Elastic analysis of defects and cracks in thin films and layered structures

Abstract

Proposed in this paper is the correspondence between anisotropic and isotropic elasticity for two-dimensional deformation, that is, the isotropic elasticity can be reconstructed in the same framework of the anisotropic elasticity, when the interface between dissimilar media lies along a straight line. Therefore, many known solutions for an anisotropic bimaterial are valid for a bimaterial, of which one or both of the constituent materials are isotropic. The usefulness of the correspondence is that the solutions for singularities and cracks in an anisotropic/isotropic bimaterial can easily be obtained without solving the boundary value problems directly. As general solutions, the interaction solutions of singularities, interfaces, and cracks in infinite anisotropic bimaterials are summarized. Conservation integrals also have the similar analogy between anisotropic and isotropic elasticity so that J integral and J-based mutual integral M are expressed in the same complex forms for anisotropic and isotropic materials, when both end points of the integration paths are on the straight interface. Schwarz-Neumann’s alternating technique is applied to singularity problems in an anisotropic `trimaterial`, which denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. It is well known that if the solution is known for singularities in a homogeneous anisotropic medium, the solution for the same singularities in an anisotropic bimaterial can be constructed by the method of analytic continuation. It is shown here that the solution for singularities in a homogeneous medium may also be used as a base of the solution for the same singularities in a trimaterial. The alternating technique is applied to derive the trimaterial solution in a series form, whose convergence is guaranteed. The energetic forces exerted on a dislocation due to interfaces are also evaluated from the trimaterial solution. The trimaterial solution studied her...