Singular Integral Equation Approach For Multiple-edge Crack Problems Of Half-plane In Antiplane Elasticity

In this paper, the multiple-edge crack problems for half-plane in antiplane elasticity are investigated systematically by using complex potentials of dislocation model and the singular integral equation approach. And the numerical solutions of many multiple- edge crack problems are solved.The elementary solution of a single-edge crack problem for half-plane is proposed, which is obtained by the elementary solution of a point dislocation for infinite plane and distributing the dislocation density along the crack configuration, and satisfies the traction-free condition along the boundary of the half-plane. The elementary solution is a function of the distributing dislocation density and composed of the principal part and the complementary part. The multiple-edge crack problem of half-plane can be considered as a superposition of many single-edge crack problems. Thus, a group of Cauchy singular integral equations can be formulated, where the distributing dislocation density serves as the unknown function. By using a semi-open quadrature rule, the singular integral equations are solved. And the stress intensity factor (SIF) values at the crack tips are calculated, which are paid more attention to by engineers in practice. The interactions end the reciprocal effects between cracks are exposed quantificationally. Meanwhile, the crack opening displacement (COD) of multiple-edge crack for half-plane is solved.The multiple-edge crack problem of dense crack and the edge internal branch crack problem in a semi-infinite region are also considered on the base of previous studies. Furthermore, the multiple-edge crack problem of the concentrated force that is applied in half-plane is studied. The 'shadow effect' of multiple-edge crack and the elementary solution of the concentrated force for half-plane are observed.All the conclusions in this paper can be further used to investigate the multiple-edge crack problems in antiplane elasticity. Using the approach proposed in this paper makes SIF values calculated more easily and more accurately. There are lots of numerical examples given. The numerical results and charts in this paper can be applied directly into practice.