System reliability analysis of fatigue-induced sequential failure

Abstract

Various structural systems are subjected to the risk of fatigue-induced failures. If such structural systems do not have an adequate level of redundancy, local failures may initiate sequential failures toward system-level failures. In order to analyze the reliability of fatigue-induced sequential failures of such structures, the Branch-and-Bound method employing system reliability Bounds method (termed as B3 method) was recently developed. Using a disjoint cut-set formulation, the B3 method identifies critical sequences of fatigue-induced failures in the decreasing order of their likelihood as it systematically updates both lower and upper bounds on the system failure probability without additional system reliability analyses. The updated bounds provide reasonable criteria for terminating the B3 analysis without missing critical sequences or estimating the system-level risk inaccurately. However, the original B3 method is not readily applicable to continuum structures because of its limitations in describing general stress distributions in limit-state formulations, evaluating stress intensity range based on the crack length, and dealing with slow convergence of the bounds for structures with high redundancy. In this paper, the B3 method is generalized to overcome these limitations, and demonstrated by a numerical example of aircraft longeron structure.