功能梯度材料与均质材料交界面上Ⅰ-型裂纹对简谐动载的响应分析

在忽略界面裂尖端裂纹面相互叠入的条件下,对功能梯度材料与均质材料交界面上Ⅰ-型裂纹对简谐动载响应问题进行了分析。利用傅立叶变换,将问题的求解转换为对以裂纹面上位移差为未知函数的对偶积分方程的求解。为了求解对偶积分方程,将裂纹面上的位移差函数展开为雅可毕多项式的级数形式。最终给出了裂纹长度、入射波频率和材料性质对应力强度的影响。结果表明,当界面材料不连续时,获得了具有普通1/2奇异性的近似解。     

关于界面下裂纹对界面裂纹的屏蔽参数

讨论了界面下裂纹对界面裂干涉的合理屏蔽参数问题。对于一条在远场载荷作用下、受到附近界面下裂纹干涉的界面裂纹,采用伪力法计算不同长度单位时界面裂纹的G／G0、k1/k10和k11/k110以及K1／K10和K11／K110（G是能量释放率、k1 ik110是通常定义的应力强度因子、K10＋iK110是含标定长度的应力强度因子;G0、k10 ik110、K10＋iK110对应单一界面裂纹情况）。结果表明,G／G0、K1／K10和K11／K110是较为合理的描述界面下裂纹对界面裂纹屏蔽的参数。     

薄膜涂层材料中币形界面裂纹的弹性波散射

研究了薄膜涂层材料中币形界面裂纹的弹性波散射问题,建立了含有币形界面裂纹的覆层半空间模型,采用Hankel积分变换,将裂纹对弹性波散射的问题转化为求解矩阵形式的奇异积分方程。结合渐近分析和围道积分技术得到积分方程的解,进一步推导了散射波的应力场和位移场,以及动应力强度因子的理论计算公式。在数值算例中,分析了不同材料组合和裂纹尺寸情况下动应力强度因子与入射波频率的关系,并给出了裂纹张开位移的结果。为薄膜涂层材料的动态破坏分析提供了一定的理论基础。     

Crack problems of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces. The explicit analytic solutions are obtained for a single crack in piezoelectrics or on the interfaces of piezoelectric bimaterials. A class of boundary problems involving many cracks is also solved. For homogeneous materials it is found that the normal electric displacementD ₂ induced by the crack is constant along the crack faces which depends only on the applied remote stress field. Within the crack slit, the electric fields induced by the crack are also constant and not affected by the applied electric field. For the bimaterials with realH, the normal electric displacementD ₂ is constant along the crack faces and electric fieldE ₂ has the singularity ahead of the crack tip and a jump across the interface. The project is supported by the National Natural Science Foundation of China(No. 19704100) and the Natural Science Foundation of Chinese Academy of Sciences(No. KJ951-1-201).     

有限尺寸下双材料界面附近裂纹位置对裂纹尖端的影响

随着复合材料的应用和发展,不同材料组成的界面结构越来越受到人们的重视.界面层两侧材料的性能相异会引起材料界面端奇异性,同时界面和界面附近存在裂纹会引起裂尖处的应力奇异性.因此双材料界面附近的力学分析是比较复杂的.论文建立双材料直角界面模型,在材料界面附近预设初始裂纹,计算了有限材料尺寸对界面应力场及其附近裂纹应力强度因子的影响.运用弹性力学中的Goursat公式求得直角界面端在有限尺寸下的应力场以及其应力强度系数.通过叠加原理和格林函数法进一步得到在直角界面端附近的裂纹尖端应力强度因子.计算结果表明,在适当范围内改变材料内裂纹与界面之间的距离,界面附近裂纹尖端的应力强度因子随着裂纹与界面距离的增加而减少,并且逐渐趋于稳定.分析结果可以为预测双材料结构复合材料界面失效位置提供参考.     

一种适合橡胶类材料的非线性粘弹性本构模型

借助非线性流变模型建立大变形情况非线性粘弹材料的本构关系,考虑到大多数橡胶类材料具有的几乎不可压缩性,以及体积响应和剪切响应的流变性能不同,将变形梯度乘法分解为等容部分和体积变形部分,给出了一种适合橡胶类材料的非线性粘弹性本构模型,并模拟了粘滞效应。对于极快或极慢的过程,该模型退化为橡胶弹性理论;在小变形情况下退化为经典的广义Maxwell粘弹性材料。模型与热力学第二定律相容,适合于大规模数值分析。     

粘弹性界面裂纹奇异场

对于许多粘弹性问题,通常可以利用对应性原理,即由弹性问题的结果得到对应的粘弹性问题在拉普拉斯变换域内的解,再通过反演变换求得最终时域中的解.但是,由于界面裂纹场存在着振荡奇异性,弹性问题解的形式就已经非常复杂,对应的粘弹性问题要通过反演变换直接求得准确的解析解几乎是不可能的.本文在利用对应性原理时做了更简单的准静态处理,即将弹性结果中的材料参数用粘弹性材料参数做对应替代,得到了粘弹性界面裂纹场近似的经典解,并与有限元分析结果作了比较.同时,利用Comninou接触模型,对粘弹性界面裂纹在远场拉剪混合加载情况下的裂尖应力场和接触区做了考察,并与经典解作了比较.     

