Stochastic simulation of woven composites forming

Abstract

A stochastic forming simulation procedure is developed and implemented to investigate the effect of geometric variability in pre-impregnated woven textiles on manufacturing. Image analysis is used to characterise variability in tow directions and unit cell size in a pre-impregnated carbon/epoxy satin weave textile. It is found that variability in tow orientations is significant, whereas variability in the unit cell size is negligible. Variability in the weft direction is higher than in the warp direction. Highly anisotropic spatial autocorrelation of weft tow orientations is observed with the major direction of autocorrelation normal to the corresponding set of tows. The extent of autocorrelation is 6–20 unit cells. The autocorrelation structure is modelled using a two-parameter stochastic process, the Ornstein–Uhlenbeck sheet, and an efficient parameter estimation technique is developed based on maximum likelihood. The resulting stochastic process is simulated using Cholesky decomposition which is combined with a simplified forming model within a Monte Carlo scheme. The forming model incorporates non-linear strain-rate dependent behaviour and wrinkling due to tow buckling in a truss formulation. Execution of the integrated scheme shows that geometric variability of the woven material has significant influence on the forming process. The coefficient of variation of minimum and average wrinkling strain in the formed component is in the range of 10–20%. Variability affects the results of forming optimisation and it should be taken into account in process design. Although applied to the case of woven textile forming, the stochastic scheme presented in this paper is general and can be applied to any material system with imperfect stru