The formation of multiple adiabatic shear bands

In a previous paper, Zhou et al. [2006. A numerical methodology for investigating adiabatic shear band formation. J. Mech. Phys. Solids, 54, 904-926] developed a numerical method for analyzing one-dimensional deformation of thermoviscoplastic materials. The method uses a second order algorithm for integration along characteristic lines, and computes the plastic flow after complete localization with high resolution and efficiency. We apply this numerical scheme to analyze localization in a thermoviscoplastic material where multiple shear bands are allowed to form at random locations in a large specimen. As a shear band develops, it unloads neighboring regions and interacts with other bands. Beginning with a random distribution of imperfections, which might be imagined as arising qualitatively from the microstructure, we obtain the average spacing of shear bands through calculations and compare our results with previously existing theoretical estimates. It is found that the spacing between nucleating shear bands follows the perturbation theory due to Wright and Ockendon [1996. A scaling law for the effect of inertia on the formation of adiabatic shear bands. Int. J. Plasticity 12, 927-934], whereas the spacing between mature shear bands is closer to that predicted by the momentum diffusion theory of Grady and Kipp [1987. The growth of unstable thermoplastic shear with application to steady-wave shock compression in solids. J. Mech. Phys. Solids 35, 95-119]. Scaling laws for the dependence of band spacing on material parameters differ in many respects from either theory.     

粉末烧结钨合金材料的绝热剪切研究

在分离式霍普金森压杆装置上对斜圆柱粉末烧结钨合金试件进行了冲击实验,由于斜圆柱结构中剪切分量在冲击压缩中的持续作用,实验中观察到了宏观破断现象。利用光学显微镜和扫描电子显微镜分别对试件断面和试件的纵截面进行了分析,观察到了贯通钨颗粒的绝热剪切带这一变形局部化现象。对粉末烧结钨合金绝热剪切破坏机制进行了分析。     

Shear band formation in thermo-viscoplastic solids under plane strain compression

The plane strain compression of a rectangular block is numerically investigated for the study of dynamic shear band development in thermo-elasto-viscoplastic materials from an internal inhomogeneity. As expected, it plays an important role in triggering the onset of shear, localization as well as thermal softening. And the competition between the strain, strain-rate hardening and thermal softening exists throughout the process. It is found that shear band develops at a 45-degree angle to the compression axis. In the light of given patterns of deformation and temperature, shear band evolution accelerated by thermal softening is retarded by the inertial effects. Interestingly, a similar temperature band is also formed along the trajectory of the localized deformation band. The calculations also show the energy evolution during the coupled thermo-mechanical process of shear band propagation. Finally, the mesh effect is discussed in terms of the numerical results from two different meshes. The project is supported by the National Natural Sciences Foundation of China.     

The growth of shear bands in composite microstructures

Shear band formation in materials with inhomogeneous and composite microstructures is influenced by factors that usually do not come into play in monolithic materials. Experiments and calculations have shown that inhomogeneities in material properties enhance the localization of deformation. This investigation concerns the propagation of shear bands in a two-phase tungsten composite under the conditions of nominally pure shear deformation. Finite element calculations are carried out to delineate the effects of different grain–matrix morphologies. In the numerical models, the initiation of shear bands is triggered by a notch, simulating the effect of defects such as microcracks and microvoids in materials. Calculations demonstrate that phase morphology, particle size and the relative location of initiation site have significant influences on the development of localized deformation. The work and energy evolutions are tracked for each constituent phase in the microstructures. In addition, the exchange of thermal energy through heat flow between the phases is analyzed. The results show that a strong correlation exists between the course of shear band propagation and the thermomechanical coupling between microscopic phases.     

