Stress intensity factor analysis of a three-dimensional interfacial corner between anisotropic piezoelectric multi-materials under several boundary conditions on the corner surfaces

Abstract

Asymptotic solutions around an interfacial corner can be obtained by a combination of the Stroh formalism and the Williams eigenfunction method. The H-integral method, which is derived from Betti’s reciprocal theorem, is useful for analyzing the stress intensity factors (SIFs) of cracks and corners. By expanding these theories for a three-dimensional interfacial corner between anisotropic piezoelectric multi-materials, we develop a modified H-integral method. This method has high generality that can deal with a jointed corner with a varied number of materials and boundary conditions on corner surfaces. We proposed a new definition for the SIFs of an interfacial corner between anisotropic piezoelectric multi-materials, which is compatible with the SIF definitions of a crack in a homogeneous material and an interfacial crack, as well as applicable in various coordinate systems. The accuracy of obtained SIFs was confirmed by comparing the asymptotic solutions obtained from the SIFs with the stress/electric-displacement field directly obtained by the finite element method (FEM). We also propose a numerical method for degenerate materials, which cause numerical problems in the Stroh formalism.