# Investigation on Residual Stress Loss during Laser
## 4 Simulation Results and Discussion
### Effect of Laser Power Density  
Laser power density is one of the most critical parameters in the LPT process. Figure 11a,b show the residual stress under different laser power densities along depth and radial direction, respectively. It is found from Figure 11a that the variation trends of residual stress along depth direction under different laser power densities are similar. The minimum residual stress is not located on the surface, but on the subsurface. With the increase of depth, the residual stress decreases to the maximum residual compressive stress \(\sigma_{\rm{ymin}}\) at a certain depth, then the residual stress increases and finally tends to be zero. The maximum residual compressive stress \(\sigma_{\rm{ymin}}\) and the thickness of the residual compressive stress zone \(\Delta\rm{Y}_{\rm{depth}}\) increase with laser power density. It means that larger laser power density leads to greater laser shock pressure, resulting in more obvious residual compressive stress, which is helpful for the mechanical performance of the target material. Figure 11b shows that variations of residual stress along radial direction under different laser power densities are similar as well. The surface residual stress firstly decreases to a certain value and then increases to a maximum residual tensile stress at the edge of the dimple. When the laser power density increases from 2.21 GW/cm\({}^{2}\) to 4.97 GW/cm\({}^{2}\), the width of the residual compressive stress zone \(\Delta\rm{X}_{\rm{radial}}\) has an increasing trend. When the laser power density continues increasing, however, due to the appearance of residual stress loss, \(\Delta\rm{X}_{\rm{radial}}\) decreases and even drops to zero when the laser power density increases to 13.80 GW/cm\({}^{2}\). Figures 12 and 13 show the effect of laser power density on the magnitude and the affecting zone size of the residual stress loss, respectively. It is found that \(\sigma_{0}\), \(\Delta\sigma_{\rm{depth}}\), \(\Delta\sigma_{\rm{radial}}\), \(\rm{y}_{\rm{min}}\), and \(\rm{x}_{\rm{min}}\) all increase with laser power density, which means that the phenomenon of residual stress loss becomes more obvious. In detail, when the laser power density is 2.21 GW/cm\({}^{2}\) or 4.97 GW/cm\({}^{2}\), the residual stress of the surface on laser spot center \(\sigma_{0}\) is compressive, meanwhile, \(\Delta\sigma_{\rm{depth}}\), \(\Delta\sigma_{\rm{radial}}\), \(\rm{y}_{\rm{min}}\), and \(\rm{x}_{\rm{min}}\) are relatively small. When the laser power density is set as 8.83 GW/cm\({}^{2}\) or 13.80 GW/cm\({}^{2}\), however, \(\sigma_{0}\) even becomes positive tensile stress, which is detrimental to the mechanical and physical performance of the target material. Therefore, it can be concluded the increase of the laser power density is not conducive to restrain the phenomenon of residual stress loss. Figure 11: Residual stress along (**a**) depth direction and (**b**) radial direction under different laser power densities (\(R\) = 200 μm). As discussed in Section 4.2, based on the generation mechanism of residual stress loss, it is known that if the laser power density is small, which means low laser shock pressure applied on the specimen, the release wave arriving at the spot center will be weak, so the reverse loading effect will not be strong enough to generate dramatic residual stress loss. With the increase of the laser power density, the laser shock pressure increases, and the release wave becomes stronger, thus the residual stress loss becomes more and more obvious. Actually, as concluded by [PERSON] [34], when the laser shock peak pressure is larger than 2.5 times the Hugoniot Elastic Limit (HEL) of the target material, there will be relatively serious residual stress loss phenomenon.