Plastic deformation of aluminium alloy under abruptly-changing loading or strain paths

The effect of deformation history on the plastic behaviour of thin-walled tubular specimens of aluminium alloy 5056 was examined for three types of abruptly-changing loading or strain paths: namely, reverse loading after pre-loading, orthogonal straining after pre-strain, and orthogonal reloading after pre-loading and then perfect unloading, by applying combined loadings of axial force and torque. The experimental results revealed the following trends. The relation between the magnitudes of stress and strain after the comer is expressed for every pre-strain by a single curve parallel to the extension of the pre-loading curve, when the strain after the corner exceeds 1.2 per cent. Moreover, the relations between the stress reduced by pre-stress and strain after the corner for various values of the same type of pre-strain agree with each other; however, the relation for the tensile pre-strain differs clearly from that for the torsional pre-strain. Thus, A.A. Il'yushin's postulate of isotropy does not hold accurately for the above loading histories for the aluminium alloy even if the effect of the third invariant of stress deviator is eliminated.     

304不锈钢室温和高温单轴循环塑性的实验研究

对304不锈钢进行了室温和高温单轴应变控制和应力控制下的系统循环试验。揭示和分析了循环应变幅值、平均应变及其历史和温度历史对材料应变循环特性的影响以及应力幅值、平均应力及其历史以及温度对循环棘轮行为的影响。也讨论了应变循环和应力循环间交互作用对材料循环塑性行为的影响。研究表明,无益单轴应变循环特性还是非对称单轴应力循环下的棘轮效应不仅取决于当前温度和加载状态,而且强烈依赖于其加载历史。研究得到了一些有助于304不锈钢室温和高温单轴循环行为本构描述的结果。     

Uniaxial and non-proportionally multiaxial ratcheting of SS304 stainless steel at room temperature: experiments and simulations

The uniaxial and non-proportionally multiaxial ratcheting behaviors of SS304 stainless steel at room temperature were initially researched by experiment and then were theoretically described by a cyclic constitutive model in the framework of unified visco-plasticity. The effects of cyclic stress amplitude, mean stress, and their histories on the ratcheting were experimentally investigated under uniaxial and different multiaxial loading paths. The shapes of non-proportional loading paths were linear, circular, elliptical and rhombic, respectively. In the constitutive model, the rate-dependent behavior of the material was reflected by a viscous term; the cyclic flow and cyclic hardening behaviors of the material under asymmetrical stress-controlled cycling were reflected by the evolution rules of kinematic hardening back stress and isotropic deforming resistance, respectively. The effect of loading history on the ratcheting was also considered by introducing two fading memorization functions for maximum inelastic strain amplitude and isotropic deformation resistance, respectively, into the constitutive model. The effect of multiaxial loading path on the ratcheting was reflected by a non-proportional factor defined in this work. The predicting ability of the developed model was proved to be good by comparing the simulations with corresponding experiments.     

Structural strength: Gasketed vs non-gasketed flange joint under bolt up and operating condition

This paper presents results of an experimental study of the behaviour of the stress variation at the flange of a gasketed and non-gasketed flanged pipe joints during both the bolt up (pre-loading) and operating (internal pressure loading) conditions. Stress variations showing flange yielding, flange rotation, effects of joint tightening sequence, identification of the mode of response to loading (static or dynamic) is discussed. In addition the effects of re-tightening, importance of high quality bolting with proper surface treatment and use of proper tooling are also discussed.     

Incorporation of yield surface distortion in finite deformation constitutive modeling of rigid-plastic hardening materials based on the Hencky logarithmic strain

In this paper a constitutive model for rigid-plastic hardening materials based on the Hencky logarithmic strain tensor and its corotational rates is introduced. The distortional hardening is incorporated in the model using a distortional yield function. The flow rule of this model relates the corotational rate of the logarithmic strain to the difference of the Cauchy stress and the back stress tensors employing deformation-induced anisotropy tensor. Based on the Armstrong–Fredrick evolution equation the kinematic hardening constitutive equation of the proposed model expresses the corotational rate of the back stress tensor in terms of the same corotational rate of the logarithmic strain. Using logarithmic, Green–Naghdi and Jaumann corotational rates in the proposed constitutive model, the Cauchy and back stress tensors as well as subsequent yield surfaces are determined for rigid-plastic kinematic, isotropic and distortional hardening materials in the simple shear deformation. The ability of the model to properly represent the sign and magnitude of the normal stress in the simple shear deformation as well as the flattening of yield surface at the loading point and its orientation towards the loading direction are investigated. It is shown that among the different cases of using corotational rates and plastic deformation parameters in the constitutive equations, the results of the model based on the logarithmic rate and accumulated logarithmic strain are in good agreement with anticipated response of the simple shear deformation.     

