# Numerical Study on the Evolution Mechanism of the Crater under a Millisecond Laser
## 2 Numerical Simulation  
A two-dimensional model with a height of 480 \(\upmu\)m and a width of 1500 \(\upmu\)m was considered here. The laser source is a Gaussian beam with a diameter of 400 \(\upmu\)m and was applied to the center of the upper surface of the model. The material is GCr15, and its physical properties were obtained from JMatPro, as shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Elements** & **C** & **Si** & **Mn** & **Cr** & **Mo** & **N** & **Pi** & **S** & **Fe** \\ \hline wt\% & 1 & 0.2 & 0.34 & 1.5 & 0.01 & 0.08 & 0.013 & 0.003 & Balanced \\ \hline \end{tabular}
\end{table}
Table 1: Chemical composition of GCr15.  
Laser irradiation causes an increase in the temperature of the surface of the material, and a molten pool is formed as the temperature exceeds the melting point. The surface of the molten pool was subjected to thermo-capillary stress and Young-Laplace stress, while the interior of the molten pool was subjected to gravity and buoyancy. With the temperature, which continues to rise to the evaporation temperature, a recoil pressure was produced by the evaporated material, which acts on the surface of the molten pool. After the termination of laser irradiation, the molten pool cools and solidifies, the theoretical model of which is shown in Figure 1. Thus, the complete process involved multiple physical processes of heat transfer and fluid flow. Two modules of fluid heat transfer and laminar flow were used to establish the numerical model, based on the following assumptions:  
1. The physical properties of materials, obtained from JMatPro, are curves about temperature. For the convenience of calculations, the physical properties of each phase were replaced by constants, as shown in Table 2.  
2. The intensity distribution of the laser is considered to follow the ideal Gaussian distribution, and the energy of the process is constant.  
3. The solid metal is regarded as a fluid with high viscosity (\(5\times 10^{5}\) kg\(/\)(m\(\cdot\)s)). The molten metal in the molten pool was treated as an incompressible Newtonian fluid, while the flow in the molten pool was treated as laminar flow [10].  
\begin{table}
\begin{tabular}{c c c} \hline
**Property** & **Symbol** & **Value** \\ \hline Liquid phase density & \(\rho_{l}\) & 6500 kg\(/\)m\({}^{3}\) \\ Solid phase density & \(\rho_{s}\) & 7600 kg\(/\)m\({}^{3}\) \\ Liquid phase thermal conductivity & \(k_{l}\) & 20 W\(/\)(m\(\cdot\)K) \\ Solid phase thermal conductivity & \(k_{s}\) & 26 W\(/\)(m\(\cdot\)K) \\ Melting temperature & \(T_{m}\) & 1700 K \\ Vaporizing temperature & \(T_{V}\) & 2610 K \\ Latent heat of fusion & \(L_{m}\) & \(2.2\times 10^{5}\) J/kg \\ Latent heat of vaporization & \(L_{V}\) & \(6.24\times 10^{6}\) J/kg \\ Specific heat of liquid phase & \(C_{P,s}\) & 660 J/kg \\ Specific heat of solid phase & \(C_{P,J}\) & 840 J/kg \\ Surface tension of pure metal & \(\gamma_{m}\) & 1.943 N/m \\ Constant in surface tension gradient & \(A_{\gamma}\) & \(3\times 10^{-4}\) N/(m \(\cdot\) K) \\ Mushy zone constant & \(A_{unish}\) & \(10^{7}\) \\ Coefficient of heat transfer & \(h\) & 10 W/(m\({}^{2}\)K) \\ Radiation emissivity & E & 0.7 \\ Retro diffusion coefficient & \(\beta_{r}\) & 0.2 \\ Temperature transition interval of melting & \(\Delta\)T & 50 K \\ Absorption coefficient & H & 0.39 \\ \hline \end{tabular}
\end{table}
Table 2: Material properties of GCr15.  
Figure 1: Model schematic.