Gradient plasticity with the tangential-subloading surface model and the prediction of shear-band thickness of granular materials

An extended gradient elastoplastic constitutive equation is formulated, which is capable of describing the plastic strain rate due to the rate of stress inside the yield surface and the inelastic strain rate due to the stress rate component tangential to the subloading surface by incorporating the tangential-subloading surface model. Based on the extended constitutive equation, the post-localization analysis of granular materials is performed to predict the shear-band thickness. It is revealed that the shear-band thickness is almost determined by the gradient coefficient characterizing the inhomogeneity of deformation, although the stress–strain curve is strongly dependent on material properties.     

准脆性材料的弹塑性各向异性损伤耦合本构模型研究

针对准脆性材料的非线性特征：强度软化和刚度退化、单边效应、侧限强化和拉压软化、不可恢复变形、剪胀及非弹性体胀,在热动力学框架内,建立了准脆性材料的弹塑性与各向异性损伤耦合的本构关系。对准脆性材料的变形机理和损伤诱发的各向异性进行了诠释,并给出了损伤构形和有效构形中各物理量之间的关系。在有效应力空间内,建立了塑性屈服准则、拉压不同的塑性随动强化法则和各向同性强化法则。在损伤构形中,采用应变能释放率,建立了拉压损伤准则、拉压不同的损伤随动强化法则和各向同性强化法则。基于塑性屈服准则和损伤准则,构建了塑性势泛函和损伤势泛函,并由正交性法则,给出了塑性和损伤强化效应内变量的演化规律,同时,联立塑性屈服面和损伤加载面,给出了塑性流动和损伤演化内变量的演化法则。将损伤力学和塑性力学结合起来,建立了应变驱动的应力-应变增量本构关系,给出了本构数值积分的要点。以单轴加载-卸载往复试验识别和校准了本构材料常数,并对单轴单调试验、单轴加载-卸载往复试验、二轴受压、二轴拉压试验和三轴受压试验进行了预测,并与试验结果作了比较,结果表明,所建本构模型对准脆性材料的非线性材料性能有良好的预测能力。     

EVALUATION OF DUCTILE FRACTURE CRITERIA IN A GENERAL THREE-DIMENSIONAL STRESS STATE CONSIDERING THE STRESS TRIAXIALITY AND THE LODE PARAMETER

This paper is concerned with evaluation of various ductile fracture criteria in a general three-dimensional stress state of stress triaxiality, the Lode parameter and the equiva- lent plastic strain to fracture. Evaluation is carried out by comparing fracture loci constructed by fracture criteria to experimental results of A12024-T351. Comparison demonstrates that the Modified Mohr-Coulomb criterion and a newly proposed criterion provide sufficient predictabil- ity of fracture strain. Moreover, evaluation is emphasized on the predicted cut-off value for stress triaxiality. The evaluation demonstrates that the Cockcroft-Latham, Brozzo, Oh, Ko-Huh and the new criteria coupled a reasonable cut-off value for ductile materials.     

对膨胀壳体材料失稳的一种简化处理

提出一种简化的塑性失稳处理并被作为高应变率拉伸下材料破坏的粗估判据。这种准则假设局部化失稳在如下条件下发生:应变及应变率硬化率恰被几何及热软化率平衡。指出了经验本构方程及本征本构方程对膨胀断裂应变的影响。通过算例也说明了热软化壳体在内压作用下的破裂过程。     

An exact semi-analytic solution for residual stresses and strains within a thin hollow disc of pressure-sensitive material subject to thermal loading

There is considerable current interest in the development of constitutive equations for pressure-dependent plastic materials. In particular, in contrast to classical plasticity there is no commonly accepted relation to connect stress and strain or strain rate for such materials. Analytic and semi-analytic solutions are convenient to compare qualitative features of boundary value problems solved for different models. Such comparative studies can be useful to choose this or that model for specific applications. Analytic and semi-analytic solutions are also necessary to verify numerical codes. In the present paper, a new semi-analytic solution for a thin hollow disc subject to thermal loading is developed. A numerical method is only necessary to solve transcendental equations. The constitutive equations for connecting the plastic portion of the strain rate tensor and the stress tensor consist of the Drucker-Prager yield criterion and its associated flow rule. Therefore, the main distinguished feature of the solution is that the material is plastically compressible.     

Stress and strain fields in rotating elastic/plastic annular disks of pressure-dependent material

The Drucker–Prager yield criterion is used in conjunction with its associated flow rule to find the elastic/plastic stress and strain distributions within the rotating annular disks under plane stress conditions. The main distinguished feature of the model, as compared to typical models used for analysis of disks, is that the material is plastically compressible. Using an approach proposed elsewhere, the solution for strain rates is reduced to one nonlinear ordinary differential equation and two linear ordinary differential equations. These equations can be solved one by one, which significantly simplifies the numerical treatment and increases the accuracy of solution.     

