Interactions Among General Systems of Cracks and Anticracks: An Integral Equation Approach

Cracks and rigid line inclusions, or anticracks, are commonly observed in many engineering materials, such as ceramics, intermetallics, etc. Interactions among these cracks and anticracks can significantly affect the load-carrying capacities and other mechanical properties of these materials. Accordingly, modeling of the interactions among general systems of cracks and anticracks subject to general loading conditions is the main thrust of this paper. An integral equation approach based on the fundamental solutions due to point loads and point dislocations in an elastic body is utilized for this purpose. A Gauss-Chebychev quadrature is used to reduce the integral equations to a system of linear equations consisting of the distributions of Burger’s dislocation vectors and forces on the cracks and the anticracks, respectively. The proposed solution procedure also allows direct determination of the rigid-body rotations for the anticracks. For a collinear crack-anticrack system, the results obtained from the present analysis are verified against those obtained from a Green’s function approach. Numerical results are also presented for sample systems of cracks and anticracks, and salient features of amplification and shielding of stress singularities are investigated.