考虑表面弹性效应时正三角形孔边裂纹反平面剪切问题的断裂力学分析

基于表面弹性理论和保角映射技术,研究了远场作用反平面剪切载荷作用下考虑表面弹性效应时正三角形孔边裂纹问题的断裂性能.给出了孔边应力场的精确解,获得了裂纹尖端应力强度因子的解析解答.数值算例中讨论了裂尖应力强度因子随三角形孔尺寸、裂纹长度和表面性能的变化规律.结果表明:当三角形孔的尺寸在纳米量级时,无量纲应力强度因子具有显著的尺寸效应;随着三角形孔尺寸的增大,论文结果趋近于经典断裂理论解答;无量纲应力强度因子随孔边裂纹长度的增加,先增大而后减小;当孔边裂纹长度较小时,表面效应影响较弱;应力强度因子的尺寸效应受表面性能影响显著.     

考虑表面效应时正三角形孔边裂纹反平面剪切问题的断裂力学分析

基于表面弹性理论和保角映射,研究了远场反平面剪切载荷作用下考虑表面效应时正三角形孔边裂纹问题的断裂性能。给出了孔边应力场解答,获得了裂纹尖端应力强度因子解析解答。数值算例讨论了应力强度因子随三角形孔尺寸、裂纹长度和表面性能的变化规律。结果表明：当三角形孔尺寸在在纳米量级时,无量纲应力强度因子受孔隙尺寸影响显著;随着三角形孔尺寸的增大,本文结果趋近于经典断裂理论解答;无量纲应力强度因子随裂纹长度的增加,数值先增大而后减小;裂纹相对长度较小时,表面效应影响较弱;应力强度因子的尺寸效应受表面性能影响显著。     

功能梯度材料涂层平面裂纹分析

研究粘接于均质基底材料上功能梯度涂层平面裂纹问题. 假设功能梯度材料剪切模量的倒数为坐标的线性函数，而泊松比为常数. 采用Fourier变换和传递矩阵法将该混合边值问题化为奇异积分方程组，通过数值求解获得 应力强度因子. 考察了材料梯度变化形式、结构几何尺寸和材料梯度参数对裂纹应力强度因子的影响，发现 功能梯度材料涂层尺寸、裂纹长度以及材料梯度参数均对应力强度因子有显著影响.     

功能梯度压电材料反平面裂纹问题

基于三维弹性理论和压电理论，导出了材料系数在横观各向同性平面内梯度分布的压电体的状态方程，进而对材料系数指数函数规律分布的半无限大压电体中的反平面裂纹问题进行了求解，利用Fourier变换给出了半无限大压电体中位移，应力，电势及电位移的解析表达式，并求得了裂纹尖端的应力强度因子和电位移强度因子，分析了不同的非均匀材料系数及几何尺寸对它们的影响。     

圆柱形界面相裂纹在扭转载荷作用下的动态断裂

本文研究了位于界面相中的圆柱形界面裂纹的扭转冲击问题.采用Laplace、Fourier变换和位错密度函数将混合边值问题转化为求解Cauchy核奇异积分方程,利用Laplace数值反演技术计算了动态应力强度因子.讨论了材料特性和结构的几何尺寸对动态应力强度因子的影响.结果表明,随着界面相厚度的增加,无量纲化的动态应力强度因子减小.当裂纹靠近剪切弹性模量大的材料时,无量纲化的动态应力强度因子增大,反之减小.界面相两侧不同的材料组合对裂尖动态应力强度因子的影响是随着剪切弹性模量和质量密度的比值的增加而减小.界面相中裂纹长度对裂尖动态应力强度因子的影响比其他因素的影响大.     

压荷载下类岩石材料中的锯齿形裂纹分析

针对类岩石材料的复杂性和非均质性，特别是材料中一些强度相对较弱的晶界的存在等，对形状较为复杂的两种锯齿形裂纹：内张型滑动裂纹和单翼滑动裂纹的应力强度因子进行了分析．结合经典的滑动裂纹模型，讨论了裂纹起裂角、侧压以及翼裂长度等对应力强度因子的影响．分析的结果为进一步研究类岩石材料的断裂损伤机理提供了理论基础．     

基于GMTS准则的岩石复合型断裂机理研究

使用国际岩石力学协会规定的半圆盘岩石试件,加工不同倾角的直裂纹试样,通过三点弯曲加载试验得到不同I-II复合比断裂的断裂韧性和初始断裂角．传统裂纹扩展准则忽视了常数项即T应力及更高阶项的影响,导致该扩展准则的理论预测结果存在较大缺陷,本文通过考虑常数项,建立广义最大周向应力准则(GMTS)．在此基础上,分别采用传统的裂纹扩展准则和考虑T应力的裂纹扩展准则预测不同复合比裂纹的断裂韧性和初始扩展角,然后对比理论预测结果和实验结果．分析可得：常数项即T应力对断裂的临界应力强度因子和初始断裂角的影响是不可忽略的,且II型断裂占比较大时影响更大,广义最大周向应力准则预测值与实验测试结果之间的误差最小．     

