A New Static Failure Criterion for Isotropic Polymers

A new static failure criterion for isotropic polymers with different strengths in tension and compression based on exponential dependence between the mean stress and the von Mises equivalent stress is proposed. The two material parameters introduced can be determined by two simple tests - the uniaxial tension and compression. The locus of the criterion is nearly conical for low hydrostatic pressures and tends to a cylindrical form if an increased hydrostatic pressure is applied. The validity of the criterion is demonstrated by experimental strength data taken from the literature for several polymers in the case of superimposed hydrostatic pressure.     

Contribution to the theory of forced high-elastic deformation of polymer materials

The large reversible and irreversible deformations of network polymers are examined. Expressions are derived for the stress tensor and for the conventional tensile stress. The uniaxial homogeneous extension curve has a maximum and a minimum if it is assumed that the coefficient of friction depends exponentially on the applied stress. The "necking" condition is derived for uniaxial tension. The results are compared with the experimental data.Mekhanika Polimerov, Vol. 4, No. 2, pp. 255–262, 1968     

非线性各向同性弹性材料热应力本构方程

在非线性各向同性弹性体张量形式的本构方程基础上,仅考虑温度初值和增值,按照表示定理,补充考虑温度影响的完备项,建立了非线性各向同性弹性材料完备的多项式形式的热应力本构方程和应变能函数．作为应用举例,利用MATLAB软件,将本构方程与现有文献中高温金属材料单向拉伸和压缩情况下弹性阶段的实验数据进行了拟合,结果表明实验值与所提出的理论模型的结果显示了良好的一致性．     

Estimation of the anisotropy of the short-time and long-time strengths of glass-reinforced plastics

A linear correlation between the tensile stress and the logarithm of the lifetime of a glass-reinforced plastic in various directions in the plane of the sheet has been experimentally established. The parametric introduction of the time factor into the criterion of the short-time strength of anisotropic materials is proposed as a first approximation. The Gol'denblat-Kopnov criterion is used to derive a simple relation describing the strength properties of glass-reinforced plastics in the uniaxial state of stress.Moscow Institute of Chemical Machine-Building. Scientific-Research Institute of Mechanics, Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 243–249, March–April, 1969.     

Long-Term Strength Criteria for Some Polymer Materials under a Plane Stress State

The problem of the choice and experimental justification of long-term failure criteria for isotropic polymer materials in creep under a plane stress state is considered. The criteria are defined by a linear two-parameter interpolation relating two stress-tensor invariants which limit the interpolation range with respect to the conditions of viscous and brittle failure and take into account the signs of principal stresses. The base experiment for determining material constants includes standard tests on long-term strength in uniaxial tension and a test on long-term strength under a plane stress state. The failure criteria have been approved in constructing unified long-term strength diagrams for thin-walled tubular specimens made of rigid polyvinylchloride and high-density polyethylene under the action of internal pressure, pressure with axial tension, torsion, and axial tension with torsion.     

On the peculiarities of a crack growth path in anisotropic solid

One of the possibilities to increase the resistance of a structure to catastrophic fracture is to force a main line crack to deviate from its path. In this connection the influence of the elastic moduli of an anisotropic material on the possibilities of crack rotation are studied. In particular a linear elastic problem for a straight Mode I crack, located on a symmetry axis of an orthotropic plane is considered. The strength properties of the material are supposed to be isotropic. For studying a direction of a crack growth path several crack models are considered. It is shown that a thin elongated elliptical hole as a crack model leads to more plausible results concerning crack rotation conditions than an ideal cut model. The maximal tensile stresses are taken as a crack growth criterion. It is shown that for some class of orthotropic materials a crack deviates from the straight path just after it starts to grow even in the conditions of uniaxial normal tension. The problem of the stability of a straight crack path under Mode I loading is also considered. This problem is reduced to the problem of the fracture direction determination for thin elongated elliptical cavity slightly inclined to the initial direction. In the frame of the proposed approach the conditions of instability are obtained. It is shown that for some class of orthotropic materials a straight crack path is unstable in the conditions of uniaxial normal tension. This class of materials is wider than one for which a crack deviates from the straight crack path just after its start. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anisotropic creep modeling based on elastic projection operators

The paper presents a unified approach for creep modeling of anisotropic materials, and is specified in more detail to the cases of isotropy, cubic symmetry and transversal isotropy. Thereby an additive decomposition of the elastic and inelastic strain tensors into dilational and isochoric Kelvin modes is assumed. Each of these modes is obtained from fourth order projection operators, resulting from solution of the eigenvalue problem for the fourth order anisotropic elasticity tensor. For simplicity the amount of strain rate for each mode is determined with a Norton type ansatz in terms of an equivalent stress, and the experimental phenomenon of primary creep is taken into account by a back stress tensor of Armstrong‐Frederick type, which is also decompose into Kelvin modes. Two numerical creep simulations investigate the crystal orientation for a compact tension specimen made out of CMSX‐4 superalloy.     

