考虑材料强化的塑性安定性分析

采用较真实的材料本构模型，在Ｐｏｎｔｅｒ和Ｋａｒａｄｅｎｉｚ提出的扩展的安定性理论以及彭得到的考虑混合强化的安定性定量的基础上，发展了计及应变强化和循环强化的结构塑性安定区的分析方法。通过将循环强化和应变强化分别引入子区域ＶＦ和ＶＳ，利用材料安定性假设，得到了较为合理的塑性安定边界，克服了以前的工作中对处于ＶＦ和ＶＳ区中材料分别采用完全各向同性强化（或假设热应力史是弹性应力史）和完全塑性的理想材料     

Plastic Flow Localization in Commercial Zirconium Alloys

The behavior of plastic flow curves and patterns of plastic strain localization were studied for tension of samples of Zr — 1% Nb (É110 alloy) and Zr — 1% Nb — 1.3% Sn — 0.4% Fe (É635 alloy) were studied. The relationship of the localization kinetics with the strain hardening law in plastic flow and transition to fracture is established. The dislocation microstructure of the alloys in strain localization and prefracture zones is examined.     

APPLICATION AND THEORETICAL ANALYSIS OF C/SiC COMPOSITES BASED ON CONTINUUM DAMAGE MECHANICS

Based on the thermodynamic theory, an orthotropic damage constitutive model was developed to describe the nonlinear mechanical behavior of C/SiC composites. The different nonlinear kinematic and isotropic hardening functions were adopted to describe accurately the damage evolution processes. The damage variables were defined with the damaged modulus and the initial undamaged modulus on energy equivalence principle. The initial orthotropy and damage coupling were presented in the damage yield function. Tensile and in-plane shear loading and unloading tests were performed, and a good agreement between the model and the experimental results was achieved.     

Equations of an Elastic Anisotropic Layer

Differential equations of an elastic orthotropic layer are constructed on the basis of expansion of the solutions of the elasticity theory in terms of the Legendre polynomials. The order of the system of differential equations is independent of the form of the boundary conditions on the layer surfaces, which allows a correct formulation of conditions on contact surfaces.     

理想正交各向异性弹塑性材料平面应变条件下静止裂纹尖端场

以Hill唯象理论为基础,建立正交各向异性弹塑性材料的本构关系,给出理想正交各向异性弹塑性材料在平面应变条件下混合型静止裂纹尖端的弹塑性场.与J.Pan的解不同,采用自相似假定,可以用解析方法求得不存在应力间断的应力场.对满塑性区条件和应变的奇异性加以讨论,这些为建立断裂准则提供了理论的依据.     

一种正交各向异性板的等效各向同性板计算法

上、下表面平整的正交各向异性板的有效抗扭刚度是2个主方向抗弯刚度的几何平均值. 根据这一特性、从正交各向异性板挠曲面的偏微分方程出发,保持一个主方向尺寸不变,另一主方向的尺寸做线性缩放,保持弹性模量与第一主方向相同,泊松比取2个主方向泊松比的几何平均值,将这类正交各向异性板等效为一块各向同性板;通过分析得到：各向同性板任意点的挠度就是原正交各向异性板对应点的挠度,各对应点内力之间存在简单的比例关系,该文的方法将为工程技术人员提供方便,同时可以更加直观的认识正交各向异性板的受力.     

Distortion of Anisotropic Hyperelastic Solids Under Pure Pressure Loading: Compressibility, Incompressibility and Near-Incompressibility

The purpose of this note is to examine distortion during pure pressure loading for anisotropic hyperelastic solids. We contrast the corresponding issues in compressible and incompressible hyperelasticity, and then use these results to examine nearly incompressible materials. An anisotropic compressible hyperelastic solid will generally exhibit both volume change and distortion under hydrostatic pressure loading. In contrast, an incompressible hyperelastic solid—both isotropic and anisotropic—exhibits no change to its current state of deformation as the hydrostatic pressure is varied. Nearly incompressible hyperelastic materials are compressible, but approach an incompressible response in an appropriate limit. We examine this limiting process in the context of transverse isotropy. The issue arises as to how to implement a nearly incompressible version of a given truly incompressible material model. Here we examine how certain implementations eliminate distortion under pure pressure loading and why alternative implementations do not eliminate the distortion.     

