# Investigation on Residual Stress Loss during Laser
## 4 Simulation Results and Discussion
### Effect of Laser Spot Radius  
Laser spot radius is also one of the most important parameters in the LPT process. The variations of residual stress along depth and radial direction under four different laser spot radii are shown in Figure 14.  
From Figure 14a, it is found that under the same laser power density, large laser spot radius leads to great thickness of residual compressive stress zone \(\Delta\mathrm{Y_{depth}}\). The probable reason is as follows. When the spot radius is large, the shock wave could be treated as a plan wave whose attenuation speed is slow, leading to a thick residual compressive stress zone. When the spot radius is small, however, the shock wave tends to be a spherical wave whose scattering is relatively serious. Thus, its attenuation speed is fast, resulting in a relatively thin residual compressive stress zone. This conclusion agrees well with previous findings of [PERSON] et al. (18).  
Figure 14b shows that with the increase of laser spot radius, the width of residual compressive stress \(\Delta\mathrm{X_{radial}}\) increases, but simultaneously, the range of residual tensile stress at the edge of the spot increases too. In addition, it is interesting to see from Figure 14a,b that the magnitudes of maximum residual compressive stress along depth direction \(\sigma_{\mathrm{ymin}}\) and those along radial direction \(\sigma_{\mathrm{xmin}}\) decrease with the increase of laser spot radius. These results might be related with the phenomenon of residual stress loss.  
In order to investigate the influence of laser spot radius on residual stress loss, the variations of \(\sigma_{0}\), \(\Delta\sigma_{\mathrm{depth}}\), \(\Delta\sigma_{\mathrm{radial}}\), \(\mathrm{y_{min}}\), and \(\mathrm{x_{min}}\) with laser spot radius are shown in Figures 15 and 16. From these two figures, it is seen that when laser spot radius is set as 100 \(\upmu\)m, the values of \(\Delta\sigma_{\mathrm{depth}}\), \(\Delta\sigma_{\mathrm{radial}}\), \(\mathrm{y_{min}}\), and \(\mathrm{x_{min}}\) are all zero, indicating that the residual stress loss does not appear. As a result, both the maximum residual compressive stress along depth direction \(\sigma_{\mathrm{ymin}}\) and that along radial direction \(\sigma_{\mathrm{xmin}}\) equal to \(\sigma_{0}\), which locates at the spot center.  
For the cases of 200 \(\upmu\)m, 300 \(\upmu\)m, and 400 \(\upmu\)m, it is found that the values of \(\sigma_{0}\), \(\Delta\sigma_{\mathrm{depth}}\), \(\Delta\sigma_{\mathrm{radial}}\), \(\mathrm{y_{min}}\), and \(\mathrm{x_{min}}\) all increase with laser spot radius. Moreover, when the laser spot radius increases by 100% from 200 \(\upmu\)m to 400 \(\upmu\)m, the values of \(\Delta\sigma_{\mathrm{depth}}\), \(\Delta\sigma_{\mathrm{radial}}\), \(\mathrm{y_{min}}\), and \(\mathrm{x_{min}}\) increase by more than 360%, 740%, 150%, and 160%, respectively. The above results show that laser spot radius has a significant effect on residual stress loss and large laser spot radius leads to more obvious residual stress loss. This might be the reason why \(\sigma_{\mathrm{ymin}}\) and \(\sigma_{\mathrm{xmin}}\) decrease with the increase of laser spot radius mentioned above.  
Figure 14: Residual stress along (**a**) depth direction and (**b**) radial direction under different laser spot radius (\(l_{0}=2.21\) GW/cm\({}^{2}\)).