Fracture toughness correction due to the in- and out-of-plane constraints

This work generalizes O’Dowd’s and Shih’s formula for the stress field in front of a crack in an elastic–plastic body in a plane strain situation for a three-dimensional case. The Guo Wanlin formula was used for this purpose. This formula extends the solution of Hutchinson, Rice and Rosengren from a plane strain case to a three- dimensional case. The second term in this generalized formula, the Q parameter, becomes a function of the Tz parameter introduced by Guo to characterize the stress triaxiality. This parameter is now computed numerically using an assumption of large strains and experimentally recorded and calibrated constitutive equations. The parameter Q calculated in such a way was used to estimate the fracture toughness taking into account both in- and out-of-plane constraint measures.