Energy rates and crack stability in small scale yielding

Crack stability in small scale yielding is traditionally analysed using the R-curve approach with toughness indexed by either of the linear elastic fracture mechanics parameters K or G. In ductile materials stable tearing commences well before crack instability and progresses under increasing GR. This is often assumed to mean that toughness is increasing with crack growth. It is shown in this paper that a rising GR curve is generated even when a crack propagates with constant toughness (constant energy dissipation rate). The paper demonstrates that this apparent anomaly occurs because G does not represent the energy input rate for a crack advancing under increasing load in an elastic-plastic material. The constant energy dissipation rate model is consistent with a size independent GR curve; also crack instability predictions are identical with both theories. The GR curve approach has practical advantages, but use of energy dissipation rate offers better physical insight and greater versatility when analysing tough materials.