The Paris law for fatigue crack growth in terms of the crack tip opening displacement

A reference Paris law for K-valid fatigue cracks, with the threshold rate at the Burgers vector b and a threshold range of stress intensity E root(2b),is compared with data from the literature. The faster growth rates of microstructurally short or highly loaded cracks, not K-valid, are compared with the crack tip displacement Delta CTOD from: alternating slip on one or two planes, J-mechanics (uncertain for shallow cracks), and the continuum sliding off from fans at a non-hardening plastic crack tip (predicting striated branch cracks). Low rates arise from roughening, closure, and obstacles requiring polyslip. In harder alloys, the smaller Delta CTOD for a given Delta K appears to be offset by reductions in roughening and resistance to polyslip.