压电体内孔边裂纹的应力强度因子

本文研究含有Ⅲ型孔边裂纹压电弹性体的反平面问题.根据Muskhelishvili的数学弹性力学理论,并利用保角变换和Cauchy积分的方法,对含有圆孔孔边单裂纹和双裂纹的压电弹性体分别进行了分析.基于电不可穿透裂纹模型,得到了在反平面剪力和面内电载荷的共同作用下裂纹尖端应力强度因子的解析解.最后,通过数值算例,讨论了应力强度因子随裂纹长度变化的规律.结果表明:应力强度因子随着裂纹和孔的相对尺寸的增加而增加,并且单边裂纹的应力强度因子要比双边裂纹的应力强度因子大.     

焦散线法确定应力强度因子的条件

基于焦散线的形成原理及含裂纹受力试件在裂尖附近区域的应力分布,得到了焦散线法确定应力强度因子的条件：初始曲线半径与试件厚度之比大于0．5。当满足该条件时,对光学各向同性材料及光学各向异性材料前表面反射的情形,只需测量焦散线沿横向的最大尺寸便可较精确地确定应力强度因子;而对于光学各向异性材料的透射或后表面反射情形,只有在忽略远场非奇异应力的影响后,才可借助焦散线的横向尺寸近似确定应力强度因子。     

常幅载荷下结构元件断裂可靠度估算的应力强度因子模型

给出了一个估算结构元件疲劳可靠度的应力强度因子模型,系统阐述了元件在常幅载荷下疲劳可靠性的分析方法。该模型研究了常幅载荷作用下材料瞬时裂纹长度和应力强度因子的分布形式,建立了应力强度因子与断裂韧性之间的干涉关系。对7075-T7351铝合金中心裂纹试件试验数据分析的结果表明：裂纹的瞬时扩展长度和可靠度的预测结果均与试验结果符合很好,本文给出的基于应力强度因子的可靠性分析模型是合理的。     

Further investigation of subinterface cracks

Summary Further investigation of subinterface cracks in bimaterial solids is presented. The traction method is proposed permitting easy calculation of the stress intensity factors of the cracks. The elastic T-terms of the cracks are determined. The J ₁ and J ₂ integrals are analyzed for a contour enclosing all the cracks in the global coordinate system x,y, where the x-axis is parallel to the interface. Numerical examples are given, and the results are presented for two kinds of material combinations, Cu/Al₂O₃ and Ni/MgO. Accepted for publication 24 November 1996     

弹性T项对裂尖参数和裂纹扩展路径稳定性的作用

研究了弹性T项在主裂纹与近裂尖微空洞干涉问题中对裂尖参数和裂纹扩展路径稳定性的影响作用.利用“伪力”法,并通过解决主裂纹与近裂尖微空洞干涉问题,对远场纯1型载荷和远场弹性T项载荷下,该干涉问题中弹性T项的影响作用进行了分析从数值结果可以看出：由于空洞的存在;释放了弹性T项所引起的应力,弹性T项对裂尖参数;应力强度因子和J积分都有直接显著的影响,因而,它对该载荷下的裂纹扩展路径的稳定性有控制作用。     

Stress state around cracks on the boundary of a hole in a photoelastic orthotropic plate under creep

The stress–strain state near cracks on the boundary of a circular hole in a linear elastic orthotropic composite plate under tension is analyzed. The distribution of stress intensity factors (SIFs) at the crack tip is found from photoelectric measurements. The dependence of the SIFs on the ratio of crack length to hole radius and on the mechanical properties of the material is established     

Elastic wave scattering from a penny-shaped interface crack in coated materials

This paper is concerned with the elastic wave scattering induced by a penny-shaped interface crack in coated materials. Using the integral transform, the problem of wave scattering is reduced to a set of singular integral equations in matrix form. The singular integral equations are solved by the asymptotic analysis and contour integral technique, and the expressions for the stress and displacement as well as the dynamic stress intensity factors (SIFs) are obtained. Using numerical analysis, this approach is verified by the finite element method (FEM), and the numerical results agree well with the theoretical results. For various crack sizes and material combinations, the relations between the SIFs and the incident frequency are analyzed, and the amplitudes of the crack opening displacements (CODs) are plotted versus incident wavenumber. The investigation provides a theoretical basis for the dynamic failure analysis and nondestructive evaluation of coated materials.     

The thermoelastic equilibrium of a transversally isotropic medium with an elliptic crack under symmetric loading

The stress intensity factors (SIFs) are evaluated for flat elliptical cracks located in a transversally isotropic material (cracks are assumed perpendicular to the transtropy axis) under an arbitrary load and symmetric temperature. The SIFs for an elliptical crack in a transversally isotropic medium are determined using the formulas (derived by the author in his previous studies) of transition from an isotropic to transversally isotropic material and the relative problem for an isotropic medium. It is proved that these formulas can be employed for an arbitrary homogeneous transversally isotropic material (no matter whether the roots of some characteristic equation of the material are real or complex) with an arbitrary flat crack or a system of coplanar flat cracks, including elliptical ones, under an arbitrary load and symmetric temperature. A transversally isotropic material with two coplanar elliptical cracks is considered as an illustrative example. The dependences of the SIFs on the parameters of cracks and their arrangement at a decreasing temperature are presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 96–105, April, 2000.     

