Evaluation of the T-stress for multiple cracks in an elastic half-plane using singular integral equation and Green’s function method

Abstract

This paper studies the T-stress problem for multiple cracks in an elastic half-plane using the singular integral equation and Green’s function method. In the relevant perturbation field, the boundary of the elastic half-plane is traction free. In the solution, the complex potentials are decomposed into two parts, the principal part and the complementary part. The principal part of the complex potentials is derived from dislocation distributions along the crack faces. The role of the complementary part is to eliminate the traction along the boundary of half-plane caused by the principal part. Finally, a singular integral equation is formulated in which the dislocation distributions are unknown function. The explicit formulae for evaluating the stress intensity factors and the T-stresses at the crack tips are provided. Several numerical examples are presented.