Incorporation of the Effects of Temperature and Unloading into the Strain Rate Dependent Analysis of Polymer Matrix Materials Utilizing a State Variable Approach

A previously developed analytical formulation has been modified in order to accurately model the nonlinear, strain rate dependent deformation of polymeric materials, including the effects of hydrostatic stresses. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J₂ plasticity theory definitions of effective stress and effective inelastic strain are appropriately modified. To account for the effects of temperature on the nonlinear, strain rate dependent deformation of polymers, the isothermal equations were still applied, but some of the material constants were allowed to vary with temperature. Preliminary efforts to model the nonlinear unloading observed in polymers indicated that the methods used to compute the value of a state variable which controls the inelastic flow must be modified to account for the nonlinear unloading. To verify the developed formulation, the room temperature shear and tensile deformation response of a representative polymer has been computed across a wide range of strain rates. The high strain rate (several hundred per second) torsion response, and the low strain rate (quasi-static) tensile and torsion response of the polymer has also been simulated. In all cases, the results computed using the developed constitutive equations correlate well with experimental data. Techniques which can be used to incorporate the model into the analysis of the strain rate dependent deformation of polymer matrix composites, through the use of micromechanics techniques, are also described.