A simple plasticity model for prediction of non-coaxial flow of sand

A bounding surface plasticity model for non-coaxiality, another aspect of anisotropic behavior of sands under rotation of principal stress axes; is developed in the critical state framework. Numerous experimental evidences exist that corroborate dependence of plastic shear strain rate direction on inherent fabric anisotropy. At first, general expressions for plastic strain rate with respect to possible emerge of non-coaxial flow are obtained. Consequently, using an anisotropy state parameter that is specially developed for this model and accounts for the interaction between imposed loading and soil fabric; effect of anisotropy on plastic flow direction is taken into account. Besides, novel circumstances are proposed for plastic modulus and dilatancy under rotation of principal stress axes. Finally, it is shown that the model is able to simulate successfully the non-coaxial behavior of sands subjected to principal stress axes rotation.     

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.     

考虑塑性和刚度不匹配的焊接残余应力估算

现有残余应力计算方法未能考虑材料塑性变形和焊接接头刚度不匹配的影响,使得焊接残余应力计算结果和实际残余应力存在较大偏差.在2219-T87铝合金钨极氩弧焊焊接头残余应力测试基础上,提出一种基于非线性有限元和材料弹性模量分区的残余应力—释放应变曲线的残余应力计算方法,研究了材料塑性变形和接头刚度不匹配对焊接残余应力计算的影响.结果表明,焊接接头中非均质材料塑性不匹配可以引起对于残余应力计算的较大误差;材料塑性变形对残余应力的影响大于接头刚度不匹配对残余应力的影响.所提出方法修正了传统方法在焊接接头的残余应力计算中由于未考虑接头非均质材料塑性不匹配而引起的误差.     

Nonlocal gradient-dependent modeling of plasticity with anisotropic hardening

This work addresses the formulation of the thermodynamics of nonlocal plasticity using the gradient theory. The formulation is based on the nonlocality energy residual introduced by Eringen and Edelen (1972). Gradients are introduced for those variables associated with isotropic and kinematic hardening. The formulation applies to small strain gradient plasticity and makes use of the evanescent memory model for kinematic hardening. This is accomplished using the kinematic flux evolution as developed by Zbib and Aifantis (1988). Therefore, the present theory is a four nonlocal parameter-based theory that accounts for the influence of large variations in the plastic strain, accumulated plastic strain, accumulated plastic strain gradients, and the micromechanical evolution of the kinematic flux. Using the principle of virtual power and the laws of thermodynamics, thermodynamically-consistent equations are derived for the nonlocal plasticity yield criterion and associated flow rule. The presence of higher-order gradients in the plastic strain is shown to enhance a corresponding history variable which arises from the accumulation of the plastic strain gradients. Furthermore, anisotropy is introduced by plastic strain gradients in the form of kinematic hardening. Plastic strain gradients can be attributed to the net Burgers vector, while gradients in the accumulation of plastic strain are responsible for the introduction of isotropic hardening. The equilibrium between internal Cauchy stress and the microstresses conjugate to the higher-order gradients frames the yield criterion, which is obtained from the principle of virtual power. Microscopic boundary conditions, associated with plastic flow, are introduced to supplement the macroscopic boundary conditions of classical plasticity. The nonlocal formulation developed here preserves the classical assumption of local plasticity, wherein plastic flow direction is governed by the deviatoric Cauchy stress. The theory is applied to the problems of thin films on both soft and hard substrates. Numerical solutions are presented for bi-axial tension and simple shear loading of thin films on substrates.     

Effect of porosity on the properties of strain localization in porous media under undrained conditions

Within the general framework of mixture theory and by introducing the fictitious “fluid phase” as a mixture of a liquid and a gas, the conditions for localization of deformation into a shear band in the incremental response of partially saturated and fully saturated elastic–plastic porous media under undrained conditions are derived. The effect of porosity is included in the derivation. The explicit analytical expressions of the direction of shear band initiation and the corresponding hardening modulus of the porous media for the plane strain case are deduced, and a parametric analysis is made of the influence of the porosity on the properties of strain localization based on Mohr–Coulomb yield criterion. It is found that the dependence of the shear banding properties of partially saturated porous media on the porosity is related to the stress states and Poisson's ratio. However, the properties of the strain localization for the fully saturated porous media are almost independent of Poisson's ratio. Finally, on the basis of Mohr–Coulomb yield criterion, some solutions of the shear banding orientation for water-saturated granular materials are obtained, which are proved to be in good agreement with the experimental results reported by other researchers.     

