A physical–statistical model of overload retardation for crack propagation and application in reliability estimation

Crack propagation subjected to fatigue loading has been widely studied under the assumption that loads are ideally cyclic with a constant amplitude. In the real world, loads are not exactly cyclic, due to either environmental randomness or artificial designs. Loads with amplitudes higher than a threshold limit are referred to as overloads. Researchers have revealed that for some materials, overloads decelerate rather than accelerate the crack propagation process. This effect is called overload retardation. Ignoring overload retardation in reliability analysis can result in a biased estimation of product life. In the literature, however, research on overload retardation mainly focuses on studying its mechanical properties without modeling the effect quantitatively and, therefore, it cannot be incorporated into the reliability analysis of fatigue failures. In this article, we propose a physical–statistical model to quantitatively describe overload retardation considering random errors. A maximum likelihood estimation approach is developed to estimate the model parameters. In addition, a likelihood ratio test is developed to determine whether the tested material has either an overload retardation effect or an overload acceleration effect. The proposed model is further applied to reliability estimation of crack failures when a material has the overload retardation effect. Specifically, two algorithms are developed to calculate the failure time cumulative distribution function and the corresponding pointwise confidence intervals. Finally, designed experiments are conducted to verify and illustrate the developed methods along with simulation studies.