Applicability of Two-Step Homogenization in High-Crimp Woven Composites

Abstract

In the present work, we analyze the applicability of two-step homogenization applied to 3D woven composites with high crimp reinforcement. The available micromechanical homogenization approaches (Hashin, Chamis, Hashin-Shtrikman bounds etc.) were developed and validated for unidirectional composites. These formulas have also been used by the community to homogenize tows in 2D and 3D woven composites including reinforcement architectures with high crimp ratios. However, a rigorous study of their applicability to high-crimp geometries is yet to be performed. We utilize Finite Element Analysis (FEA) to calculate the overall engineering constants (Young’s moduli and shear moduli) of tows having various crimp (𝐶𝑅) and wavelength-to-fiber diameter (𝜆/𝑑) ratios. For this analysis, periodic sinusoidal unit cells following shapes of individual fibers are used. Fiber volume fraction is set to 70% and is the same in all cases. Transversely isotropic carbon fiber and isotropic epoxy matrix are used. The results are compared with overall responses of tows modeled using homogenized tow properties obtained from micromechanics and FEA as well as explicitly modeled tows containing multiple parallel fibers. The results of our analysis show dependence of the overall elastic properties on both crimp ratio and the normalized wavelength. Separation of fiber/tow scales is achieved at 𝜆/𝑑 = 50.