## 2 Materials and Methods
### Heat Transfer Model  
In this paper, the finite element method was used to simulate the temperature field. The current model has some assumptions. (1) This model is without regard for the convection of the liquid in the molten pool. (2) The volume shrinkage caused by the solidification of the powder layer is not considered in this model. (3) This model ignores the mass transport of heat. During the LPBF process, a laser beam is used as a heat source, the powder on the laser path is heated directly by the laser beam, and the heat is transferred to the surrounding space through heat convection and heat radiation. Moreover, the heat is conducted to the powder bed, causing the powder to go through the process of melting and cooling. Together, these three processes determine the temperature distribution inside the material. The transient spatial distribution of the temperature satisfies the following differential equations of 3D heat conduction in a domain region D, which can be described as [26; 27; 28]:  
\[\frac{\partial H}{\partial t}=\frac{\partial}{\partial x}\bigg{(}k\frac{ \partial T}{\partial x}\bigg{)}+\frac{\partial}{\partial y}\bigg{(}k\frac{ \partial T}{\partial y}\bigg{)}+\frac{\partial}{\partial z}\bigg{(}k\frac{ \partial T}{\partial z}\bigg{)}+Q,\ \ (x,\ y,\ z\in D) \tag{1}\]  
where \(H\) is the enthalpy (J/m\({}^{3}\)), \(T\) is the temperature (\({}^{\circ}\)C), \(t\) is the time (s), \(k\) is the thermal conductivity (W/m\({}^{\circ}\)C), and Q is the heat generated per unit volume of the interior (W/m\({}^{3}\))  
The enthalpy can be expressed as a function of temperature [28; 29]:  
\[\mathrm{H(T)}=\left\{ \begin{array}{c}\int_{T_{s}}^{T_{s}}\rho(T)c(T)dT\ (T<T_{s})\\ \int_{T_{s}}^{T_{s}}\rho(T)c(T)dT+\int_{T_{s}}^{T_{s}}\rho(T)c(T)dT+\int_{T_{s }}^{T_{s}}\rho(T)c(T)dT+\int_{T_{s}}^{T_{s}}\rho(T)c(T)dT\ (T\geq T_{l})\end{array} \right. \tag{2}\]  
where \(\rho\) is the density of AlSi10 Mg (kg/m\({}^{3}\)), \(c\) is the specific heat capacity (J/kg.\({}^{\circ}\)C), T\({}_{s}\) is the solidus temperature (\({}^{\circ}\)C), T\({}_{1}\) is the liquidus temperature (\({}^{\circ}\)C), T\({}_{r}\) is a reference temperature that is below T\({}_{s}\) (\({}^{\circ}\)C), and L is the latent heat (J/kg). Before the LPBF process begins, the initial temperature is equal to 20 \({}^{\circ}\)C and can be expressed as:  
\[T(x,y,z)_{t=0}=T_{0},\ \ (x,\ y,\ z\in D) \tag{3}\]  
The natural boundary condition that occurs on the free surface, including the inside conduction, surface convection, and radiation, can be described as [30]:  
\[k\frac{\partial T}{\partial N}-q+q_{c}+q_{r}=0,\ \ (x,\ y,\ z\in S) \tag{4}\]  
where S represents the surfaces that are attached to imposed heat fluxes, convection, and radiation; \(N\) is the normal vector of surface; the input heat flux is presented by Equation (7); \(q_{c}\) is the heat convection; and \(q_{r}\) is the heat radiation, which can be expressed by:  
\[q_{c}=h_{c}(T-T_{0}) \tag{5}\]  
\[q_{r}=\sigma_{SB}\epsilon\Big{(}T^{4}-{T_{0}}^{4}\Big{)} \tag{6}\]  
where \(h_{c}\) is the convective heat transfer coefficient, \(\sigma_{SB}\) is the Stefan-Boltzmann constant, and \(\epsilon\) is the emissivity of the powder bed. On the laser processing surface, the laser intensity distribution is approximately a Gaussian distribution. In this paper, the Gaussian body heat source model is used as the heat source model. This model considers the laser distribution in the direction of the vertical machining surface and assumes that the laser intensity decreases with the increase in depth.