# Investigation on Residual Stress Loss during Laser
## 4 Simulation Results and Discussion
### Mechanism for the Generation of Residual Stress Loss  
The investigation on the generation mechanism of residual stress loss will be helpful for understanding this phenomenon and explaining the effect of laser shock parameters on residual stress. In order to explore the relationship between residual stress loss and release waves, the release waves at different solution time are obtained from the simulation with a laser power density of 4.97 GW/cm\({}^{2}\) and a laser spot radius of 200 \(\upmu\)m (see Figure 7).  
Figure 5: The typical plastic deformation of the target material from (**a**) experimental result and (**b**) simulation result.  
Figure 6: Comparison between simulation and experiment (**a**) dimple profile (**b**) dimple depth.  
It is found from Figure 7 that the release wave generates at the edge of the laser spot and reaches the maximum at about 30 ns. After stopping laser radiation, the release wave continues to propagate along the spot center and longitudinal direction and arrives at the spot center at about 100 ns. Then, the release wave propagates towards the edge of the spot again, but it attenuates gradually.  
Furthermore, the time histories of the radial stress and the displacement of the laser spot center due to surface deformation are obtained, as shown in Figure 8. When the solution time increases from 100 ns to 230 ns, the radial stress changes from compressive stress \(-\)2478 MPa to tensile stress 257 MPa. After 230 ns, although the release wave attenuates to a low level and the stress state at the spot center gets back to compression, the radial stress tends to be stable at \(-\)221 MPa, which is much higher than the minimum radial stress of \(-\)2478 MPa. Generally speaking, the radial stress and the displacement have sharp changes at about 100 ns at which the release wave reaches the spot center, as shown in Figure 7. This validates that release wave has a close relationship with the residual stress loss, as [PERSON] et al. [18] put forward.  
Figure 8: Radial stress and displacement of the laser spot center along depth direction at different solution time (\(l_{0}=4.97\) GW/cm\({}^{2}\), \(R=200\) μm).  
Figure 7: Release waves at different solution time (\(l_{0}=4.97\) GW/cm\({}^{2}\), \(R=200\) μm).  
Through the above analysis, the generation of the residual stress loss can be summarized as follows: Under the loading of laser shock pressure, the material inside of the laser spot is compressed in the depth direction. But in the radial direction, the material expands first and then the expansion is confined by surrounding materials. Release wave occurs at the edge of the spot and propagates towards the spot center. When it arrives at the center, the reverse loading is generated, which makes the material compressive in the radial direction and expands in the depth direction. If the shock pressure exceeds a certain value, reverse plastic deformation will be induced by the release wave, which will weaken the limitation of the surrounding material on the spot of the laser. As a result, the compressive stress at laser spot center will decrease and even become tensile stress if the reverse plastic deformation is severe enough.