Rate-dependent constitutive equations and process modeling of polymer materials

Rate and temperature dependent constitutive equations based on existing isotropic formulations of viscoplasticity are presented that are capable of simulating some of the important features of deformation exhibited by amorphous and semi-crystalline polymers. The theory does not require the use of a yield surface nor loading/unloading boundary conditions; instead, the evolution of the flow stress is assumed to depend on the rate of deformation, temperature and an appropriate set of internal variables. The internal variable for amorphous polymer materials describes the evolution of the intermolecular resistance that gives rise to the strain softening phenomena. The semi-crystalline polymer internal variable describes the evolution of the macrostructural resistance to slip, twinning and martensitic transformation that gives rise to viscoplastic and subsequent hardening behavior. The theory is capable of modeling the yield, strain softening and the orientation hardening exhibited by amorphous polymers as well as the initial viscoplastic and subsequent nonlinear hardening exhibited by semi-crystalline polymers at large deformations.;Uniaxial tensile tests with uniform and hourglass specimens were made at temperatures ranging from 23 to 100 deg C and various cross-head speeds, using amorphous polycarbonate and semi-crystalline polypropylene in order to obtain experimental stress-strain data and material constants. Load relaxation experiments were also conducted to obtain necessary material constants describing the rate and temperature dependence of flow stress for polypropylene.;The constitutive model is incorporated into an existing two-dimensional elastic-plastic non-isothermal finite element formulation. A simple rigid surface contact algorithm is also developed and incorporated into the finite element formulation in order to carry out the analysis of realistic boundary value problems. The finite element model and coupled constitutive equations are then used to numerically simulate an actual forming process--the draw forming of polypropylene sheets. Predicted analysis results compare with experimental observations with good agreement. The constitutive model used is shown to describe the complex deformation behavior of both amorphous and semi-crystalline polymers, and can be applied as a predictive tool in the analysis of deformation processing operations.