## 3.1 Influence of LSP power density on residual stress field

Three distinct power densities of 1.9GWcm− 2, 3.9 GWcm− 2, and 5.2 GWcm− 2 were chosen for numerical simulation based on the best peak range of shock wave pressure. Figure 6 depicts the residual stress nephogram and residual stresses in surface and depth directions of different power density., as laser power density increases, the maximum surface residual compressive stresses are − 300.7MPa, -332.0MPa and − 385.3MPa, respectively, while the uniformity of its distribution declined. At a power density impact of 5.9 GWcm− 2, residual tensile stress is even seen in certain parts of the surface (Fig. 6c).

Figure 6(d) depicts residual stress numerical extraction path in the direction of surface and depth. From low to high power densities, the average surface residual stresses are − 182.14MPa, -180.92MPa, and − 159.61MPa. The residual stress on the surface reduces clearly as power density increases. When compared to the residual stress in depth direction, it is discovered that while the maximum residual compressive stress on the surface of 5.9 GWcm− 2 is the greatest, the compressive stress layer on the surface of 5.9 GWcm− 2 is the shallowest, whereas 3.9 GWcm− 2 has a larger surface compressive stress and a deeper surface compressive stress layer. In general, as the laser power increases, the overall strengthening effect showed a trend of first increased and then decreased. The laser power density is estimated to be about 3.9 GWcm− 2based on the computed findings.

The higher laser power density increases the plastic strain, therefore the residual compressive stress rises. However, the component is a thin-walled pipe, and the propagation of stress waves within the component is extremely complicated, resulting in uneven distribution of residual stress. The stress wave propagation of the final hit is chosen for study, and the findings are illustrated in Fig. 7. It can be found that the maximum mises stress on the top surface reflected by 5.9 GWcm− 2, 3.9 GWcm− 2 and 1.9 GWcm− 2 is 891.0MPa, 776.0MPa and 633.3MPa. It may be discovered that a larger power density still has a bigger stress wave after reflection, which can still produce plastic strain of the material, and thus some residual tensile strains occur on the surface under the operation of 5.9 GWcm− 2.

## 3.2 Effect of spot size on residual stress field by LSP

From the simulation findings of LSP at various power densities, while the residual stress distribution at 3.9 GWcm− 2 power density is the best, it still has the disadvantages of uneven distribution and small value. Vasu et al. [21] discovered that increasing the curvature of convex model increases the compressive residual stress in materials. However, it is impossible to modify the curvature of real pipe fittings such as aircraft pipe.

Figure 8 shows the stress wave propagation of the pipe (Fig. 8b) compared with the plane member (Fig. 8a). It is obvious that the stress wave propagating over the curved surface has a horizontal extrusion, the horizontal component decreases as the diameter of the spot decreases (Fig. 8c). The effect of varied spot sizes on the pipe's residual stress is investigated in this paper.

Numerical simulation of LSP with spot diameters of 0.5mm, 1mm and 2mm is carried out. Figure 9 illustrates the residual stress nephogram and residual stresses in surface and depth directions of different spot diameters. The residual stress distribution is more uniform over the surface of the 0.5mm spot, with a maximum residual compressive stress of -439.9MPa. On a 1mm spot surface, the highest residual compressive stress is -332.0MPa. The greatest residual compressive stress on a 2mm spot surface is -378.5MPa, while certain parts of the surface exhibited residual tensile stress.

The mean values of surface residual stress are − 301.56MPa, -180.92MPa, and − 156.49MPa. As the diameter of the spot grows larger, the residual stress on the surface drops dramatically. It is found that the residual compressive stress on the surface of the 0.5mm spot is the largest, but the thickness of the compressive stress layer is the shallowest, while the compressive stress and the compressive stress layer on the surface of the 1mm spot are relatively large and deep.

The bigger spot creates a stronger squeezing component, which inhibits the downward propagation of the stress wave, resulting in a residual stress smaller than that of the small light spot in the surface and subsurface region. The stress wave is reflected several times in the depth direction by the thin-walled member, and the hindrances of large laser spots to downward propagation reduce the intensity of the stress wave after reflection, weakening the influence of the wave system after multiple reflection coupling on the residual stress field, and thus the residual compressive stress depth of small light spots is smaller than that of large light spots.

The stress wave propagation of the final hit is chosen for study. Figure 10 illustrates the findings. The stress waves are examined at the time of surface loading, at the time of the waves reaching the bottom surface, and at the time of the waves reaching the top surface. It is discovered that when the diameter of the spot increases, the area of the reflected stress wave on the top surface increases. When the diameter of the spot is increased, the diameter of the stress wave reflected on the top surface rises by 32%, 47%, and 50%. As seen in Fig. 10 (d), when a larger light spot acts, the influence range of the reflected wave is increased, resulting in a greater effect on the unloaded region by the reflected tensile wave, certain regions are impacted by the surrounding area's loading, leaving a residual tensile stress area. As a result, this effect can be reduced by using a smaller spot.

**3.3 Influence of guided wave material on residual stress field by LSP**

Although various power densities and spot sizes had been investigated before, and reasonably suitable laser parameters had been sought, the intense stress wave after reflection in the thin-walled pipe resulted in an uneven distribution residual compressive stress filed. As a result, the pipe was filled with a guided wave material to minimize stress wave reflection and to enhance the residual stress field. The residual stress nephogram and residual stresses in surface and depth directions of filled and unfilled guided wave materials is represented in Fig. 11. As seen in the image, the filled guide material raises the maximum residual stress of the surface residual stress to -578.6MPa, which is 70% more than the value for the pipe without the filled guide material.

The mean surface residual stress distributions of filled and unfilled guided wave materials are − 351.76MPa and − 180.92MPa. After filling the guided wave material, the surface's residual stress is significantly reduced. When residual stress is compared in the depth direction, it is discovered that the maximum residual compressive stress on the surface of the filled waveguide material is significantly enhanced, while the compressive stress layer is increased by about 0.2mm in depth.

After filling the guided wave material, the reflection of stress waves in thin-walled pipe is minimized. As seen in Fig. 12, the stress wave propagation of the most recent hit is chosen for investigation. When the stress wave reaches the bottom surface, the majority of it propagates through the interface and into the waveguide material. With continuous stress wave propagation, the energy of the stress wave is lost throughout the propagation process in the guided wave material, and it is difficult to affect the material's plastic strain during following propagation. Thus, the LSP's effect of thin-walled pipe can be improved effectively by filling with guided wave material.