Finite block method for interface cracks

Abstract

The finite block method in both the Cartesian coordinate and polar coordinate systems is developed to evaluate the stress intensity factors and the T-stress for interface cracks in bi-materials. The first order partial differential matrices can be constructed straightaway based on the Lagrange series interpolation. The nodal values of displacement can be obtained from a set of linear algebraic equations in strong form from both the governing equation and the boundary conditions. In order to capture the stress intensity factors and the T-stress at the crack tip accurately, the asymptotic expansions of the stress and displacement around the crack tip are introduced with a singular core technique. For elastodynamic fracture problems, the Laplace transform method and the Durbin’s inverse techniques are utilised. The accuracy and the convergence of the finite element method are demonstrated in three examples. Comparisons have been made with numerical solutions by using the boundary collocation method and the finite element method. Satisfactory numerical solutions are obtained with very few blocks in each example.