Formulation of a viscoplasticity model for unidirectional carbon fiber-reinforced composites with differences in off-axis tensile and compressive behaviors

Formulation of a phenomenological viscoplasticity model that accounts for differences in tensile and compressive nonlinear rate-dependent behaviors of unidirectional carbon fiber-reinforced composites in a given off-axis direction is attempted. Effective stress and effective viscoplastic strain for transversely isotropic materials are derived from a three-dimensional pressure-modified Hill's anisotropic yield criterion, and they are reduced to the forms for plane state of stress. A plane-stress viscoplasticity model furnished with a capability to predict the phenomena raised above is formulated on the basis of the concept of overstress and the irreversible thermodynamics with internal variables. A shear constraint parameter, in which the influence of the compressive transverse stress on the shear flow resistance is reflected, is taken into account in defining a modified form of effective viscoplastic strain rate to enhance the predictive capability of the viscoplasticity model. The viscoplasticity model discussed in the present study is designed so as to be reduced to the viscoplasticity model of the Gates-Sun type developed in the previous study, which allows easy identification of material constants. Validity of the proposed viscoplasticity model is evaluated by comparing with results of off-axis tension and compression tests on a unidirectional carbon/epoxy composite at different strain rates.