基于二阶组构张量的各向异性屈服准则

将四个屈服准则:Tresca准则、Mises准则、Mohr-Coulomb准则以及Drucker-Prager准则归类为剪切屈服准则。Tresca准则和Mohr-Coulomb准则是关于最不利截面的剪切屈服准则,而Mises准则和Drucker-Prager准则是关于各方向截面的剪应力和正应力的某种综合度量的八面体剪应力和八面体正应力的剪切屈服准则。从方向函数(ODF)的概念入手,将各方向截面的剪应力和正应力综合度量直接取为所有方向截面上的剪应力和正应力的平均。对各向同性材料,提出了平均剪切屈服度准则:当平均剪应力和平均正应力的组合达到某一极限值时,材料开始屈服。研究表明,平均剪切屈服准则与Drucker-Prager准则具有相同的形式,当不考虑平均正应力对屈服的影响时,它与Mises准则具有相同的形式。针对由各向异性损伤导致的材料各向异性强度问题,定义截面上的有效正应力和有效剪应力则分别为截面上的法向力和切向力与有效承载面积之比,基于截面上的有效应力提出了各向异性材料的平均剪切屈服准则。各向异性损伤引起的截面上有效应力放大系数为方向函数,可以采用二阶组构张量来近似表示,在任意坐标系中,各向异性屈服准则为应力分量的二次齐次式,导出了其中的系数与二阶组构张量之间的显式关系式。在二阶组构张量的主轴坐标系内,各向异性屈服准则与殷有泉的拓展Hill准则形式完全相同,当不考虑正应力对屈服的影响时,它与Hill准则具有相同的形式。     

纤维增强复合材料的基体和界面控制破坏的强度理论

本文简略地回顾了各向同性和各向异性材料的破坏准则.在文献[1]和[2]的基础上,更完整地提出了以基体和界面破坏判定复合材料在复杂应力下破坏的准则.准则方程的形式取决于基体的破坏特征;方程的系数可由组份性能、含量和界面粘接状况所确定.这就揭示了这些参数对复合材抖强度的作用和影响,对复合材料的材料和结构设计有直接的指导意义.偏轴拉伸强度的理论计算结果与试验结果很一致.     

混凝土与各向同性岩石强度理论研究进展

强度理论是研究复杂应力状态下材料是否破坏的理论,该文总结了古典强度理论以及混凝土和各向同性岩石等两类现代强度理论,将各项同性现代强度理论分为剪应力强度理论、八面体强度理论与主应力强度理论。通过收集国内外已有相关三轴实验数据对各种主要强度理论进行论述、比较与评价,在此基础上对混凝土和各向同性岩石的主应力空间损伤比强度理论进行展望。     

横观各向同性地层井壁应力分析

目前关于实钻井壁应力分布计算大都基于岩石的各向同性,在实际工况分析中存在误差。该文应用各向异性材料力学理论,将层状地层简化为横观各向同性岩石材料,建立了各向异性地层井孔周围应力计算模型。应用弹性力学广义平面应变问题的复变函数解法,结合井孔周围受力边界条件及相关坐标转换,得到横观各向同性地层斜井壁围岩应力解析解。对井壁围岩主应力影响因素的分析表明,层理面弹性参数、层理面倾角、水平原地应力比和井斜角方位角对井壁应力分布均会造成影响。在进行层理性地层井壁稳定分析时,应格外注意层理面倾角、原地应力比以及井斜参数的影响。该结果对现场施工设计有很好的指导意义。     

中应变率加载下云杉各向异性力学行为研究

采用高速加载INSTRON设备对云杉开展100 s-1~102 s-1中应变率压缩实验,研究了材料沿顺纹、横纹径向、弦向、以及径(弦)切面内与顺纹呈15°、30°、45°、60°和75°夹角方向的力学性能。实验表明随着加载方向由顺纹向横纹径(弦)向变化,材料屈服强度逐渐减小,应力-应变曲线塑性流动段由"塑性软化"向"塑性硬化"转变;试件沿不同方向压缩屈服强度表现出较强应变率敏感性。冲击压缩下云杉宏观破坏模式与加载方向相关,沿顺纹方向加载时,试件中部向外膨胀,产生褶皱、纤维屈曲折断;当载荷方向与顺纹夹角逐渐增大时,材料失效模式体现为木材纤维分层滑移、撕裂。采用简化Hill强度理论对中低应变率下云杉空间屈服行为进行了理论描述,不同应变率下云杉空间屈服面为椭圆柱曲面,屈服曲面半径长度随应变率提高而增加。实验与理论分析表明,云杉沿空间不同方向具有各向异性力学特性,屈服强度受应变率和加载方向影响较大,而破坏模式则主要依赖于载荷方向。     

