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.     

双周期裂纹压电材料反平面剪切问题断裂力学分析

研究压电材料双周期裂纹反平面剪切与平面电场作用的问题．运用复变函数方法，获得了该问题严格的闭合解，并由此给出了裂纹尖端应力强度因子和电位移强度因子的精确公式．数值算例显示了裂纹分布特征对材料断裂行为的重要影响．叠间小裂纹能够对主裂纹的应力和电位移场起着屏蔽作用，相反行间小裂纹却起着放大作用，至于钻石形分布裂纹的影响规律则更为复杂．对于某些特殊情形给予了解答并导出一系列有意义的结果。     

集中力作用下含尖孔无限域的反平面剪切问题

论文采用了一种新的方法求解含孔元发域的反平面剪切问题，以闭合形式导出了在集中力作用下，孔口尖点的应力强度因子表达式。同时，给出了对称翼状尖孔、内摆线状尖孔、震状尖孔及圆孔径向边裂纹的应力强度因子，其结果在理论上和应用中都具有重要的意义。     

曲线裂纹和反平面圆形夹杂相交问题

建立了和反平面圆夹杂界面相交的曲线裂纹的弱奇异积分方程,利用Cauchy型奇异积分方程主部分析方法研究了穿过反平面圆夹杂界面的曲线裂纹在交点处的奇性应力指数以及交点处角形域内的奇性应力,并根据奇性应力定义了交点处的应力强度因子.通过对弱奇异积分方程的数值求解,可得裂纹端点和交点处的应力强度因子.     

圆形域多圆孔多裂纹反平面问题研究

本文运用复变函数及积分方程方法，求解了圆形域多圆孔多裂纹反平面问题，建立了两种类型的基本解。复叠加原理和所得的基本解并沿国圆孔和裂纹表面取待定的基本解密度函数，可得到一组以基本解密度函数为未知函数的Ｆｒｅｄｈｏｌｍ积分方程。通过该积分方程组的数值可以得到密度函数的离散值，进而得到了裂纹尖端的应力强度因子。     

周期裂纹和刚性线尖端场干涉效应研究

研究双周期裂纹和刚性线夹杂非均匀材料的反平面剪切问题。基于保角变换技术和椭圆函数理论,获得了问题应力场的全场精确解,给出了裂纹和刚性线尖端应力强度因子的封闭形式解答,讨论了裂纹和刚性线尖端场的干涉效应。数值结果表明：改变水平和垂直分布周期对裂纹和刚性线尖端场影响明显不同;裂纹长度2a逐渐增大时(0≤a/ω1≤0.5),裂纹尖端应力强度因子从1逐渐增大到无限大,而刚性线的尖端场变化不大;刚性线长度2d逐渐增大时(0≤d/ω2≤1),刚性线尖端应力强度因子逐渐减小,而裂纹的尖端场仅略微增大。     

双周期平行四边形排列裂纹反平面问题的有限元分析

提出了双周期平行四边形排列裂纹反平面问题的有限元方法,通过对单位胞元引入周期边界条件,在裂纹尖端采用奇异单元,解决了有限元分析这类问题的效率和精度问题.利用Ansys软件计算,在各种有解析解对照的情形下,应力强度因子的相对误差都在0.2%以内.与现有通常限于对称阵列的双周期裂纹的研究相比,本文发展的方法适用于一般的非对称平行四边形裂纹阵列.算例揭示了行向裂纹间的相互干涉放大应力强度因子,而叠向裂纹间的作用相互屏蔽.对于平行四边形阵列的情形,这两种相反的干涉效应使应力强度因子与裂纹错动参数间呈现非单调依赖关系.     

