Bi-material V-notch fracture analysis in functionally graded materials

Abstract

The finite block method (FBM) in the Cartesian coordinate system is developed to deal with the problems of the bi-materials V-notches in functionally graded materials (FGM) under static and dynamic loads. The first partial differential matrix is established via Lagrange series. Higher-order derivatives can be deduced from the first order partial differential matrix directly. In order to obtain the high accurate at the V-notch tip, the asymptotic expansions of the stress and displacement around the notch tip are introduced with a singular polygonal core technique. For the dynamic problems, the Laplace transform method with Durbin inverse algorithm is utilized. The degrees of accuracy and convergence of the FBM are demonstrated through four case studies. Comparisons are implemented with the finite element method (FEM) results.