too low a layer thickness will induce overlapping of the interface-affected-zone (IAZ), thereby weakening the strain hardening efficiency. The simulations track the nucleation and growth of SBs at the atomic scale, and discover that the structure can better balance HL's strength and ductility when the layer thickness is three times the grain size of the soft domain.

Atomic insights on nanoindentation-induced plastic-deformation behavior of tetrahedral amorphous carbon film

The nanoindentation-induced deformation behavior of the Cr-doped diamond-like carbon (DLC) films was clarified with Cr concentration varying from 0 to 16.5 at.% by experiment and molecular dynamics simulation. The Cr-DLC films were fabricated by a direct cathode vacuum arc technique and Cr dopants existed in the form of stripes owing to the deposition features. Results showed the addition of Cr facilitated the transformation of sp3-C bonds to sp2-C bonds, resulting in a decrease of the hardness and elastic modulus. Especially, the sp2 nano-crystallites with the lamellar structure were found in the Cr (16.5 at.%)-DLC film. During nanoindentation, the ring-like cracking on the surface and lateral crack at the interface are exhibited in the Cr-free DLC film, while the introduction of Cr makes the DLC film alleviate the cracking trend. According to the atomic-scale analysis, Cr can significantly improve the plasticity of the DLC film because the Cr-rich cluster with a high free volume can facilitate the shear transformation zones percolation and the shear bands (SBs) nucleation by collective coordinated vortex-like movements of atoms. The Cr-free DLC film can hardly accommodate high plastic strain with very few fine SBs and blockage of the SBs.

Improvement of plastic property of Ti/Al nanowires by designing the core–shell structures

Ti alloy has the disadvantages of low elastic modulus, high yield ratio, and low plasticity, therefore, improving its plasticity is very important to promote their use. In this study, the tensile behavior of Ti/Al core–shell nanowires (NWs) in the z-axis direction of single-crystal Ti with [0001] grain-oriented HCP structure and single-crystal Al with [001] grain-oriented FCC structure was investigated using molecular dynamic (MD) simulations to explore the mechanism of enhanced ductility in Ti alloy. The results indicate that the shell thickness may significantly affect the mechanical behaviors of the NWs. For the mechanical properties of core–shell NWs, Young’s modulus, ultimate tensile strength (UTS), Specific modulus, Specific strength, flow stress, and fracture strain showed sensitivity to shell thickness. Compared with core–shell NWs, single crystal Ti NW has greater strength and higher Young’s modulus, Specific strength and UTS. By contrast, core–shell NWs have better Specific modulus and plastic properties, their flow stress and fracture strain are higher than those of single crystal Ti NW. For the single crystal Ti NW, the main plastic deformation mechanisms are shear band nucleation and recrystallization. For Ti/Al core–shell NWs with shell thicknesses of 1and 2 nm, the nucleation of the twin variants replaces the dominant position of the shear bands. As the twin boundaries (TBs) expand, the dislocation slip is activated, and grain reorientation occurs, inducing the superior plastic properties of NWs. As the shell thickness increases to 3–5 nm, the interaction between the twin variants and shear bands reduces the expansion rate of the TBs, resulting in increased flow stress and fracture strain of the NWs. This study can provide theoretical guidance for the experimental study and preparation of core–shell NWs.

Large deflection deformation behavior of a Zr-based bulk metallic glass for compliant spinal fixation application