金属切屑塑性流动的稳定性

对金属正交切削过程中切屑形成机制和材料塑性流动行为进行实验研究和理论分析. 通过对4 种常用金属材料正交切削过程的实验研究和切屑形貌的微观观察,确定了连续切屑转变成锯齿切屑的临界速度. 结果表明该临界速度与材料性能相关. 在实验观察基础上,提出描述材料正交切削过程的二维分析模型. 该模型假设切屑形成区为包括主剪切区和次剪切区的一个平行四边形. 载荷有主剪切区中的剪应力和次剪切区中的正压力;通过量纲分析得到描述材料正交切削过程的无量纲主控参数和无量纲形式的基本控制方程;应用线性稳定性分析方法建立平面应变状态下评价材料塑性流动稳定性的普遍准则;求得切屑形成区内材料塑性变形的速度和应力近似解. 讨论切屑形成、形貌转变以及相关的塑性失稳机制. 分析结果表明, 表征材料惯性与阻尼之比的无量纲参数— 雷诺数可以作为主控参数描述金属切削过程以及切屑材料塑性流动的稳定性.      

Material plasticity dependence of mixed mode fatigue crack growth in commonly used engineering materials

In this paper, an investigation of fatigue crack propagation in rectangular plates containing an inclined surface crack is presented. A criterion for the three-dimensional stress state is proposed to predict fatigue crack initiation angles. It is assumed that the direction of crack initiation coincides with the direction of the minimum radius of the plastic zone defined by the von Mises yield criterion. The maximum energy release rate criterion, i.e., G_max criterion, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the consideration of the plastic strain energy. Subsequently, this concept is applied to predict crack growth due to fatigue loads. Experiments for checking the theoretical predictions from the proposed criterion have been conducted. The results obtained are compared with those obtained using the commonly employed fracture criteria and the test data.     

纯钼烧结体压缩变形本构模型建立

基于可压缩连续材料的屈服准则和塑性本构关系,推导了粉末烧结材料的压缩变形屈服条件,采用真空烧结技术制备了不同密度的钼,通过在MTS810实验机上进行单向压缩试验,研究了在不同的初始密度,变形温度和应变速率的条件下,纯钼烧结休压缩变形流变应力的变化规律.建立了其流变应力的经验回归模型,进而确定了纯钼烧结材料压缩变形的屈服...     

On stress rate and plasticity constitutive equations referred to a body-fixed coordinate system

Investigators have viewed the stress rate in two different ways: the material (body-fixed) point of view and the Eulerian point of view. We discuss the Zaremba–Jaumann rate and Oldroyd’s rate from the material viewpoint and apply them to the material formulation of a theory of plasticity for materials undergoing anisotropic plastic deformation. Significant advantages of the material formulation are that the derivation of equations is straight forward, the distortion of yield surface can be easily accounted for, and the issue of self-consistent elastic equation does not arise.     

A research note on certain loading directions in rate independent plasticity

Starting with the strain space formulation of rate independent elastic-plastic materials, the notion of “work-instability”, i.e. the possibility of an elastic plastic material undergoing spontaneous plastic deformation in a workless manner, is discussed. Some simple criteria for a material to be work stable are presented. An example of a material that satisfies Prandtl-Reuss type equations with strain softening is presented and it is demonstrated that for plane homogeneous deformations, the material shows the possibility of spontaneous plastic flow even if the in-plane strains are held fixed, if it softens beyond a critical amount.     

A generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials

In this paper, a generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials is derived. The evolution equation for the active yield surface with reference to the memory yield surface is obtained by considering the continuous expansion of the active yield surface during the unloading/reloading process. The incremental constitutive relation based on the associated flow rule is then derived for a general yield function for pressure insensitive and sensitive materials. Detailed incremental constitutive relations for materials based on the Mises yield function, the Hill quadratic anisotropic yield function and the Drucker–Prager yield function are derived as the special cases. The closed-form solutions for one-dimensional stress–plastic strain curves are also derived and plotted for materials under cyclic loading conditions based on the three yield functions. In addition, the closed-form solutions for one-dimensional stress–plastic strain curves for materials based on the isotropic Cazacu–Barlat yield function under cyclic loading conditions are summarized and presented. For materials based on the Mises and the Hill anisotropic yield functions, the stress–plastic strain curves show closed hysteresis loops under uniaxial cyclic loading conditions and the Masing hypothesis is applicable. For materials based on the Drucker–Prager and Cazacu–Barlat yield functions, the stress–plastic strain curves do not close and show the ratcheting effect under uniaxial cyclic loading conditions. The ratcheting effect is due to different strain ranges for a given stress range for the unloading and reloading processes. With these closed-form solutions, the important effects of the yield surface geometry on the cyclic plastic behavior due to the pressure-sensitive yielding or the unsymmetric behavior in tension and compression can be shown unambiguously. The closed form solutions for the Drucker–Prager and Cazacu–Barlat yield functions with the associated flow rule also suggest that a more general anisotropic hardening theory needs to be developed to address the ratcheting effects for a given stress range.     

