Random field generation of stochastically varying through the thickness permeability of a plain woven fabric

Abstract In the Vacuum Assisted Resin Transfer Molding (VARTM) process to manufacture composites, woven or stitched fabrics are stacked on top of a tool surface and resin is introduced into this porous network by drawing a vacuum. For large parts, to reduce the time for filling, highly permeable distribution media (DM) is placed on top of the fabric layers to accelerate the in-plane filling process. Many factors such as the manufacturing process, handling, variation in fabric manufacturing and placement of fabric cause heterogeneity in the permeability of fibrous materials. Due to the presence of the DM, the heterogeneous through the thickness permeability (Kpin) of a fabric can dramatically affect the flow of resin and cause air pockets or voids which are mechanical flaws resulting in the rejection of the composite as scrap. Statistical characterization of Kpin is crucial for understanding the (i) effect of heterogeneity in Kpin and its interaction with DM permeability and void formation and (ii) for generating the field of random numbers (Kpin), which can be used for simulations to predict resin flow and void formation for such materials that exhibit stochastic variability. The novelty of this study is that the observed random field (Kpin) is generated for numerical simulation through statistical analysis. First, in this study, the heterogeneity in Kpin was statistically characterized by spatial correlation with Moran's I index and semi-variogram. Then the random field of Kpin was generated by transforming the normal numbers from Karhunen–Loeve (KL) expansion to gamma numbers. A numerical flow simulation of the VARTM process with the generated random fields was performed using Monte Carlo method for three types of Distribution Media (DM). The outcome is compared with experimental results and to simulation results that used experimentally determined Kpin data as an input.