Influence of sample size on permeability of carbon-carbon composites with stochastic microstructure

Permeability is one of the key parameters for the successful densification of carbon-carbon composites (CCC), as it governs the ability of the matrix precursor to infiltrate the porous carbonized structure. Unlike the case of traditional dry fiber preforms, such as continuous or woven textiles, which exhibit a periodic microstructure having a relatively small representative volume element (RVE), the microstructure of pyrolyzed CCC is far more complex. In CCC a periodic fabric architecture is combined with a matrix that is highly stochastic exhibiting a broad distribution of pore sizes and a network of interconnected transverse cracks within tows and delaminations between layers that extend beyond the fabric intrinsic RVE dimensions. For accurate permeability measurements, the size of a statistically homogenous RVE must be determined. In this study, a T800SC 12K 2 x 2 twill weave fabric (RVE size 25 mm2) with MT35700 benzoxazine resin is pyrolyzed to form CCC with 57 % fiber volume fraction and 20 % porosity measured in a previous study. The effect of the sample size on the effective permeability of the pore network developed during pyrolysis for crossply laminates having 5 and 33 layers is investigated. The results of experiments on samples of different in-plane dimensions, ranging from 400 to 2000 mm2, are compared to numerical simulations of permeability using 70 full-thickness high-resolution computed-tomography (CT) images, with in-plane dimensions of 1.80 by 1.97 mm2, as the statistical description of the geometry of the porous microstructure. Monte Carlo simulations are performed on numerical models of the 5 and 33 ply laminates of in-plane dimensions ranging from about 3.5 mm2 to 35000 mm2. This procedure is used to identify the minimum size of the statistical representative volume element (sRVE) of the CCC microstructure. For a coefficient of variation of 5 %, the size of the sRVE was determined to be 350 mm2 for the sample of 5 plies and 130 mm2 for the sample of 33 plies. In both cases the sRVE is significantly larger than the RVE of the twill weave. The predicted effective permeability on the sRVE is found to be in agreement with the experimental permeability.