Quantification of constraint on elastic–plastic 3D crack front by the J– A2 three-term solution

Abstract

Three-dimensional (3D) modified boundary layer analyses are performed using the finite element method to study the crack-front constraint for an elastic–plastic thin plate. Far field loading is applied through the plane-stress displacement fields based on the elastic K I-field, and specimen constraint levels are varied through the T-stress applied on the far field boundary. Numerical stresses at the crack front at different planes of the plate are compared with those determined by the J–A 2 three-term solution. Results show that the in-plane-stress fields at the crack front for various K I– T loads possess the plane-strain nature throughout the thickness except for the region near the free surface, and can be characterized by the J–A 2 three-term solution under the small scale yielding condition. The transition of the stress field from the far field, in the plane-stress state, to the near crack-front field, dominated by the plane-strain state, is explained by the iso-contours of effective stress and the plane-strain constraint parameter. At the plane near the free surface, the crack-front field is close to the plane-stress state provided that the applied load is high and the plastic zone size is relatively large. Additional aspects of the 3D fields at the crack front through the thickness are also analyzed. In particular, a linear relationship between the constraint parameter A 2 and the hydrostatic stress is found in the 3D crack-front fields. It is also found that unlike the two-dimensional case where the J at the crack tip is not affected by the T-stress, the J-integrals at the crack front in the 3D case vary with the applied far field T-stress.