Generalization of the Prandtl problem for a creep model

An approximate solution to the problem of compression of an infinite layer of material between rough parallel plates is constructed with the creep equations being fulfilled. Constitutive relations in accordance with which the equivalent stress tends to a finite value as the equivalent strain rate tends to infinity are used. The behavior of the solution in the neighborhood of the maximum friction surface is studied. It is shown that the existence of the solution depends on one of the parameters included in the constitutive equations. If the solution exists, the equivalent strain rate tends to infinity in the neighborhood of the maximum friction surface, and the asymptotic behavior of the solution depends on the same parameter. It is established that there is a range of this parameter in which the nature of the change in the equivalent strain rate near the maximum friction surface is the same as in the solutions for rigid plastic materials.     

A finite volume cell‐centered Lagrangian hydrodynamics approach for solids in general unstructured grids

A finite volume cell‐centered Lagrangian hydrodynamics approach, formulated in Cartesian frame, is presented for solving elasto‐plastic response of solids in general unstructured grids. Because solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum, and energy conservation laws. The total stress is split into deviatoric shear stress and dilatational components. The dilatational response of the material is modeled using the Mie‐Grüneisen equation of state. A predicted trial elastic deviatoric stress state is evolved assuming a pure elastic deformation in accordance with the hypo‐elastic stress‐strain relation. The evolution equations are advanced in time by constructing vertex velocity and corner traction force vectors using multi‐dimensional Riemann solutions erected at mesh vertices. Conservation of momentum and total energy along with the increase in entropy principle are invoked for computing these quantities at the vertices. Final state of deviatoric stress is effected via radial return algorithm based on the J‐2 von Mises yield condition. The scheme presented in this work is second‐order accurate both in space and time. The suitability of the scheme is evinced by solving one‐ and two‐dimensional benchmark problems both in structured grids and in unstructured grids with polygonal cells. Copyright © 2013 John Wiley & Sons, Ltd.     

A finite deformation fractional viscoplastic model for the glass transition behavior of amorphous polymers

The stress response of amorphous polymers exhibits tremendous change during the glass transition region, from soft viscoelastic response to stiff viscoplastic response. In order to describe the temperature-dependent and rate-dependent stress response of amorphous polymers, we extend the one-dimensional small strain fractional Zener model to the three-dimensional finite deformation model. The Eyring model is adopted to represent the stress-activated viscous flow. A phenomenological evolution equation of yield strength is used to describe the strain softening behaviors. We demonstrate that the stress response predicted by the three-dimensional model is consistent with that of one-dimensional model under uniaxial deformation, which confirms the validity of the extension. The model is then applied to describe the stress response of an amorphous thermoset at various temperatures and strain rates, which shows good agreement between experiments and simulation. We further perform a parameter study to investigate the influence of the model parameters on the stress response. The results show that a smaller fractional order results in a larger yield strain while has little effect on the yield stress when the temperature is below the glass transition temperature. For the stress relaxation tests, a smaller fractional order leads to a slower relaxation rate.     

ASYMPTOTIC SOLUTIONS OF MODE I STEADY GROWTH CRACK IN MATERIALS UNDER CREEP CONDITIONS

An asymptotic analysis is made on problems with a steady-state crack growth coupled with a creep law model under tensile loads. Asymptotic equations of crack tip fields in creep materials are derived and solved numerically under small scale conditions. Stress and strain functions are adopted under a polar coordinate system. The governing equations of asymptotic fields are obtained by inserting the stress field and strain field into the material law. The crack growth rate rather than fracture criterion plays an important role in the crack tip fields of materials with creep behavior.     

Pseudo plane stress plastic field for mode I crack growth

The pseudo plane stress field for a mode I crack growth is analyzed for both perfectly plastic and power law hardening plastic materials. When finite strain is taken into account, it is found that for perfectly plastic materials, the plastic domain is a narrow strip ahead of the crack tip. For power law hardening plastic material, the plastic domain contains a strip and a region ahead of the strip. The fracture criterion is discussed. The energy dissipated in the plastic strip is found to be proportional to the square of the thickness. Singular solutions to the field are ruled out by analysis.     

The constitutive equations for mixed hardening orthotropic material

IntroductionAyieldingcriterionandtheassociatedflowtheorywereproposedbyHill[1]forinitiallyorthotropicmetalsin 1 948,whichareusedbroadly .AquadraticformofstressesisusedastheplasticpotentialthatisindependentofhydrostaticstressinHillplasticitytheory .Butcompressedbyhydrostaticstress,considerabledeformationwillbeproducedinorthotropicmaterials.Inthecaseofcyclicloading ,duetoBauschingereffect,thekinematichardeningcannotbeneglected .Inthispaper,kinematichardeningandproportionalhardeningareconsidered…