Probability Distribution of the Lengths of Fatigue Cracks in Riveted Joints of an Aircraft

Abstract

In the case of cyclic loading of aircraft structures, fatigue cracks are initiated and grow in riveted joints, which may lead to a decrease in the residual strength and to the sudden widespread fatigue damage. This phenomenon is induced by multiple-site damage, which is usually described by statistical methods. Since the crack length in multiple-site damage is bounded by the distance between the neighboring holes, it is necessary (for the prediction of the limit state in a row of rivets) to know the size distribution of fatigue cracks, which can be computed according to the distribution of operating times (i.e., the numbers of flight cycles) to fatigue-crack initiation with regard for the dependence of crack length on the number of flight cycles. We deduce a relation for the distribution of crack lengths for a given number of flights of an actual aircraft structure. With the use of the numerical values of the parameters of defect initiation and growth, we show that this distribution can be approximated by a hyperbolic-type power function.