Modeling And Numerical Simulation Of Polymer Crystallization By Revised Phase Field Method

The solidification process is a complex process which includes thermodynamics of phase transition, solidification kinetics and various transport phenomena. The solidification microstructure is formed in the solidification process, and numerical simulation of the formation of microstructure can predict the properties of control materials. The phase field method is a new numerical simulation method to research the microstructure in solidification process. The phase field method has obvious advantages over other numerical simulation methods for the growth of grain in non-equilibrium system. In this thesis, a revised phase field method is used to numerically simulate the grain growth morphology during the semi-crystalline process of polymer. The main work of this thesis is summarized as follows.Firstly, based on the existing phase field model of polymer crystallization, an improved phase field model is presented by using the construction principle of the phase field model of pure metal. The improved phase field model consists of two partial differential equations, i.e. a second-order phase field equation and a heat conduction equation respectively. Considering the grain morphology has anisotropy and random disturbance during the actual process of grain growth, the interface anisotropy and interface perturbation term are both introduced to the phase field model. The model parameters of the phase field model are obtained through the physical parameters of materials, and the model can show a variety of morphology under static situations.Secondly, the finite difference method is used to solve the phase field model. Forward difference scheme is used to discrete the time variable and the nine-point discrete format is used to discrete the Laplace operator. Fortran programming language is used to write the calculation program of growth of the grain of polymer.Thirdly, various crystallization forms of polymers(polyethylene, isotactic polystyrene) are reproduced using the new phase field model. And the research on the influences of the model parameters on crystalline morphology of isotactic polystyrene is conducted. The influence of undercooling DT, anisotropy coefficient e, latent heat °K and thermal fluctuation h on the grain morphology is investigated quantitatively. Numerical results show that supercooling strongly affects the interface structure. As the increase of the degree of supercooling, the number of secondary branches increase and the distance between them becomes smaller. The value of the anisotropy coefficient should be moderate. If the value of anisotropy coefficient is too large, it will make the grains deformed and the simulation results become distortion, which make the result inconsistent with the actual situation. The simulated results will be reasonable if the anisotropy coefficient e value is between 0.01 :0.04. Numerical results also show that latent heat release rate is faster than the thermal conductivity near the interface and it makes grain growth rate decline when the value of °K is greater than a certain fixed value. Adding thermal disturbance can trigger side branches so that the numerical simulation results are more in line with the actual situation.