Evolution of shear bands in bulk metallic glasses under dynamic loading

Shear band spacing in Zr-based bulk metallic glasses (BMGs) under dynamic loads is found to vary with position and local strain rate in the indented region. To investigate the dependence of shear band evolution characteristics on local strain rate and normal stress, a micromechanical model based on momentum diffusion is proposed. The thermo-mechanical model takes into account the normal stress dependence of yield stress, the free volume theory and the associated viscosity change within the shear band region. Temperature rise is obtained from the balance between the heat diffusion to the adjacent regions from a shear band and the heat generation due to the accumulated plastic work in a shear band. The parametric study has revealed that thermal effects play a minor role when the critical shear displacement is below 10 nm (as in nanoindentation) but become significant when the shear displacement accumulated in a shear band is of the order of hundreds of nanometers (as in uniaxial compression and in dynamic indentations). Finally, it is found that the normal stress plays a crucial role in the deformation behavior of BMGs by not only decreasing the time for shear band formation but also increasing the temperature rise significantly.     

Damage evaluation and damage localization of rock

Knowledge of damage accumulation and corresponding failure evolution are prerequisite for effective maintenance of civil engineering so as to avoid disaster. Based on statistical mesoscopic damage mechanics, it was revealed that there are three stages in the process of deformation, damage and failure of multiscale heterogeneous elastic–brittle medium. These are uniformly distributed damage, localized damage and catastrophic failure. In order to identify the transitions from scattering damage to macroscopically localized one, a condition for damage localization was given. The experiments of rock under uniaxial compression with the aid of observations of acoustic emission and speckle correlation do support the concept of localization. This provides a potential approach to properly evaluate damage accumulation in practice. In addition, it is found in the experiments that catastrophic failure displays critical sensitivity. This gives a helpful clue to the prediction of catastrophic failure.     

Shear bands in dense metallic granular materials

In this paper, the phenomenon of strain localization, i.e., shear banding, in densely distributed metallic assemblies has been studied. A discrete element methodology for analyzing metallic granular materials has been put forward. In this numerical model, elastoplastic contact, as well as friction, rolling resistance and cohesion between spheres, are explicitly taken into account. The calculations reveal that the shear banding mechanism in dense assemblies can be thought as an instability triggered by initial imperfections. Within a band, the motion, deformation and rearrangement of spheres soften the resistance of the aggregate, as these mechanisms create additional geometric imperfections. Additionally, the simulations showed that the shear-band width does not change conclusively with the friction, rolling resistance and plasticity parameters. However, cohesive strength, even in small amounts, drastically increased the shear-band width. Finally, the shear-band thickness and inclination angles are strongly dependent on the degree of initial imperfection. Whereas for a perfect assembly the shear band inclinations were consistently around 60°, more heterogeneous assemblies lead to shear band angles closer to the continuum mechanics solution, which is 45°. This was found to be in agreement with recent experimental observations.     

Simulation and interpretation of diffuse mode bifurcation of elastoplastic solids

The diffuse mode bifurcation of elastoplastic solids at finite strain is investigated. The multiplicative decomposition of deformation gradient and the hyperelasto-plastic constitutive relationship are adapted to the numerical bifurcation analysis of the elastoplastic solids. First, bifurcation analyses of rectangular plane strain specimens subjected to uniaxial compression are conducted. The onset of the diffuse mode bifurcations from a homogeneous state is detected; moreover, the post-bifurcation states for these modes are traced to arrive at localization to narrow band zones, which look like shear bands. The occurrence of diffuse mode bifurcation, followed by localization, is advanced as a possible mechanism to create complex deformation and localization patterns, such as shear bands. These computational diffuse modes and localization zones are shown to be in good agreement with the associated experimental ones observed for sand specimens to ensure the validity of this mechanism. Next, the degradation of horizontal sway stiffness of a rectangular specimen due to plane strain uniaxial compression is pointed out as a cause of the bifurcation of the first antisymmetric diffuse mode, which triggers the tilting of the specimen. Last, circular and punching failures of a footing on a foundation are simulated.     

