Three-dimensional crack front fields in a thin ductile plate

Abstract

Based on detailed finite element solutions, various aspects of the 3-D fields near a crack front in a thin ductile plate are analysed. In particular, the stress field in the immediate crack front vicinity is carefully investigated. The existence and size of local J-dominated fields are determined from a comparison of the complete near tip stress field with the plane strain HRR solutions using a dominance parameter. In conjunction with an estimated size of the finite deformation zone, the loss of HRR-dominance along the crack front is also studied. Physically, the loss of HRR-dominance at higher load occurs when the finite deformation region outgrows the (local) plane strain region, the size of which is essentially limited by the geometry of a thin plate. Alternatively, the existence (at the mid-plane) of plane strain HRR-dominance in a low hardening material under (in-plane) small scale yielding requires the thickness of a thin plate to exceed 0̃.5(K 1/σ 0) 2, thus limiting the maximum in-plane extent of the plastic zone to a fractio of plate thickness. Furthermore, such a restriction on the plastic zone size precludes the coexistence of local plane strain and surrounding plane stress HRR-fields within a thin plate.