Material aspects of dynamic neck retardation

Neck retardation in stretching of ductile materials is promoted by strain hardening, strain-rate hardening and inertia. Retardation is usually beneficial because necking is often the precursor to ductile failure. The interaction of material behavior and inertia in necking retardation is complicated, in part, because necking is highly nonlinear but also because the mathematical character of the response changes in a fundamental way from rate-independent necking to rate-dependent necking, whether due to material constitutive behavior or to inertia. For rate-dependent behavior, neck development requires the introduction of an imperfection, and the rate of neck growth in the early stages is closely tied to the imperfection amplitude. When inertia is important, multiple necks form. In contrast, for rate-independent materials deformed quasi-statically, single necks are preferred and they can emerge in an imperfection-free specimen as a bifurcation at a critical strain. In this paper, the interaction of material properties and inertia in determining neck retardation is unraveled using a variety of analysis methods for thin sheets and plates undergoing plane strain extension. Dimensionless parameters are identified, as are the regimes in which they play an important role.     

On the evolution of isotropic and kinematic hardening with finite plastic deformation Part I: compression/tension loading of OFHC copper cylinders

Compression tests followed by tension tests after re-machining were performed on annealed oxygen-free-high-conductivity copper cylinders. These tests were conducted at nine levels of maximum strain ranging from 5 to 50%. From this data, isotropic and kinematic hardening were calculated using 50, 1000 and 2000 microstrain offset definitions. Both isotropic and kinematic hardening were found to depend on the yield definition. Isotropic hardening, which increased with plastic strain with no signs of saturation, also increased with larger offset definition of yield. Kinematic hardening, which increased to 40% strain and appeared to saturate thereafter, decreased with higher offset definitions of yield.     

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     

塑性预应变对屈服条件影响的实验研究

本文介绍了确定具有塑性予应变板材后继屈服条件的实验方法。铝合金板LY12～M12的实验研究表明:随着塑性予应变的增加,将依次出现各向同性强化、运动强化以及组合强化。     

One plasticity model for problems of plastic metal working

Scalar and tensor models of plastic flow of metals extending plasticity theory are considered over a wide range of temperatures and strain rates. Equations are derived using the physico-phenomenological approach based on modern concepts and methods of the physics and mechanics of plastic deformation. For hardening and viscoplastic solids, a new mathematical formulation of the boundary-value plasticity problem taking into account loading history is obtained. Results of testing of the model are given. A numerical finite-element algorithm for the solution of applied problems is described. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 159–169, November–December, 2008.     

Axisymmetric thermoelastoplastic stress-strain state of flexible laminated transversely isotropic shells

The paper presents a technique for numerical analysis of the elastoplastic stress-strain state of flexible laminated shells of revolution made of isotropic and transversely isotropic materials and subjected to axisymmetric loading and heating. The technique is based on the Kirchhoff-Love hypotheses for the whole laminate. The deformation of the isotropic materials is described using the theory of deformation along paths of small curvature. The deformation of the transversely isotropic material is described using the flow theory with isotropic hardening. The process of loading is divided into steps at each of which the stress-strain state is determined by the method of successive approximations. A numerical example is given __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 76–86, December, 2006.     

Anisotropic plastic fields at a rapidly propagating crack-tip

Under the condition that all the stress components at a crack-tip are the functionsofθonly,making use of the equations of steady-state motion,stress-strain relationsand Hill anisotropic yield conditions,we obtain the general solutions at a crack-tip inboth the cases of anti-plane and in-plane strains.Applying these general solutions tothe concrete cracks,the anisotropic plastic fields at the rapidly propagating tips ofmodeⅢand modeⅠcracks are derived.     

