Probabilistic method for the analysis of widespread fatigue damage in structures

A probabilistic method was developed to model structural failure associated with widespread damage as a stochastic chain of crack initiation and growth, linkup, and final failure. The major feature of this method is that multiple sites (fastener holes) have individual crack-initiation and crack-growth characteristics. These individual characteristics are established by Monte Carlo simulation. Stress analysis of undamaged and cracked structures is performed incrementally using a finite element method incrementally and the crack length increment is determined at a given time increment by using an equation for crack growth. Consequent application of the Monte Carlo simulation results in empirical distributions for (a) life to crack initiation, (b) residual life and (c) total life of the structure. A worst-case scenario of multiple cracks is introduced by assigning equal cracks growing simultaneously with highest speed at all sites. This case establishes the threshold of residual life of a structure. Utilizing the threshold, Monte Carlo simulations are conducted in conjunction with a three-parameter lognormal probability distribution for the residual life of a structure. Numerical studies were performed for panels with rows of holes and for a panel stiffened by stringers. The proposed method makes it possible to assess the probability of occurrence of a structureʹs failure associated with widespread damage as a function of time.