*3.3. Residual Stress Analysis*

The analysis results of temperature and stress field are applied to the cladding layer as loads, and a line constraint is imposed on both sides of the matrix surface, the stress distribution of the workpiece in all directions after cooling for 3.5 h was analyzed, the stress is also the residual stress of the workpiece.

In order to study the residual stress distribution at different positions of the formed part, the middle position of the cladding layer was selected and cut along the plane. The junction between the cladding layer and the matrix along the axis is selected as the path1, and the path from the apex of the cladding layer to the vertical direction of the matrix along the axis is selected as the path2 to study the distribution of residual stress at different positions, as is shown in Figure 9.

**Figure 9.** Path location diagram.

Figure 10 shows the residual stress distribution of the two paths. Figure 10a shows that in the horizontal direction of path 1, the residual stress is symmetrically distributed with a single track as the central axis. In X direction, the residual stress increases sharply when it is close to the boundary area of the cladding layer (0.7 mm ≤ *y* ≤ 1.4 mm), and the maximum axial tensile stress is about 414 MPa. Because heat dissipation is relatively faster at the boundary between the cladding layer and the substrate, and the temperature gradient increases, thereby increasing the stress value. In the cladding layer, the closer to the center of the light spot, the smaller the temperature gradient, and the lower the stress value relative to the boundary of the cladding layer. Compressive stress is present in the part far away from the cladding layer, which is due to the high energy input, large temperature gradient, fast cooling rate, and difference in material properties during processing. After cooling, the substrate will hinder the shrinkage of the nickel-based coating, causing the cladding layer to bear tensile stress. Because of the limitation of the single-pass cladding width, the deformation resistance in the direction is small, and the stress value is also relatively small. However, the maximum residual stress in the y direction is concentrated on both sides of the cladding layer close to the substrate, cracks in the cladding layer often appear in this area. The tensile stress in Z direction is very small and can be ignored.

**Figure 10.** Residual stress distribution in two paths. (**a**) Residual stress distribution in path 1.(**b**) Residual stress distribution in path 2.

Figure 10b shows that there is a high tensile stress at the interface between the deposited layer and the substrate plane along the vertical direction of Path 2 due to the difference in thermophysical properties between substrate and nickel-based coating, and the maximum tensile stress at z = 3 mm is 432 Mpa. In x direction, as the depth continues to increase, the energy delivered by the laser becomes smaller and smaller, and the temperature gradient decreases, resulting in a gradual decrease in tensile stress. In y direction, as the depth of the cladding layer increases, the tensile stress gradually decreases and transforms into compressive stress in the middle of the substrate. But the compressive stress is transformed into tensile stress again at the bottom of the substrate z = 6 mm, because the local temperature is relatively high during the processing, and the temperature gradient of the entire cladding layer and its edges is large relative to the substrate, the shrinkage rate of the substrate is smaller than that of the entire single track. When the cladding layer is cooled and solidified, the substrates on both sides and the bottom of the cladding layer hinder the shrinkage of the cladding layer, so the single-pass cladding layer bears the tensile stress from the surrounding matrix. Because the cladding layer runs through the entire surface of the substrate along the axis, the overall deformation in the axial direction is an arc with a low center and high sides. Because the substrate is thicker, when the deposited layer is cooled and solidified, the compressive stress in the middle of the substrate and the tensile stress of the cladding layer balance each other according to the force balance principle, while the substrates on both sides move closer to the middle of the cladding layer, the bottom of the substrate bears the tensile stress. The residual stress value in z direction is relatively small, showing a small tensile stress in the upper position of the cladding layer and the substrate, it gradually shows a slight compressive stress as the depth increases.
