An edge dislocation near an anticrack in a confocal elliptical coating

Abstract

We present an analytical study of the problem associated with an edge dislocation near a completely coated finite anticrack (or rigid line inhomogeneity). The two foci of the elliptical coating-matrix interface are located at the two tips of the anticrack. In addition, the coating and the matrix have identical shear moduli but distinct Poisson’s ratios. By means of conformal mapping and analytic continuation, we obtain a closed-form representation of a specifically constructed auxiliary function defined in the entire image plane. This auxiliary function is then used to derive analytical expressions (in the image plane) of the two pairs of analytic functions which characterize the corresponding stress and displacement distributions. A closed-form expression representing the rigid-body rotation of the anticrack is presented by satisfying moment balance on a circular disk with sufficiently large radius. The mode I and mode II stress intensity factors at the two anticrack tips are determined explicitly.