Analysis of flexible bending behavior of woven preform using non-orthogonal constitutive equation

Previous studies by Yu et al. [Yu WR, Pourboghrat F, Chung K, Zampaloni M, Kang TJ. Non-orthogonal constitutive equation for woven fabric reinforced composites. Composites Part A 2002;33:1095-1105; Yu WR, Zampaloni M, Pourboghrat F, Chung K, Kang TJ. Sheet hydroforming of woven FRT composites: non-orthogonal constitutive equation considering shear stiffness and undulation of woven structure. Compos Struct 2003;61:353-62; Yu WR, Zampaloni M, Pourboghrat F, Liu L, Chen J, Chung K, Kang TJ. Sheet forming analysis of woven FRT composites using picture-frame shear test and non-orthogonal constitutive equation. Int J Mater Prod Tech 2004;21(1/2/3):71-88] have illustrated the validity of the non-orthogonal constitutive relationship for predicting deformation behavior and changes in fiber angle in situations where woven preform was constrained by tools such as the die and blank holders. In the previous studies, the bending rigidity for out-of-plane deformation was assumed to be dependent on the in-plane stiffness; thereby the non-orthogonal constitutive equation being developed was based on the in-plane deformation geometry. The assumption for the bending rigidity was modified in this study by modeling the bending property using an asymmetric axial modulus. The asymmetric axial modulus was considered in order to utilize its ease in calculating bending rigidity from the in-plane stiffness, defining bilinear behavior over the range of tension to compression. The asymmetric factor, the ratio of compression and tensile modulus, for a woven preform was determined through simple cantilever deflection in the warp and weft directions, the validity of which was proven by conducting a cantilever deflection test and simulation in the bias direction. Finite element simulation of three-dimensional bending deformation was performed by using a non-orthogonal constitutive equation and the asymmetric axial modulus. The results show that the draped shape obtained numerically is in good agreement with the experiments in both overall deflected shape and projected contour. A shaping process was also simulated to show the usefulness of the current approach. By including the gravity and contact loading, successful prediction was made but a need was identified that extends linear asymmetric factor into nonlinear form in order to simulate large deformation in bending.