表面粗糙度对TC4钛合金柱壳剪切带形成的影响

剪切带是材料在高应变率加载条件下特有的变形和损伤形式之一,关于影响金属材料中剪切带形成的敏感性因素及其机理的研究,一直是科学研究和工程设计中关注的重点问题. 在柱壳高速坍塌过程中,剪切带优先在内表面形核, 其形核及扩展行为受内表面介观状态的影响显著.本文采用爆轰加载厚壁圆筒坍塌实验技术,结合材料表面处理技术、微结构表征技术和剪切带理论模型分析,研究了内表面粗糙度变化对TC4钛合金柱壳剪切带形成影响的细观动力学规律.结果表明, 在爆炸加载形成的高应变率条件下,表面粗糙度对TC4钛合金柱壳中剪切带形成具有明显影响. 在相同的变形条件下,随着试样内表面粗糙度的增大, 剪切带数量、长度和形核速率均增大;表面粗糙度越大, 部分剪切带扩展速率越快, 剪切带长度差异越大,剪切带的屏蔽效应增强. 分析表明,实验获得的剪切带间距与W-O模型和M模型预测结果基本吻合,具体数值受试样内表面粗糙度影响, 随着表面粗糙度的增大,实验结果逐渐小于预测数值.      

Quantification of large and localized deformation in granular materials

Quantifying large deformation in granular assemblies using concepts originating from continuum mechanics is a challenging task because of (1) the discontinuous nature of granular displacement, which does not allow the definition of a continuum measure of deformation, and (2) the almost inevitable shear band localization. These problems exist in both real-world granular materials and their numerical idealizations using particle-based simulations. In this work a new method is developed in order to address these issues. Instead of creating a meshed equivalent continuum for quantifying small engineering strains, the new method performs independent random queries on the velocity gradient characteristics of arbitrary sub-domains in the assembly through the novel concept of overlapping reference triangles, thus, enabling rigorous handling of large deformations which are usually associated with localization. The proposed method is illustrated and validated by discrete element method (DEM) simulation of a biaxial compressive test, in which apparent shear banding takes place. The homogenized deformation quantifications based on the new method match the estimations from the imposed boundary conditions. The numerical examples are also applied to (1) quantifying the heterogeneous distribution of deformation over the specimen, (2) visualizing the nucleation process of shear bands, and (3) characterizing shear flow patterns in shear bands. An investigation on the effects of the reference triangle sizes yields some inspiring and practically significant results.     

Computations of size effects in granular bodies within micro-polar hypoplasticity during plane strain compression

The numerical investigations of size effects in granular bodies during a plane strain compression test are performed. To describe a mechanical behaviour of a cohesionless granular material during a monotonous deformation path in a plane strain compression test, a micro-polar hypoplastic constitutive model was used. It includes particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. In the paper, deterministic and statistical size effects in geometrically similar granular specimens are analysed. The deterministic calculations were carried out with a uniform distribution of the initial void ratio. To investigate a statistical size effect, in order to reduce the number of realizations without loosing the accuracy of the calculations, a Latin hypercube method was applied to generate Gaussian truncated random fields in a granular specimen. The results show that the statistical size effect is significantly stronger than the deterministic one. The shear resistance decreases and the rate of softening increases with increasing specimen size. The effect of the boundary roughness on shear localization is pronounced.     

Microstructural effects on shear instability and shear band spacing

A constitutive relation that accounts for the thermally activated dislocation motion and microstructure interaction is used to study the stability of a homogeneous solution of equations governing the simple shearing deformations of a thermoviscoplastic body. An instability criterion and an upper bound for the growth rate of the infinitesimal deformations superimposed on the homogeneous solution are derived. By adopting Wright and Ockendon's postulate, i.e., the wavelength of the dominant instability mode with the maximum growth rate determines the minimum spacing between shear bands, the shear band spacing is computed. The effect of the initial dislocation density, the nominal strain-rate, and parameters describing the initial thermal activation and the initial microstructure interaction on the shear band spacing are delineated.     

