An integral-equation solution for cracked half-planes bonded together and containing debondings along their interface

Abstract

The general solution of an arbitrary system of microdefects (i.e. cracks and/or holes) in an isotropic elastic half-plane bonded partially, along an infinite number of straight line segments to another half-plane consisting of a different isotropic elastic material, is formulated in this paper using the complex variable technique. The solution in terms of complex potentials is given by integrals over the cracks and/or holes with integrands expressed in terms of Green's functions and an unknown complex density function. Finally, the problem is reduced to the solution of a singular integral equation for the complex density function only along the microdefects. The appropriate Green's functions are derived from the solution of the problem of a concentrated force or a dislocation existing in either of the two half planes. Numerical results are presented for the stress intensity factors in three different cases.