Stress Intensity of Debonding for A Rigid Inclusion Near An Angle Dislocation

Abstract

The study of debonding is of importance in providing a good understanding of the bonded interfaces of dissimilar materials. The problem of debonding of an arbitrarily shaped rigid inclusion in an infinite plate with a point dislocation of thin plate bending is investigated in this paper. Herein, the point dislocation is defined with respect to the difference of the plate deflection angle. An analytical solution is obtained by using the complex stress function approach and the rational mapping function technique. In the derivation, the fundamental solutions of the stress boundary value problem are taken as the principal parts of the corresponding stress functions, and through analytical continuation, the problem of obtaining the complementary stress function is reduced to a Riemann-Hilbert problem. Without loss of generality, numerical results are calculated for a square rigid inclusion with a debonding. It is noted that the stress components are singular at the dislocation point, and a stress concentration can be found in the vicinity of the inclusion corner. We also obtain the stress intensity of a debonding in terms of the stress functions. It can be found that when a debonding starts from a corner of the inclusion and extends to another corner progressively, the stress intensity of the debonding increases monotonously; once the debonding extends over the corner points, the value of the stress intensity of the debonding gradually decreases. The relationships between the stress intensity of the debonding and the direction and position of the dislocation are also presented in this paper.