Discussion: “Computationally Efficient Micromechanical Models for Woven Fabric Composite Elastic Moduli” (Tanov, R., and Tabiei, A., 2001, ASME J. Appl. Mech., 68, pp. 533–560)

In their paper, Tanov and Tabiei presented two micromechanics-based models to evaluate the elastic moduli of woven fabric reinforced composites. After going through their numerical examples shown in the paper, the present reader has a strong feeling that the accuracy and hence the efficiency of their models is suspect.

The fabric investigated by Tanov and Tabiei is schematically shown in Fig. 1, where $af$ and $aw$ are the fill and warp yarn widths, and $gf$ and $gw$ are the inter-yarn gaps between the fill and warp yarns. After the fabric is impregnated with a polymer matrix, the areas in between the inter-yarn gaps have no reinforcement. Namely, they become pure matrix regions in the woven composite. Apparently, these pure matrix regions can significantly reduce the overall stiffness and strength of the woven composite. The amount of reduction depends on the gap-yarn ratios $gf/af$ and $gw/aw.$ It has been shown by this author (see 1) that when the gap-yarn ratio $g/a$ (supposing $gf/af=gw/aw=g/a$⁠) is only 4%, a reduction of as high as 22% in the in-plane elongation modulus can be recognized. The larger the gap-yarn ratio, the lower the in-plane modulus of the resulting woven composite. Therefore, in order to achieve as high a mechanical performance as possible, the woven composites have been generally fabricated with as small (if not zero) inter-yarn gaps as possible.

However, the three examples of woven fabric reinforced epoxy (with modulus between 3.45 to 4.51 GPa) matrix composites investigated by Tanov and Tabiei were all assumed to have very large gap-yarn ratios (using the term of Ref. 2, the gap-yarn ratio was given by $1−Vy/Vy,$ see Fig. 1 and Fig. 2 of Ref. 2), being 85.7%, 284.6%, and 72.4%, respectively. From the input data of the yarns, epoxy matrices, and the yarn volume fractions provided in Ref. 2, we can easily estimate the maximum possible in-plane moduli for the three woven composites without any inter-yarn gaps, which are given by those of the corresponding cross-plied laminates [0 deg/90 deg]. The estimation for the properties of the unidirectional (0 deg) lamina is made based on the bridging micromechanics model (Ref. 3, with bridging parameters β=0.35 and α=0.45) by assuming that it is fabricated from the yarn (fiber) and the matrix with the given yarn (fiber) volume fraction. The classical lamination theory is then applied to obtain the in-plane modulus of the cross-plied laminate. The maximum possible in-plane moduli for the three woven composites thus obtained are: 18.21 GPa, 11.77 GPa, and 45.1 GPa, respectively. In light of the fact reported in Ref. 1 that a 50% gap-yarn ratio would cause nearly 300% reduction in the in-plane modulus of a woven composite, the predicted moduli of the woven composites with the aforementioned very large gap-yarn ratios, i.e., 17.85 GPa, 11.86 GPa, and 45.08 GPa from Tanov and Tabiei’s four-cell model, or 18.21 GPa, 11.93 GPa, and 45.17 GPa from their single-cell model, would be hardly possible.