Influence of edge effects on the state of stress and strength of carbon composites in tension

Conclusions A difference has been found between the theoretical and experimental strength values. The theoretical strength of flat strips with straight edges, obtained on the basis of the two-dimensional solution within the elastic range for a composite with fiber angle < 30°, is higher than the actual strength. The difference is due to the failure to take account of interlaminar shear. The strength tensor is applied to a monolayer with respect to which the internal state of stress and the nature of the interrelationship between the layers are not taken into account. In this connection, it is desirable to supplement the given criterion with a condition which would take account of the difference between the stresses _xy in adjacent layers. If the directions of reinforcement > 30°, then the agreement between the theoretical strength of flat strips of variable width, obtained on the basis of the two-dimensional solution within the elastic range using the tensor strength criterion, is in good agreement with the actual strength obtained experimentally. The big differences between the actual and theoretical strengths for the three-dimensional solution are attributable to the physical and geometric nonlinearity in the boundary zone between the elementary layers of the composite.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 263–270, March–April, 1985.     

Anisotropic stress-softening model for compressible solids

A general constitutive theory for anisotropic stress softening in compressible solids is presented. The constitutive equation describes anisotropic strain induced behaviour of an initially “isotropic” virgin material. Parameters which characterise damage are proposed together with a concept of damage function. In order to develop an anisotropic stress-softening theory for compressible materials in close parallel to a recent incompressible anisotropic theory, the right stretch tensor is decomposed into its isochoric and dilatational parts. The ’free’ energy is expressed as a function of the dilatation, modified principal stretches, a volume change parameter and invariants of the dyadic products of the principal directions of the right stretch tensor and two structural tensors. A class of free energy functions is discussed and a special form of this class which satisfies the Clausius–Duhem inequality is proposed. Results of the theory applied to uniaxial tension, bulk compression and simple shear deformations are given. A sequence of deformations involving shear, hydrostatic-compression and hydrostatic-tension deformations is also investigated. In the case of hydrostatic-tension deformation, the stress softening is due to cavitation damage. The theoretical results obtained are consistent with expected behaviour and compare well with experimental data.     

Strength of glass-reinforced plastics in the complex stress state

A new criterion of strength is proposed for anisotropic materials of the glass-reinforced plastic type. This criterion takes into account not only the different ultimate strengths in tension and compression in each direction but also the dependence of the ultimate shear strengths on the sign (direction) of the shear stresses. The criterion is given in tensor invariant form, so that it can be rewritten for any direction of the glass fibers. The criteria proposed by other authors, in particular, R. Hill's condition of plasticity [1], follow from the new generalized criterion as special cases. The results of experiments conducted both by the authors of the present article and by other investigators provide good confirmation of the proposed criterion.Mekhanika Polimerov, Vol. 1, No. 2, pp. 70–78, 1965     

Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion

This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic – perfectly plastic materials obeying a Drucker–Prager or Mohr–Coulomb yield criterion. Under suitable assumptions on the data, it is proved that the stress tensor has a spatial gradient that is locally squared integrable. As a corollary, the usual measure theoretical flow rule is expressed in a strong form using the quasi-continuous representative of the stress.     

三维四向编织复合材料刚度和强度的理论预测

以单胞模型为基础,将三维四向编织复合材料中相同走向的纤维束视为单向复合材料,利用桥联模型确定了单向复合材料的柔度矩阵,再将具有不同材料主向的单向复合材料的刚度矩阵通过体积平均,得到了三维四向编织复合材料的总体刚度矩阵,从而得到其工程弹性常数．然后,以单向复合材料为基础,基于等应变假设和桥联模型,确定出材料内各组分（纤维束和基体）的细观应力分布,且对纤维束采用Hoffman失效准则,对基体采用Mises失效准则,预报了三维四向编织复合材料的拉伸强度．     

