Stress intensity factor and effective stiffness of a solid containing aligned penny-shaped cracks

The stress state and effective elastic moduli of an isotropic solid contain ing equally oriented penny-shaped cracks are evaluated accurately. The geom etric model of a cracked body is a spatially periodic medium whose unit cel l contains a number of arbitrarily placed aligned circular cracks. A rigoro us analytical solution of the boundary-value problem of the elasticity theo ry has been obtained using the technique of triply periodic solutions of th e Lame equation. By exact satisfaction of the boundary conditions on the cr acks' surfaces, the primary problem is reduced to solving an infinite set o f linear algebraic equations. An asymptotic analysis of the stress field ha s been performed and the exact formulae for the stress intensity factor (SI F) and effective elasticity tensor are obtained. The numerical results are presented demonstrating the effect of the crack density parameter and arran gement type on SIF and overall elastic response of a solid and comparison i s made with known approximate theories. (C) 2000 Elsevier Science Ltd. All rights reserved.