Crack-tip plastic blunting under gross section yielding and implications for modelling physically short cracks

Abstract

The plastic blunting behaviour at the tip of a mode I crack embedded in a grossly plastic material is analysed, with a view to identifying a consistent scaling parameter for correlating the growth rates of short and long fatigue cracks. Numerical analysis is first carried out using a finite element method that accounts for the large deformation and non-proportional straining near the crack tip. It is found that the crack-tip plastic blunting is uniquely characterized by a single size scale, despite the fact that the J-dominance on the stress-strain field exists only at a distance greater than the crack-tip opening displacement. An improved formula is constructed based on the finite element results to relate this size scale to the remote loading and the materials' cyclic deformation properties. A solution has been derived to quantify the influence of cyclic plasticity on the closure of short cracks, which is shown to correlate well with experimental results. When plotted in terms of the present crack-tip blunting parameter, the growth rates of physically short cracks seem to fall within a band comparable to the scatter band of the experimental data.