刚度微分法计算压电材料平面断裂问题

把计算应变能释放率的刚度微分法推广到压电材料平面断裂问题．在此基础上，利用压电材料平面断裂问题的有限元数值解作为真实场，用Ｓｏｓａ的平面问题裂端渐近解作为辅助场，由推广的交互Ｍ积分法求得了应力强度因子ＫＩ，ＫＩＩ和电位移强度因子ＫＩＶ．算例表明，计算结果与理论解符合得很好     

用围线积分法计算压电材料面外剪切问题的应力强度因子

本文把Ｂｅｔｉ功互等原理推广到压电材料的面外剪切问题中，并且根据Ｐａｋ的压电材料Ⅲ型裂纹问题复势解，给出了其裂端位移、电势、应力和电位移的渐近解及相应的辅助场具体形式。然后，把有限元数值解作为真实平衡状态，把推导出的辅助场作为辅助平衡状态，利用围线积分法计算出了压电材料Ⅲ型裂纹问题的应力强度因子ＫⅢ和电强度因子ＫⅣ。算例表明，计算结果与理论解符合得很好     

用围线积分法计算压电材料面外剪切问题的应力强度因子

本文把Ｂｅｔｔｉ功互等原理推广到压电材料的面外剪切问题中，并且根据Ｐａｋ的压电材料Ⅲ型裂纹问题复势解，给出了其裂端位移，电势，应力和电位移的渐近解及相应的辅助场具体，然后，把有限元数值作为真实平衡状态，把推导出的辅助场作为辅助平衡状态，利用围线积分法出了压电材料Ⅲ型裂纹问题的应力强度因子ＫⅡ和电强度因子ＫⅣ。算例表明，计算结果与理论解符合得很好。     

LY12复合型断裂的实验研究

应用有限元方法和断裂实验对铝合金ＬＹ１２在Ｉ＋Ⅱ型复合载荷作用下的弹塑性断裂行为进行了研究，给出了复合型弹塑性断裂的Ｊ积分准则，结果表明：（１）不同复合型下启裂Ｊ积分值满足ＪＩｉ／ＪＩｃ＋ＪⅡｉ／ＪⅡｃ＝１，ＪＭＣ＝ＪＩｉ＋ＪⅡｉ的关系，随Ⅱ型分量增加，启裂的Ｊ积分值ＪＭＣ增加ＪＩＣ为ＪＩＣ的两部；（２）ＪＭＣ值与复合比满足ＪＭＣ＝Ｋ＾２Ｉ．ＪＩＣ／（Ｋ＾２１＋αＫ＾２ＩＩ）＋αＫ＾２Ｉ．ＪＩＣ／     

一维六方准晶中椭圆孔边裂纹的静态与动态分析

通过构造保角映射函数,借助复变函数方法,研究了一维六方准晶中椭圆孔边裂纹的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子的解析解.当椭圆的长、短半轴以及裂纹长度变化时,所得结果不仅可以还原为Griffith裂纹的情形,而且得到孔边裂纹问题、T型裂纹问题和半无限平面边界裂纹问题的应力强度因子的解析解.就声子场而言,这些解与经典弹性的结果完全一致.接着对椭圆孔边裂纹的动力学问题进行了研究,并得到了Ⅲ型动态应力强度因子的解析解.当裂纹速度V→0时,动力学解还原为静力学解.这些解在科学与工程断裂中有着潜在的应用价值.     

用电阻应变片测量应力强度因子方法的研究

本文利用Ｗｉｌｉａｍｓ应力函数导出的应变场渐进表达式和电阻应变片测量技术，测量张开型（Ｉ型）裂纹尖端附近两点应变来确定应力强度因子ＫＩ。通过对不同裂纹体的测试结果表明，该技术具有较好的适用性。     

计算K_I时裂纹尖端塑性区修正的讨论

本文讨论在小范围屈服条件下，裂纹尖端塑性区修正问题，指出用等效裂纹计算ＫＩ的不足之处及其改进方式．     

计算K_I时裂纹尖端塑性区修正的讨论

本文讨论在小范围屈服条件下，裂纹尖端塑性区修正问题，指出用等效裂纹计算ＫＩ的不足之处及其改进方式．     

应变损伤材料I型动态扩展裂纹尖端场的渐近分析

研究了应变损伤材料Ｉ型动态扩展的裂纹尖端场。假定材料服从Ｊ２流动理论，且损伤规律以幂律应变软化的规律给出。对于塑性区引进了应力函数φ，ψ０借助于动力学方程的分析，给出了渐近方程及数值解。结果表明，对于可压缩材料Ｉ型平面应变尖端场是完全由塑性区组成，没有弹性卸载区。在裂纹尖端附近，应力和应变分别具有如下的奇异性：σ￣（ｌｎＲ／ｒ）＾－ｎ／ｎ＋１，ε￣（ｌｎＲ／ｒ）＾１／ｎ＋１。     

