LAMELLAR INHOMOGENEITIES IN A UNIFORM STRESS-FIELD

Solutions for lamellar inhomogeneities in an infinitely extended isotr opic solid subjected to a uniform stress field at infinity are obtaine d by using Eshelby's equivalent inclusion method. First, two limiting cases are studied: cracks (i.e. inhomogeneities with elastic moduli id entically zero), and anticracks (i.e. inhomogeneities with infinitely large elastic moduli). Solutions are obtained for different modes of u niform loading in plane strain (biaxial load and in-plane shear), and anti-plane strain. It is observed that the stress field of an anticrac k under biaxial load has an inverse square root singularity at the tip of the anticrack. The stress held arises from the contribution of a p lanar dislocation distribution and a dislocation dipole distribution. Finally the most general case of inhomogeneities with finite non-zero elastic moduli, which here are called quasicracks, is considered and n ew solutions are provided. Quasicracks are useful to model fibers in f iber-reinforced materials. Analytical solutions are provided for the s tress held in the matrix, including the interface shear stress.