Phase-field Model Of Polycrystalline Multiphase Solidification System

The non-equilibrium solidification process is characterized by polycrystalline and multi-phase complex interactions.The microstructure formed by these interactions has a significant effect on the material properties.It is difficult to observe the microstructure evolution of polycrystalline and multiphase interactions in real time under the existing experimental conditions.As an effective tool for simulating the evolution of microstructure morphology at mesoscopic scale,the phase-field method can be applied to study the complex interaction process of non-equilibrium solidification.Therefore,we proposed a phase-field model suitable for polycrystalline and multiphase system,and designed the corresponding program to achieve dynamical simulation of the solidification process.Traditionally,the analysis of phase-field dynamical equation is based on perturbation method.In this papar,an operator analysis method is proposed to derive and analyze the properties of this dynamical equation,which obtains the same conclusion as the perturbation method,but greatly simplifies the analysis and derivation process.This operator analysis method not only establishes the equivalent relationship between the diffuse interface and the traditional sharp interface,but also clarifies the calculation technique of the physical parameters related to the phase-field equation,which further reveals the theoretical mechanism of the solidification process at mesoscopic scale.Based on the Kim-Kim-Suzuki(KKS)model,polycrystalline phase-field model and multiphase field model,we proposed a phase-field model suitable for polycrystalline multiphase solidification.In order to solve the low efficiency problem of Newton's iterative scheme in KKS model,a parabolic approximation scheme is proposed to calculate the phase compositions and driving force used in the numerical simulation,which greatly improves the calculation efficiency.Based on the MPI parallel explicit finite difference algorithm,we designed a solidification simulation package with multi-field coupling function.The microstructure evolution simultion of the complex solidification system can be achieved by this modular package.As an example of multiphase solidification,we studied the Fe-C peritectic solidification process,which includes the interaction of liquid-ferrite-austenite three phases and the the diffusion of carbon.The simulation consists of three parts:a single dendritic arm,a single anisotropic equiaxed grain,and a polycrystalline grains system with random orientations.Several microscopic physical characteristics of Fe-C peritectic solidification are clarified by this simulation,which includes the heterogeneous nucleation of austenite on the ferrite-liquid interface,the control of carbon diffusion on various interfacial movements,the formation mechanism of liquid channels and micro-melting pools,and the interaction of grains with different orientations.This study not only validates the validity of the model,but also reveals the microstructure evolution mechanism of the Fe-C peritectic solidification process,which can provide a theoretical basis for process control and optimization of engineering production.As an example of polycrystalline growth of grains with random orientations,we studied the graphene aerogel preparation by ice template method,and simulated the process of polycrystalline nucleation,anisotropic growth and interaction of ice crystal grains.In this study,the redistribution and diffusion process of graphene suspended particles during solidification of ice crystal grains is clarified,which reveals the formation mechanism of microscopic wall structure of graphene aerogel.In addition,the simulation also presents the relationship between the scale and morphology of this microstructure and the nucleation rate.Therefore,this study provides a theoretical reference for the microstructure control of the graphene aerogels preparation.In summary,the main works is briefly described as follows.Firstly,an operator analysis method is proposed to analyze the dynamical characteristics of the diffuse interface in phase-field model.Secondly,a phase-field model coupling with multi-field is constructed to simulate the polycrystalline multiphase solidification system,in which a parabolic approximation scheme is applied to improve the numerical calculation efficiency.Based on this model,a modular parallel solver package is designed for numerical simulation.Finally,we take the Fe-C peritectic solidification as the example of multiphase system and the graphene aerogel preparation by ice template method as the example of polycrystalline system to study the microstructure formation mechanism of steel solidification and the microscopic wall structure evolution mechanism of graphene aerogel respectively.These simulations verify the effectiveness of the package and provide theoretical guidance and analysis strategies for the material preparation process.