Probabilistic considerations of the growth and detection of delaminations for repeated impact on composites

Repeated impact of foreign bodies on laminated composites may give rise to delamination damage. In this paper, experimental information is employed to formulate a growth law for delamination damage in terms of the impact energy per impact and number of impacts. The growth of regions of delamination is considered a stochastic problem, and hence the growth law is placed in a probabilistic setting by considering the evolution of a probability density function of delamination damage as the number of impacts increases. For a specific number of impacts, this formulation is used to determine the probability of a delamination in a selected range of delamination sizes. The formulation has been extended to include the effect of probability of detection as well as the effect of variable impact energy according to a probability density function. Finally, random variation of impact location is taken into account by the equivalent effect of a discrete probability function for the number of impacts at a fixed location.