In-plane and out-of-plane constraint characterization of different constraint parameters for semi-elliptical surface cracks in pipes

Six constraint parameters (namely T-stress, Q, h, T-z, A(d) and A(p)) have been numerically calculated for semi-elliptical surface cracks in pipes so as to comparatively investigate their capability, applicability and ease of use for characterizing in-plane and out-of-plane constraints. The results show that the parameters T-stress and T-z can separately characterize in-plane and out-of-plane constraints. The crack depth a/t and aspect ratio a/c of semi-elliptical cracks can influence both in-plane and out-of-plane constraints. With decreasing a/c (increasing crack length) and increasing crack depth a/t, both in-plane and out-of-plane constraints increase. The parameters Q and stress triaxiality factor h are equivalent, and they can capture both in-plane and out-of-plane constraints for the cracks in pipes. But they may overestimate constraint for longer cracks with lower a/c. The parameters A(d) and A(p) based on crack-tip plastic deformation (or strain) can equivalently characterize both in-plane and out-of-plane constraints for the cracks in pipes. The advantages and limitations of different constraint parameters in terms of their engineering applications are analyzed and appropriate parameters are recommended.