Manifold embedding of heterogeneity in permeability of a woven fabric for optimization of the VARTM process

Abstract

In Vacuum Assisted Resin Transfer Molding (VARTM), fabrics are placed on a tool surface and a Distribution Media (DM) is placed on top to enhance the flow in the in-plane direction. Resin is introduced from one end and a vacuum is applied at the other end to create the pressure gradient needed to impregnate the fabric with resin before curing the resin to fabricate the composite part. Heterogeneity in through the thickness permeability of a woven fabric is one of the causes for the variability in the quality of the final composite part fabricated using the VARTM process. The heterogeneity is caused by the varying sizes of pinholes which are meso-scale empty spaces between woven tows as a result of the weaving process. The pinhole locations and sizes in the fabric govern the void formation behavior during impregnation of the resin into the fabric. The pinholes can be characterized with two parameters, a gamma distribution function parameter α and Moran's I (MI). In this work, manifold embedding methods such as t – Distributed Stochastic Neighborhood Embedding (t_SNE) and Principal Component Analysis (PCA) are used to visually characterize fabrics of interest with the two variables, α and MI, through the reduction of dimensionality. To demonstrate the manifold embedding method, a total of 450 training sample data with ranges of α from 1 to 3 and MI from 0 to 0.5 were used to create a map in three-dimensional space for ease of visualization and characterization. The method is validated with a plain-woven fabric sample in a testing step to show that the two parameters of the fabric are identified with its corresponding α and MI using these machine learning algorithms. Numerical flow simulations were carried out for varying α, MI, and DM permeability, and the results were used to predict final void percentage. The quick online identification of the fabric parameters with machine learning algorithms can instantly provide expected variability in void formation behavior that will be encountered in a VARTM process.