Three-parameter approach for elastic–plastic stress field of an embedded elliptical crack

A three-parameter approach for an embedded center-elliptical crack under tension is presented by systematic three-dimensional (3D) elastic–plastic finite element. It is shown that even in the well embedded condition, the conventional two-dimensional HRR solution and the extended J–Q description which considers the in-plane constraint modification can hardly provide satisfied description for the crack front fields with the increase of radial distances (r/(J/σ0)) and strain hardening exponent n. Thus, a consideration of the out-of-plane constraint and use of the three-parameter description is necessary and efficient to predict the 3D stress fields in the whole plastic zone.