Materials Science, Vol. 49, No. 2, September, 2013 (Ukrainian Original Vol. 49, No. 2, March–April, 2013) PROBABILITY DISTRIBUTION OF THE LENGTHS OF FATIGUE CRACKS IN RIVETED JOINTS OF AN AIRCRAFT S. R. Ignatovich, 1,2 E. V. Karan, 1 and V. S. Krasnopol’skii 1 UDC 620.178.2(045) 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 num- bers 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 ini- tiation and growth, we show that this distribution can be approximated by a hyperbolic-type power func- tion. Keywords: multiple-site damage, aircraft structure, fatigue cracks, crack initiation, crack growth, distri- bution of crack lengths. It is customary to guarantee the safety of aircraft structures from the viewpoint of their strength by follow- ing the traditional principle of “safe service life” or the modern concepts of the “admissibility of damage” and “fracture (damage) safety” [1]. It is stressed in the standard specifications that, in analyzing the admissibility of damage, one should take into account the possibility of appearance of multiple-site damage caused by fatigue with regard for the rate of defect (crack) propagation, the reliability of their detection in the course of operation, and also the expected mutual location of the sites of their initiation [1, 2]. Otherwise, the total admissible oper- ating time of controlled critical sites of the structure (articles whose durability and survivability determine the level of safety according to the conditions of strength of the structure as a whole) should not exceed a half of the total durability determined in laboratory fatigue tests [1]. Hence, the multiple-site damage (MSD) is one of the determining factors in estimating the strength, reliability, and durability of aircraft structures. Multiple-site damage is usually defined as the state of a structure damaged by numerous fatigue cracks [1, 3]. As a rule, these defects are typical of the elements of aircrafts containing numerous holes for riveted joints arranged in a row and regarded as potential sources of fatigue crack initiation induced by stress concentration. In addition, even if the sizes of these cracks are relatively small, we encounter the hazard of rapid destruction of the bridges between the neighboring holes, especially in the case of their growth toward each other and merging of the cracks. It is worth noting that the problem of MSD is important in estimating the serviceability, specifying the periodicity of inspections, and prediction of the residual strength of the park of aging aircrafts [4, 5]. Since the number of riv- eted joints in the structure of contemporary flying vehicles is quite large, it is clear that one should estimate the parameters of their residual strength and reliability in the probabilistic aspect. 1 National Aviation University, Kiev, Ukraine. 2 Corresponding author; e-mail: ignatovich@nau.edu.ua. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 49, No. 2, pp. 109–115, March–April, 2013. Original article submitted December 18, 2012. 1068-820X/13/4902–0257 © 2013 Springer Science+Business Media New York 257