Ⅰ型裂纹试件裂端三维应力结构分析之一——裂端约束参数与断裂参数分析

本文利用大型通用结构有限元分析程序ADINA对16Mn材料制的两种不同厚度的Ⅰ型CT试样进行了计算与分析,结果表明,厚度方向的约束状态将试样分成两部分:具有相同约束状态的心部高约束区(Z₁)和约束显著变化的外边缘区(Z₂);有限元计算和实验测定结果证实了这两部分分别与试样断口上的纤维区及剪切唇相对应.所以,Ⅰ型裂纹试件裂端应力、应变场可分别通过这两个区域加以分析获得.本文对一些断裂参数如裂纹尖端张开位移(CTOD)和空穴扩张比(V_g)参数也进行了考察,结果表明这两个参数在厚度方向有相类似的变化规律,在一定程度上都可反映试样的厚度效应及外载荷水平效应.     

一类不可压缩材料平面应力问题的裂纹尖端场

本文采用完全非线性弹性理论,研究了一类不可压缩橡皮类材料[1]在Ⅰ型荷载作用下的平面应力问题.指出裂尖变形由两个收缩区和一个扩张区三部分组成.裂纹尖端应力、应变分别具有R-1、R-1/n的奇异性,当趋近裂尖时,厚度以R1/4n的方式趋于零,n为材料常数.     

三维变形状态下Ⅰ型裂纹裂尖应力场结构的有限元分析*

本文用ADINA(Automatic Dynamical Incremental Nonlinear Analysis)有限元程序计算了三维变形条件下,幂硬化材料紧凑拉伸(CT)试样的应力应变场,并根据计算结果分析了Ⅰ型裂纹裂尖应力场的结构,发现在厚度方向的任一平面上,裂尖应力场的表达式都可写成r,θ坐标变量分离的形式,从而r的函数部分可展成罗朗级数,且三个正应力分量具有相同的数量级.这两个结论为从理论上求解Ⅰ型裂纹裂尖应力场的数学表达式提供了两个有根据的假设条件,可大大减化求解过程.     

复合材料对称层合板单向拉伸与面内剪切下的三维应力分析

本文给出了单向拉伸与面向剪切载荷下复合材料对称层合板中心区域的应力和应变沿板厚的数值计算分布规律。计算结果表明，在斜交对称辅层的层合板中心区域层间界面附近存在着层间边界层效应。层间界面处纤维走向的突变导致局部的三维应力状态和很强的应力集中。     

非应变盖层对应变结构中净应力的影响 *

分析了应变外延层中非应变盖层厚度和在应变层上下界面的失配位错数目差对净应力的影响 ,对现有的单结点和双结点位错模型的净应力的表达式进行了修正 ,得到一个能将单、双结点模型统一起来且对任意盖层厚度都适用的表达式 .从而进一步完善了描述应变外延层中失配位错的产生和运动机制的理论     

高速扩展平面应力裂纹尖端的各向异性塑性场

在裂纹尖端的应力分量都只是θ的函数的条件下,利用定常运动方程,Hill各向异性屈服条件及应力应变关系,我们得到高速扩展平面应力裂纹尖端的各向异性塑性场的一般解.将这个一般解用于四种各向异性特殊情形,我们就导出这四种特殊情形的一般解.最后,本文给出X=Y=Z情形的高速扩展平面应力Ⅰ型裂纹尖端的各向异性塑性场.     

引用复变量伪应力函数来解幂硬化材料平面应力问题

本文引用复变量伪应力函数将幂硬化材料平面应力问题的协调方程化为双调和方程,从而使此类有强化材料的弹塑性平面应力问题能像线弹性力学平面问题那样采用复变函数法进行求解.本文推导出了幂硬化材料平面应力问题的应力、应变及位移分量的复变函数表达式,可推广应用于满足全量理论的一股弹塑性平面应力问题.作为算例,文中给出了含圆孔幂硬化材料无限大板单向受拉问题的解答,并和有关文献用摄动法获得的同一问题的渐近解进行了比较.     

