Modeling of textural anisotropy in granular materials with stochastic micro-polar hypoplasticity

The paper deals with a numerical analysis of the effect of textural anisotropy on the behaviour of cohesionless granular materials with consideration of shear localization. For a simulation of the mechanical behaviour of a granular material during a monotonic deformation path, an isotropic micro-polar hypoplastic constitutive model was used. To describe textural effects, spatially correlated random fields of the initial void ratio were subject to rotation against the horizontal axis. The 2D random fields were generated using a conditional rejection method. The results were compared with those obtained with an anisotropic micro-polar constitutive model for a uniform distribution of the initial void ratio. The calculations were carried out with an initially dense granular specimen during plane strain compression under constant lateral pressure.     

Boundary effects on behaviour of granular material during plane strain compression

The paper investigates the boundary effect on the behaviour of granular materials during plane strain compression using finite element method. A micro-polar hypoplastic constitutive model was used. The numerical calculations were carried out with different initial densities and boundary conditions. The behaviour of initially dense, medium dense and loose sand specimen with very smooth or very rough horizontal boundary was investigated. The formation of shear zones gave rise to different global and local stress and strain. Comparisons of the mobilized internal friction, dilatancy and non-coaxiality between global and local quantities were made.     

Comparative FE-studies of shear localizations in granular bodies within a polar and non-local hypoplasticity

Paper presents a FE-analysis of shear localizations in granular bodies with a finite element method based on a hypoplastic constitutive law. The law can reproduce essential features of granular bodies in dependence on the void ratio, pressure level and deformation direction. To simulate the formation of a spontaneous shear zone inside of cohesionless sand during plane strain compression, a hypoplastic law was extended by polar and non-local terms. The effect of both models on the thickness of a shear zone was compared.     

Effects of texture on shear band formation in plane strain tension/compression and bending

In this study, effects of typical texture components observed in rolled aluminum alloy sheets on shear band formation in plane strain tension/compression and bending are systematically studied. The material response is described by a generalized Taylor-type polycrystal model, in which each grain is characterized in terms of an elastic–viscoplastic continuum slip constitutive relation. First, a simple model analysis in which the shear band is assumed to occur in a weaker thin slice of material is performed. From this simple model analysis, two important quantities regarding shear band formation are obtained: i.e. the critical strain at the onset of shear banding and the corresponding orientation of shear band. Second, the shear band development in plane strain tension/compression is analyzed by the finite element method. Predictability of the finite element analysis is compared to that of the simple model analysis. Third, shear band developments in plane strain pure bending of a sheet specimen with the typical textures are studied. Regions near the surfaces in a bent sheet specimen are approximately subjected to plane strain tension or compression. From this viewpoint, the bendability of a sheet specimen may be evaluated, using the knowledge regarding shear band formation in plane strain tension/compression. To confirm this and to encompass overall deformation of a bent sheet specimen, including shear bands, finite element analyses of plane strain pure bending are carried out, and the predicted shear band formation in bent specimens is compared to that in the tension/compression problem. Finally, the present results are compared to previous related studies, and the efficiency of the present method for materials design in future is discussed.     

Inelastic behavior of an AS4/PEEK composite under combined transverse compression and shear. Part I: experiments

The nonlinear behavior in shear and transverse compression of unidirectional AS4/PEEK and their interaction are investigated experimentally. The composite is rate dependent even at room temperature and its rate exponent is similar to that of neat PEEK. The material is tested under pure shear, pure compression and under biaxial loading histories. The biaxial tests are performed in a custom facility on thin strips of the material. The facility allows freedom to choose the loading path in the biaxial stress and strain spaces of interest. Tests are performed for three biaxial loading paths. In the first, the specimen is sheared then compressed while the shear stress is held constant; in the second, the specimen is compressed then sheared while the compressive stress is held constant; and in the third, the specimen is loaded simultaneously by proportional amounts of compression and shear. It was found that the induced deformation is influenced significantly by the loading history followed. Also, initial loading in shear or compression has only a modest effect on subsequent loading of the other type. An unorthodox yielding behavior for the composite results from this lack of interaction. Finally, the stresses at failure are found to trace an elliptical path in the shear–transverse compression plane, but the failure stress state is not significantly affected by the loading path followed.     

Large Deformation of Nitinol Under Shear Dominant Loading

Full-field quantitative strain maps of phase transformation and plasticity in Nitinol under large shear-dominated deformation are presented. To achieve a shear-dominated deformation mode with relatively uniform stresses and strains, a shear compression specimen (SCS) geometry was utilized. Shear deformation appears to impede the development of the strain localization during phase transformation that is seen in uniaxial testing. The shear-dominant deformation of Nitinol in the plastic regime exhibits low hardening and results in the development of significant strain inhomogeneity.     