夹杂和裂纹相互影响时的界面应力分析

本文结合无限域上单根夹杂和单根裂纹的基本解,将裂纹与夹杂相互作用的问题归结为解一组柯西型奇异积分的积分方程组,使问题得到解决。本文还使用夹杂两侧的未知界面应力差,进一步推导了夹杂两侧的界面应力,并做了数值计算。有关这方面的计算可以作为研究与设计纤维与基体的联结强度的工程参考。     

各向异性双材料界面裂纹扩展裂尖场

应用界面断裂力学理论和Stroh方法,研究了广义平面变形下动态裂纹沿着各向异性双材料界面扩展时的裂尖奇异应力及动态应力强度因子.双材料界面的动态裂尖区域特性主要由两个实矩阵W和D确定,且裂尖奇异应力和动态应力强度因子可以由包含这两个矩阵的柯西奇异积分方程确定,同时给出了动态应力强度因子和能量释放率的显示表达式.算例得出当裂纹以小速度扩展时,裂尖振荡因子ε与静态时几乎相同,当界面裂纹扩展速度接近瑞利波速时,ε趋于无穷大;同时得出应力强度因子及能量释放率随裂纹扩展速度的变化关系.     

梯度非均匀有限层-基结构界面裂纹动态断裂的数值分析

研究了具有一个界面裂纹的有限尺寸梯度非均匀层-基结构在面内冲击载荷作用下的动态响应问题;提出了分析这类问题的一种数值方法,其核心是计算具有一定宽度的裂缝位移场,通过对到缝端距离及缝宽的双重插值求裂尖处动态应力强度因子。文中对涂层是弹性模量及密度连续变化的梯度非均匀材料,基体是各向同性均匀材料的层-基结构作了具体计算,数值结果清楚地显示出动态应力强度因子的时程变化规律,及有关参数(梯度参数,层厚,层长)对它的影响。     

Dynamic Out of Plane Displacement Fields for an Inclined Crack in Graded Materials

A generalized elastic solution for an arbitrarily propagating crack in Functionally Gradient Materials (FGMs) is obtained through an asymptotic analysis. The shear modulus and mass density of the FGM are assumed to vary exponentially along the gradation direction. The mode mixity due to the inclination of property gradient is accommodated in the analysis through superposition of the opening and shear modes. Using this asymptotic solution, contours of constant out of plane displacement are generated. The effect of inclination of property gradation direction and the crack speed on these contours is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

正交异性复合材料界面上反平面动态自相似扩展裂纹问题的解

采用复变函数论的方法，对复合材料界面上的裂纹扩展问题进行研究。并根据任意的自相似指数的断裂动力学问题，进行自相似求解，导出解析解的一般表示。应用该法可以迅速地将所论问题转化为Riemann-Hil-bert问题，并可以相当简单地得到问题的闭合解。文中分别对裂纹中心受阶跃载荷，裂纹面受到瞬时脉冲载荷作用下的界面裂纹扩展问题进行求解。得到了裂纹的位移。尖端的应力和动态应力强度因子的解析解。应用该解并通过叠加原理。就可以很容易的求得任意复杂问题的解。     

幂硬化弹塑性-刚性界面Ⅲ型定常扩展裂纹尖端的渐近场

对幂硬化弹塑性材料－刚性材料界面上裂纹以定常方式扩展的Ⅲ型问题进行弹塑性渐近分析，给出裂纹尖端的应力，应变和位移场解。通过数值计算，考察了不同Mach数以及裂纹尖端混合参数对场解的构造以及应力，应变分布的影响，为给出合理的断裂准则提供理论依据。     

垂直裂缝在砂泥岩层理界面上拐折扩展特性研究

首先以大庆油田薄差油藏的砂泥岩储层力学参数为基础,根据相似原理,制备了砂泥岩相似材料试件。然后通过三点弯曲实验构建了Ⅰ型裂缝扩展,并采用数字散斑相关方法,获得了裂缝扩展过程中试件表面散斑场的变化规律。由此给出了界面位置处裂尖的应力奇异性阶数及应力强度因子,了解了材料强度差异对裂缝在界面扩展特性的影响。分析表明,当垂直裂缝从高强度材料一侧扩展时,界面的应力奇异性阶数大,界面的应力集中效应高,KⅡ/KⅠ比值小,裂缝拐折程度小,反之亦然。     