岩石变形演化诱致灾变破坏过程的同步实验观测

将试样变形场演化特征与试样的宏观载荷位移曲线的演化特征结合起来研究是揭示非均匀脆性介质变形演化诱致灾变破坏的一个重要途径.本文发展了一套实验系统,通过对试样表面变形场的演化、宏观载荷和位移信号的同步观测,对单轴加载下岩石试样变形演化和灾变破坏的过程进行了实验研究.揭示了试样变形场由加载初期的随机涨落到灾变破坏前出现明显的变形局部化的演化特征现象,试样最终在变形局部化区内形成宏观破裂面.     

Length scale effects on the shear localization process in metallic glasses: A theoretical and computational study

Some recent experiments on sub-micron and nano-sized metallic glass (amorphous alloy) specimens have shown that the shear localization process becomes more stable and less catastrophic when compared to the response exhibited by large sample sizes. This leads to the discovery that the shear localization process and fracture can be delayed by decreasing sample volume. In this work we develop a non-local and finite-deformation-based constitutive model using thermodynamic principles and the theory of micro-force balance to study the causes for the aforementioned observations. The constitutive model has also been implemented into a commercially available finite-element program by writing a user-material subroutine. With the aid of finite-element simulations, our constitutive model predicts that metallic glass samples have the intrinsic ability to exhibit: (a) the delaying of (catastrophic) shear localization with decreasing sample size, and (b) homogeneous deformation behavior for sample volumes smaller than the shear band nucleus.The cause for the observations listed above is the increasing influence of a non-local interaction stress with decreasing sample volume. This interaction stress has energetic origins and it affects plastic deformation due to the strong coupling between plastic shearing and free-volume generation. Akin to strain-gradient plasticity theory, the role of the interaction stress is to strengthen the material at locations where the defect density/free volume is higher compared to the rest of metallic glass sample.     

Diffuse mode bifurcation of soil causing convection-like shear investigated by group-theoretic image analysis

Diffuse mode bifurcation of soil under plane-strain compression test is shown, by means of an image analysis based on group-theoretic bifurcation theory, to trigger convection-like shear and to precede shear band formation. First digital photos of Toyoura sand specimens are processed by PIV (particle image velocimetry) to gather digitized images of deformation. Next bifurcation from a uniform state is detected by expanding these images into the double Fourier series and finding a predominant harmonic diffuse bifurcation mode based on that theory. This harmonic bifurcation mode, which is the mixture of a few harmonic functions, expresses complex convection-like shear. Last bifurcation from a non-uniform state is detected by decomposing each image into a few images with different symmetries to extract non-harmonic diffuse bifurcation modes. Diffuse modes of bifurcation, which hitherto were hidden behind predominant uniform compressive deformation, have thus been made transparent by virtue of the group-theoretic image analysis proposed. A possible course of deformation suggested herein is the evolution of diffuse mode bifurcation with a convection-like bifurcation mode breaking uniformity and symmetry, followed by the formation of shear bands through localization.     

多孔铁电陶瓷冲击压缩响应与损伤演化的离散元数值模拟

采用flat-joint粘结模型,建立多孔铁电陶瓷在一维应变冲击压缩下的PFC (particle flow code)颗粒流离散元模型,通过数值模拟再现了平板撞击实验中实测的自由面速度剖面历史,并揭示了多孔铁电陶瓷在冲击压缩下的响应过程与损伤演化机制。多孔铁电陶瓷在冲击压缩下的响应过程可分4个阶段:弹性变形、失效蔓延、冲击压溃变形、冲击Hugoniot平衡状态;其中,失效蔓延的内在机制是由剪切裂纹的成核与增长,而冲击压溃变形的主要机制是孔洞的塌缩以及层状剪切裂纹的形成与扩展;冲击速度与孔隙率对铁电陶瓷的响应有显著的影响,Hugoniot弹性极限强烈依赖于孔隙率,但与冲击速度的大小无关,宏观损伤累积随着冲击速度和孔隙率的增加而增加。     

Effect of material parameters on shear band spacing in work-hardening gradient dependent thermoviscoplastic materials

