Analysis of the stress singularity for a bi-material V-notch by the boundary element method

A new algorithm coupling the boundary element technique with the characteristic expansion method is proposed for the computation of the singular stress field in the V-notched bi-material structure. After the stress asymptotic expansions are introduced into the linear elasticity equilibrium equations, the governing equations at the small sector dug out from the bi-material V-notch tip region are transformed into the ordinary differential eigen-equations. All the parameters in the asymptotic expansions except the combination coefficients can be achieved by solving the established eigen-equations with the interpolating matrix method. Furthermore, the conventional boundary element method is applied to modeling the remaining structure without the notch tip region. The combination coefficients in the asymptotic expansion forms can be computed by the discretized boundary integral equations. Thus, the singular stress field at the V-notch tip and the generalized stress intensity factors of the bi-material notch are successfully calculated. The accurate singular stress field obtained here is very useful in the evaluation of the fracture property and the fatigue life of the V-notched bi-material structure.