| In most polymer processing applications, the final structure of the material is determined by the extent of crystallization. The energy flow/cooling patterns should be coupled with the thermodynamic and rheological properties of the polymer for optimum product design. However, classical Stefan's approach is limited to equilibrium processes with small temperature gradients. In processing of semi-crystalline polymers, the temperature gradients are large, process times are small and the local equilibrium theories seldom hold. Hence, in this study, the crystallization kinetics of the material are introduced by modifying the phase change temperature through a mathematical model that couples the cooling rate of a hypothetical control volume in the solid (crystalline) domain to the crystallization rate of the material. The constitutive equation for temperature dependence of the crystallization rate may be determined either from the experiments or from the thermodynamical formulation.;Two different techniques are used to obtain the numerical solution, the finite difference method and the boundary element method. Examining the effects of various cooling rates reveals that the movement of the interface slows down considerably as the phase change temperature is allowed to vary. Effects of the temperature dependence of crystallization rate are analyzed by using different kinetics constitutive relations. The results indicate that depending on the cooling rate and the parameters in the kinetics model, there may be undercooling during the process. Then, the temperature field and residual stress predictions of traditional phase change approaches are compared with the new approach. Next, the predictions of the derived theoretical non-isothermal crystallization rate method are demonstrated by a sample study. And finally, the coupled model is extended to two-dimensional problems using BEM.;Also, an experimental set-up is designed and fabricated to examine the movement of the phase change front and to monitor the temperature profiles during the process. Both the phase change front position and the phase change temperature predictions of the coupled model agree very well with the experimental observations. |