岩石三维强度准则的研究

结合非线性统一强度理论与Hoek-Brown强度准则,以Hoek-Brown强度准则构建子午面上的强度曲线,以非线性统一强度理论构建偏平面上的强度曲线,通过应力空间变化方法将子午面上强度曲线与偏平面上强度曲线进行结合,从而建立一种新的岩石三维强度准则。建立的强度准则在子午面上为非线性,考虑岩石材料的静水压力效应;在偏平面上强度线涵盖了从上限Drucker-Prager圆到下限Matsuoka-Nakai曲线之间的所有区域,可较好模拟岩石材料的中间主应力效应。强度面光滑、外凸,可用于建立岩石的屈服函数。强度准则共有3个材料参数m_t、σ_c、m_i,各参数可通过岩石试验数据确定且具有明确的物理意义。另外,该文提出一种m_t的近似求解公式,总的参数可退化为σ_c和m_i,与Hoek-Brown准则基本参数一致,可由岩石常规三轴压缩试验按Hoek-Brown提出的回归公式确定。与国内外学者已开展的岩石材料三轴试验结果进行对比,建立的强度准则与试验数据吻合良好,可合理描述岩石材料的非线性强度特性。其次,通过引入地质强度指标GSI,建立的强度准则可应用于较为完整的岩体（GSI>25）,对于较为破碎岩体（GSI<25）需做进一步的研究。     

横观各向同性饱和土中单桩竖向振动的简化模型求解

基于饱和多孔介质理论,将土体视为横观各向同性饱和两相介质,利用分离变量法求解了横观各向同性饱和土层的竖向振动,在此基础上建立横观各向同性饱和土中单桩竖向振动的控制方程,借助桩端边界条件和三角函数的正交性对桩竖向振动问题进行了求解,并分析了相关参数对竖向振动的影响。研究表明:桩-土系统存在共振现象,复刚度的变化受激振频率的影响较大;在高频和低频时,各向异性参数对动刚度的影响不同,各向异性参数越大,复刚度的峰值越小。     

非圆截面纤维增强复合材料的弹塑性性能

基于Tandon和Weng(1988)建立的理论框架,应用细观力学方法,本文提出了非圆截面纤维增强复合材料的弹塑性理论。对于两种复合材料,即单向排列纤维形成的正交各向异性材料和在截面内随机排列纤维形成的横观各向同性材料,作出了割线模量,基体应力增大系数及屈服条件曲线。通过各种截面纤维之间的比较,得出结论:在横观各向同性材料情况下,片状纤维增强材料的力学性能优于其它材料。      

短纤维增强三元乙丙薄膜拉伸破坏率相关Tsai-Hill强度准则

短纤维增强三元乙丙（EPDM）薄膜材料是一种应用于固体火箭发动机装药的新型绝热结构材料,其密度小、耐烧蚀且力学性能良好。基于正交各向异性单向板的Tsai-Hill强度准则,引入率相关函数法和率强度因子法改进,预测材料在不同偏轴方向下的抗拉强度,从而建立一种适用于准静态条件下的率相关各向异性通用准则。研究表明：轴向强度和抗剪强度随应变率的增加而增加;相比于率强度因子法,基于率相关函数法的Tsai-Hill强度准则对材料抗拉强度的预测精度较高;率强度因子法预测抗拉强度的误差与参考速率的选取和率强度因子的函数表达式有关。     

关于横观各向同性体在其各向同性面内弹性问题的一个常数

研究了在平面应力和平面应变情况下, 横观各向同性材料在其各向同性面内的应力2应变关系以及用位移表达的平衡方程可以被表示成与各向同性材料完全相同的形式。这种等同关系是通过引入一个与横观各向同性材料的泊松比有关的常数得到的。该常数的引入消除了已发表的文献中求解横观各向同性材料平面问题时出现的矛盾。这个常数的引入也便于正确计算单向纤维增强复合材料的横向切变模量。      

Modelling of anisotropic elastic properties in alloy 718 built by electron beam melting

ABSTRACT

Owing to the inherent nature of the process, typically material produced via electron beam melting (EBM) has a columnar microstructure. As a result of that, the material will have anisotropic mechanical properties. In this work, anisotropic elastic properties of EBM built Alloy 718 samples at room temperature were investigated by using experiments and modelling work. Electron backscatter diffraction data from the sample microstructure was used to predict the Young’s modulus. The results showed that the model developed in the finite element software OOF2 was able to capture the anisotropy in the Young’s modulus. The samples showed transversely isotropic elastic properties having lowest Young’s modulus along build direction. In addition to that, complete transversely isotropic stiffness tensor of the sample was also calculated.

