A Bayesian Framework for Assessing the Strength Distribution of Composite Structures with Random Defects

Abstract

This paper presents a novel stochastic framework to quantify the knock down in strength from out-of-plane wrinkles at the coupon level. The key innovation is a Markov Chain Monte Carlo algorithm which rigorously derives the stochastic distribution of wrinkle defects directly informed from image data of defects. The approach significantly reduces uncertainty in the parameterization of stochastic numerical studies on the effects of defects. To demonstrate our methodology, we present an original stochastic study to determine the distribution of strength of corner bend samples with random out-plane wrinkle defects. The defects are parameterized by stochastic random fields defined using Karhunen-Lo\'{e}ve (KL) modes. The distribution of KL coefficients are inferred from misalignment data extracted from B-Scan data using a modified version of Multiple Field Image Analysis. The strength distribution is estimated, by embedding wrinkles into high fidelity FE simulations using the high performance toolbox 'dune-composites' from which we observe severe knockdowns of $74\%$ with a probability of $1/200$. Supported by the literature our results highlight the strong correlation between maximum misalignment and knockdown in coupon strength. This observations allows us to define a surrogate model providing fast assessment of predicted strength informed from stochastic simulations utilizing both observed wrinkle data and high fidelity finite element models.