弹性-应变软化粘塑性材料反平面剪切动态扩展裂纹尖端的渐近解*

本文首先给出了一种用于描述材料软化,并存在有粘塑性的材料模型.用这种模型对反平面剪切型动态扩展状态下,裂纹尖端的弹粘塑性场进行了渐近分析,给出了弹性－应变软化粘塑性材料反平面剪切动态扩展裂纹尖端的渐近解方程.分析结果表明,在裂纹尖端应变具有(ln(R/r))1/(n＋1)的奇异性,应力具有(ln(R/r))-n/(n＋1)的奇异性.从而本文揭示了应变软化粘塑性材料反平面剪切动态扩展裂纹尖端的渐近行为.     

带裂纹三点弯曲试样的动态应力强度因子分析

提出了计算带单边裂纹三点弯曲试样动态应力强度因子的新方法．首先由权函数的普遍形式和两种参考载荷下的应力强度因子,得到了带单边裂纹三点弯曲试样的权函数,然后考虑试样的转动惯性和剪切变形,根据振动理论推导出无裂纹梁内的动应力响应和分布,最后由权函数的思想推导出了带裂纹三点弯曲试样动态应力强度因子公式．通过有限元数值计算,验证了该方法的正确性,结果比较表明公式具有较高的精度．另外,还研究了冲击载荷下三点弯曲试样的动态应力强度因子随裂纹长度和加载速率的变化规律．     

加捻纤维复合材料三维残余应力分析

本文提供一种对于含有加捻纤维束的复合材料由于固化而产生的热残余应力的分析研究.纤维束中的纤维经过加捻产生了一种螺旋形状,这种形状所产生的三维热弹性力学问题可以利用能量法获得解答.这个问题的热残余应力场可以表示为纤维、基体材料的性质以及纤维束几何参数的函数.纤维/基体界面上的残余应力(包括环向和径向的应力)都可以从这些分析中得到.本文分析的结果表明:加捻纤维束构成的复合材料,由于纤维的适当加捻,可以减弱由于纤维与基体各具不同的热膨胀系数而产生的热固化残余应力.     

Three-Dimensional Computational Analysis of Stress State Transition in Through-Cracked Plates

Stress state is a main parameter within fracture mechanics. It has a major influence on different phenomena, namely those involving diffusion, plastic deformation, and brittle fracture. As is well-known, in the near-surface regions of a crack front, the plane stress state dominates, while at interior positions the plane strain state prevails. The main objective here is to examine the extent of surface regions in through-cracked planar geometries subjected to cyclic loading. Two constitutive material models were developed to characterise the stress state along the crack front. A new criterion based on the h stress triaxiality parameter was proposed to define the transition between surface and near-surface regions. Finally, a linear relation between the stable value of the extent of surface region and the maximum stress intensity factor was established.     

Coupling effect of thickness and shear deformation on size-dependent bending of micro/nano-scale porous beams

A unified nonlocal strain gradient beam model with the thickness effect is developed to investigate the static bending behavior of micro/nano-scale porous beams. Size-dependent governing equations and corresponding analytical solutions for the bending of hinged-hinged beams are obtained by employing minimum total potential energy principle, the Navier solution method as well as the variational-consistent boundary conditions. For nonlocal strain gradient theory (NSGT) with thickness effect, virtual strain energy function of shear beams can contain additional nonlocal shear stress and high-order nonlocal shear stress related to the thickness direction in comparison with that of Euler–Bernoulli beam, so the coupling of the shear and thickness effects should be drawn huge attention. By means of detailed numerical analysis, it is found that, the stiffness-hardening effect is underestimated in NSGT without the thickness effect, and the stiffness-hardening and stiffness-softening effects of NSGT with the thickness effect can be not only length-dependent but also thickness-dependent. Interestingly, the generalized Young’s modulus depends on half-wave number, which means that the generalized Young’s modulus may be different due to applied load types. In the context of NSGT with the thickness effect, the deflection of Euler–Bernoulli beam predicted is smaller than that of shear beam, especially for thick beams. Furthermore, porosities distributed in the top or bottom of beams can possess a greater influence on the decrease of overall stiffness of beam than those distributed in the vicinity of the middle plane of beams.     