电可通纳米尺度孔边均布多裂纹的电弹断裂分析

解析研究了面内电载荷和反平面机械载荷作用下压电体中纳米尺度圆孔边均布电可通多裂纹问题的断裂性能。基于Gurtin-Murdoch表面弹性理论,利用保角映射方法和复变弹性理论给出了裂纹尖端电弹场分布、电弹场强度因子及能量释放率的解析结果。阐述了无量纲电弹场强度因子、无量纲能量释放率的尺寸依赖效应,讨论了裂纹数量和缺陷几何参数对无量纲场强度因子和无量纲能量释放率的影响。结果表明：无量纲电弹场强度因子和无量纲能量释放率具有显著的尺寸依赖效应;考虑表面效应,孔径和裂纹长度相当时,电弹场强度因子达到最大;裂纹/孔径比对电弹场强度因子随裂纹数量变化的制约会随着裂纹数量的增加而逐渐消失;过大或过小的裂纹孔径比会削弱裂纹长度对能量释放率的影响。     

电可通纳米尺度孔边均布多裂纹的电弹断裂分析

解析研究了面内电载荷和反平面机械载荷作用下压电体中纳米尺度圆孔边均布电可通多裂纹问题的断裂性能。基于Gurtin-Murdoch表面弹性理论,利用保角映射方法和复变弹性理论给出了裂纹尖端电弹场分布、电弹场强度因子及能量释放率的解析结果。阐述了无量纲电弹场强度因子、无量纲能量释放率的尺寸依赖效应,讨论了裂纹数量和缺陷几何参数对无量纲场强度因子和无量纲能量释放率的影响。结果表明：无量纲电弹场强度因子和无量纲能量释放率具有显著的尺寸依赖效应;考虑表面效应,孔径和裂纹长度相当时,电弹场强度因子达到最大;裂纹/孔径比对电弹场强度因子随裂纹数量变化的制约会随着裂纹数量的增加而逐渐消失;过大或过小的裂纹孔径比会削弱裂纹长度对能量释放率的影响。     

压电体中考虑表面效应时开裂孔洞的断裂特征

研究了反平面机械载荷和面内电载荷作用下压电体中考虑表面效应时孔边双裂纹问题的断裂特征.基于Gurtin-Murdoch表面理论模型,通过构造映射函数,利用复势电弹理论获得了应力场和电位移场的闭合解答.给出了裂纹尖端应力强度因子、电位移场强因子和能量释放率的解析解.讨论了开裂孔洞几何参数和施加力电载荷对电弹场强因子和能量释放率的影响.     

基于表面弹性理论的开裂椭圆孔断裂力学研究

研究纳米尺度时开裂椭圆孔的III型断裂性能。基于表面弹性理论和保角映射技术,利用复势函数理论获得了缺陷(裂纹和椭圆孔)周围应力场和裂纹尖端应力强度因子的闭合解答。所得结果具有一般性,许多已有和新的解答可由本文退化的特殊情形得到。利用解析结果讨论了缺陷的绝对尺寸、椭圆孔的形状比以及裂纹的相对尺寸对应力强度因子的影响。结果表明：考虑表面效应且缺陷尺寸在纳米尺度时,应力强度因子具有显著的尺寸依赖效应;应力强度因子随椭圆孔形状比的变化规律受缺陷表面常数的影响;缺陷表面效应的影响取决于椭圆孔的形状比,非常大的形状比屏蔽了表面效应的影响;裂纹相对尺寸非常小时表面效应影响较弱,裂纹相对尺寸较大时表面效应较为明显。     

Dynamic analysis of a cracked magnetoelectroelastic medium under antiplane mechanical and inplane electric and magnetic impacts

The transient analysis of a magnetoelectroelastic medium containing a crack is made under antiplane mechanical and inplane electric and magnetic impacts. The crack is assumed to penetrate through the solid along the poling direction. By using the Fourier and Laplace transforms, the associated mixed boundary value problem is reduced to a Fredholm integral equation of the second kind, which is solved numerically. By means of a numerical inversion of the Laplace transform, dynamic field intensity factors are obtained in the time domain. Numerical results are presented graphically to show the effects of the material properties and applied electric and magnetic impacts on the dynamic intensity factors of COD and stress, and dynamic energy density factors. The results indicate that except for the intensity factors of electric displacement and magnetic induction, other field intensity factors exhibit apparent transient feature. Moreover, they depend strongly on mechanical input as well as electric and magnetic impacts.     

