Retroextrapolation of crack growth curves using phenomenological models based on cumulative distribution functions of the generalized extreme value family

Abstract

In this work, the evolution of crack lengths under fatigue load is interpreted as a sample function of a cumulative damage process which, once normalized, allows a phenomenological model to be satisfactory applied using cumulative distribution functions (cdfs) of the generalized extreme value family (GEV). The denoted “retroextrapolation” procedure is used to determine the complete evolution of the a-N crack growth curve from the final fragment of the curve recorded during the test implying the consideration of additional crack growth phases, namely, prior to the pre-crack length and subsequent to the failure, respectively. The proposed methodology verifies excellent fitting of the a-N curves. It also ensures its conversion to fatigue crack growth rate curves (CGR) and, as a result, promotes the analysis of the transition from micro- to macrocracks, depending on the resulting parameters for the material tested, the specimen geometry and test type. Lastly, it allows a probabilistic analysis on the prediction of fatigue life originated from random initial sizes of cracks, smaller or larger than those induced in the experimental program to determine the a-N curve. In this way, a statistically reliable basis is provided for the application of the damage tolerance concept to the practical component design.