Incorporating the effects of fabric in the dilatant double shearing model for planar deformation of granular materials

The objective of this paper is to incorporate the effects of fabric and its evolution into the Dilatant Double Shearing Model [Mehrabadi, M.M., Cowin, S.C., 1978. Initial planar deformation of dilatant granular materials. J. Mech. Phys. Solids 26, 269–284] for granular materials in order to capture the anisotropic behavior and the complex response of granular materials in cyclic shear loading. An important consequence of considering the fabric is that one can have unequal shearing rates along the two slip directions. This property leads to the non-coaxiality of the principal axes of stress and strain rate, which is more appropriate for a material that exhibits initial and induced anisotropy. In addition, we employ a fabric-dependent elasticity tensor with orthotropic symmetry. The model developed in this paper also predicts one of the experimentally observed characteristics of granular materials: the gradual concentration of the contact normals towards the maximum principal stress direction.We implement the constitutive equations into ABAQUS/Explicit by writing a user material subroutine in order to predict the strength anisotropy of granular materials in a plane strain biaxial compression test and investigate the mechanical behavior of granular materials under the cyclic shear loading conditions. The predictions from this model show good quantitative agreement with the experiments of [Park, C.S., 1990. Anisotropy in deformation and strength properties of sands in plane strain compression, Masters Thesis, University of Tokyo; Park, C.S., Tatsuoka, F., 1994. Anisotropic strength and deformation of sands in plane strain compression. In: XIII ICSMFE, New Delhi, India; Okada, N., 1992. Energy dissipation in inelastic flow of cohesionless granular media. Ph.D. Thesis, University of California, San Diego].     

Fatigue-crack-tip plastic strains by the stereoimaging technique

The stereoimaging technique is an accurate, high-resolution means of measuring the in-plane displacements resulting from the deformation of a specimen so that the corresponding components of the strain tensor can be computed independently of the stresses. The example used in this paper is a fatigue-cracked specimen of a microscopically homogeneous experimental powder-metallurgy aluminum alloy, analyzed to determine the displacement and strain fields accompanying the opening of the fatigue crack. The displacement measurements are processed by a computer program which compensates for measurement fluctuations in the displacement data by smoothing, and derives the strain magnitudes. The principal strains and the maximum shear strain are determined using Mohr's circle, and the latter strain is then used to estimate the plastic-zone size. The crack-opening mode may be inferred from the displacement map, and the state of stress (plane stress or plane strain) inferred by applying the in-plane compatibility equation.     

粒料固有各向异性的离散元模拟与细观分析

料在摊铺后形成的颗粒定向排列将导致其力学性质的固有各向异性. 依据粒料的实际不规则形状, 构建了可模拟粒间咬合嵌挤作用的三维离散元复杂形状颗粒; 生成了5 种不同沉积方向的各向异性试件和1种各向同性试件, 对比了各试件在三轴压缩试验中的宏观力学特性差异; 引入组构张量以量化各向异性程度, 利用玫瑰图表达接触法向与接触力的分布特征, 探究了粒料各向异性的细观发展规律. 结果表明: 颗粒长轴愈趋向水平排布, 峰值应力比愈大, 剪缩与剪胀程度愈明显; 相较于各向同性试件, 沉积角$\theta$为料在摊铺后形成的颗粒定向排列将导致其力学性质的固有各向异性. 依据粒料的实际不规则形状, 构建了可模拟粒间咬合嵌挤作用的三维离散元复杂形状颗粒; 生成了5 种不同沉积方向的各向异性试件和1种各向同性试件, 对比了各试件在三轴压缩试验中的宏观力学特性差异; 引入组构张量以量化各向异性程度, 利用玫瑰图表达接触法向与接触力的分布特征, 探究了粒料各向异性的细观发展规律. 结果表明: 颗粒长轴愈趋向水平排布, 峰值应力比愈大, 剪缩与剪胀程度愈明显; 相较于各向同性试件, 沉积角$\theta$为$0^\circ$时, 峰值应力比和最大体积压缩应变分别提高了12.6\%和18.8\%, 其原因在于加载过程中颗粒旋转和滑动百分比更小, 内部调整时间更短、更易被剪密; 固有各向异性对颗粒法向接触力分布的影响不大, 但显著影响接触法向分布特征; 剪切过程中, $\theta$为$90^\circ$时的接触法向各向异性系数先快速减小后逐渐增大, 而$\theta$为$0^\circ$到$60^\circ$时则呈现出增大后稍有回落或趋于稳定的趋势, 且$\theta$ 愈小的试件各向异性系数增大愈快.     