钛镍形状记忆合金冲击变形后形状记忆效应的研究

采用SHPB技术和可控速率循环加温条件下变形恢复量测定装置研究了冲击及静载变形后的TiNi形状记忆合金的单程及双程形状记忆特性。发现马氏体状态下的TiNi合金的力学特性显示出明显的应变率强化效应 ,并且高应变率压缩应力应变曲线呈现流动平台。应变率对形状记忆效应的影响具有双重性 ,当外加应力或残余应变较小 ,可逆非弹性变形机制起主导作用时 ,提高应变率可以增加其单程形状记忆效应 ;而随外加应力或残余应变增大 ,当基于位错机制的不可逆非弹性变形机制起主导作用时 ,应变率提高却抑制了其单程形状记忆效应。应变率对TiNi合金双程形状记忆效应的影响视塑性变形的大小而异 ,高应变率动载后的双程形状记忆效应在较小塑性应变时 ,比静载后的要强 ;但在较大塑性应变时两者差别不大。     

True triaxial cyclic behavior of concrete and rock in compression

Results from true triaxial cyclic tests on concrete are presented and compared with corresponding ones for dense rocks (mainly marbles) obtained under the same laboratory conditions. Common basic characteristics are confirmed regarding the essential effect of intermediate stress, the cataclastic mode of deformation under low confinement, the coupling between volumetric strain and deviatoric stress, the dependence of the equivalent modulus E_q and the hysteresis loops. Common characteristics are also revealed in meridian and deviatoric sections of peak strength surfaces, moreover a stress invariant and its work conjugate plastic strain increment are approximately equal. Concrete behavior is different on the postpeak plastic contraction under high confinement, on the creep rate, on the validity of the condition of convexity and on the considerable degree of violation of the condition of normality. A simple empirical equation is proposed and experimentally verified for predicting deviatoric sections of strength surfaces.     

基于有限变形单晶塑性滑移的微观热-力耦合模型及其有限元计算

基于率相关的晶体塑性滑移理论,论文考虑晶体内部塑性变形产生的热以及快速热冲击作用下温度急剧变化产生热应力的热-力双向耦合效应,建立起微观单晶的瞬态热-弹-塑性耦合模型,推导出与温度有关的剪应变率和弹塑性切模量公式.根据论文建立的模型,对ABAQUS软件进行二次开发[1],数值模拟出<001>/{100}单晶Cu在单轴拉伸状态下的应力、应变与温度的关系和弹性模量的变化,结果如下:轴向应力随温度升高先呈线性增加再呈非线性减小,轴向应变随温度增加而增加;弹性模量随塑性变形的增加而降低,与分子动力学模拟的趋势[2]是一致的.数值实验表明,论文建立的模型和算法是正确合理的,且计算量远远小于分子动力学模拟.     

Generalization of the Prandtl solution to the case of axisymmetric deformation of materials obeying the double shear model

A semianalytic solution of the problem on the compression of an annular layer of a plastic material obeying the double shear model on a cylindrical mandrel is obtained. The approximate statement of boundary conditions, which cannot be satisfied exactly in the framework of the constructed solution, is based on the same assumptions as the statement of the classical plasticity problem of compression of a material layer between rough plates (Prandtl’s problem). It is assumed that the maximum friction law is satisfied on the inner surface of the layer. The solution is singular near this surface. The strain rate intensity factor is calculated, and its dependence on the process and material parameters is shown.     

Roles of plastic spin in shear banding

In this paper, the effects of plastic spin on shear banding and simple shear are examined systematically. Three types of plastic constitutive model with plastic spin are considered: (i) a non-coaxial model in which the direction of the plastic strain rate depends on that of the stress rate; (ii) a strain-softening model based on the J₂ flow theory; and (iii) the pressure-sensitive porous plasticity model. All the constitutive models are formulated in viscoplastic forms and in conjunction with non-local concepts that have been recently focused and discussed. First, behavior in simple shear is examined by numerical analysee with the aforementioned constitutive models. Moreover, some experimental evidences for stress response to simple shear are shown; that is, several large torsion tests of metal tubes and bars are carried out. Next, finite element simulations of shear banding in plane strain tension are performed. A critical effect of plastic spin on shear banding is observed for the noncoaxial model, while an almost negligible effect is observed for the porous model. The identical effects of plastic spin are observed, whether nonlocality exists or not. Finally, we discuss the relationship between the behavior in simple shear and the shear band formation. It is emphasized that this is a critical issue in predicting shear banding in macroscopic grounds.     