Boundary element analysis of crack problems in functionally graded materials

The present study examines the crack problems in a functionally graded material (FGM) whose upper and bottom surfaces are fully bonded with dissimilar homogeneous materials. A so-called generalized Kelvin solution based boundary element method is used in the numerical examination. The multi-region method and the eight-node traction-singular boundary elements are used for the crack evaluation. The layer discretization technique is utilized to approximate the depth material non-homogeneity of the FGM layer. The proposed method can deal with any depth variations in both the shear modulus and the Poisson ratio of the FGMs. Results of the present analysis are compared very well with the exact analytical solutions available in the literature, which demonstrates that the proposed method can accurately evaluate the stress intensity factors (SIFs) for cracks in FGMs. The paper further evaluates the effect of the functionally graded variations in the Poisson ratio on the stress intensity factors. The paper also assesses the elliptical cracks in the FGM system. The paper presents the influence of both the non-homogeneity and the thickness of the FGM layer on the three SIFs associated with the elliptical cracks.     

夹杂对两相材料界面裂纹的影响

根据界面上应力和位移的连续条件,得到了单向拉伸状态下,含有椭圆夹杂的无限大双材料组合板的复势解。进一步通过求解Hilbert问题,得到了含有夹杂和半无限界面裂纹的无限大板的应力场,并由此给出了裂尖的应力强度因子K。计算了夹杂的形状、夹杂的位置、夹杂的材料选取以及上、下半平面材料与夹杂材料的不同组合对裂尖应力强度的影响。计算结果表明夹杂到裂尖的距离和夹杂材料的性质对K影响较大,对于不同材料组合,该影响有较大差异。夹杂距裂尖较近时,会对K产生明显屏蔽作用,随着夹杂远离裂尖,对K的影响也逐渐减小。另外,软夹杂对K有屏蔽作用,硬夹杂对K有反屏蔽作用,而夹杂形状对K几乎没有影响。     

半无限横观各向同性体中共面双裂纹边界元分析

基于双横观各向同性材料基本解的对偶边界元方法,分析了半无限横观各向同性材料中两条共面裂纹的相互作用问题。裂纹面上分别作用着法向和切向两种均布荷载,材料的各向同性面及裂纹面平行于半无限域自由面。数值计算得到了该类裂纹的应力强度因子(SIF)值和两条共面裂纹相互作用的SIF值影响系数。根据数值结果分析了自由面对该类裂纹SIF值的影响,以及裂纹间距与形状、自由面对SIF值影响系数的影响。结果表明,自由面对作用法向力时的该类裂纹SIF值有明显的影响,裂纹间距与形状对SIF值影响系数影响较大,但自由面对SIF值影响系数基本无影响。     

Three-dimensional mixed-mode stress intensity factors for cracks in functionally graded materials using enriched finite elements

Three-dimensional enriched finite elements are used to compute mixed-mode stress intensity factors (SIFs) for three-dimensional cracks in elastic functionally graded materials (FGMs) that are subject to general mixed-mode loading and constraint conditions. The method, which advantageously does not require special mesh configuration/modifications and post-processing of finite element results, is an enhancement of previous developments applied so far on isotropic homogeneous and isotropic interface cracks. The spatial variation of FGM material properties is taken into account at the level of element integration points. To validate the developed method, two- and three-dimensional mixed-mode fracture problems are selected from the literature for comparison. Two-dimensional cases include: inclined central crack in a large FGM medium under uniform tensile strain and stress loadings, a slanted crack in a finite-size FGM plate under exponentially varying tensile stress loading and an edge crack in a finite-size plate under shear traction load. The three-dimensional example models a deflected surface crack in a finite-size FGM plate under uniform tensile stress loading. Comparisons between current results and those from analytical and other numerical methods yield good agreement. Thus, it is concluded that the developed three-dimensional enriched finite elements are capable of accurately computing mixed-mode fracture parameters for cracks in FGMs.     

Stress state of a piezoelectric ceramic body with a plane crack under antisymmetric loads

The static equilibrium of an electroelastic transversely isotropic space with a plane crack under antisymmetric mechanical loads is studied. The crack is located in the plane of isotropy. Relationships are established between the stress intensity factors (SIFs) for an infinite piezoceramic body and the SIFs for a purely elastic body with a crack of the same form under the same loads. This makes it possible to find the SIFs for an electroelastic body without the need to solve specific electroelasitc problems. As an example, the SIFs are determined for a piezoelastic body with penny-shaped and elliptic cracks under shear __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 32–42, February 2006.