Obtaining S–N curves from crack growth curves: an alternative to self-similarity

A crack growth model that allows us to obtain the S–N curves from the crack growth rate curves is presented in an attempt to harmonize the stress based and fracture mechanics approaches in lifetime prediction of long cracks propagation. First, using the Buckingham theorem, the crack growth rate curve $$\frac{da}{dN}-\varDelta K$$dadN-ΔK is defined over all its range as a cumulative distribution function based on a normalized dimensionless stress intensity factor range $$\varDelta K^+$$ΔK+. Then, a relevant theorem is derived that provides an alternative to self-similarity allowing significant reduction of experimental planning. In this way, different $$a-N$$a-N crack growth curves for different stress ranges $$\varDelta \sigma $$Δσ and initial crack lengths $$a_0$$a0 can be obtained from a particular crack growth curve under some conditions. The S–N field is obtained from the crack growth curves, showing the close relation between the fracture mechanics and stress approaches. Finally, the model is applied to a particular set of experimental data to obtain the crack growth rate curve and the S–N curves of a certain material for a subsequent fatigue lifetime assessment