Viscoelastic composite with a cracked layer under anti-plane shear

A viscoelastic cracked sandwich composite under anti-plane load is presented via the application of the Laplace transform and the complex variable formulation. Using a special technique of analytical continuation associated with the method of image, the triple-layered problem is reduced to a singular function by simple algebraic manipulations. The superposition method and the singular integral equation is applied to deal with the concentrated load and crack problem. Finally, some typical viscoelastic models and its corresponding stresses and stress intensity factors are also discussed. The results show that the time dependent stress intensity factor is affected by the relative strength of creep compliances of each layer.     

Fracture analysis of a single edge cracked strip under thermal shock

For a single edge crack in a long strip quenched on the cracked side, the time-dependent stress intensity factors have been calculated by means of the methods of weight functions, finite elements and boundary elements. These quantitative results support a recently developed heuristic fracture-mechanical approach to thermal shock damage due to single and multiple crack growth.     

Fracture analysis of functionally graded coatings: antiplane deformation

A new model for approximate analysis of a functionally graded coating with arbitrary variation of properties has been developed. In this model, the coating is divided into several sublayers. In each sublayer the material properties vary in a linear manner along the thickness direction and the material properties are continuous at each subinterface. With this new model, the crack problem of a functionally graded coating bonded to a homogeneous half-plane under static antiplane shearing load is investigated. By using transfer matrix method and Fourier integral transform technique, the problem is reduced to the solution of a Cauchy singular integral equation. Stress intensity factors are calculated. Comparisons are made between the present model and other models. The results show some advantages of the present model.     

Stress singularity analysis of anisotropic multi-material wedges under antiplane shear deformation using the symplectic approach

Symplectic approach has emerged a popular tool in dealing with elasticity problems especially for those with stress singularities. However, anisotropic material problem under polar coordinate system is still a bottleneck. This paper presents a subfield method coupled with the symplectic approach to study the anisotropic material under antiplane shear deformation. Anisotropic material around wedge tip is considered to be consisted of many subfields with constant material properties which can be handled by the symplectic approach individually. In this way, approximate solutions of the stress and displacement can be obtained. Numerical examples show that the present method is very accurate and efficient for such wedge problems. Besides, this paper has extended the application of the symplectic approach and provides a new idea for wedge problems of anisotropic material.     

Oblique edge crack in an anisotropic material under antiplane shear

An oblique edge crack in an anisotropic material under antiplane shear loadings is investigated. The antiplane problems are formulated based on a linear transformation method. An anisotropic solid containing an edge crack subjected to concentrated forces is first considered. The stress intensity factor for the edge crack with concentrated forces is obtained from the solution of the transformed edge crack in an isotropic material which is solved by using conformal mapping technique and complex function theory. The solution of the edge crack under concentrated loads is used to construct the stress intensity factor for the oblique edge crack in the anisotropic material subjected to antiplane distributed loads. Some numerical computations are carried out to calculate the stress intensity factors for the edge crack in inclined orthotropic materials subjected to point forces as well as distributed tractions.     

A unified treatment of the elastic elliptical inclusion under antiplane shear

Summary A generalized and unified treatment is presented for the antiplane problem of an elastic elliptical inclusion undergoing uniform eigenstrains and subjected to arbitrary loading in the surrounding matrix. The general solution to the problem is obtained through the use of conformal mapping technique and Laurent series expansion of the associated complex potentials. The resulting elastic fields are derived explicitly in both transformed and physical planes for the inclusion and the surrounding matrix. These relations are universal in the sense of being independent of any particular loading as well as the geometry of the matrix. The complete field solutions are provided for an elliptical inclusion under uniform loading at inifinity, and for a screw dislocation interacting with the elastic elliptical inclusion.