J–Mp based criteria for bifurcation assessment of a crack in elastic–plastic materials under mixed mode I–II loading

In this work, a set of J–Mp based criteria is proposed to assess the bifurcation angle of an elastic–plastic crack in plane strain under mixed mode loading. We first establish a criterion in order to study the competition between the tensile fracture (T-type fracture) and the shear fracture (S-type fracture) in the frame of RKR conception [J. Mech. Phys. Solids 21 (1973) 395]. Based on the generalized HRR [ASTM STP 560 (1974) 187] solution and on the knowledge of the mixity parameter Mp, the RKR based criterion is transformed into a J–Mp based criterion. When the crack grows in tensile manner, the maximum circumferential stress criterion is adopted to determine the crack bifurcation angle. When the crack grows in shear manner, the traditional theory of plasticity, according to which the plastic flow develops essentially along one of the slip bands immediately ahead of the crack tip, is used to determine the crack growth direction. All these proposed criteria are given as function of the mixity parameter Mp and the hardening exponent n of the material. Finally, we carry out some numerical computations by applying the proposed criteria and then compare the obtained results with experimental data gathered in literature. It is shown that these criteria are physically reasonable and highly accurate. Another advantage is that the parameters used are easy to identify numerically and experimentally, therefore, these criteria are simple to apply in engineering structures.