This paper is part of a thematic issue on Nuclear Materials.     

Orientation-dependent piezoelectric Eshelby S-tensor for a lamellar structure in a transversely isotropic medium

Summary.  This paper provides explicit expressions for the orientation-dependent piezoelectric Eshelby S-tensor with a lamellar structure in a transversely isotropic medium. Many piezoelectric or ferroelectric materials prefer to form a lamellar structure during a change of nano-scale microstructure and domain switch; such a lamellar morphology is energetically more favorable than other shapes in a diffusionless process. According to the above observation, this paper seeks to derive the Eshelby tensor in a coupled field with the consideration of lamellar structure. In general, Eshelby's tensor can be obtained through a Green's function technique, but it is usually given in an integral form. Due to the geometric simplicity of a lamellar structure, a simple explicit form of piezoelectric S-tensor can be obtained directly from the interfacial continuous conditions. In a transversely isotropic medium, the angle between the global symmetric axis and one of the local parallel to the surface of the lamellar inclusion is the key geometrical factor in the construction of the S-tensor. Two special cases with 90° and 180° orientation that bear significant relevance to domain switch in ferroelectric ceramics are discussed in detail. Received September 2, 2002; revised December 3, 2002 Published online: May 8, 2003 This work was supported by the National Science Foundation, Surface Engineering and Materials Design Program, under grant CMS-0093808.     

Constraints on the applicability range of Hill’s criterion: strong orthotropy or transverse isotropy

Commonly used orthotropic Hill’s criterion of plastic flow initiation (Hill in Proc R Soc Lond A 193:281–297, 1948) suffers from some constraints and inconsistencies, which are of two different origins. Firstly, in case of high orthotropy degree, the quadratic form corresponding to Hill’s criterion may change type from convex and closed elliptic to concave and open hyperbolic in the deviatoric stress space (Ottosen and Ristinmaa in the mechanics of constitutive modeling, Elsevier, Amsterdam, 2005). Secondly, application of classical Hill’s criterion to transversely isotropic materials shows a discrepancy between Hill’s limit curves in the transverse isotropy plane and the Huber-von Mises prediction for isotropic materials (Huber 1904; von Mises 1913). The basic result of the present paper is to propose the new transversely isotropic von Mises–Hu–Marin’s-type criterion of hexagonal symmetry that is free from both constraints. The new enhanced Hu–Marin’s-type limit surface represents an elliptic cylinder, the axis of which is proportional to stress/strength, in contrast to Hill’s-type limit surface possessing the hydrostatic axis. Hence, this condition does not exhibit the deviatoricity property, which is a price for coincidence with the Huber–von Mises condition in the transverse isotropy plane, but with cylindricity ensured for an arbitrarily high orthotropy degree. The hybrid-type transversely isotropic Hu–Marin’s criterion of mixed symmetry based on additional biaxial bulge test, capable of fitting experimental findings for some complex composites, is also proposed. Application of this criterion has been verified for a unidirectional SiC/Ti composite examined by Herakovich (Thermal stresses V, Lastran Corp. Publ. Division, pp 1–142, 1999).     

Explicit formulations of tangent stiffness tensors for isotropic materials

A compact explicit expression for the tangent stiffness tensor is presented. Throughout the analysis, the formulation holds for general isotropic elastic materials and does not require solving eigenvector problems. On the theoretical side, a very simple solution of a tensor equation is obtained. Then the expressions for the derivatives of general symmetric isotropic tensor functions of a symmetric tensor are developed. On the computational side, particular attention is given to the consideration of the special case, Green elastic materials, in which the strain energy does not admit a closed‐form expression in terms of principal invariants. Finally, a simple formulation of the tangent stiffness tensor for Ogden material model is supplied. Copyright © 2006 John Wiley & Sons, Ltd.     

Stress concentration around a strongly oblate spheroidal cavity in a transversely isotropic medium

Expressions for the Eshelby tensor of a strongly oblate spheroidal region in a transversely isotropic medium are given explicitly. Based on the equivalent inclusion method, three dimensional stress concentration around the spherodal cavity subjected to remote uniform loading is analyzed and the associated stress concentration factor is determined. Analogously to two-dimensional blunted cracks, the so called stress rounding factor is introduced so that the connection between the crack tip stress and the stress intensity factor in linear fracture mechanics is established. Numerical values of the stress rounding factor for several representative cases of transversely isotropic symmetry are given.     

