International Journal of Fracture 79: 27--48, 1996. 27 (~) 1996 Kluwer Academic Publishers. Printed in the Netherlands. An incremental analysis of plane strain fully plastic crack growth in strain-hardening materials under extension QING ZHOU* and TOMASZ WIERZBICKI Massachusetts Institute of Technology, Cambridge, MA 02139, USA Received 10 October 1995; accepted 11 April 1996 Abstract. Analyses of inelastic fracture have mainly followed two directions. One is crack-tip-field analysis in strain-hardening materials (e.g., the HRR solution). The other is whole field analysis in non-hardening materials (e.g., McClintock's slip-line approach). In this paper, a theoretical approach that combines the two directions is presented to account for large crack growth. As an example, plane strain mode I fully plastic crack growth in a single-edge-cracked-specimenunder extension is analyzed. The incremental analysis based on the deformed configuration is developed for large crack growth in strain-hardening materials. A kinematically admissible dis- placement increment field with crack-tip singularity is first constructed in a presumed symmetrical triangular deformation zone extending from the crack tip to the back flank of the ligament (whole field). Then the size of the deformation zone is determined by minimizingthe total force in each incremental step. The strain histories of all material points in the ligament are traced and a fracture criterion based on the hole growth theory is applied. The comparisons between the present study and the experiments existing in the literature show the validity of the present approach. 1. Introduction Fully plastic crack growth is a very common feature in structural and material failures. From the structural safety point of view, it is desirable that fully plastic conditions be attained before fracture and that the load does not fall rapidly during crack growth. Stable crack growth in structures and materials is another desirable feature in accidents because the significant plastic flow provides considerable crack-growth resistance. To understand large crack-growth behavior including crack-growth ductility, it is important to predict the relation between load and displacement during crack growth. Ductile fracture processes are usually characterized by the so-called R-curves defined as nonlinear elastic energy release J versus crack extension Aa and obtained from the crack-tip- field analyses (see Section 2 for more discussions). However, in metal plate tearing, cutting of metal sheets, and some pressure vessel failures, cracks penetrate through the full thickness of structural components. For such a deep extension having an order of the ligament thickness, the far-field-boundary-conditions and the damage accumulated in the entire ligament ahead of the crack tip may significantly affect the crack-growth behavior. Beyond J validity range which is a small distance from the crack tip (see Section 2), R-curves expressed in terms of deformation theory would have been misleading (Landes et al. [1]). A typical load versus crack extension curve of ductile fracture from an existing sharp- tipped crack is shown in Figure 1. The first rapidly rising stage is usually due to the elasticity of material and the blunting of the initially sharp crack tip. Then the load continues to increase due to initiation of crack growth, strain-hardening and plastic flow until reaching its maximum. * Present address: General Motors Corporation, Mail Code 480-106-256, 30500 Mound Road, Warren, MI 48090-9055, USA.