**4.1. Experimental process**

**Figure 14.** Simulation results of residual stress field of SP (σxx) on the whole surface; (a) 3D result; (b) 2D result of surface.

**Figure 14(a)**). In addition, it is obvious that the max CRS appears in the subsurface, and after SP treatment of 200% coverage rate, the deformation of surface layer can be observed from the cross section (in **Figure 14(a)**) and the surface (in **Figure 14(b)**). Comparing with the residual stress distribution on the surface of homogeneous material in **Figure 5**, the stress distribution on surface of composite in **Figure 14(b)** is not uniform because the influence of reinforcements. The value of max CRS and tensile residual stress in **Figure 14(b)** are increased a little comparing the results in **Figure 5(b)**. The detailed discussion will be carried out in the following section.

The stress difference between the reinforcement and matrix is mainly due to the large mechanical differences between them. During the SP process, the matrix material and the reinforcement are deformed by the pressure caused by the impact of shot balls. The matrix material is deformed easily due to the small Young's modulus and yield strength. But the Young's modulus of the reinforcement is very large. The reinforcement in the surface undergoes bending under the vertical impact of shot balls, the reinforcement in the deeper area of plastic deformation zone is mainly deformed elastically. Some of the surface reinforcements are deformed in the plastic and result in high tensile residual stress (in **Figure 14(a)**). After SP,

**3.3. Influence of reinforcements on residual stress distribution**

40 Finite Element Method - Simulation, Numerical Analysis and Solution Techniques

SP treatment was performed using an air blast machine (Carthing Machinery Company, Shanghai, China). The SP intensities were: 0.15, 0.30, and 0.45 mmA. The distance between nozzle and samples was 100 mm and the diameter of peening nozzle was 15 mm. The shot media was cast steel ball with hardness of 610 HV and average radius of 0.3 mm. In order to obtain the uniform stress field on surface, the coverage rate of SP process was 200%. Residual stresses were measured by X-ray stress analyzer (LXRD, Proto, Canada) with Cu-*Ka* radiation under 30 kV/25 mA and Ni filter. The diffraction peak of Ti (213) was detected in the measurements and then the residual stresses were determined according to the sin2 *ψ* method [44] and the range of tilting angles was 0–45°. The schematic figure of residual stress measurement coordinate was shown in **Figure 15(a)** and the photo of residual stress measurement using X-ray stress analyzer was presented in **Figure 15(b)**. For obtaining the stress distribution along the depth, the thin top surface layer was removed one by one via chemical etch method with a solution of distilled water, nitric acid, and hydrofluoric acid in proportion of 31:12:7.
