Modeling of Tension-Compression Asymmetry in Off-axis Nonlinear Rate-dependent Behavior of Unidirectional Carbon/Epoxy Composites

A phenomenological anisotropic theory of viscoplasticity that takes account of the difference between the nonlinear rate-dependent behaviors of unidirectional carbon fiber-reinforced composites under off-axis tensile and compressive loading conditions is presented. The plane-stress representation of the effective stress associated with the pressure-modified Hill's anisotropic yield criterion is modified into a new form that allows consideration of the difference between the shear flow stress levels under transverse tension and compression, i.e., a shear flow differential effect, as well as of the difference between the transverse tensile and compressive flow stress levels, i.e., a transverse flow differential effect. The shear flow differential effect is modeled in two ways by assuming the sensitivity and insensitivity to transverse stress, respectively. The rate-dependent plastic deformation of unidirectional composites is modeled on the basis of the concept of overstress and the irreversible thermodynamics with internal variables. The viscoplasticity model proposed in the present study can be reduced to the form developed in an earlier study, which facilitates identification of material constants and comparison with other existing theories. Validity of the proposed viscoplasticity model is evaluated by comparing with the off-axis tension and compression test results on a unidirectional carbon/epoxy composite at different strain rates. It is demonstrated that consideration of both the transverse and shear flow differential effects is crucial for accurate prediction of the different nonlinear rate-dependent behaviors of unidirectional composites under off-axis tensile and compressive loading conditions and those two kinds of flow differential effects have successfully been modeled in the proposed theory of viscoplasticity.