页岩储层各向异性对水平井坍塌压力的影响

为揭示层理页岩强度各向异性对水平井井壁坍塌压力的影响规律,对取自四川盆地龙马溪组页岩钻井不同层理角度的岩芯,通过岩芯观测、偏光显微镜、扫描电镜试验分别从宏观和微观角度研究了页岩层理特征,并基于单轴抗压强度研究了页岩强度各向异性特征.层理结构发育导致页岩呈现出显著的各向异性特征,粗略地将页岩视为各向同性体及简单采用Mohr-Coulomb准则作为破坏判据,使得预测的维持井壁稳定的坍塌压力不能满足安全钻井的需要.该文在研究层理地层岩石力学特性的基础上,采用横观各向同性地层井周应力分析模型,研究了弹性模量及地应力各向异性比对井周应力的影响;并结合考虑中间主应力的Mogi-Coulomb判据,分析了井壁坍塌压力对弹性模量E和Poisson(泊松)比ν各向异性比值变化的敏感性.实例分析结果表明:弹性模量和水平地应力各向异性比值的变化会对井周应力产生较大影响;Poisson比各向异性对井壁坍塌压力没有明显影响,而弹性模量比值的变化对井壁坍塌压力影响较大;横观各向同性地层中井壁坍塌压力与储层水平和垂直方向的硬脆性强弱关系有关,弹性力学参数各向异性既有可能利于井壁稳定,也可能更易导致井壁的剪切破坏;在实际工程中应根据储层岩石水平和垂直方向的硬脆性强弱关系,确定安全钻井液密度窗口.该结果对现场施工具有很好的指导意义.     

带弹性范围物质理论和背应力定义

在推广Lucchesi和Podio-Guidugli(1988)的带弹性范围物质理论的基础上,表明了背应力作为Cauchy应力空间中屈服面“中心”的定义存在问题.背应力是Lagrange型变量,只能定义在Lagrange型应力空间上.     

Limiting stresses in spatially reinforced composites with components-having different structural geometries nd elastic properties

A model which is proposed for calculating structural stresses in spatially reinforced composites and an invariant-polynomial criterion for evaluating their limiting values are used to predict the effect of the elastic and strength properties of the components and their relative content on the limiting stress-strain state of composites of different structures. Emphasis is given to tri-orthogonal and 4D cubic structures, in addition to structures with hexagonal and angle-ply fiber reinforcement schemes in the plane and perpendicular to it. The types of composite loading typical of standard tests are examined in separate numerical experiments for shear, tension, compression, and their proportional combination. A computational variant of a criterional estimate of the limiting stresses is substantiated for an anisotropic composite of variable strength. The limiting-stress surface is obtained along with contour maps showing stress isolines as a function of the properties of the components and the geometry of the structure. The maps are suitable for practical use. The cases of maximum resistance to shear, tension, compression, and combination loading of 3D and 4D composites are compared to the analogous cases for two-dimensional structures.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 616–639, September–October, 1995.     

关于损伤张量的阶次

本文首先讨论了较为广泛的连续介质材料的应力变形本构关系,得到了通常以泛函表示的应力变形本构关系的张量表达式.以此为基础,研究了各向异性材料各向异性损伤时,无论从连续介质力学模型出发还是从缺陷模型出发,描述损伤的张量都存在最高阶次的限制;指出了在什么条件下,损伤变量可用低于最高阶次的张量来描述.     

A network evolution model for the anisotropic Mullins effect

In this contribution, a micro-mechanical constitutive model for filled rubberlike materials is proposed. Rubber network is decomposed into two parts, elastic rubber network and polymer-filler network. As a consequence of filler contribution, the last one is subjected to damage. A non-Gaussian strain energy function for a single chain with a constant valence angle has been postulated. Damage in different directions is governed by the corresponding maximal micro-stretch and is considered as a result of network evolution. Directional network rearrangement as a consequence of network evolution has been employed in order to describe induced anisotropy and permanent set. The model shows good agreement with experimental data on uniaxial tension tests in two orthogonal directions. (© 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

理想弹塑性I型平面应力裂纹线场的精确解

本文纠正了过去在裂纹弹塑性场匹配上存在的问题,采用线场分析方法,通过求得塑性区应力场的合理解答,使之与弹性精确场在裂纹线附近的弹塑性边界上匹配。本文就远场受单向拉伸及双向拉伸的理想弹塑性平面应力裂纹无限板,在完全放弃了小范围屈服条件的情况下求得了塑性区应力场、塑性区长度以及弹塑性边界的单位法向量在裂纹线附近足够精确的表达式。结果表明,无论单向拉伸和双向拉伸,塑性区应力分量σ_y,σ_xy,塑性区长度以及弹塑性边界的单位法向量在裂纹线附近的表达式完全相同,但塑性区沿X方向的正应力σ_x存在差别。