激光金属沉积GH4169在不同应变率下的剪切特性及破坏机理研究

为了能在传统的分离式Hopkinson压杆上准确可靠地测试激光金属沉积GH4169的动态剪切特性，基于数值模拟方法对比分析了三种不同动态剪切试样形式及尺寸对剪切区应力分布的影响，结果表明:经过尺寸优化后的双剪切试样的剪切区剪应力占主导地位，可实现近似纯剪切的动态剪切实验。利用此试样形式，系统测试了不同取向（扫描方向、沉积方向）的LMD GH4169试样在不同应变率下的剪切应力应变曲线，并对破坏后试样进行了SEM分析观察。结果表明:(1) 本文中选用的试样形式剪切纯度高，应力沿剪切区宽度厚度分布均匀，可以更好地得到材料的动态剪切特性；(2) 对实验所得剪应力-剪应变曲线进行分析，发现本材料在扫描路径方向和沉积方向并没有表现出明显的各向异性，但随着应变率的增加，具有明显的应变率强化效应；将单轴压缩和动态剪切应力应变曲线同时转换为等效应力应变曲线，对比证实了试样形式能很好反应材料的剪切特性；(3) 通过对LMD GH4169剪切变形破坏试样的微观分析发现，随着应变率升高，断口韧窝尺寸和深度减小，韧性降低，在更小的变形量下容易剪切失效。初始微观缺陷容易导致材料的动态剪切破坏。     

Large Strain Shear Compression Test of Sheet Metal Specimens

A hybrid experimental-computational procedure to establish accurate true stress-plastic strain curve of sheet metal specimen covering the large plastic strain region using shear compression test data is described. A new shear compression jig assembly with a machined gage slot inclined at 35° to the horizontal plane of the assembly is designed and fabricated. The novel design of the shear compression jig assembly fulfills the requirement to maintain a uniform volume of yielded material with characteristic maximum plastic strain level across the gage region of the Shear Compression Metal Sheet (SCMS) specimen. The approach relies on a one-to-one correlation between measured global load–displacement response of the shear compression jig assembly with SCMS specimen to the local stress-plastic strain behavior of the material. Such correlations have been demonstrated using finite element (FE) simulation of the shear compression test. Coefficients of the proposed correlations and their dependency on relative plastic modulus were determined. The procedure has been established for materials with relative plastic modulus in the range 5?×?10^?4?<?(E _p /E)?<?0.01. It can be readily extended to materials with relative plastic modulus values beyond the range considered in this study. Nonlinear characteristic hardening of the material could be established through piecewise linear consideration of the measured load–displacement curve. Validity of the procedure is established by close comparison of measured and FE-predicted load–displacement curve when the provisional hardening curve is employed as input material data in the simulation. The procedure has successfully been demonstrated in establishing the true stress-plastic strain curve of a demonstrator 0.0627C steel SCMS specimen to a plastic strain level of 49.2 pct.     

基于PVDF薄膜传感器的猪肝动态压缩力学性能测试

瞬态冲击载荷作用下肝脏的力学响应是损伤生物力学的重要研究内容。本文提出了一种可用于软组织动态压缩力学特性测试的改进SHPB(分离式霍普金森压杆,Split Hopkinson Pressure Bar)方法。该方法采用PVDF(聚偏氟乙烯,Polyvinylidene Fluor)压电薄膜传感器测量实验过程中试件两端面的受力,以此来计算试件的应力,从而无需测量透射杆上的微弱透射信号。猪肝试样前后端面的PVDF压电信号对比表明,加载过程中试样达到了动态应力平衡状态。试样动态压缩中的惯性效应主要在加载的初始阶段对透射应力信号造成较大影响,在大变形阶段惯性效应引起的轴向应力较小。利用此方法对猪肝组织进行三种高应变率(1800s^-1,2500s^-1,3500s^-1)的动态压缩实验,并采用基于真实应变的惯性效应公式对实验数据进行修正计算。结果表明:猪肝组织在准静态与高应变率时的应力应变曲线都呈现出凹向上的非线性特征,即曲线初始阶段应力增长较缓慢,当应变达到15%后应力值则迅速增大;猪肝组织也具有明显的应变率效应,即随着应变率的增加,应力应变曲线的整体应力值也随之增大。最后,采用黏超弹性本构模型描述了猪肝组织的动态应力应变曲线。     

