Simulating stress intensity factors for anisotropic materials by the least-squares method

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.

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Stress Intensity Factor Analyses of Interface Cracks Between Anisotropic Media in Electronic Packages

2003 International Electronic Packaging Technical Conference and Exhibition, Volume 2 ◽

10.1115/ipack2003-35146 ◽

2003 ◽

Author(s):

Toru Ikeda ◽

Koh Yamanaga ◽

Noriyuki Miyazaki

Keyword(s):

Finite Element Method ◽

Stress Intensity ◽

Interface Crack ◽

Stress Intensity Factors ◽

Anisotropic Materials ◽

Electronic Packages ◽

Strain Condition ◽

The Finite Element Method ◽

Intensity Factors ◽

Generalized Plane Strain

Delamination from interfaces between dissimilar materials is the primary cause of failure in electronic packages. Fracture mechanics is a powerful tool for the evaluation of delamination. However, many materials used in electronic packages such as composite materials and single crystals are anisotropic materials. Stress intensity factors of an interface crack between dissimilar anisotropic materials which proposed by Hwu are useful for evaluating the reliability of plastic packages. However, numerical methods that can analyze the stress intensity factors of an interface have not been developed. We propose herein a new numerical method for the analysis of an interface crack between dissimilar anisotropic materials. The stress intensity factors of an interface crack are based on the generalized plane strain condition. The energy release rate is obtained by the virtual crack extension method in conjunction with the finite element method for the generalized plane strain condition. The energy release rate is separated into individual modes of stress intensity factors, KI, KII, and KIII, using the principal of superposition. The target problem to be solved is superposed on the asymptotic solution of displacement in the vicinity of an interface crack tip, which is described using the Stroh formalism. Analyses of the stress intensity factors of center interface cracks between semi-infinite dissimilar anisotropic media subjected to concentrated self-balanced loads on the center of crack surfaces as well as to uniform loads are demonstrated. The present method accurately provides the mode-separated stress intensity factors using relatively course meshes for the finite element method.

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