Large strain responses of elastic-perfect plasticity and kinematic hardening plasticity with the logarithmic rate: Swift effect in torsion

A new Eulerian rate type elastic-perfectly plastic model has recently been established by utilizing the newly discovered logarithmic rate. It has been proved that this model is unique among the objective elastic-perfectly plastic models with all objective corotational stress rates and other known objective stress rates by virtue of the self-consistency criterion: the hypoelastic formulation intended for elastic behaviour must be exactly integrable to deliver a hyperelastic relation. The finite simple shear response of this model has been studied and shown to be reasonable for both shear and normal stress components. On the other hand, a kinematic hardening plasticity model may be formulated by adopting the logarithmic rate. The objective of this work is to further study the large deformation responses of the foregoing two kinds of idealized models, in particular the well-known Swift effect, in torsion of thin-walled cylindrical tubes. A complete, rigorous analysis is made for the orders of magnitude of all stress components. A closed-form solution is obtained for the kinematic hardening plastic case, and an analytical perturbation solution is derived for the elastic-perfectly plastic case. It is shown that the simple idealized kinematic hardening model with the logarithmic rate, which uses only two classical material constants, i.e., the initial (tensile) yield stress and the hardening modulus, may arrive at satisfactory explanation for and reasonable accord with salient features of experimental observation.     

循环荷载下岩石阻尼行为的试验研究

为了深入地了解岩石的阻尼特性,利用WDT–1500多功能材料试验机,对砂岩、砾岩和砂砾岩进行了循环荷载试验,研究了岩石的动剪切模量和阻尼参数对应力、应变幅值和应力水平的响应特性,得到了动弹性模量和阻尼参数随应力幅值、应力水平及含水率的变化规律,讨论了其变化机理。证实了双曲线关系能够描述分级循环荷载作用下岩石的应力-应变关系,得到了动剪切模量和阻尼比与动应力、动应变之间的关系,建立了不同应力水平和不同应力幅值条件下岩石的动剪切模量与阻尼比关系模型,结果表明该模型能够描述分级循环荷载过程中阻尼行为。     

Application of a discrete polycrystal model to the analysis of cyclic straining in copper

A discrete polycrystal model, designed to simulate a metal aggregate macro-element, is applied to the study of cyclic straining in copper. The numerical method of solution (an adaptation of the “finite element method”) incorporates a convergent discrete Green's function within the constrained minimum principle which governs the (crystallographic) plastic shear increments at each load step. Isothermal elastic moduli of copper crystals and Taylor's hardening rule with constant hardening modulus are used in the calculations. Numerical results are obtained for macroscopic elastic properties, cyclic stress-strain curves (which indicate the contribution of aggregate heterogeneity to macroscopic hardening), macroscopic plastic work, and residual (latent) strain energy through four loading cycles between fixed macrostrain limits. Other estimates for elastic properties also are included, and all results are compared, both qualitatively and quantitatively, with published experiments. The predictions of the model are in general satisfactory.     

Reverse shear on inclined planes at the tip of a sharp crack

Plane strain plastic yielding at a crack tip has been represented by edge dislocations with Burgers vectors parallel to symmetrical planes inclined at 70° and 45° to the plane of the crack. The plastic displacement and the stresses near the crack tip were calculated by a numerical method and the effect of a reduction in applied stress was determined. Removal of the whole or a part of the initial load produces reverse shear in regions of the slip band nearest the crack tip. The amount of reverse shear depends only on the reduction in the load and not on its initial value. The reverse shear is associated with the presence of negative dislocations and the stresses near the crack tip may become compressive even though the applied (remote) stress is still tensile. The degree and extent of compression depends on the reduction in applied stress and on its original value. It is argued that the residual compressive stresses produced under fluctuating loads may produce crack closure and crack arrest. The effect of residual plasticity in a slip band left behind a growing crack has been estimated. It is shown that after an overload the excess residual plasticity opposing crack opening rises to a maximum value when the crack tip has advanced some distance from the point where the overload was applied.     

