拉－扭复合加载下不锈钢的弹塑性本构关系——Ⅱ．理论

提出应力是塑性应变空间内蕴几何学参数的泛函．一般情况下，塑性应变空间是非欧几何空间，而其度量张量是塑性应变和其历史的函数，但在初始各向同性和不可压的情况下可取成欧氏空间．本文在Ｉｌｙｕｓｈｉｎ理论，和Ｖａｌａｎｉｓ理论的基础上，提出在拉－扭复合加载下的εｐ１－εｐ３空间中新的积分型弹塑性本构关系，所建理论预测的结果和实验［１］相当一致，表明理论是合理的     

钻孔法测定焊接残余应力时的εp

用钻孔法测定焊接残余应力，孔边塑性变形对测量精度有很大影响。本文对孔边屈服过程进行了研究。克服了以往在误差修正方法中的不足，确定了塑性释放应变εｐ与主应力δ１、δ２和主方向角β的函数关系：εｐ＝ｆ（δ１、δ２、β），用以修正这塑变引起的测量误差，使得在二维应力状态下最大值近２０％的测量误差降至２％以下。     

应变损伤材料I型动态扩展裂纹尖端场的渐近分析

研究了应变损伤材料Ｉ型动态扩展的裂纹尖端场。假定材料服从Ｊ２流动理论，且损伤规律以幂律应变软化的规律给出。对于塑性区引进了应力函数φ，ψ０借助于动力学方程的分析，给出了渐近方程及数值解。结果表明，对于可压缩材料Ｉ型平面应变尖端场是完全由塑性区组成，没有弹性卸载区。在裂纹尖端附近，应力和应变分别具有如下的奇异性：σ￣（ｌｎＲ／ｒ）＾－ｎ／ｎ＋１，ε￣（ｌｎＲ／ｒ）＾１／ｎ＋１。     

拉─扭复合加载下不锈钢的弹塑性本构关系─I．实验

讨论了１Ｃｒ１８Ｎｉ９Ｔｉ不锈钢薄壁圆管试件沿三段折线、不同曲率的圆形和椭圆应变路径承受拉－扭复合载荷的实验．在塑性应变空间中，观察加载路径的内蕴几何参数对应力矢量大小、方向影响的规律．结果表明：响应的延迟角、瞬时软化和重新强化性质与路径的内蕴几何学密切相关；Ｌｅｎｓｋｙ的“局部确定性”假设不完全符合事实；变形历史和应变分量相互间的耦合效应对响应存在显著的影响．初步的电镜实验表明，材料中的位错组态和塑性应变历史密切相关     

描述大应变率范围下材料响应的粘塑性本构模型

以位错动力学理论中的Ｏｒｗａｎ和Ｇｉｌｍａｎ关系为基础建立描述率相关材料非弹性响应的基本方程，选择材料准静态实验的单轴响应作为强化演化的规律，并考虑应变率敏感程度随变形产生变化的特性，建立了适用于大应变率范围内率相关材料的统一型粘塑性本构模型。对铝１１００－０在应变率范围１０－５～１０４ｓ－１内产生的有限塑性应变的单轴响应进行了理论预测，与Ｋｈａｎ和Ｈｕａｎｇ［１］的实验数据及模型预测结果进行了比较，结果表明本文模型具有较高的预测精度，在高应变率和较大应变下不容忽视率敏感参数随变形的变化。     

COMP．B复合炸药动态力学性能和塑性流动本构关系的研究

利用自制的含能材料动态变温三轴压缩实验装置，采用准静态应变速率（１０－４／ｓ）和中等应变速率（３／ｓ），对国产复合炸药Ｃｏｍｐ．Ｂ进行了三轴压缩实验．测试了Ｃｏｍｐ．Ｂ在不同温度、不同应变速率条件下的杨氏模量Ｅ，泊松比ν和屈服强度Ｙ．实验结果表明，Ｃｏｍｐ．Ｂ具有明显的应变率相关和热软化效应．基于热激活模型，作了适当的改进，根据实验数据建立了含能材料塑性流动模型，分析表明该模型能合理地描述率相关材料的塑性流动，同时考虑了应变率和温度对塑性流动的影响．这些基础研究为含能材料动态力学性能的研究和炸药早爆机理的理论分析提供了依据     

人造多晶冰抗压强度实验研究

对实验室制作的平均粒径为４ｍｍ的宏观各向同性粒状多晶冰，在冰温分别为－０．５、－２、－５和－１０℃及应变率分别为４．２×１０－４、５．５×１０－５、５．５×１０－６及３．５×１０－７ｓ－１下进行了单轴抗压强度实验。结果表明，极限抗压强度与负温和应变率的对数均呈正比例关系；在较高应变率下（４．２×１０－４ｓ－１），在－５℃时，出现韧脆性转折点。     