A shear-compression specimen for large strain testing

A new specimen geometry, the shear-compression specimen (SCS), has been developed for large strain testing of materials. The specimen consists of a cylinder in which two diametrically opposed slots are machined at 45° with respect to the longitudinal axis, thus forming the test gage section. The specimen was analyzed numerically for two representative material models, and various gage geometries. This study shows that the stress (strain) state in the gage, is three-dimensional rather than simple shear as would be commonly assumed. Yet, the dominant deformation mode in the gage section is shear, and the stresses and strains are rather uniform. Simple relations were developed and assessed to relate the equivalent true stress and equivalent true plastic strain to the applied loads and displacements. The specimen was further validated through experiments carried out on OFHC copper, by comparing results obtained with the SCS to those obtained with compression cylinders. The SCS allows to investigate a large range of strain rates, from the quasi-static regime, through intermediate strain rates (1–100 s⁻¹), up to very high strain rates (2×10⁴s⁻¹ in the present case).     

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.     

Comparison of Test Specimens for Characterizing the Dynamic Properties of Rubber

Dynamic material properties inferred via experiment can be strongly influenced by the choice of test specimen geometry unless care is taken to ensure that mechanical fields (stress, strain, etc.) within the specimen adequately reflect the ideal homogeneous deformation state. In this work, finite element models of simple shear, cylindrical compression, simple tension, and bi-conical shear test specimens were analyzed in order to quantify the relative conformity of each specimen to its corresponding ideal. Three metrics of conformity were evaluated, based respectively on the distributions of stress, strain, and strain energy density. The results show that a simple shear specimen provides superior conformity. Other factors involved in the selection of test specimen geometry are also discussed. Such factors include relative linearity and symmetry of measured stress–strain data, grip slip, and heat build up.     

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.     

压应力对压剪裂纹扩展的影响研究

本文针对压剪裂纹的启裂及扩展问题,研究了脆性材料中裂纹面压应力变化对其扩展的影响规律.借助双轴加载试验机可自由调节两个轴位移和力的优势,设计了一种单边对称双裂纹压剪试样.试验中,施加裂纹面压应力至不同的预设值后,使剪应力单调增大直至裂纹启裂及扩展,得到不同预设压应力下压剪裂纹启裂及扩展规律. 随着预设压应力增大,启裂角增大,裂纹扩展路径与初始裂纹的偏角也增大.但随着压应力增大,启裂角增大至一定值后趋于稳定,实验发现,依据裂纹是否闭合,压应力对压剪裂纹扩展的作用大致可分为两个阶段:闭合前,压应力对裂纹启裂载荷及启裂角、扩展路径均有影响,预设压应力增大,裂纹启裂载荷增大、启裂角增大,扩展路径愈来愈偏离初始裂纹方向;闭合后,压应力虽然增大,启裂角和临界压剪应力比始终恒定,压应力对临界剪力和扩展路径存在一定影响.研究表明,裂纹启裂角与启裂时的压剪应力比存在一定的对应关系.启裂时的压剪应力比增大,启裂角增大,启裂时的压剪应力比恒定,启裂角不变.      

Stress analysis of an orthotropic material under diametral compression

The diametral compression test is commonly used to determine the tensile strength of brittle materials. For isotropic materials a simple relation based on specimen geometry and the applied load at failure is used to calculate the tensile strength. Previous to this work the effect of material orthotropy and material orientation on the specimen stress state had not been completely determined. In this study, both isotropic and orthotropic specimens were analyzed using a finite element analysis and experimentally verified by strain gage and photoelastic measurements. Further, this work investigated the effect of the applied load area on the specimen stress state. Results of this work show that there is a significant difference between the theoretical calculations based on the assumption of material isotropy when compared to an orthotropic material. This difference can be as much as 45 percent depending on the degree of orthotropy and the orientation. It was also determined that the applied load area and material orientation significantly influence the specimen stress state. An applied load area of 8 percent of the circumference was found to reduce the stresses in the applied load region.     

Numerical validation of the shear compression specimen. Part I: Quasi-static large strain testing

The shear compression specimen (SCS), which is used for large strain testing, is thoroughly investigated numerically using three-dimensional elastoplastic finite element simulations. In this first part of the study we address quasi-static loading. A bi-linear material model is assumed. We investigate the effect of geometrical parameters, such as gage height and root radius, on the stress and strain distribution and concentration. The analyses show that the stresses and strains are reasonably uniform on a typical gage mid-section, and their average values reflect accurately the prescribed material model. We derive accurate correlations between the averaged von Mises stress and strain and the applied experimental load and displacement. These relations depend on the specimen geometry and the material properties. Numerical results are compared to experimental data, and an excellent agreement is observed. This study confirms the potential of the SCS for large strain testing of material.