A novel compliant spinal fixation designed based on the concept of compliant mechanisms can reduce the stress-shielding effect and adjacent segment degeneration (ASD) effectively, but propose higher requirements for the properties of the used materials. Bulk metallic glasses (BMGs), as a kind of young biomaterials, exhibiting excellent comprehensive properties, which are attractive for compliant spinal fixation. Here, according to the practical service condition of the basic elements in compliant spinal fixation, large deflection deformation behaviors of Zr61Ti2Cu25Al12 (at.%, ZT1) BMG beam, including elastic, yielding and plastic were investigated systematically. It was shown that the theoretical nonlinear analytical solution curve as the benchmark not only with the capacity to predict the nonlinear load-deflection relation within the elastic deformation regime, but also assists to capture the yielding event roughly, which can be used as a powerful design tool for engineers. To capture the beginning of the yielding event exactly, bending proof strength (σp,0.05%) accompanied with tiny permanent strain of 0.05% was proposed and determined for BMGs in biomedical implant applications, which is of significance for setting the allowable operating limits of the basic flexible elements. By approach of interrupted loading-unloading cycles, plastic deformation driven by the bending moment can be classified into two typical stages: the initial stage which mainly characterized by the nucleation and intense interaction of abundant shear bands when the plastic strain below the critical value, and the second stage which dominated by the progressive propagation of shear bands and coupled with the emergence of shear offsets on tensile side. The plasticity of BMG beam structures depends on the BMG's inherent plastic zone size (rp). When the half beam thickness less than that of the rp, the plastic deformation of BMGs will behave in a stable manner, which can be acted as the margin of safety effectively.

Microstructure evolution and recrystallization kinetics of Al-Cu-Li alloy during thermo-mechanical treatment with overaging and electrically-assisted annealing

An improved thermomechanical treatment (N-ITMT) containing electrically-assisted recrystallization annealing (EARA) was proposed for manufacturing fine-grained Al-Cu-Li alloys, based on overaging, cold asymmetric rolling and EARA. The corresponding microstructure evolution and mechanical properties were investigated. The coarse precipitates introduced by overaging changed the deformed microstructure, produced particle affected zones and weakened the shear band (SB) compared with that with no precipitates. The combined action of electric current and coarse precipitates completed the recrystallization within 5 s and the solution process within 180 s, refined the grain size, and improved the strength and ductility. Discontinuous static recrystallization (dSRX) and continuous static recrystallization (cSRX) were both considered recrystallization mechanisms for specimens with or without coarse precipitates. The dSRX for specimens with coarse precipitates mainly featured particle-stimulated nucleation (PSN), while it featured shear band nucleation for specimens with no precipitates. The athermal effect of electric current not only decreased the activation energy, increasing the nucleation rate during dSRX, but also accelerated the diffusion of atoms and vacancies, promoting recrystallization and solution treatment. The proposed N-ITMT containing EARA possesses the synergetic capacity of optimizing the microstructure and improving the strength and ductility of Al-Cu-Li alloys.

Structural mechanisms of enhanced mechanical property in ZrCu metallic glass at low temperatures

The application of traditional crystalline materials as structural materials cannot meet critical design challenges due to low-temperature brittleness. To address this issue, this study investigates the deformation behavior of Zr2Cu metallic glass (MG) model at ambient and low temperature states by molecular dynamics (MD) simulations to unravel the governing mechanisms associated with mechanical performance. Structurally representative amorphous models of the MG were developed and their evolutions under tensile loadings at ambient (300 K) and low temperatures (250 K, 200 K, 150 K, 100 K, 50 K) were captured. Notably, significant variations in maximum stress and corresponding strains characterized the stress-strain behavior as elastic-plastic properties increased with decreasing temperatures. Stress activations of the atomic mass were rapidly incipient at the ambient condition, but largely constrained at low temperatures by which the density variations of activated zones and the emerging strain of first shear transformation zones (STZ's) established a negative correlation with temperature as inferred by the wider strain range of deformation. Disparities in strain thresholds accounted for the higher free volume content at the ambient state, but as temperatures declined, fine structural differences stimulated the formation of densely-packed structures in the amorphous model at low temperatures by the spontaneous annihilation of excessive free volumes. Consequently, the higher growth rates of the average atomic potential energy and the retarded emergence of high-potential-energy atomic mass suggest that at low temperatures, there is a higher resistance to shear band nucleation and higher barrier for atomic migration. As a result, the generation of free volumes, formation of STZs and shear bands were retarded, leading to the enhanced ductility. Thus, at low temperatures, unique tuning mechanisms of structural performance were evolved in the amorphous model that suitably enhanced the constitutive properties of Zr2Cu MG.

