Stress intensity factors for two offset parallel circular cracks: Part III — Elastic layer

Part III of this work is concerned with the interaction of two penny-shaped cracks in the mid-plane of an elastic layer. Two cases, namely the stress free boundary case and the fixed boundary case, are considered. It is shown that these two cases are mathematically equivalent. As in Part I (G.A.C. Graham and Q. Lan, J. Theor. Appl. Fract. Mech. 20, 207–225 (1994) 1])_for the problems of an infinite solid and Part II (G.A.C. Graham and Q. Lan, J. Theor. Appl. Fract. Mech. 20, 227–237 (1994) 2]) of a semi-infinite solid, the problem is reduced to a system of Fredholm integral equations of the second kind. These integral equations are then solved when the crack size is small compared to the distance between them and the cracks are far away from the boundaries. It is also shown that the problem decouples when the cracks are subjected to normal loading and shear loading. Asymptotic solutions are presented for these two loadings.