[Metal Growth] Simulation of metallic nickel grain growth based on phase field with matlab code

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Content introduction

In the fields of modern science and engineering, the research and application of metallic materials has always been an important topic. The growth process of metal grains has an important impact on the properties and structure of materials. Therefore, it is critical to understand and control the mechanism of metal grain growth.

Phase field simulation is a commonly used method to simulate and predict the microstructure and evolution of materials. In the study of metal grain growth, phase field simulations can provide information about grain shape, size, orientation and distribution. This article will introduce the metallic nickel grain growth algorithm process based on phase field simulation.

First, we need to define the basic parameters of the simulation. These parameters include the size of the simulation region, the initial orientation of the grains, the time step of grain growth, etc. By adjusting these parameters, we can control the accuracy and computational efficiency of the simulation.

Next, we need to build the phase field model. The phase field model is a mathematical model that describes the phase change and phase separation process of materials. In the simulation of metal grain growth, the phase field model can be used to describe the morphology and evolution of grains. Commonly used phase field models include Allen-Cahn equation and Cahn-Hilliard equation.

Then, we need to set boundary conditions. Boundary conditions refer to constraints on the boundaries of the simulation area. In the simulation of metal grain growth, boundary conditions can affect the direction and rate of grain growth. Common boundary conditions include fixed grain orientation, periodic boundary conditions and free growth boundary conditions.

Next, we can start performing phase field simulations. Phase field simulations typically use numerical methods to solve the phase field equations. Common numerical methods include finite difference method, finite element method and spectral method. By iteratively solving the phase field equation, we can obtain the evolution process of the grain and the final grain structure.

Finally, we need to analyze and verify the simulation results. Analyzing simulation results can help us understand the mechanism and rules of grain growth. Validating simulation results allows you to evaluate the accuracy and reliability of the simulation by comparing it to experimental data.

To sum up, the process of the metal nickel grain growth algorithm based on phase field simulation includes the steps of defining simulation parameters, constructing a phase field model, setting boundary conditions, performing phase field simulation and analyzing and verifying the simulation results. Through this algorithm process, we can deeply study the mechanism of metal grain growth and provide basic support for the design and application of metal materials.

Metal grain growth is a complex and important process that has a significant impact on the properties and structure of materials. Phase field simulation is an effective method that can help us understand and predict the behavior of metal grain growth. By continuously improving and optimizing phase field simulation algorithms, we can better control and design the microstructure of metal materials, achieving improvement in material performance and innovation in applications.

Part of the code

m=0.05; eps=0.005; r=0.08; % kinetic coefficient, interface related parameters, anisotropy coefficient
Tm=1728; L=2350; DT=0.155; Cp=5.42; % melting point, latent heat, thermal diffusivity, specific heat
Delta=-0.55; R=0.05; alfa=400; % dimensionless supercooling, nucleation radius, coupling related parameters alfa
Lamda=30; % coupling coefficient
EPS=eps^2;A=m/EPS;B=(m/EPS)*EPS;C=eps*alfa*(-Delta);D=Lamda/(-Delta);
%Meshing------------------------------------------------ --------------------------
N=50; NTimeSteps=5000; Dx=0.02; Dy=Dx; Dt=1e-5; E=(m*Dt)/eps^2; DXX=Dx^2;
[x,y]=meshgrid(0:Dx:1); t=100; T=0; h=Dt/Dx/Dx;
%Initial conditions----------------------------------------------- -------------------
nn = length(x);
for i=1:nn
    for j=1:nn
        phy_n(i,j)=0.5*(tanh((sqrt((x(i,j).^2 + y(i,j).^2)))-R)/(2*sqrt(2)*eps )) + 1);
        U_n(i,j)=Delta*phy_n(i,j);
    end
end

Run results

[Metal Growth] Simulation of metal nickel grain growth based on phase field with matlab code_drone

[Metal Growth] Simulation of metal nickel grain growth based on phase field with matlab code_path planning_02

[Metal Growth] Simulation of metal nickel grain growth based on phase field with matlab code_drone_03

References

[1] Sun An. Simulating dendrite growth of pure metals using phase field method [D]. Ningxia University, 2009. DOI: 10.7666/d.y1682868.

[2] Hu Weiying, Chen Changle. Optimization of pure metal dendrite growth parameters simulated by phase field method [J]. Special Casting and Nonferrous Alloys, 2007, 27(3):3.DOI:10.3321/j.issn:1001-2249.2007 .03.007.

[3] Xue Xianjie. Phase field simulation of ternary alloy crystal growth based on adaptive finite element method [J]. Shanghai Jiao Tong University, 2007.

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