A Combined Viscoelasticity-Viscoplasticity-Anisotropic Damage Model With Evolving Internal State Variables Applied To Fiber Reinforced Polymer Composites

A thermodynamically-consistent large strain viscoelasticity-viscoplasticity-damage Internal State Variable (ISV) constitutive material model integrated with a mixture theory combining each individual constituent is formulated to describe the highly nonlinear, rate-dependent thermomechanical behavior of Fiber Reinforced Polymer (FRP) composites. The model is formulated in an intermediate configuration where unloading the specimen is viscoelastic. In our model, a rate-dependent yield surface is employed to identify initial yielding of the material. At small deformations, which occurs before yielding, the viscoelastic behavior of FRPs is described using the generalized Maxwell model, while at large deformation, three physically based evolving ISVs are used to capture the hardening and softening behaviors caused by their polymeric constituents. The complicated damage state of the FRPs is captured by a second rank tensor, which is further decomposed to model the subscale damage phenomena of microvoids/cracks nucleation, growth and coalescence. Finally, the mixture theory in combination with certain homogenization procedures are adopted to formulate the overall stress, strain, and damage of the composite in terms of the individual constituents. To demonstrate the model's usage, two examples are presented. First, the ISV model is calibrated to a Polyamide 6,6 reinforced with glass fibers with the aim of showing its capacity to predict the viscoelastic and damage coupled behaviors of a composite. Second, a glass fiber reinforced epoxy with the purpose of describing the temperature dependence and the interphase effect is illustrated.