Micromechanics based elasto-visco-plastic response of long fibre composites using functionally graded interphases at quasi-static and moderate strain rates

A unit cell model is developed to capture the elasto-visco-plastic response of a long fibre composite using a 3-dimensional finite element model. Using a glass rubber model, the elasto-visco-plastic response of the matrix is analysed and the fibre is considered to deform elastically. A functionally graded interphase zone is defined in the region surrounding and encompassing a reinforcing fibre. The model subdivides the interphase zone into an infinite number of concentric rings where stress and strain compatibility is preserved. This model aims to improve on the computational efficiency of micromechanics models where the fibre and matrix are modeled as separate materials. The mechanics of the fibre deformation are governed by a transformation tensor for transversely isotropic materials based on Eshelby’s method. The model is calibrated using experimental data for the transverse compression of a unidirectional composite; it is then validated using axial compression and shear data for quasi static strain rates. For moderate strain rate the model is also calibrated for one of the transverse strain rates then validated using the other strain rates and axial compression. The proposed unit cell model is capable of predicting the elasto-visco-plastic response of long fibre composites to a very high accuracy.