Research progress on the shear band of metallic glasses

Metallic glasses have received considerable attention in the fields of materials science and condensed matter physics. The disordered structure of metallic glasses gives rise to unique mechanical properties, such as high strength, large elasticity and a distinct deformation mechanism in contrast to conventional crystalline alloys. The plastic deformation of metallic glasses at temperatures well below the glass transition is generally carried out through the formation of highly localized shear bands. Therefore, a thorough understanding of shear banding behavior is vital for improving the mechanical properties of metallic glasses and tailoring the properties of post-deformed metallic glasses. This review article aims to provide an up-to-date overview of the atomic mechanisms underlying shear band nucleation, propagation and interaction. Additionally, the dynamics of shear bands and their correlation with plasticity are also presented. This article also focuses on the progress in the fundamental structure and properties of mature shear bands, such as density fluctuation, medium-range order, shear-band affected zone, and diffusivity. Furthermore, the fracture mechanism based on the development of cavities is elaborated. Finally, we identify a number of key unsolved issues on this subject.

Unraveling structural relaxation induced ductile-to-brittle transition from perspective of shear band nucleation kinetics in metallic glass

Structural relaxation induced ductile to brittle transition seriously hampers the practical applications in metallic glasses. Although there have been many researches focusing on the hidden physical mechanism of ductile to brittle transition, the correlation between ductile to brittle transition and shear band nucleation kinetics is still unclear. In this work, by applying for one new studying strategy based on the nanoindentation, the evolution of the thermodynamic property, the macroscopic mechanical behavior and the corresponding shear band nucleation kinetics including the nucleation site type, the nucleation site density and the nucleation rate with annealing time at one Sub-glass transition temperature, were systematically investigated. We found that there appears one critical annealing state corresponding to the ductile to brittle transition and then the ductile-to-brittle transition induced by structural relaxation is the comprehensive result of the transition of the shear band nucleation mode, the nucleation site density and the nucleation rate. These results provide new enlightenment for the structural relaxation effect on the shear band nucleation and the macroscopic deformation behaviors, and for developing new metallic glasses with improved mechanical properties.

Twin boundary spacing and loading direction dependent tensile deformation of nano-twinned Al10(CrCoFeNi)90 high-entropy alloy: An atomic study

Experiments have shown that nanotwins play an important role in strengthening and toughening high-entropy alloys (HEAs), which are closely associated with twin boundary (TB) spacing. Understanding the TB spacing dependent deformation mechanisms is helpful to design strong and ductile HEAs. In this work, the TB spacing dependent tensile deformation of equiaxed- and columnar-grained Al10(CrCoFeNi)90 HEA with various TB spacings has been studied via molecular dynamics simulation. The results show that equiaxed-grained samples with nanotwins have higher strength than twin-free counterpart. De-twinning at small TB spacing softens equiaxed-grained samples, which is similar to that observed in nano-twinned Cu. However, for the columnar-grained samples, it is interesting to find that no softening occurs with decreasing TB spacing when the loading direction is parallel or vertical to TB. In the case of parallel loading, the main dislocation activities change from hairpin- to necklace-like dislocations with decreasing TB spacing, and this dislocation mode transformation leads to a slow-to-sharp-increase transition in strength. Our theoretical analysis indicates that the sharp increase in strength is related to the severe lattice distortion in HEAs which makes the de-pinning process of necklace-like dislocation unit difficult. In the case of vertical loading, the dominated dislocation motions shift from dislocation slipping in the twin and matrix regions to dislocation cutting through TBs as TB spacing decreases from 6.2 to 0.62 nm, the latter of which leads to shear bands nucleation and expansion. Yet, the strength still shows a monotonous increase due to the increasing difficulty of dislocation nucleation in the initial plastic deformation that produces significant strengthening.