弹塑性材料的平面应力非连续分岔

基于平面应力非连续分岔特性的一般描述,运用统一强度理论,得出了非相关流动情形的弹塑性材料平面应力非连续分岔的起始方位角以及相应的最大硬化模量的统一解析解,并且分析了材料拉压异性以及不同程度的中间应力对结果的影响,进而发现所得的结果一强度准则的选取有关,揭示了在分岔研究中正确选取符合材料特性的强度准则的重要性。最后,同特线理论比较发现平面应力剪切带型非连续分岔同平面应力特征线重合。     

The significance of pure measures of distortion in nonlinear elasticity with reference to the Poynting problem

The objective of this paper is to show the significance of expressing the strain energy function in terms of a scalar pure measure of dilatation and a tensor pure measure of distortion, which were essentially introduced by Flory [1]. It is shown that convenient representations for the strain energies of dilatation and distortion, and the pressure and deviatoric Cauchy stress may be recorded in terms of these deformation measures. After specializing to the case of an isotropic material, specific constitutive equations are proposed and the Poynting problem is considered. It is shown that the Poynting effect (extension of a bar in torsion) is significantly influenced by coupling between dilatational and distortional strain energies, which is caused by the dependence of the shear modulus on dilatation.     

Theory and calculation of stress transfer between fiber and matrix

For the better use of composites and a deeper insight into the fracture propagation and stress transfer of the interface between fiber and matrix, a theoretical solution of closed form is presented with the assumed bilinear local bond-slip law and a parabolic shear stress distribution along the thickness of the matrix. The load-displacement relationship and interfacial shear stress are obtained for four loading stages. Finally, the effects of Young's modulus of fiber (matrix) and bond length on the performance of the interface are illustrated.     

基于微纳米压入法提取无铅焊料合金弹塑性力学参数的研究

本文通过微纳米压入法结合数值模拟研究了无铅焊料合金SnAg3.5 的弹塑性力学性能，分别采用圆柱形压头及两种不同锥角压头对无铅焊料合金进行压入测试：基于圆柱形压头测试过程中接触面积恒定的特点得到了无铅焊料的弹性模量，进一步采用塑性应变梯度理论对两种锥角压头的测试结果予以修正并通过数值模拟反分析得到相应的特征应力值，同时基于压入特征塑性应变与压头锥角的关系式得到两种不同锥角压头下的特征应变值，在此基础上经求解方程组得到焊料合金的初始屈服应力与应变强化因子，进而得到了焊料合金的幂强化弹塑性本构关系．该方法剔除了压入尺度效应的影响并保证了所得本构关系的唯一性，给出了一种通过原位压入测试表征金属材料弹塑性力学性能的有效方法．     

Statistical continuum theory for inelastic behavior of a two-phase medium

A statistical continuum mechanics formulation is presented to predict the inelastic behavior of a medium consisting of two isotropic phases. The phase distribution and morphology are represented by a two-point probability function. The isotropic behavior of the single phase medium is represented by a power law relationship between the strain rate and the resolved local shear stress. It is assumed that the elastic contribution to deformation is negligible. A Green’s function solution to the equations of stress equilibrium is used to obtain the constitutive law for the heterogeneous medium. This relationship links the local velocity gradient to the macroscopic velocity gradient and local viscoplastic modulus. The statistical continuum theory is introduced into the localization relation to obtain a closed form solution. Using a Taylor series expansion an approximate solution is obtained and compared to the Taylor’s upper-bound for the inelastic effective modulus. The model is applied for the two classical cases of spherical and unidirectional discontinuous fiber-reinforced two-phase media with varying size and orientation.     

Rheology of concentrated microgel solutions

Viscosity, modulus, and yield stress for 0–6 wt% aqueous solutions of Carbopol 941 were investigated using constant shear rate, constant shear stress, and dynamic oscillatory experiments. The microgel character of the polymer was evident from the solid-like behavior of the solutions above 1 wt%. Yield stress increased with concentration, but yield occurred at a critical shear strain of 40%, independent of concentration. The static stress-strain relationship became non-linear at ~ 25% strain, in fair agreement with the onset of non-linear response in the storage modulus at ~ 10% strain. Small strain moduli from static and low frequency measurements agreed rather well; modulus values obtained from the recoverable strain after yielding were 30–40% smaller. Solutions flowed at near-constant stress in the low shear rate regime; at higher rates the stress increases with shear rate more rapidly. The viscosity did not obey the Cox-Merz rule. Steady-state viscosity scaled with polymer concentration to the 3/4 power. Results were interpreted using a cellular, deformable sphere model for the polymer, in analogy to emulsions and foams.