Mathematical model of riveted joint multiple site damage

Abstract

Multiple Site Damage (MSD) is one of the significant damaging factors that limit the airworthiness of aging fleet aircrafts. In case of MSD multiple fatigue cracks initiates and propagates at the rivet holes. Those cracks are relatively short in length, but with a sufficiently large number of them and an unfavorable arrangement along the rivet joint, they can join together and form a crack of a dangerous length. To prevent this type of damage it is necessary to have adequate methods for predicting the boundary state of riveted joints during MSD. A useful approach is a numerical experiment based on Monte-Carlo simulation of the MSD main random factors – the formation of initial cracks and their growth. This paper presents a probabilistic model for predicting the initial stage of MSD – destruction of at least one bridge between the adjacent holes. A level I model is considered, which describes the process of fatigue failure of specimens without rivets but with multiple holes, which are typical for riveted joints. The initiation of fatigue cracks and their growth are modeled taking into account the laws of damage development obtained experimentally on specimens with multiple cracks. So, to simulate the random initiation of cracks in time the Weibull distribution is used. The parameters of this distribution depend on the applied stress. The growth of cracks is described by the Paris' equation, taking into account the experimentally confirmed correlation between the coefficients of this equation. The model assumes that each initiated crack propagates according to a random value of the Paris' equation exponent. The distribution of such a random value corresponds to a logarithmically normal law with experimentally obtained parameters. The criterion for the possible join of opposite cracks growing from adjacent holes is the uniting of plastic deformation zones at the tips of such cracks. The results of modeling are presented in the form of multiple site damage realization field of points in the coordinates of the number of cycles before the initiation of cracks vs. the number of cycles before the destruction of the bridge between holes.

Keywords

• усталость
• многоочаговое повреждение
• образование трещин
• рост трещин
• численное моделирование