求解界面裂纹应力强度因子的围线积分法

本文基于Ｂｅｔｔｉ功互等定理和双材料界面裂纹辅助场，提出了一种求解界面裂纹应力强度因子的方法，即远场围线积分法。此方法与积分径的选择无关，用有元元法计算出远离裂纹尖端的位移场和应力场，应可通过计算绕裂尖围线的积分，精确地给出界面裂纹应力强度因子ＫＩ和ＫⅡ。     

Mode II dynamic fields near a crack tip growing in an elastic-perfectly-plastic solid

An asymptotic solution is given for Mode II dynamic fields in the neighborhood of the tip of a steadily advancing crack in an incompressible elastic—perfectly-plastic solid (plane strain). It is shown that, like for Modes I and III (Gao and Nemat-Nasser, 1983), the complete dynamic solution for Mode II predicts a logarithmic singularity for the strain field, but unlike for those modes which involve no elastic unloading, the pure Mode II solution includes two elastic sectors next to the stress-free crack surfaces. This is in contradiction to the quasi-static solution which predicts a small central plastic zone, followed by two large elastic zones, and then two very small plastic zones adjacent to the stress-free crack faces. The stress field for the complete dynamic solution varies throughout the entire crack tip neighborhood, admitting finite jumps at two shock fronts within the central plastic sector. This dynamic stress field is consistent with that of the stationary crack solution, and indeed reduces to it as the crack growth speed becomes zero.     

An exact transient analysis of plane wave diffraction by a crack in an orthotropic or transversely isotropic solid

A transient plane strain analysis of diffraction of plane waves by a semi-infinite crack in an unbounded orthotropic or transversely isotropic solid is performed. The waves approach the crack at a general oblique angle, and are of two types, a normal stress pulse and a shear stress pulse, i.e. a P- and an SV-wave, respectively, in the isotropic limit. A class of materials that includes this limit and beryl, cobalt, ice, magnesium and titanium is chosen for illustration, and exact solutions are obtained for the initial/mixed boundary value problems.In contrast to related work, a factorization in the Laplace transform space is used to simplify the solution forms and the Wiener-Hopf component of the solution process, and to yield a more compact expression for the Rayleigh wave speed. Calculations for this speed, the two allowable, direction-dependent, plane wave speeds, and quantities related to the Mode I and Mode II dynamic stress intensity factors are given for the five anisotropic materials mentioned.     

孔边裂纹对SH波的散射及其动应力强度因子

采用Ｇｒｅｅｎ函数法研究任意有限长度的孔边裂纹对ＳＨ波的散射和裂纹尖端场动应力强度因子的求解．取含有半圆形缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解作为Ｇｒｅｅｎ函数,采用裂纹“切割”方法并根据连接条件建立起问题的定解积分方程,得到动应力强度因子的封闭解答．最后给出了孔边裂纹动应力强度因子的算例和结果,并讨论了圆孔的存在对动应力强度因子的影响     

Circular welding problems with a crack

In this paper,the problem of an infinite plane with acircular hole welded by a nearly circular plate with a crackof different material is considered.The problem is tran-sformed into solving a certain boundary value problem ofanalytic functions and then reduced to solving a singularintegral equation along the crack.The formulas and somenumerical results of the factors of stress intensityfor the cases Mode Ⅰ and Mode Ⅱ are obtained at the endof this paper.     

A novel singular finite element of mixed-mode crack problems with arbitrary crack tractions

A novel singular finite element is presented to study cracked plates with arbitrary traction acting on crack surfaces. Firstly, the analytical solution around crack tips is determined using the symplectic dual approach. Subsequently, the solution is used to develop a novel singular finite element, which depicts accurately the characteristic of singular stresses field near crack tips. And the novel element can be applied to solve cracked plates, and both Mode I and Mode II stress intensity factors can be determined directly and accurately. Lastly, two numerical examples are given to illustrate the present method.     