On the modeling and simulation of induced anisotropy in polycrystalline metals with application to springback

The presence of initial, and the development of induced, anisotropic elastic and inelastic material behavior in polycrystalline metals, can be traced back to the influence of texture and dislocation substructural development on this behavior. As it turns out, via homogenization or other means, one can formulate effective models for such structure and its effect on the macroscopic material behavior with the help of the concept of evolving structure tensors. From the constitutive point of view, these quantities determine the material symmetry properties. Most importantly, all dependent constitutive fields (e.g., stress) are by definition isotropic functions of the independent constitutive variables, which include these evolving structure tensors. The evolution of these tensors during loading results in an evolution of the anisotropy of the material. From an algorithmic point of view, the current approach leads to constitutive models which are quite amenable to numerical implementation. To demonstrate the applicability of the resulting constitutive formulation, we apply it to the case of metal plasticity with combined hardening involving both deformation- and permanently induced anisotropy. Comparison of simulation results based on this model for the bending tension of aluminum-alloy sheet-metal strips with corresponding experimental ones show good agreement.     

Effect of the rate dependence of nonlinear kinematic hardening rule on relaxation behavior

Relaxation experiments for metallic materials and solid polymers have exhibited nonlinear dependence of stress relaxation on prior loading rate; the relaxed stress associated with the fastest prior strain rate has the smallest magnitude at the end of the same relaxation periods. Modeling capability for the basic feature of relaxation behavior is qualitatively investigated in the context of unified state variable theory. Unified constitutive models are categorized into three general classes according to the rate dependence of kinematic hardening rule, which defines the evolution of the back (equilibrium) stress and is the major difference among constitutive models. The first class of models adopts the nonlinear kinematic hardening rule proposed by Armstrong and Frederick. In this class, the back stress appears to be rate-independent under loading and subsequent relaxation conditions. In the second class of models, a stress rate term is incorporated into the Armstrong–Frederick rule and the back stress then becomes rate-dependent during relaxation condition even though it remains rate-independent under loading condition. The final class proposed here includes a new nonlinear kinematic hardening rule that causes the back stress to be rate-dependent all the time. It is shown that the apparent rate dependence of the back stress during relaxation enables constitutive models to predict the influence of prior loading rate on relaxation behavior.     

316L不锈钢随动强化模型改进研究

本文对316L不锈钢进行了单轴与多轴非比例路径下的应力控制棘轮试验,考察了应力幅值、平均应力和加载历程对棘轮特性的影响。同时进行了应变控制循环试验以研究材料的应力松弛特性。试验结果表明轴向棘轮效应在对称剪切荷载下效果明显,同时棘轮应变随应力幅值和平均应力的增加而增加。研究了Chen-Jiao随动强化模型与Jiang-Sehitoglu随动强化模型采用的单轴与多轴参数对背应力分量增量方向的影响,将Chen-Jiao模型中的多轴系数替换为界面饱和率,并在此基础上引入新的参数对塑性模量系数进行修正,计算结果表明修正后的模型能提升应力控制下多轴棘轮的预测精度,并能很好的预测应力松弛现象,表明了新模型的正确性与有效性。     

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.     

