Unitary phenomenological approach to the fatigue crack growth curve based on the analytical definition of the a-N curve

Abstract

A phenomenological unitary methodology is applied for the analytical deduction of the Fatigue Crack Growth Rate ($FCGR$) curve. It encompasses: First, the analytical definition of the $a-N$ curve from the data recorded in the crack growth test, identified as a Weibull cumulative distribution function (cdf) by applying the retro-extrapolation (REX) model. Second, the identification of the $FCGR$ data as a relation between the $\mathrm{da}/dN-a$ curve and the conventional expression of the maximum stress intensity factor, $K_M$, as combining the stress condition, crack length and specimen geometry. Lastly, the identification of the normalized $\mathrm{da}/dN-K_M$ curve, as a Gumbel cdf, according to the model of Castillo et al. The methodology thus applied ensures an improved estimation of both lower and higher asymptotic values, $K_{M,th}$ and $K_{M,up}$, respectively, and a more reliable definition of the $\mathrm{da}/dN-K_M$ curve, even outside the monitored test data. In this way, a robust fatigue crack propagation characterization of the material is achieved for lifetime prediction of components and structures in the damage tolerance design. The satisfactory fit obtained from external crack growth results proves the suitability of the procedure in the solution of this kind of mechanism of failure.