Interaction of penny-shaped cracks with a half-plane crack

Abstract Three-dimensional interactions between a half-plane crack and penny-shaped cracks which are not necessarily located in the same plane are analysed using the “weight function” method of three-dimensional crack analysis. Analytical expressions are given for the interaction kernels in the integral equations with the opening displacements of penny-shaped cracks as unknown functions. By using the Rayleigh-Ritz method the singularities of the kernels are weakened to make them suitable for finite element calculations. The weak form equations are also solved by a simple method after approximating the opening displacement over each crack by a constant times a square root function of the distance from its edge. This simple method of solution is shown to give results which are in excellent agreement with those of Laures and Kachanov (1991, Int. J. Fract . 48 , 255–279).

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