晶粒数量对多晶集合体初始各向异性的影响

Taylor类多晶晶体粘塑性模型被用于研究晶粒数量对随机分布多晶体拉伸塑性各向异性的影响。分别沿包含不同晶粒数量的多晶集合体的各方向进行单向拉伸数值模拟实验，得到多晶集合体各方向在一定等效应变下的等效应力，并用云图和等高线表示在多晶体的参考球面上。定义了描述多晶集合体各向异性程度的参考指标。讨论了三种确定晶体随机取向的方法。计算结果表明：晶粒数量有限的多晶集合体的应力应变响应仍有一定的各向异性，且随着晶粒数量增多，多晶集合体的各向异性程度降低；就所包含晶粒数相同的多晶集合体来说，在确定晶粒随机取向时，选取不同的方法对它的各向异性程度也有一定的影响。     

Anisotropic hardening model and its application to cyclic loading

The experimental study of evolution rules of two state variables: back street _ij and yield stress R are first discussed. It is shown that back stress evolution is affected by the maximal prestress, and asymptotic value of yield stress depends on strain amplitude. The constitutive model is presented next, and its prediction for cyclic loading program is compared with experimental data.     

Analytical solutions for anisotropic bimaterials under several boundary conditions on the interface

Summary Analytical solutions are proposed for the stress and displacement fields induced by in-plane loading of a bimaterial under several boundary conditions. The two joined orthotropic layers forming the bimaterial are allowed to possess different types of anisotropy with their planes of elastic symmetry arbitrarily inclined with respect to the horizontal.     

Influence of the Direction of the Principal Anisotropy Axes in a Rectilinearly Orthotropic Material on the Stress State of a Compound Solid of Revolution Subject to Nonaxisymmetric Heating

A technique for analysis of the temperature fields and the stress state of isotropic and orthotropic laminated bodies of revolution under nonaxisymmetric loading is described. The influence of the direction of the principal anisotropy axes in a rectilinearly orthotropic material on the stress state of a three-layer body of revolution under nonaxisymmetric loading is studied     

Finite strain analysis of simple shear using recent anisotropic yield criteria

The finite strain response of a rectangular block subjected to constrained simple shearing deformations is considered in order to evaluate the predictive capability of some recently proposed anisotropic yield functions. It is shown that, in the presence of plane anisotropy, the prediction of realistic second order normal stresses cannot be expected since every different initial orientation of the material axes relative to the loading axes results in a different response due to the rotation of the material axes with shear. Parametric studies are performed in order to determine possible limits on the material constants so that the predicted normal stresses remain second order with respect to the shear stress itself. Our numerical results indicate that, in particular, the commonly employed range of one parameter associated with grain related anisotropy renders results which no longer imply predicting a proper second order effect but rather introduces errors of the first order. The results suggest that the modelling of anisotropy with such phenomenological anisotropic yield functions should be limited to near-quadratic yield surfaces for applications involving stress states outside the biaxial tensile stress range.     

Photoelastic-coating analysis of dynamic stress concentration in composite strips

Dynamic stress concentration in high-velocity tension is investigated for fiber-reinforced composite strips with a central circular hole. The photoelastic-coating technique is utilized with a newly constructed nine-frame Cranz-Schardin high-speed reflection-type camera. The excellent reflective plane is the key to obtaining clear isochromaticfringe patterns. Four different kinds of composites in a very wide range of anisotropy are tested to study the effects of anisotropy, loading direction and the hole-diameter/specimenwidth ratio on the dynamic-stress distribution. Dynamic-stress and strain distribution around a hole is found to vary remarkably with the change in anisotropy of each composite. In some tests, dynamic fractures caused by stress concentration are also detected in high-speed photos. Photoelastic-coating results are then compared with the results obtained by straingage experiments and finite-element numerical analysis in order to verify the validity of the present dynamic photoelasticoating analysis.while the present research was conducted.Paper was presented at 1982 SESA/JSME Spring Meeting held in Oahu and Maui, HI on May 23–30, 1982.     

Precise measurement of plastic behaviour of mild steel tubular specimens subjected to combined torsion and axial force

In the present paper, as an investigation for obtaining detailed information about the plastic behaviour of real materials, precise measurement of plastic deformation of thin-walled tubular specimens of initially-isotropic mild steel was performed under combined loading of torsion and axial force having trajectories consisting of two straight lines at a constant rate of the effective strain.From the experimental results, it is found that the effect of the third invariant of the strain tensor appeared even for proportional deformation consisting of torsion and axial force. Moreover, it may be seen that the effective stress drops suddenly with increasing effective strain, and coaxiality between the stress deviator and the plastic strain increment tensor is seriously disturbed just after the corner of the strain trajectory. However, these local disturbances are recovered along the second branch of the trajectory.The effect of the third invariant of the strain tensor was eliminated from the experimental results by the introduction of the modified local stress space for isolating the influence of anisotropy due to the deformation history. This permits a systematic evaluation of the influence of anisotropy for various types of combined loading.     

