# Effect of Process Parameters on Distortions Based on the Quantitative Model in the SLM Process
## 2 Materials and Methods
### Simulation Details  
A thin-walled model is established (shown in Figure 1a) to investigate the distortion mechanism. The substrate dimensions are 8 \(\times\) 2 \(\times\) 3 mm\({}^{3}\), and the powder bed region is 6.6 \(\times\) 0.64 \(\times\) 0.8 mm\({}^{3}\). The powder bed region, which is dramatically heat-affected and undergoes a phase change, is finely meshed with 100 \(\times\) 40 \(\times\) 40 \(\upmu\)m\({}^{3}\) cubic element to improve the calculation efficiency. The substrate is meshed using coarse tetrahedrons. First, a thin-walled part with twenty layers and one track (6 mm length) within each layer is fabricated using a fixed scan speed of 800 mm/s. Other detailed process parameters are detailed in Table 3. Then, to investigate the effect of the height on the distortion, more simulations are conducted with various layers ranging from four to fifteen. This study is also to examine the effect of scanning speed on distortion. Therefore, six thin-walled parts with a height of 240 \(\upmu\)m are manufactured at different scanning speeds ranging from 500 mm/s to 1000 mm/s. The stiffness of support structures depends on the elastic modulus and the porosity. The substrate of the thin-walled model is modified into a columnar structure (as shown in Figure 1b) to explore the effect of support structures \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Temperature** **(K)**} & \multicolumn{2}{c}{**Thermal**} & \multirow{2}{*}{**Elastic Modulus** **Coefficient** **\(\mathbf{\kappa_{th}}\) **(I/K)**} & \multirow{2}{*}{**Elastic Modulus** **E (GPa)**} & \multirow{2}{*}{**Yield Stress** **\(\mathbf{\sigma_{y}}\) **(MPa)**} & **Plastic Tangent** **Modulus** **H\(\mathbf{p}\) **(GPa)** \\ \hline
296 & 8.78 & 125 & 1000 & 0.7 \\
366 & 9.83 & 110 & 630 & 2.2 \\
477 & 10 & 100 & 630 & 2.2 \\
589 & 10.7 & 100 & 525 & 2.2 \\
700 & 11.1 & 80 & 500 & 1.9 \\
811 & 11.2 & 74 & 446 & 1.9 \\
922 & 11.7 & 55 & 300 & 1.9 \\
1033 & 12.2 & 27 & 45 & 2 \\
1144 & 12.3 & 20 & 25 & 2 \\
1366 & 12.4 & 5 & 5 & 2 \\
1923 & 12.5 & 0.1 & 0.1 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical properties of Ti-6 Al-4V (data is obtained from Reference [26]). stiffness on the distortion. The gap between each column determines the stiffness. As the column gap increases, the stiffness of support structures decreases. Five simulations at different column gaps in support structures ranging from 150 \(\upmu\)m to 750 \(\upmu\)m are performed. The height of the thin wall is 200 \(\upmu\)m. A plate model shown in Figure 1c is built for exploring the relationship between scan strategies and distortions. The dimensions of the substrate are 4 \(\times\) 4 \(\times\) 3 mm\({}^{3}\), and the powder zone is 2.6 \(\times\) 2.6 \(\times\) 0.016 mm\({}^{3}\). Similar to the thin-walled model, the powder zone of this model is divided into 50 \(\times\) 50 \(\times\) 40 \(\upmu\)m\({}^{3}\) cubic elements. The scanning speed is fixed at 800 mm/s, and the scanning scale is 2 \(\times\) 2\(\times\) 0.016 mm\({}^{3}\) (four layers). Figure 2 shows six different scanning patterns employed in the simulation model. Case (a) is unidirectional scanning, where the scanning direction of each layer stays the same. In Case (b), the scanning movement rotates 90\({}^{\circ}\) between layers. Case (c) also has a 90\({}^{\circ}\) rotation, but the scanning direction is at a 45\({}^{\circ}\) angle to the boundary of the powder bed. The rotation angle in Case (d) is 45\({}^{\circ}\), and the initial scanning movement is along the \(x\)-direction. The contour scanning pattern is widely adopted in the SLM process [27]. Case (e) and Case (f) are the out-in and the in-out scanning strategy, respectively. Figure 1: Simulation models: (**a**) the thin-walled model with twenty layers; (**b**) the thin-walled model with the columnar support structures; (**c**) the plate model.