In-Plane Analysis of Micro-Cracks Using Modified Couple-Stress Elasticity

Abstract

Based upon the modified couple stress theory, we devise a procedure to analyze multiple interacting micro-cracks subject to the mixed mode deformation in an isotropic elastic plane. First, we carry out the asymptotic analysis of the displacement field at the tip of a stationary crack. The dominant term of displacement field reveals that the symmetric part of the stress tensor, which is energy conjugate to the strain tensor, is not singular. In contrast, the couple stress tensor has square root singularity at a crack tip. Furthermore, we use the Fourier integral transform to obtain the solution to an edge dislocation in an isotropic plane. Asymptotic analysis of the obtained solutions shows Cauchy singularity in the location of the edge dislocation. The integral equations for several interacting parallel micro-cracks are constructed via the distributed dislocation technique. These equations are solved numerically for the density of dislocations on a micro-crack surface. The effects of intrinsic material length scale on the stress field of a crack and the interaction between two parallel micro-cracks are studied.