Microscopic stress analysis at crack tip in heterogeneous media by multi-scale method

In the development of various advanced materials by controlling their heterogeneous microstructures, there is a growing need for the multi-scale analysis. There have been many studies on the correlation between the heterogeneous microstructure and the macroscopic properties mainly using the asymptotic homogenization method with the help of the finite element method. Although the consideration of fracture origin in components such as interface crack is important in the multi-scale stress analysis, it was impossible to calculate the microscopic stress under high gradient of macroscopic strain/stress field at the crack tip. Furthermore, the representative dimension of the fracture origin lies between the microscopic scale and the macroscopic one. Hence, this paper proposes a novel three-scale computational method that employs both the homogenization method and the enhanced mesh superposition method to study the correlation among microstructure, component and fracture origin simultaneously. An equation solver for large-scale 3 D analysis by the mesh superposition method is also presented. A demonstrative 3 D example of porous thin film with interface crack, whose finite element model has approximately 78 thousand solid elements, is shown.