梯度塑性的有限元分析及应变局部化模拟

对梯度塑性连续体提出了一个有限元方法．内状态变量的Ｌａｐｌａｃｉａｎ的确定基于它在求积点邻域的最小二乘方多项式近似．具体地考虑了具有一点求积和Ｈｏｕｒｇｌａｓｓ控制特点的基于胡海昌－Ｗａｓｈｉｚｕ变分原理的混合应变元和单元平均意义下的ｖｏｎ－Ｍｉｓｅｓ屈服准则．解析地导出了梯度塑性下一致性单元切线刚度矩阵和速率本构方程的一致性积分算法．在所建议的非局部化途径中求积点的一致性条件在非局部化意义下逐点精确满足．数值例题表明所提出的非经典连续体的有限元方法求解应变局部化问题的有效性     

16Mn钢在低、常温下对冲击拉伸载荷的响应

对１６Ｍｎ钢在２０℃、－４０℃、－８０℃温度场下，进行了应变率为４０ｓ－１和４８０ｓ－１的冲击拉伸的试验研究．得出其动态本构关系及其相关参数．揭示了１６Ｍｎ钢不仅属于应变率敏感材料，而且亦属于温度敏感材料     

梯度塑性的有限元分析及应变局部化模拟

对梯度塑性连续体提出了一个有限元方法．内状态变量的Ｌａｐｌａｃｉａｎ的确定基于它在求积点邻域的最小二乘方多项式近似．具体地考虑了具有一点求积和Ｈｏｕｒｇｌａｓｓ控制特点的基于胡海昌－Ｗａｓｈｉｚｕ变分原理的混合应变元和单元平均意义下的ｖｏｎ－Ｍｉｓｅｓ屈服准则．解析地导出了梯度塑性下一致性单元切线刚度矩阵和速率本构方程的一致性积分算法．在所建议的非局部化途径中求积点的一致性条件在非局部化意义下逐点精确满足．数值例题表明所提出的非经典连续体的有限元方法求解应变局部化问题的有效性     

An integral elasto-plastic constitutive theory

This paper proposes an integral elasto-plastic constitutive equation, in which it is considered that stress is a functional of plastic strain in a plastic strain space. It is indicated that, to completely describe a strain path, the arc-length and curvature of the trajectory, the turning angles at the corner points and other characteristic points on the path must be considered. In general, the plastic strain space is a non-Euclidean geometric space, hence its measure tensor is a function of not only properties of the material but also the plastic strain history. This recommended integral elasto-plastic constitutive equation is the generalization of Ilyushin, Pipkin, Rivlin and Valanis theories and is suited to research the responses of material under the complex loading path. The predictions of the proposed theory have a good agreement with the experimental results.     

Formulation of stress-strain relation for plastic deformation of mild steel for strain trajectory consisting of two straight branches

A relation between the stress and incremental strain deviators, which are not coaxial, is derived by considering the characteristics in tensor space. On the bases of this relation and of precise experimental results for mild steel, a specific plastic stress-strain relation is formulated for a strain trajectory with a comer in a 3D-vector space corresponding to the strain deviator, as a typical example of plastic behaviour under complex loading. It may be confirmed that the effects of plastic anisotropy and of the third invariant of the strain deviator on the plastic behaviour of mild steel under complex loading are expressed precisely by means of the above formulation.     

On nonlocal rate-independent plasticity

A nonlocal rate-independent large strain theory for elastic-plastic bodies consistent with thermodynamic theory is derived. The theory is based on a strain space formulation, where plastic strain is regarded as a primitive variable, characterised by an appropriate constitutive equation for its rate. Stress and free energy are assumed to be functions of a set of nonlocal variables, constructed from a collection of basic state functions, constituted by strain, plastic strain and a scalar measure of strain hardening. A yield function is introduced depending on the same set of independent, nonlocal variables. Yield criteria, flow rules, and loading conditions are formulated. The consistency condition is not, as in local theory, expressed by an algebraic equation, but by an integral equation defined throughout the region of plastic loading.     