正交异性体反平面问题另一形式自相似解的推导

正交异性体的反平面运动方程有几种表达方式，而以自相似解表达方式尤为简单。由于在弹性动力学问题的计算中可以获得解析解，使得考虑的问题相应地简化，并具有一定的普遍性，因此对自相似形式的解的推导具有重要的意义。本文针对这一问题进行研究，利用复变函数论的方法导出另一形式自相似解的一般表达式。应用该法可以很容易地将所讨论的问题转化为Riemann—Hilbert问题，而后一问题可以用同通常的Muskhelishvili方法求解，并且可以相当简单地得到问题的闭合解。这些解在断裂动力学以及弹性动力学问题当中具有重要的应用价值。     

Thermoelastoplastic Stress—Strain State of Laminated Transversely Isotropic Shells under Axisymmetric Loading

A method is proposed for determining the thermoelastoplastic stress–strain state of laminated shells of revolution, made of isotropic and transversely isotropic materials, under axisymmetric loading. The method is based on the Kirchhoff–Love hypotheses for a layer stack, the theory of deformation along paths of small curvature for isotropic materials, and Hill's flow theory with isotropic hardening for transversely isotropic materials. The loading history is accounted for. The problem is solved by the method of successive approximations. Numerical examples are given     

Asymptotic integration of elasto-plastic constitutive relation for isotropic hardening material and its computational precision

In this paper, an asymptotic expansion solution of the constitutive equation of hardening materials is presented. Its 1st asymptotic integration can give an approximate one with good enough accuracy and the second asymptotic one improves the precision of solutions further. The steps of its algorithms are fairly simple and clear, and its computational workload is considerably reduced. It can be easily incorporated into a general purpose finite element program.The Chinese original of this article was published in the Chinese edition ofActa Mechanica Solida Sinica, No. 1, 1986.     

Propagation of Quasiacoustic Pulses in an Elastoplastic Medium

Expressions for the velocity of a plastic shock wave and phase velocity of longitudinal waves in an elastoplastic medium with hardening are obtained in a quasiacoustic approximation. An analytical solution of the problem of shockpulse attenuation is constructed. A special feature of the amplitude of the attenuating plastic shock wave is that it reaches the amplitude of the elastic precursor in a finite time, whereas in hydrodynamics, the amplitude of a quasiacoustic shock pulse tends to zero asymptotically.     

Anisotropic work hardening of steel sheets under plane stress

This work is a follow-up of the previous report by Kim and Yin [Kim, K.H., Yin, J.J., 1997. Evolution of anisotropy under plane stress. J. Mech. Phys. Solids 45, 841–851] regarding the anisotropic work hardening of cold rolled steel sheets. Tensile prestrain has been applied at angles to the rolling direction and then tensile uniaxial yield stress and R-value distributions are measured. As reported earlier, the orientations of local maxima and minima in the yield stress are altered when the prestrain axis is not in the rolling direction. This led Kim and Yin [Kim and Yin (1997)] to suggest that the orientations of orthotropy axes are altered by the tensile prestrain at angles to the rolling direction. However, R-value distribution is found to be hardly affected by the prestrain. The unchanging R-value distribution shows that the material remembers the rolling direction even after the prestrain. An attempt is made to approximate the observed yield and flow behavior based upon isotropic-kinematic hardening with the quadratic yield function (Hill, 1948). The degree of approximation raises the issues of yield point definition, flexibility of yield function, non-associated flow rules, distortional hardening and others.     

Numerical Nonaxisymmetric Thermostress Analysis of Compound Solids of Revolution with Damage

A technique is proposed to allow for deformation damage of cylindrically orthotropic elastic materials in a thermoelastoplastic stress–strain analysis of composite bodies of revolution under nonaxisymmetric loading and heating