【摘要】 假设沿分叉裂纹各分支和板条边界有某位错分布,利用半平面内分叉裂纹问题的复势函数,将板条分叉裂纹问题转化为半平面内的多分叉裂纹问题处理。根据板条边界和裂纹面上的应力边界条件,建立以集中位错强度和分布位错密度为未知函数的Cauchy型奇异积分方程,利用半开型积分法则将该奇异积分方程化为代数方程求解。最后,由位错密度函数得到各裂纹分支端的应力强度因子值。文中分别给出集中力和分布力作用情况下内分叉和边缘分叉裂纹的3个算例,其极限情况的计算结果与精确解是一致的。更多还原

【Abstract】 The branch crack problems in a finite-width strip were solved by using the complex potential of a branch crack of half-plane,in which the distributed dislocations were assumed along all the branches and one boundary of the strip. Then by matching the traction along the branches and the boundary of the strip,Cauchy singular equations were obtained,in which the point dislocation and the distributed dislocation density served as the unknown function. Finally,by using a semi-open quadrature rule,the singular integral equations were transformed to algebra equations. It can be solved easily,and the SIF(stress intensity factor) values at the crack tips were calculated by the distributed dislocation function. Some examples are calculated,which contains the inner branch cracks and the edge branch cracks under the loading conditions of concentration force or distribution force. The results of the special cases agree well with the exact results.更多还原