类岩石材料中表面裂纹扩展模式的实验研究

采用粘贴式轴拉方法实现了类岩石材料的直接拉伸实验,通过在类岩石材料试件中预制表面裂纹研究了类岩石材料中表面裂纹的扩展模式.研究发现,粘贴式轴拉方法可以满足一般类岩石材料的直接拉伸实验;类岩石材料中表面裂纹首先从试件正面开始扩展;表面裂纹的存在极大地影响着材料的破坏模式,类岩石材料在试件的正面上会表现出明显的二维穿透性裂纹的扩展形态,但是受其影响裂纹在厚度方向扩展会发生偏转,从而使得试件背面的最终贯通方向没有与加载方向垂直,而是呈一倾角,并且和表面裂纹的倾角和深度有关.     

Stress Analysis of an Elliptic Inclusion with Imperfect Interface in Plane Elasticity

In this paper, a semi-analytic solution of the problem associated with an elliptic inclusion embedded within an infinite matrix is developed for plane strain deformations. The bonding at the inclusion-matrix interface is assumed to be homogeneously imperfect. The interface is modeled as a spring (interphase) layer with vanishing thickness. The behavior of this interphase layer is based on the assumption that tractions are continuous but displacements are discontinuous across the interface.Complex variable techniques are used to obtain infinite series representations of the stresses which, when evaluated numerically, demonstrate how the peak stress along the inclusion-matrix interface and the average stress inside the inclusion vary with the aspect ratio of the inclusion and a representative parameter h (related to the two interface parameters describing the imperfect interface in two-dimensional elasticity) characterizing the imperfect interface. In addition, and perhaps most significantly, for different aspect ratios of the elliptic inclusion, we identify a specific value (h ^*) of the (representative) interface parameter h which corresponds to maximum peak stress along the inclusion-matrix interface. Similarly, for each aspect ratio, we identify a specific value of h (also referred to as h ^* in the paper) which corresponds to maximum peak strain energy density along the interface, as defined by Achenbach and Zhu (1990). In each case, we plot the relationship between the new parameter h ^*and the aspect ratio of the ellipse. This gives significant and valuable information regarding the failure of the interface using two established failure criteria.     

An Interface Crack for a Functionally Graded Strip Sandwiched Between Two Homogeneous Layers of Finite Thickness

In this paper, the behavior of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness subjected to an uniform tension is resolved using a somewhat different approach, named the Schmidt method. The Fourier transform technique is applied and a mixed boundary value problem is reduced to two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surface. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. This process is quite different from those adopted in previous works. Numerical examples are provided to show the effects of the crack length, the thickness of the material layer and the materials constants upon the stress intensity factor of the cracks. It can be obtained that the results of the present paper are the same as ones of the same problem that was solved by the singular integral equation method. As a special case, when the material properties are not continuous through the crack line, an approximate solution of the interface crack problem is also given under the assumption that the effect of the crack surface interference very near the crack tips is negligible. Contrary to the previous solution of the interface crack, it is found that the stress singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials.     

Interface crack problems for mode II of double dissimilar orthotropic composite materials

The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized hi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.     

基于神经网络的界面裂纹尖端场分析

通过构造反向传播神经网络,对裂纹尖端的应力场进行模拟,进而实现对裂纹尖端应力场甬数的逼近。得到的网络具有较高的联想、记忆能力和相当的稳定性,并且可以快速、准确地得到带裂纹构件的裂纹尖端应力场,从而确定裂纹尖端的塑性区和分析裂纹的扩展。数值计算给出了LY12-CZ材料裂纹扩展方向的计算结果,与实验结果吻合较好,还给出了两相材料含界面裂纹在复合型载荷作用下的塑性区形状的变化情况,并对两相材料含界面裂纹在复合型载荷作用下裂纹的扩展方向进行了预测。     

压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题

分析了压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题。利用傅立叶变换,使问题的求解转换为对一对以裂纹表面上的位移差为未知变量的对偶积分方程的求解。为了求解对偶积分方程,把裂纹面上的位移差展开为雅可比多项式形式,进而得到了裂纹长度、入射波波速及入射波频率对裂纹应力强度因子的影响。从数值结果可以看出,压电压磁复合材料中可导通裂纹的反平面问题的动应力奇异性与一般弹性材料中的反平面断裂问题动应力奇异性相同。