# Numerical Study on the Evolution Mechanism of the Crater under a Millisecond Laser
## 3 Results and Discussion  
### Effect of Ablation Rate on Morphology and Verification of Numerical Model  
Figure 4 illustrates the comparison of microstructure morphology after cooling, with and without the ablation amount, when the peak power density is \(3\times 10^{9}\) W/m\({}^{2}\). It can be seen that the two curves have a high coincidence degree with a height of about 1.55 \(\upmu\)m, a depth of about 1.78 \(\upmu\)m, and a radius of about 110 \(\upmu\)m, which are consistent with the experimental results (Figure 5). This can be considered from the temperature distribution diagram (Figure 6), where the highest temperature at 1 ms is only 2650 K and the molten pool flows outwardly at a maximum velocity of 0.21 m/s. Although ablation has already taken place at this time, its corresponding ablation speed is lower (as shown in Figure 7), which is derived from Equation (21). In this case, the higher the temperature is, the more drastic the ablation speed would be. Thus, the ablation speed corresponding to 2650 K is around to 0.5 mm/s. Consequently, the influence of the ablation amount at the peak power density could be ignored. Figure 4: Comparison of molten pool with and without the ablation rate for \(I=3\times 10^{9}\) W/m\({}^{2}\), \(\tau=1\) ms, \(t=10\) ms.  
Figure 3: The schematic of the crater. Figure 8 compares the surface morphology of molten pool with and without the Hertz-Knudsen ablation rate, when the peak power density is \(5\times 10^{9}\) W/m\({}^{2}\) and the pulse width is 1 ms. It can be seen that the difference between the diameters and depths of the molten pool surface is less than 0.5 \(\upmu\)m, while the difference between the heights is more than 3.5 \(\upmu\)m at the end of laser heating. The temperature and flow velocity distribution of the molten pool, at 1 ms, are, respectively, shown in Figure 9.  
Figure 5: **(a)** Comparison of crater morphology from Comsol and NanoFocus \(\upmu\)surf explorer confocal microscope system for \(\tau=1\) ms, \(I=3\times 10^{9}\) W/m\({}^{2}\), **(b)** Three-dimensional diagram of a crater from the NanoFocus \(\upmu\)surf explorer confocal microscope system. Figure 6: Transient melt flow during laser heating for \(t=1\) ms, \(\tau=1\) ms, \(I=3\times 10^{9}\) W/m\({}^{2}\). Figure 7: Variation curve of the ablation rate with the temperature from Equation (21). Figure 9. The maximum temperature is 2750 K, while the corresponding ablation velocity is around 9 mm/s, which results in the reduction of the molten pool and its flow to the edge. In addition, the removal of materials reduces the temperature from 2750 K to 2740 K, which weakens the influence of recoil pressure and causes the flow rate to decrease from 0.64 m/s to 0.46 m/s; it also reduces the accumulation at the edge of the molten pool. Figure 8. Comparison of the molten pool with and without the ablation rate for \(I=5\times 10^{9}\) W/m\({}^{2}\), \(\tau=1\) ms, \(t=1\) ms.  
Figure 9. Transient melt flow during laser heating for \(t=1\) ms, \(\tau=1\) ms, \(I=5\times 10^{9}\) W/m\({}^{2}\), temperature field (color surface contour), and velocity field (colored arrow plots). (**a**) Ablation rate considered (**b**) Without the ablation rate. Figure 10 shows the temperature and flow velocity distribution diagrams in the cooling stage of 1.03 ms. It can be seen that the melt in the molten pool has a flow velocity of 1.39 m/s (when the ablation rate is ignored) and 1.14 m/s (when the ablation rate is considered). It can be considered that the height of the edge bulge possesses a positive correlation with the curvature of the molten pool surface, which makes the Young-Laplace stress increase. Consequently, the molten pool was affected by it and possessed a higher flow rate and reflux quantity in the cooling stage, making the center depth of the microstructure decrease, compared to the addition due to the Hertz-Knudsen ablation rate.