The Mixed-Mode Fracture Analysis of Multiple Embedded Cracks in a Semi-Infinite Plane by an Analytical Alternating Method

An efficient analytical alternating method is developed in this paper to evaluate the mixed-mode stress intensity factors of embedded multiple cracks in a semi-infinite plane. Analytical solutions of a semi-infinite plane subjected to a point force applied on the boundary, and a finite crack in an infinite plane subjected to a pair of point forces applied on the crack faces are referred to as fundamental solutions. The Gauss integrations based on these point load fundamental solutions can precisely simulate the conditions of arbitrarily distributed loads. By using these fundamental solutions in conjunction with the analytical alternating technique, the mixed-mode stress intensity factors of embedded multiple cracks in a semi-infinite plane are evaluated. The numerical results of some reduced problems are compared with available results in the literature and excellent agreements are obtained.