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 containing equally oriented penny-shaped cracks are evaluated accurately. The geometric model of a cracked body is a spatially periodic medium whose unit cell contains a number of arbitrarily placed aligned circular cracks. A rigorous analytical solution of the boundary-value problem of the elasticity theory has been obtained using the technique of triply periodic solutions of the Lame equation. By exact satisfaction of the boundary conditions on the cracks' surfaces, the primary problem is reduced to solving an infinite set of linear algebraic equations. An asymptotic analysis of the stress field has been performed and the exact formulae for the stress intensity factor (SIF) and effective elasticity tensor are obtained. The numerical results are presented demonstrating the effect of the crack density parameter and arrangement type on SIF and overall elastic response of a solid and comparison is made with known approximate theories.