π平面上原状土的空心扭剪试验

为了通过空心扭剪试验获得原状土在π 平面上的屈服特性,在分析空心扭剪试验仪加载过程和加载特点的基础上,研究了空心圆柱试样可实现的应力状态,并设计了相应的加载路径．与重塑试样不同,原状土样的初始应力状态位于K0 固结线上而不是等倾线上,因此,其加载路径应从原点开始沿K0 固结线行至原始应力状态,然后再在π 平面上进行以初始应力为起点的等p 试验．在考虑原状土的初始应力状态和各项异性的基础上,针对具有不同主应力方向角的平行试样,给出了等p 条件下保持主应力方向角不变的加载路径实现方法,采用该方法可得到任意平均主应力时π 平面上六分之一范围内的屈服曲线,该范围对应于大主应力方向角从-45o~45o．本文设计的加载方案可完成真三轴试验的部分功能,但经济成本相对较低,操作方法简单易行．     

Finite and transversely isotropic elastic cylinders under compression with end constraint induced by friction

This paper derives an exact solution for the non-uniform stress and displacement fields within a finite, transversely isotropic, and linear elastic cylinder under compression with a kind of radial constraint induced by friction between the end surfaces of the cylinder and the loading platens. The main feature of the present work is the introduction of a general solution form for Lekhnitskii’s stress function such that the governing equation and all end and curved boundary conditions of the cylinder are satisfied exactly. Two different solutions were obtained corresponding to the real or complex characteristic roots of the governing equation, depending on the combination of the elastic material constants. The solution by Watanabe [Watanabe, S., 1996. Elastic analysis of axi-symmetric finite cylinder constrained radial displacement on the loading end. Structural Engineering/Earthquake Engineering JSCE 13, 175s–185s] for isotropic cylinders under compression test can be recovered as a special case. Our numerical results show that both the non-uniform stress distribution and the difference between the apparent and the true Young’s moduli of the cylinder are very sensitive to the anisotropy of Young’s moduli, Poisson’s ratios and shear moduli. A more distinct bulging shape of the cylinder is expected when anisotropy in shear modulus is strong, the cylinder is relatively short, and the end constraint is large. The bulging shape, however, does not depend strongly on anisotropy of either Poisson’s ratio or Young’s modulus.     

三维结构安定分析的直接算法

基于线性随动强化理论和Von. Mises屈服准则,对蒙板结构直接安定分析法进行了扩展,建立了结构的三维安定直接分析法。根据投射原理,推导出结构发生塑性安定的存在条件,便于调整控制加载步长和载荷历程。采用逐次增量加载方式,确定出背应力的偏移范围,克服了原始直接分析法不能获得安定极限的缺陷,并得到安定极限条件下结构中残余应力与应变的分布状况。该数值方法将弹塑性问题分解为弹性问题和特征应变决定的残余问题,节约计算时间,提高计算效率,将该算法应用于相关算例,并与有关数值结果相比较,验证了该算法的有效性。     

Numerical simulation study on particle breakage behavior of granular materials in confined compression tests

In order to study the fragmentation law, the confined compression experiment of granular assemblies has been conducted to explore the particle breakage characteristic by DEM approach in this work. It is shown that contact and contact force during the loading process gradually transform from anisotropy to isotropy. Meanwhile, two particle failure modes caused by different contact force states are analyzed, which are single-through-crack failure and multi-short-crack failure. Considering the vertical distribution of the number of cracks and the four characteristic stress distributions (the stress related to the maximum contact force, the major principal stress, the deviatoric stress and the mean stress), it is pointed out that the stress based on the maximum contact force and the major principal stress can reflect the distribution of cracks accurately. In addition, the size effect of particle crushing indicates that small size particles are prone to break. The lateral pressure coefficient of four size particles during the loading process is analyzed to explain the reason for the size effect of particle breakage.