Fabrication to Performance: A Comprehensive Multiscale Stochastic Predictive Model for Composites

摘要

We propose a comprehensive framework for uncertainty management within themanufacturing process of non-crimp fiber composites (NCF), including the forming,resin injection, curing, and distortion. The challenge of meeting performancerequirements while having incomplete knowledge about the fundamental physicalprocesses is addressed with the objective of proposing manufacturing guidelines thatare agnostic to these uncertainties. We accomplish this by making the functionaldependence of uncertainties in the performance metrics and uncertainties in thevarious parameters and models explicit. We tackle the issues associated withdimensionality, which has hampered similar efforts in the past, through a basisadaptation procedure that permits the development of functional dependencies, forrealistic systems, without any loss of accuracy. These representations are uniquelysuited for design optimization as they provide explicit, yet highly accurate, stochasticreduced order models (SROM) that can be analytically differentiated and integrated.We compute several Quantities of Interest (QoI) as functions of random variables andprocesses of material properties and process conditions. During the forming stage, weconsider the mechanical properties of the fibers and the local fiber directions to berandom. The deformation of the fabric was computed via a reduced model consistingof an effective shell with embedded upscaling algorithms at the integration points.Forming induces stochastic fluctuations in the relative shearing angles of the fabric,which are mapped, through a stochastic model, into spatial fluctuations of thepermeability field. The simulations were carried out using the PAM-COMPOSITES™ solvers. The sequence of these four linked manufacturing models involves a total of 74random variables describing the various uncertainties. An adapted Polynomial ChaosExpansion (PCE) is then constructed to map these input variables into stochasticrepresentations for each QoI.