Multiple-factor dependence of the yielding behavior to isotropic ductile materials

Extensively experimental evidences have shown that the yielding behaviors for many isotropic materials exhibit both the pressure and stress-state dependence. The strength-differential in tension and compression results not only from the hydrostatic stress, but also from the loading type. Different materials often demonstrate different yielding features in stress space even though they have the same ratio of compression yield-stress to tension yield-stress. Bases on a physical hypothesis introduced herein, a yield criterion is proposed to fulfill the experimental observations. The yield criterion can be represented finally with three independent invariants of the stress tensor and the deviatoric stress tensor. The yield criterion can well predict the yielding behavior arising from the yielding mechanism of the multiple-factor dependence. The yielding analysis with the effect of the hydrostatic stress does not have a limit when regardless of the strength-differential in tension and compression. The yield criterion assures the convexity in a wider range of material properties so that it can be used as the plastic potential in the implementation of predicting the subsequent yield surface. The yield criterion reveals a clearly transforming procedure with respect to its simplified form when applied to different materials from a general compressive isotropic material to an ideal incompressive isotropic material, back to the Mises’s criterion. Divers experiments on metallic and polymeric materials are compared. The results show that the new yield criterion is in fairly good agreement with all referred experiments.     

Modeling the effective elastic properties of nanocomposites with circular straight CNT fibers reinforced in the epoxy matrix

In the present study, the consistent effective elastic properties of straight, circular carbon nanotube epoxy composites are derived using the micromechanics theory. The CNT composites are known to provide high stiffness and elastic properties when the shape of the fibers is cylindrical and straight. Accordingly, in the present work, the effective elastic moduli of composite are newly obtained for straight, circular CNTs aligned in the specified direction as well as distributed randomly in the matrix. In this direction, novel analytical expressions are proposed for four cases of fiber property. First, aligned, and straight CNTs are considered with transverse isotropy in fiber coordinates, and the composite properties are also transversely isotropic in global coordinates. The short comings in the earlier developments are effectively addressed by deriving the consistent form of the strain tensor and the stiffness tensor of the CNT nanocomposite. Subsequently, effective relations for composites reinforced with aligned, straight CNTs but fibers isotropic in local coordinates are newly developed under hydrostatic loading. The effect of the unsymmetric Eshelby tensor for cylindrical fibers on the overall properties of the nanocomposite is included by deriving the strain concentration tensors. Next, the random distribution of CNT fibers in the matrix is studied with fibers being transversely isotropic as well as isotropic when CNT nanocomposites are subjected to uniform loading. The corresponding relations for the effective elastic properties are newly derived. The modeling technique is validated with results reported, and the variations in the effective properties for different CNT volume fractions are presented.     

Three-dimensional stress intensity factors of a central square crack in a transversely isotropic cuboid with arbitrary material orientations

In this paper, we present the dual boundary element method (dual-BEM) or single-domain BEM to analyze the mixed three-dimensional (3D) stress intensity factors (SIFs) in a finite and transversely isotropic solid containing an internal square crack. The planes of both the transverse isotropy and square crack can be oriented arbitrarily with respect to a fixed global coordinate system. A set of four special nine-node quadrilateral elements are utilized to approximate the crack front as well as the outer boundary, and the mixed 3D SIFs are evaluated using the asymptotic relation between the SIFs and the relative crack opening displacements (COD) via the Barnett–Lothe tensor.Numerical examples are presented for a cracked cuboid which is transversely isotropic with any given orientation and is under a uniform vertical traction on its top and bottom surfaces. The square crack is located in the center of the cuboid but is oriented arbitrarily. Our results show that among the selected material and crack orientations, the mode-I SIF reaches the largest possible value when the material inclined angle ψ₁=45° and dig angle β₁=45°, and the crack inclined angle ψ₂=0° and dig angle β₂=0°. It is further observed that when the crack is oriented vertically or nearly vertically, the mode-I SIF becomes negative, indicating that the crack closes due to an overall compressive loading normal to the crack surface. Variation of the SIFs for modes II and III along the crack fronts also shows some interesting features for different combinations of the material and crack orientations.     

爆破动应力对岩质边坡损伤破坏作用机理

分析了爆破动应力在岩质边坡中的分布规律,推导出了爆破动应力与质点振速及岩体物理力学参数间关系的计算表达式。分析讨论了由爆破产生的附加动应力与岩质边坡中的应力场及岩体介质中的裂纹损伤场相互耦合作用机理,并推导出了裂纹初裂强度表达式。从断裂力学及损伤力学的理论出发,建立了节理裂隙岩体的等效柔度张量以及在爆破动应力作用下裂隙岩体的附加柔度张量。从所建立的柔度张量关系式中可知,当有爆破动应力存在时,增大了岩体的柔度张量,削弱了岩体的强度。