The anti-plane branch crack problems of strip were solved by using complex variable function and singular integral equation approach. Firstly, complex potential of single branch crack of half-plane which satisfied the traction-free condition along the boundary (also the lower boundary of the strip) was given. The problem was converted to the multiple branch cracks problem in half-plane by replacing the upper boundary of the strip with a two equal branch crack to satisfy the traction-free condition along the upper boundary. Next by matching the traction along the cracks, Cauchy singular integral 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 solved. Thus, the SIF values at the crack tips were calculated. At last, Two numerical examples were given.
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马丽娜 王钟羡. 板条内分叉裂纹的Ⅲ型应力强度因子[J]. 科学技术与工程, 2007, (17): 4260-4264. MA Li-na, WANG Zhong-xian.[J]. Science Technology and Engineering,2007,(17):4260-4264.