A Finite-Element Analysis of Stable Crack Growth—I

Abstract

A finite-element methodology is developed to study the phenomenon of stable crack growth in two-dimensional problems involving ductile materials. Crack growth is simulated by (1) the translation in steps, of a core of sector elements, with embedded singularities of Hutchinson-Rice-Rosengran type by an arbitrary amount, Δa in each step, in the desired direction; (2) reinterpolation of the requisite data in the new finite-element mesh; and (3) incremental relaxation of tractions in order to create a new crack face of length Δa. Steps 1 and 2 were followed by corrective equilibrium-check iterations. A finite deformation analysis based on the incremental updated Lagrangian formulation of the hybrid-displacement finite-element method is used. The present procedure is used to simulate available experimental data on stable crack growth, and thus to study the variation during crack growth of certain physical parameters that may govern the stability of such growth and the subsequent onset of rapid fracture. Attention is focused in this study on the following parameters: G*Δ, the energy release to the crack tip per unit crack growth, for growth in finite steps Δa, calculated from global energy balance considerations; GpzΔ the energy release to a finite “process zone” near the crack tip per unit crack growth, for growth in finite steps Δa, calculated again from global energy balance considerations; and the crack opening angles. However, the work reported here is limited to the first phase of our study, that is, to simulation of available experimental data.