Fracture analysis of ultra-thin coating/substrate structures with interface cracks

Abstract

Abstract This paper presents a fracture analysis of ultra-thin coating/substrate structures with interface cracks. For this purpose, an advanced boundary element method (BEM) is adopted. To correctly describe the oscillatory displacement and stress fields near the interfacial crack-tip, a new set of novel special crack-tip elements are implemented. The complex interfacial stress intensity factors (SIFs) can be directly and accurately computed at the collocation points extremely close to the crack-tip by using the proposed computational strategy based on the novel special crack-tip elements. Furthermore, the troublesome nearly-singular boundary integrals, which are crucial in the application of the BEM for both crack-like and ultra-thin structural problems, are calculated accurately by using a nonlinear coordinate transformation method. It is shown that the advanced BEM based on the novel special crack-tip elements and appropriate technique for evaluating nearly-singular boundary integrals provides an accurate and robust numerical tool for interfacial crack analysis of ultra-thin coating structures. Accurate and reliable BEM results with only a small number of boundary elements can be obtained for a relative coating-to-substrate thickness as small as 10-9, which is important for modeling ultra-thin coating structures as used in smart materials and micro/nano-electro-mechanical systems (MEMS/NEMS). Several representative numerical examples will be presented and discussed to reveal the effects of the key geometrical and material parameters, the crack configuration and the loading conditions on the interfacial fracture parameters such as energy release rate and complex SIFs.