Stress Intensity Factor Analysis of an Interfacial Corner Between Piezoelectric Bimaterials in a Two Dimensional Structure Using the H-Integral Method

Abstract

A corner of bonded dissimilar materials is one of the main causes of the failure of electronic packages or MEMS structures. These materials are sometimes anisotropic materials and piezoelectric materials. To evaluate the integrity of a corner of bonded piezoelectric materials is useful for the reliability of electronic packages and MEMS. Asymptotic solutions around the interfacial corner between piezoelectric bimaterials can be obtained by the combination of the Stroh formalism and the Williams eigenfunction expansion method. Based on an extension of the Stroh formalism and the H-integral derived from Betti’s reciprocal principle for piezoelectric problems, we analyzed the stress intensity factors (SIFs) and asymptotic solutions of piezoelectric bimaterials. The eigenvalues and eigenvectors of an interfacial corner between dissimilar piezoelectric anisotropic materials are determined using the key matrix. The H-integral for piezoelectric problems is introduced to obtain the scalar coefficients, which are related to the SIFs. We propose a new definition of the SIFs of an interfacial corner for piezoelectric materials, and we demonstrated the accuracy of the SIFs by comparing the asymptotic solutions with the results obtained by the finite element method (FEM) with very fine meshes. Proposed method can analyze the stress intensity factors of a corner and a crack between dissimilar isotropic materials, anisotropic materials and anisotropic piezoelectric materials.