弹性圆域中Ⅲ型分叉裂纹的应力强度因子  

Stress intensity factor for the branch cracks of the circular region in elastic longitudinal shear problem

作　　者：杜红珊[1] 石少广[1] 张蕾[1] 

机构地区：[1]临沂师范学院数学系,山东临沂276005

出　　处：《山东大学学报（理学版）》2007年第9期101-106,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10671086);山东省自然科学基金资助项目(Y2005A12)

摘　　要：采用位错分析法,研究弹性纵向剪切情况下圆域中分叉裂纹问题.在给出无限大域中点位错复势的基础上,引入补充项以满足圆边界自由的条件,得到圆域中分叉裂纹问题的基本解.通过裂纹面上的应力边界条件,建立一组以位错密度为未知函数的Cauchy型奇异积分方程.由位移单值条件可以得到另一个约束方程.然后利用半开型数值积分公式把奇异积分方程化为代数方程求解,由位错密度直接得到裂纹尖端处的应力强度因子值.这种解析数值相结合求解应力强度因子的方法,充分利用了解析方法精度高和数值方法适用性广的特点,同时又克服了保角变换等解析解的局限,各裂纹位置可以是任意的.算例中所得的图表可以应用于工程实际.The branch cracks problems of circular region in elastic longitudinal shear are investigated by the dislocatious analysis method. Based on the complex potential of a point dislocation in an infinite region, a complementary term was introduced to satisfy the traction-free condition along the circular boundary, and then the elementary solution for branch crack problems in the circular region was obtained. By matching the traction along the cracks, Cauchy singular integral equatious for the branch cracks in the circular region were derived. A coustraint equation was formulated for the displacement single value condition. By using a semi-open quadrature rule, the singular integral equatious were transformed to algebraic equatious, and finally the stress inteusity factors at the crack tips were obtained. This semi-analytical method is accurate and widely used. It overcomes the limitation of the analytical solution such as conformal mapping. The position of cracks can be arbitrary. The results can be applied to actual projects.

关 键 词：分叉裂纹 纵向剪切 圆域 奇异积分方程 应力强度因子 

分 类 号：O346.1[理学—固体力学]