On Delamination Branching of Anisotropic Bimaterials

Abstract

The phenomena of delamination branching/kinking from the interface of general anisotropic bimaterials are investigated based on the elegant Stroh’s sextic formulism of dislocation theory in matrix notation. A set of compact form of Green’s functions for two kinds of dislocation — an interface dislocation and a dislocation in one medium of the bimaterial elastic solid is obtained. Using these Green’s functions, the whole delamination including the interface part and the part branching into either one of the dissimilar anisotropic materials is modeled as a continuous distribution of the two kinds of dislocations. An interesting observation from this method is that the traction along the dislocation line when the dislocation is inside one medium, mathematically has similar form as the traction on the interface surface due to an interface dislocation. Thus a non-homogeneous Hilbert problem with discontinuous coefficients for this anisotropic bimaterials is formulated and a general solution to this problem is obtained. Consequentially, a preferable value of the branching angle for a given pair of anisotropic bimaterial media can be obtained by maximizing the energy release rate of the kinking-cracked solid. The comparison of other approaches which have appeared in the literature are discussed.