Statistical modeling of microstructurally short crack growth in high cycle fatigue

Abstract

Capturing the behavior of short cracks under fatigue conditions has become a challenge for researchers. The early stage of crack propagation is influenced by microstructural features, such as grain boundaries and orientations, which leads to significant statistical variations. Models such as the ones developed by Navarro and De Los Rios have been able to describe the process by considering the average properties of the material and estimating the number of cycles related to the short crack stage. However, fatigue should be seen as an extreme value process. In the present work, a more realistic model was developed to consider the statistical nature related to grain orientations to estimate fatigue life dispersion. Eleven crack propagation criteria have been used to compute the number of cycles spent in the short crack stage. Parameters such as the Schmid factor, the potential crack length, and the various angles describing the misorientation between adjacent grains were considered. One thousand random scenarios for short crack growth were studied for each propagation criterion and some statistical analyzes were run to estimate the worst-case scenario out of one million. Results can be well described using the generalized extreme value distribution, capturing the stochastic nature of the fatigue life.