Modeling And Numerical Simulation Of Non-isothermal Crystallization Of Quaternary Alloy By Fourier Spectrum Method

This paper first establishes and adds the temperature field equation derived from the law of conservation of enthalpy on the basis of the microstructure evolution field equation of the multi-component alloy system driven by the reduction of free energy controlled by the Cahn–Hilliard and Allen–Cahn equations;using Fourier The spectral method is used to solve the discrete microstructure and the phase field model of temperature field and flow field.Finally,the process of alloy precipitation and evolution is simulated numerically.The main contributions are as follows:Firstly,a non-isothermal phase field model is established based on the phase field model of a quaternary alloy at constant temperature,which is controlled by phase field equation and temperature field equation,the main work is as follows: 1)changing the constant temperature to linear temperature;2)adding the non-constant temperature field derived from the law of Conservation of enthalpy;3)combining with the fact that the alloy precipitation is greatly influenced by the temperature,and the shape of each component in the precipitation process is influenced by the temperature and forced convection in the non-constant temperature field;4)changing the concentration of each component and the velocity of flow field.Secondly,the phase-field model is solved by fourier spectrum method.The phase-field simulation of quaternary alloy precipitation process is realized by Matlab programming,and the alloy precipitation process is visualized by paraview software.And finally,the relevant conclusions are obtained through visualization.The changes of the alloy precipitation behavior with the temperature field under constant temperature,linear temperature and non-constant temperature field all show that Cu precipitates first precipitate from the supersaturated solid solution,and then Mn and Ni precipitate.At linear temperature,the precipitation rate of each element of the alloy is faster,and as the aging continues,the precipitated elements will merge with each other.When the temperature continues to increase or decrease iteratively,more and more precipitates are merged.The addition of a non-constant temperature field to the phase field shows that the temperature changes with the change of the order parameter,which in turn affects the precipitation of the alloy.The addition of the temperature field makes the Cu precipitates become coarser and increase in size,and Ni and Mn move to In the interface area between the Cu precipitates and the Fe matrix,the process of finally forming the shell layer becomes shorter and faster,and the precipitation of Cu,Ni,and Mn is also faster and more obvious at higher temperatures.The higher the alloy composition,the faster the precipitation of precipitates,and the more precipitates fused.The flow field only affects the diffusion and accumulation of temperature,and has little effect on the alloy precipitation process.