A relation of unsolved issues related to crack growth rate curves

The traditional fatigue approaches, namely, the stress based, strain based and fracture mechanics approaches, being different perspectives from the same fatigue problem have more links in common as usually supposed. In fact, only four parameters can be considered as being significant in the analysis of any fatigue phenomenon, namely, crack size, driving force (stress range, strain range, J-integral range, SWT parameter, etc.), fatigue lifetime (number of cycles to failure) and probability of failure. The probability of failure encompasses its twofold interpretation: the scatter of the lifetime given the driving parameter, and that of the driving parameter given the lifetime. In the different conventional fatigue approaches (S-N field, -N field, crack growth rate curve and Kitagawa –Takahashi diagram, respectively), some of those determining parameters in fatigue are neglected or not explicitly included. Thus, though four main parameters are involved in the fatigue problem requiring all the different approaches or models to be compatible with each other, at most three of these parameters are considered at the same time. Thus, a global probabilistic fatigue approach are intended to tackle different cases of fatigue problems encompassing the stress based, strain based and fracture mechanics approaches in a unified way by elucidating the existing relations among driving force, lifetime, probability of failure and initial crack size of the material. The relevant variables involved in each fatigue problem are recognized, and the transcendence of considering compatibility conditions in the derivation of the different probabilistic models is exemplified. In order to achieve progress in this direction, the main lacks in solving the problem must be recognized.