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-Loéve (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.

Multilevel Monte Carlo Simulations of Composite Structures with Uncertain Manufacturing Defects

“…In complex composite manufacturing processes, uncertainty arises from a number of different sources, e.g. material variability [3], machine tolerance [4] and process-induced defects such as fibre waviness or ply wrinkling [5,6,7,8]. However, statistical simulations typically require a large number of analyses, and thus can become extremely computationally expensive.…”

High-performance dune modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites

“…Wrinkle defects, which can form during the manufacturing process [31,32], occur at the layer scale. They lead to strong local stress concentrations [6,33], causing premature failure. Naturally, good mesh resolution around the defect is required, leading to finite element calculations with very large number of degrees of freedom.…”

A High-Performance Implementation of a Robust Preconditioner for Heterogeneous Problems

“…In this section we describe an industrially motivated example in which we asses the strength of an airplane wingbox with a small localised wrinkle defect in one corner. Wrinkle defects often form during the manufacturing process and lead to strong local stress concentrations, which may cause premature failure [9,10]. More details on this test setup can be found in [7].…”

“…In total the laminate is made up of 39 fibrous layers and 38 resin layers. One of the corner radii contains a localised wrinkle with a parametrisation matching an observed defect in a CT-Scan of a real corner section, for further details see [10]. Two forms of loading are applied, an internal pressure of 0.109MPa, arising from the fuel, is applied to the internal surface and a thermal pre-stress induced by the manufacturing process is imposed.…”