Effect of loading orientation on plasticity in nano-laminated CoNiCrFeMn dual-phase high-entropy alloy: a molecular dynamics study

Dual-phase high-entropy alloys (DP-HEAs) have been proved to be a kind of promising materials that exhibit a combination of excellent strength and ductility. Previous studies have emphasized the effect of interface and phase volume fraction on mechanical performance in DP-HEAs. However, the deformation mechanisms such as interplays between dislocations and the constituent phases have not been fully understood. Particularly, the research concerning plastic anisotropy in DP-HEAs is still lacking. Here, molecular dynamics simulations are performed to probe the effect of loading orientation on plasticity in the nano-laminated face-centered cubic (FCC)/hexagonal close-packed (HCP) CoNiCrFeMn DP-HEA. Results reveal that a switch from strengthening to softening and back to strengthening is closely related to the activation of different slip systems when tailoring the inclination angles of the nanolaminates with respect to the tensile direction from 0° to 90°. Slip transfer across phase boundaries, phase transformation and the nucleation of shear bands dominate the plasticity in the samples with low, medium and high inclination angles, respectively. Furthermore, the evolution of microstructures, such as dislocations, stacking faults, and FCC/HCP phase are analyzed to study the underlying deformation mechanisms. These results can help understand the plastic anisotropy of DP-HEAs and design alloys with excellent mechanical properties for engineering applications.

Mechanical size effect and serrated flow of various Zr-based bulk metallic glasses

Despite superior mechanical properties, the cross-scale mechanical properties of Zr-based bulk metallic glasses (BMGs) are urgent to be revealed. Depth-sensitive nanoindentation technique was employed to directly investigate the significant depth-dependent mechanical properties of three kinds of Zr-based BMGs. Specifically, the surface hardness H and elastic modulus E are verified to increase with the decrease of indentation depth while the fracture toughness KIC decreases with the indentation depth. The mechanical size effect is closely related to the evolution of shear bands at various indentation depths, which can be equivalently revealed by the distribution of serrated flow. Based on a relatively shallow indentation depth, the comparatively minor stress gradient established inside the micro-region underneath the indenter tip induces insufficient activation energy of shear bands, which prevents the nucleation of shear bands and further restricts plastic deformation, and ultimately results in enhanced surface hardness and elastic modulus but reduced fracture toughness. In addition, the shear band morphology of residual indentation and the stress distribution obtained from the finite element simulation provide integral evidence in support of the depth-induced mechanical size effect.

Modulating mechanical performances of metallic amorphous materials through phase gradient

Increasing strength is usually at the cost of sacrificing ductility in structural materials. The tradeoff becomes even conspicuous in a category of metallic amorphous materials, the so-called metallic glasses (MGs) featured without any atomic-scale translational symmetry. Therefore, there remains little room for simultaneous optimization of strength and ductility in MGs through tailoring the morphology and kinetics of structural imperfections. Here we propose an alternative strategy for modulating the mechanical properties of MGs through introducing proper content of compositional or phase gradient inspired by the mechanistic strain gradient theory. We design two types of CuZr-based phase gradient metallic glasses (PGMGs) with different compositional concentration gradient directions in either continuous or stepped gradient form. Extensive molecular dynamics simulations demonstrate that phase gradient raises the concentration of mechanically stable icosahedral and icosahedron-like Voronoi polyhedra and, thus, increases the strength of MGs. In terms of plastic deformation, free volume mismatch between phases invalidates the autocatalytic activation mechanism of shear transformation zones, resulting in greater resistance to shear band propagation. The phase gradient also encourages branches of shear band and nucleation of multiple shear bands, which mechanism delocalizes deformation and postpones failure. These mechanisms lead to an improvement in the overall ductility of the PGMGs. The present strategy sheds light on evading the long-standing strength-ductility tradeoff in amorphous metals through extrinsic chemical and geometrical modulation that can be handled by appropriate thermal processing and fabrication technique.

Recrystallization Behavior of Warm Rolling and Cold Rolling Cr-Ti-B Steel during Annealing

To study the nucleation and recrystallization behavior of deformation bands, shear bands and grain boundaries during the recrystallization process, a heat treatment test was carried out on Cr-Ti-B low-carbon steel after warm rolling and cold rolling. The results show that recrystallization occurs preferentially in shear bands and grain boundaries. The γ deformation texture can be enhanced and the Goss texture can be weakened during the warm rolling and subsequent cold rolling process. Recrystallization of the deformation bands was observed, but the nucleation time of recrystallization in the deformation band is much slower than that in the shear band and grain boundary.