The Facet method: A hierarchical multilevel modelling scheme for anisotropic convex plastic potentials

An entirely new analytical expression describing plastic anisotropy is presented. It is designed to be used in combination with multilevel models. It makes use of the theory of dual plastic potentials, which is shortly revisited. An analysis of convexity is presented. Note that the new method is not optimal when not used in combination with a multilevel model; other methods are better suited for identification on the basis of mechanical test data. Compared with already existing methods which work with multilevel models, the new method has the following advantages: (i) it is automatically convex anywhere in the six-dimensional stress or strain rate space; (ii) it can be used for materials with a stress differential effect, such as hcp metals or pre-strained cubic materials; (iii) its identification procedure is such that not only the Taylor theory, but also more advanced theories, such as the Alamel-model or self-consistent models, can be used to identify the parameters; (iv) an analytical expression of the plastic potential can be obtained in both strain rate and stress space, which is an important advantage when implementing the model in finite element codes for metal forming. Equipotential surfaces in strain rate space and corresponding yield loci obtained by the new method for four materials (one ferrite single crystal, one aluminium alloy and two types of steel) are presented and discussed.     

基于能量等效原理的应变局部化分析:Ⅰ.一维解析解

基于热力学第一定律和非局部塑性理论,提出了一种求解应变局部化问题的非局部方法.对材料的每一点定义了局部和非局部两种状态空间,局部状态空间的内变量通过非局部权函数映射到非局部空间,成为非局部内变量.在应变软化过程中,局部状态空间中的塑性变形服从正交流动法则,材料的软化律在非局部状态空间中被引入.通过两个状态空间的塑性应变能耗散率的等效,得到了应变软化过程中明确定义的局部化区域以及其中的塑性应变分布.应用本方法导出了一维应变局部化问题的解析解.解析解表明,应变局部化区域的尺寸只与材料内尺度有关;对于高斯型非局部权函数,局部化区域的尺寸大约是材料内尺度的6倍.一维算例表明,局部化区域的塑性应变分布以及载荷-位移曲线仅与材料参数和结构几何尺寸有关,变形局部化区域的尺寸随着材料内尺度的减小而减小,同时塑性应变也随着材料内尺度的减小变得更加集中.当内尺度趋近于零时,应用本文方法得到的解与采用传统的局部塑性理论得到的解相同.     

Experimental determination of strain-induced anisotropy during nonproportional straining of an A1/Mg alloy at room temperature

A servohydraulic, computer controlled MTSn axial-torsion testing machine with a bi-axial clip-on extensometer is used to test thin-walled tubes of an A1/Mg alloy under strain control. A plastic offset strain of 10⁻⁴ determines the yield surfaces. Straining and yield surface probing is governed by a computer program which also controls digital data acquisition. Yield surfaces in stress and in strain space as well as the axial and shear stress-strain diagrams can be reconstructed from the digitally recorded data. The specimens were subjected to a strain path in the form of a regular 16-sided polygon which was followed on some specimens by a square path. The total inelastic strain path length can exceed 15% while the equivalent strain excursion is less than 2%. It is shown that yield surfaces measured on specimens withclose initial stress-strain diagrams are very consistent and that yield surface probing has an insignificant effect on subsequent yield surfaces. Yield surfaces are shown to translate, changein shape and size and to exhibit a cross effect. A post processor which includes a least square smoothing routine calculates the area and the centroid of each yield surface. The size increase is initially rapid but the rate of increase decreases as a saturation is approached. After strining for less than 1% in a fixed direction a characteristic yield surface shape is established. Yield surfaces obtained at the same point in strain space with identical prestrain direction of at least 1% but with increased amounts of accumulated plastic strain have the same shape but show an increase in size. The yield surfaces differ in shape and size when the same strain point is reached from different directions. The centroid of the yield surface in stress space moves almost in a circular path for a polygonal strain path. All stress space yield surfaces contain the origin but this is not the case for the surfaces in strain space.     

A generalized formulation of the concept of nonhardening region

A stable hysteresis loop is realized under a cyclic loading between fixed strain limits for metals. To describe this phenomenon the idea of memory hypersphere was proposed by Chabocheet al. [1979] and it has been extended by Ohno [1982] as the concept of nonhardening (strain) region, which assumes that an isotropic hardening does not proceed when a plastic strain exists inside a hypersphere in the plastic strain space. A generalized formulation for this concept is presented in this article, which concerns isotropic-kinematic hardening materials, not limited to metals, undergoing a large deformation with a material rotation.     

NONSMOOTH MODEL FOR PLASTIC LIMIT ANALYSIS AND ITS SMOOTHING ALGORITHM

By means of Lagrange duality theory of the convex program, a dual problem of Hill's maximum plastic work principle under Mises' yield condition has been derived and whereby a non-differentiable convex optimization model for the limit analysis is developed. With this model, it is not necessary to linearize the yield condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subject to linear constraints. Aimed at resolving the non-differentiability of Euclidean norms, a smoothing algorithm for the limit analysis of perfect-plastic continuum media is proposed. Its efficiency is demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems.     

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.