Dynamic stability of a propagating crack

In this work we investigate the stability of a straight two-dimensional dynamically propagating crack to small perturbation of its path. Willis and Movchan (J. Mech. Phys. Solids 43 (1995) 319; J. Mech. Phys. Solids 45 (1997) 591) constructed formulae for the perturbations of the stress intensity factors induced by a small three-dimensional dynamic perturbation of a nominally plane crack. Their solution is exploited here to derive equations for the in-plane and out-of-plane perturbations of the crack path making use of the Griffith fracture criterion and the principle of “local symmetry” (i.e the crack propagates so that local K_II=0). We consider a crack propagating in a body loaded by a pair of point body forces and subjected to a remote uniaxial stress, aligned with the direction of the unperturbed crack. We assume that the loading follows the crack as the crack advances and is such that the unperturbed crack is subjected to Mode I loading. We perform an analysis of the stability of the dynamic crack in a similar way as in earlier work (Obrezanova et al., J. Mech. Phys. Solids 50 (2002) 57) on the quasistatically advancing crack. We present numerical results illustrating the influence of the crack velocity on the crack stability. Numerical computations of the possible crack paths have been performed which show that at velocities of crack propagation exceeding about one-third of the speed of Rayleigh waves the crack may admit one or more oscillatory modes of instability.     

On the lamb solution and Rayleigh-wave-induced cracking

This paper examines the extension of surface microcracks induced by a surface or Rayleigh wave (R-wave). This problem is examined both theoretically and experimentally. The theoretical approach involves a full-field reappraisal of the Lamb solution for a surface wave propagating in a homogeneous, isotropic, elastic, two-dimensional material for the cases of plane strain and plane stress. Using the Griffith-Irwin energy-release-rate fracture criterion for cracks under combined Mode I and Mode II loading, a prediction is made of the path and final length of the surface microcrack extension produced by the R-wave. Predictions of the crack-extension direction are also obtained using the maximum normal-stress fracture criterion. The experimental approach uses dynamic photoelasticity to observe the isochromatic patterns associated with an R-wave propagating along the narrow edge of a transparent birefringent plate, examining in detail the process of crack extension. When the theoretically and experimentally obtained results are compared, reasonable agreement is obtained.     

THE THREE-DIMENSIONAL STRESS INTENSITY FACTOR UNDER MOVING LOADS ON THE CRACK FACES

The dynamic stress intensity factor history for a half plane crack in anotherwise unbounded elastic body,with the crack faces subjected to a tractiondistribution consisting of two pairs of combined mode point loads that move in adirection perpendicular to the crack edge is considered.The analytic expression for thecombined mode stress intensity factors as a function of time for any point along thecrack edge is obtained.The method of solution is based on the application of integraltransform together with the Wiener-Hopf technique and the Cagniard-de Hoop method.Some features of the solution are discussed and graphical results for various point loadspeeds are presented.     

Asymptotic fields around an interfacial crack with a cohesive zone ahead of the crack tip

This paper considers an interfacial crack with a cohesive zone ahead of the crack tip in a linearly elastic isotropic bi-material and derives the mixed-mode asymptotic stress and displacement fields around the crack and cohesive zone under plane deformation conditions (plane stress or plane strain). The field solution is obtained using elliptic coordinates and complex functions and can be represented in terms of a complete set of complex eigenfunction terms. The imaginary portion of the eigenvalues is characterized by a bi-material mismatch parameter ε = arctanh(β)/π, where β is a Dundurs parameter, and the resulting fields do not contain stress singularity. The behaviors of “Mode I” type and “Mode II” type fields based on dominant eigenfunction terms are discussed in detail. For completeness, the counterpart for the Mode III solution is included in an appendix.     

CRACK PROPAGATION IN STRUCTURES SUBJECTED TO PERIODIC EXCITATION

In the present paper,a simple mechanical model is developed to predict the dynamic response of a cracked structure subjected to periodic excitation,which has been used to identify the physical mechanisms in leading the growth or arrest of cracking.The structure under consideration consists of a beam with a crack along the axis,and thus,the crack may open in Mode I and in the axial direction propagate when the beam vibrates.In this paper,the system is modeled as a cantilever beam lying on a partial elastic foundation,where the portion of the beam on the foundation represents the intact portion of the beam.Modal analysis is employed to obtain a closed form solution for the structural response.Crack propagation is studied by allowing the elastic foundation to shorten(mimicking crack growth)if a displacement criterion,based on the material toughness,is met.As the crack propagates,the structural model is updated using the new foundation length and the response continues.From this work,two mechanisms for crack arrest are identified.It is also shown that the crack propagation is strongly influenced by the transient response of the structure.