Integral identities for fracture along imperfectly joined anisotropic ceramic bimaterials

Abstract

We study a crack lying along an imperfect interface in an anisotropic bimaterial. A method is devised where known weight functions for the perfect interface problem are used to obtain singular integral equations relating the tractions and displacements for both the in-plane and out-of-plane fields. The problem can be considered as modelling bimaterial ceramics which are joined with a thin soft adhesive substance. The integral equations for the out-of-plane problem are solved numerically for orthotropic bimaterials with differing orientations of anisotropy and for different extents of interfacial imperfection. These results are then compared with finite element computations.authorsversionPeer reviewe

Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

“…In a majority of the referenced works above, the interface is assumed to be perfectly bonded, i.e., those models assume the continuity of both the traction and displacement across the interface. Theoretical models looking into imperfect/weak interfaces have also been developed for both isotropic (Cheng et al, 1996;Antipov et al, 2001;Sudak, 2003) and anisotropic materials (Pan, 2003;Sudak and Wang, 2006;Vellender et al, 2016). These models consider spring-like boundary conditions for which the interfacial displacement jump is directly proportional to the traction.…”