Abstract
Uncertainty in the prediction of lower tail fatigue life behavior is a combination of many causes, some of which are aleatoric and some of which are systemic. The error cannot be entirely eliminated or quantified due to microstructural variability, manufacturing processing, approximate scientific modeling, and experimental inconsistencies. The effect of uncertainty is exacerbated for extreme value estimation for fatigue life distributions because by necessity those events are rare. In addition, typically, there is a sparsity of data in the region of smaller stress levels in stress–life testing where the lives are considerably longer, extending to giga cycles for some applications. Furthermore, there is often over an order of magnitude difference in the fatigue lives in that region of the stress–life graph. Consequently, extreme value estimation is problematic using traditional analyses. Thus, uncertainty must be statistically characterized and appropriately managed. The primary purpose of this paper is to propose an empirically based methodology for estimating the lower tail behavior of fatigue life cumulative distribution functions, given the applied stress. The methodology incorporates available fatigue life data using a statistical transformation to estimate lower tail behavior at much smaller probabilities than can be estimated by traditional approaches. To assess the validity of the proposed methodology confidence bounds will be estimated for the stress–life data. The development of the methodology and its subsequent validation will be illustrated using extensive fatigue life data for 2024–T4 aluminum alloy specimens readily available in the open literature.
Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications
