A multiscale model for polymer crystallization. II: Solidification of a macroscopic part

Abstract

In part I of this paper, we presented two efficient front‐tracking methods to simulate the growth of a spherulite within an imposed temperature field. In this second part we present a method that predicts the final microstructure in a macroscopic part by coupling these front‐tracking techniques with (a) a stochastic model for the nucleation of individual spherulites, (b) a cellular model for spherulite impingement and solid fraction evolution and (c) a Finite Difference Method (FDM) for latent heat release and heat diffusion. The method tracks the physical phenomena on several length scales: a course grid for the heat diffusion, a fine grid for solid fraction evolution and a very fine grid for the shape of the individual spherulites and the lamellae within them. To our knowledge this is the first time that fully coupled multiscale model has been applied to the solidification of polymers which gives realistic microstructure evolution, orientation of the different lamellae within spherulites and maps of the solid fraction and temperature fields during solidification. The model provides us with a quantitative predictive tool that can be used to optimize industrial processes.

Simulation of Polymer Crystallization under Isothermal and Temperature Gradient Conditions Using Particle Level Set Method

“…To date, a number of investigators are interested in predicting the morphological development of polymer crystallization and many research studies have been carried out on this topic [2][3][4][5][6][7][8][9][10][11][12]. In order to obtain the internal microstructure of polymer products, different approaches have been proposed for morphological modeling of polymer crystallization by researchers [7][8][9][10][11][12].…”

“…In order to obtain the internal microstructure of polymer products, different approaches have been proposed for morphological modeling of polymer crystallization by researchers [7][8][9][10][11][12]. Charbon and Swaminarayan [7,8] presented front-tracking methods to predict the evolution of microstructures during spherulitic crystallization under realistic crystallization conditions. Raabe and Godara [9] studied the topology of spherulite growth during crystallization of isotactic polypropylene (iPP) by using a cellular automata method.…”

Untitled

“…The prefactor of three dimensional spherulite density in Eq (7) can be converted to one of the two dimensional spherulite density by using the stereological relationship 7 :…”

“…There have been a few researches to study the shape evolution of a spherulite in various thermal conditions. [3][4][5][6][7] In the approach of Schulze and Naujeck, [3][4] the shape of a spherulite is analytically determined by any points that are reached by the growing fibrils from the nucleation center itself. Lovinger and Gryte 5 implemented the thermal conditions and the dependence of the growth rate on the temperature in the thermal fields.…”

“…However, this method is limited due to the difficulties of the numerical computation of the front directions when the thermal gradients are large. Swaminarayan and Charbon [6][7] proposed two methods, that is, the arborescent method and the front-tracking method in order to avoid such drawbacks. In the Arborescent method, the growth of the spherulites is modeled by following individual fibrils of which branching can be made in all possible orientations.…”