We study thermomechanical deformations of a viscoplastic body deformed in simple shear. The effect of material elasticity is neglected but that of work hardening, strain-rate hardening, thermal softening, and strain-rate gradients is considered. The consideration of strain-rate gradients introduces a material characteristic length into the problem. A homogeneous solution of the governing equations is perturbed at different values t₀ of time t, and the growth rate at time t₀ of perturbations of different wavelengths is computed. Following Wright and Ockendon's postulate that the wavelength of the dominant instability mode with the maximum growth rate at time t₀ determines the minimum spacing between shear bands, the shear band spacing is computed. It is found that for the shear band spacing to be positive, either the thermal conductivity or the material characteristic length must be positive. Approximate analytical expressions for locally adiabatic deformations of dipolar (strain-rate gradient-dependent) materials indicate that the shear band spacing is proportional to the square-root of the material charateristic length, and the fourth root of the strain-rate hardening exponent. The shear band spacing increases with an increase in the strain hardening exponent and the thermal conductivity of the material.     

金属材料平面应变拉伸变形局部化有限元分析

本文对于涉及韧性金属大变形中颈缩与剪切带断裂一类高度非线性变形局部化问题进行了弹塑性有限元数值模拟。采用改进的Ｊ２形变理论微分形式公式与交叉三角形四边形单元有限元网格，详细研究了应变硬化指数及初始表面不均匀特性的平面应变拉伸颈缩和剪切带形成的综合影响，给出此类问题的断裂机制图。     

A finite thickness band method for ductile fracture analysis

We present a finite element method with a finite thickness embedded weak discontinuity to analyze ductile fracture problems. The formulation is restricted to small geometry changes. The material response is characterized by a constitutive relation for a progressively cavitating elastic–plastic solid. As voids nucleate, grow and coalesce, the stiffness of the material degrades. An embedded weak discontinuity is introduced when the condition for loss of ellipticity is met. The resulting localized deformation band is given a specified thickness which introduces a length scale thus providing a regularization of the post-localization response. Also since the constitutive relation for a progressively cavitation solid is used inside the band in the post-localization regime, the traction-opening relation across the band depends on the stress triaxiality. The methodology is illustrated through several example problems including mode I crack growth and localization and failure in notched bars. Various finite element meshes and values of the thickness of the localization band are used in the calculations to illustrate the convergence with mesh refinement and the dependence on the value chosen for the localization band thickness.     

Localization,delocalization and compression fracture in externally pressurized thick cross-ply (very) long cylindrical shells with material non-linearity: A multi-scale and multi-physics analysis

Compression fracture in carbon fiber reinforced plastics (CFRP) involves multiple physical mechanisms operating at multiple scales ranging from angströms to cms and beyond. First, at the macro/meso-scale, combined effects of modal imperfections, transverse shear/normal deformation along with the non-linear hypo-elastic transverse shear (G_TT) material property on the emergence of interlaminar shear crippling type instability modes, related to the localization (onset of deformation softening), delocalization (onset of deformation hardening) and propagation of mode II compression fracture/damage, in thick imperfect cross-ply very long cylindrical shells under applied hydrostatic pressure, are investigated. The primary accomplishment is the (hitherto unavailable) computation of the layer-wise mode II stress intensity factor, energy release rate and kink crack band-width, under hydrostatic compression, from a non-linear finite element analysis (FEA), using Maxwell’s construction and Griffith׳s energy balance approach. Numerical results include the effects of hypoelastic (G_TT only) material property, on localization and delocalization leading to compression fracture.At the micro-scale, a novel three-dimensional eigenfunction expansion technique, based in part on separation of the cylinder length-variable and partly utilizing a modified Frobenius type series expansion in conjunction with an affine transformation to compute the local stress singularity, in the vicinity of a kinked-fiber/matrix trimaterial junction front. Such computed stress singularities represent a measure of the degree of inherent flaw sensitivity of unidirectional CFRP under compression. Finally, dislocation glide in graphite crystallites plays a dominant role in kink band nucleation and propagation at the nano-meter scale.