Reliability assessment of deteriorating component due to fatigue crack growth under a random loading

Metal fatigue is generally considered to be the most important failure mode in structural and mechanical design. But there are general large uncertainties in the design factors. Therefore it is recommended that fatigue analysis and design be based on probabilistic and/or statistical methods. To date, most of the work on reliability based design of high-cycle fatigue critical components subjected to random stresses has been based on the characteristic {dollar}S-N{dollar} approach. Reliability analysis employing the fracture mechanics crack growth model is still in its infancy. A comprehensive model for fatigue reliability assessment based on a fracture mechanics approach is presented.; The overall goal of this study is to develop a practical model and computational procedure for obtaining the statistical distribution of the time-to-failure of a single fatigue critical component under general non-zero mean and wide band stationary Gaussian stress processes. The theme of this proposed research is to merge and extend recently developed technologies on crack closure fatigue crack growth modeling, time-variant reliability and first-passage concepts, and advanced structural reliability computational methods giving full consideration to engineering applications.; A first passage approach using an advanced crack growth model and an efficient structural reliability computational procedure is proposed. Failure is defined as the event that the first time the random stress process exceeds the strength of the component. But strength degrades with time as the fatigue crack grows. Assuming a stationary Gaussian stress process, the barrier upcrossing is modeled as a Poisson clumping process. And the threshold level of residual strength is derived using a crack-closure fatigue crack growth model. Fatigue design factors are modeled as random variables. An implicit expression for time-to-fatigue-failure T is derived in terms of the random fatigue design factors. The cumulative distribution function of T can be estimated efficiently and accurately by an advanced mean value procedure together with a log transformation on select variables.; Contributions of this study include: (1) Development of a time-variant first-passage fatigue reliability model employing the Poisson upcrossing approach thereby combining the synergistic effects of fatigue and fracture failure modes. (2) The introduction of a refined fatigue crack growth model, which includes the crack opening stress concept and the rainflow cycle counting principle, to predict crack growth under wide band random stresses. The model is capable of accommodating effects of mean stress and bandwidth factor of the stress process. (3) Development and demonstration of methods and strategies of structural reliability analysis to accommodate large variances of the design factors. (4) Gaining an understanding of the physical process of fatigue fracture failure behavior by identifying the important design factors through a sensitivity study. (5) Close comparison of mathematical forms between various fatigue/fracture limit states.