Three-dimensional fracture analysis for a thin cracked hardening plate

•A new semi-analytic method for ductile fracture is proposed.•Comparison with numerical solutions shows the current analytic solutions are valid.•The current J-T solutions may depict the in-plane stress fields near the crack front. A semi-analytical method is presented to investigate fracture behavior of a mode-I crack in a thin ductile plate. In the part of theoretical analysis, a total deformation theory of plasticity, in conjunction with a power law hardening stress-strain relation, is employed. Three-dimensional Maxwell stress functions, the minimum complementary potential energy principle and three dimensional J-integrals are used to obtain crack front stress fields. In the part of numerical analysis, three dimensional finite element simulations are carried out to obtain J-integrals, the out-of-plane constraint level and crack front stress fields. Comparison with numerical results of crack front stress fields shows the analytic solutions for crack front stress fields are valid. Numerical and analytic results show that the value of the opening stress ahead of the crack front deceases with increasing z (approaching the free surface) and lies between the corresponding plane strain and plane stress solutions.