Three-dimensional fully plastic solutions for semi-elliptical surface cracks

Abstract

Nonlinear finite element analyses of semi-elliptical surface cracks are performed with the fully plastic condition, where the power-law hardening materials and the deformation theory of plasticity are assumed. To satisfy the incompressibility condition of a plastic material, two kinds of numerical techniques (the penalty function method and the Uzawa algorithm) are employed. The local distributions and the global values of the J- integral are obtained using the virtual crack extension technique for various configurations of semi-elliptical surface crack in plate subjected to uniform tension and bending, respectively. These solutions are given in the form of polynomials with geometric parameters of crack and the strain hardening exponent. Finally, an estimation scheme for the J- integral of surface crack in a plate subjected to mixed loading of tension and bending is proposed.