Parametric Model for the Analytical Determination of the Solidification and Cooling Times of Semi-Crystalline Polymers

This work presents an efficient method to quickly calculate with good accuracy (about 5%) the solidification time of an injected semi-crystalline polymer slab. Under some hypotheses this polymer can be considered as a phase change material with a constant phase change temperature. We use a noteworthy property established on the ratio between the thickness of a solidifying phase change finite medium and the solidified thickness in a semi-infinite medium. The knowledge of this ratio enables to predict analytically the solidification time in a 1D finite medium. This ratio can be parameterized as a function of characteristic numbers in phase change problems: Stefan numbers and the ratio of thermal diffusivities of both phases. The results are compared with those given by a complete model integrating the physics of the coupling between heat transfer and crystallization kinetics. The solidification times computed from both models are very close, demonstrating the relevance of the simplified model. Finally, we also get a very good accuracy in calculating the total cooling time, from injection to ejection.