对称迭层矩形板的平面应力分析

常用的对称迭层板为各向异性板．根据平面应力问题的基本方程精确地用应力函数解法求得了各向异性板的一般解析解．推导出平面内应力和位移的一般公式,其中积分常数由边界条件来决定．一般解包括三角函数和双曲函数组成的解,它能满足4个边为任意边界条件的问题．还有代数多项式解,它能满足4个角的边界条件．因此一般解可用以求解任意边界条件下的平面应力问题．以4边承受均匀法向和切向载荷以及非均匀法向载荷的对称迭层方板为例,进行了计算和分析．     

轻质热防护系统多层材料组合结构的热应力分析

提出了轻质热防护系统外面板使用多层结构的概念,设计了2种热防护材料组合构成的3种铺层方案．通过模拟飞行器再入大气层时受到的机械和热载荷条件,数值计算得到了层间剪切力、底部温度和y方向位移．计算结果发现,层间剪切力发生在边缘部位且呈反对称分布;选用高热导率和高热容材料能够减少材料内的温度梯度,进而有效地降低结构的热应力和热变形;在均匀温度场情况下,两种材料的热膨胀系数之差越小,则层间剪切力越小．该研究表明不同的材料组合和铺层次序的多层结构,可以满足不同设计要求,具有优化设计潜力．     

A Study on the Propagation of Plane Stress Waves across the Thickness of a Plate by the Method of Analytic Continuation in Time

The interaction of plane tension/compression waves propagating within a plate perpendicularly to its surface is considered. The analytic solution is obtained by a modified method of characteristics for the one-dimensional wave equation used in problems on an impact of a rigid body on the surface of a plate. The displacements, velocities, and stresses in the plate are determined by the edge disturbance caused by the initial velocity and the stationary force field of masses of the striker and the plate. The method of analytic continuation in time put forward allows a stress analysis for an arbitrary time interval by using finite expressions. Contrary to a stress analysis in the frequency domain, which is commonly used in harmonic expansion of disturbances, the approach advanced allows one to analyze the solution in the case of discontinuous first derivatives of displacements without calculating jumps in summing series. A generalized closed-form solution is obtained for stresses in an arbitrary cycle n(t), which is determined by the multiplicity of the time of wave travel across the double thickness of the plate. A method of recurrent solution based on calculating the convolution of repeated integrals of the initial form of disturbance at t = 0 is elaborated. The procedure can be used for evaluating the maximum stress and the contact time in a plane impact on the surface of a plate.     

On the uniform stress state inside an inclusion of arbitrary shape in a three-phase composite

The stress field inside a two-dimensional arbitrary-shape elastic inclusion bonded through an interphase layer to an infinite elastic matrix subjected to uniform stresses at infinity is analytically studied using the complex variable method in elasticity. Both in-plane and anti-plane shear loading cases are considered. It is shown that the stress field within the inclusion can be uniform and hydrostatic under remote constant in-plane stresses and can be uniform under remote constant anti-plane shear stresses. Both of these uniform stress states can be achieved when the shape of the inclusion, the elastic properties of each phase, and the thickness of the interphase layer are properly designed. Possible non-elliptical shapes of inclusions with uniform hydrostatic stresses induced by in-plane loading are identified and divided into three groups. For each group, two conditions that ensure a uniform hydrostatic stress state are obtained. One condition relates the thickness of the interphase layer to elastic properties of the composite phases, while the other links the remote stresses to geometrical and material parameters of the three-phase composite. Similar conditions are analytically obtained for enabling a uniform stress state inside an arbitrary-shape inclusion in a three-phase composite loaded by remote uniform anti-plane shear stresses.     

Plane strain deformation of an initially unstressed elastic medium

Selim and Ahmed [1] used the eigenvalue approach by assuming distinct eigenvalues to calculate the elastic deformation due to an inclined load at any point as a result of an inclined line load of initially stressed orthotropic elastic medium. They studied the plane strain problem and obtained the corresponding results for an unstressed orthotropic medium as a particular case. In the present paper, it is shown that all the eigenvalues do not remain distinct, but become repeated when the elastic medium is free from the initial compressive stresses. Further, the displacements and stresses for an unstressed elastic medium have been independently obtained. The variation of the displacements and stresses due to normal and tangential line load are also shown graphically.