Fracture characteristics of solids containing doubly-periodic arrays of cracks

Abstract

The stress relaxation process from the tips of doubly-periodic (rectangular and diamond-shaped) arrays of slit-like cracks contained in an infinite elastic solid is studied under both plane and anti-plane strain conditions. The displacement discontinuities due to slit-like cracks are represented by distributions of suitable dislocations. The latter are determined from singular integral equations resulting from the satisfaction of the traction-free conditions at the crack faces. In the absence of a closed form solution, these equations are solved numerically after expanding the non-singular part of the kernel in a series of Chebyshev polynomials. Results are presented for the extent of spread of plasticity from each of the cracks and for the crack-tip opening displacement as functions of the horizontal and vertical crack spacings and the externally applied stress and discussed from the point of fracture initiation from an array of stress concentrations. It is shown that an array of cracks can have a detrimental or beneficial effect on the fracture characteristics of the solid depending on the far-field state of stress. Moreover, the crack-tip opening displacement is practically independent of the horizontal separation of cracks for small values of the distance of vertical separation and depends only on the latter.