*2.2.4. Influence of shot velocity on residual stress distribution*

SP is the process of consuming shot balls' kinetic energy and transfer the kinetic energy to the deformation energy of target material. So, after SP, the elastic and plastic deformations are introduced in the surface layer of target material. The shot balls' mass and velocity directly affect the value of kinetic energy. When the material of shot balls is same, the kinetic energy increases with the improvement of shot velocity. In SP experiment by using an air blast machine, the shot velocity can be varied and obtained by adjusting the air pressure. During the flight of shot balls, the velocity will be decreased because of the collision between them and the effect of air resistance, and the attenuation is related to the distance between the nozzle and the material. The smaller diameter of shot ball, the velocity attenuation is more obvious. The attenuation rates of cast shot balls (ρ = 7.8 g/cm<sup>3</sup> ) with different diameters at different shot distances are shown in **Figure 9** [41]. From this figure, it can be found that when the shot distance is less than 2 m, the attenuation rates are proportional to the distance increment.

The shot velocity is also affected by the shot angle in addition to the attenuation with the distance. When the shot balls impact on the surface of workpiece at a certain angle, the velocity can be decomposed into two directions. One is perpendicular to the surface (normal velocity) and the other is parallel to the surface (tangential velocity). The former velocity contributes to the plastic deformation of the surface layer, but the latter only promotes the friction effect. Based on the above analysis, in the experiment of this work, the distance between nozzle and samples is 100 mm (0.1 m),

**Figure 9.** Relationship between decrement of shot velocity and shooting distance [41].

**Figure 8.** Influence of shot radius on depth distribution of residual stress (*v* = 100 m/s and coverage = 100%).

**Figure 7.** Residual stress distribution after SP with different coverage rates: (a) 100%; (b) 200%; (c) 300%. [36].

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

*<sup>v</sup>* <sup>=</sup> 16.35 <sup>×</sup> *<sup>p</sup>* \_\_\_\_\_\_\_\_\_

and 100 m/s are considered in this work.

severely and the deeper deformation layer can be obtained.

**3.1. Establishment of inhomogeneous SP model**

H2

**3. Finite element simulation on inhomogeneous SP model**

1.53 × *m* + *p*

+

*m*, *p*, and *d* represent the flux of shot balls (kg/min), the jet pressure (bar), and the diameter of shot balls (mm), respectively. In current experiment, the value of *m* is 0.5 kg/min. The different SP parameters are shown: (1) 0.15 mmA (SP intensity), 4 bar (air pressure), 0.5 min (SP time); (2) 0.3 mmA, 10 bar, 0.5 min. The average radius of shot balls *r* = 0.3 mm. Based on above parameters, the approximate shot velocities are estimated as 57 and 92 m/s, corresponding to SP intensities of 0.15 and 0.3 mmA respectively. Thus, the shot velocities of 50

During simulation, the initial shot velocity represents SP intensity. The larger velocity means the higher SP intensity. **Figure 10** indicates the residual stress distribution in depth with different initial velocities. In these figures, the variation trends are similar. While increasing velocity, both the surface and max CRS significantly increase and the depth of deformation layer is also improved. At *v* = 100 m/s, the max depth of CRS in the material reaches 600 μm with *r* = 0.6 mm and coverage = 200% (in **Figure 10(f)**). The surface residual stress is less affected by the shot velocity while *r* = 0.3 and the surface residual stress is around −100 to −200 MPa (in **Figure 10(c)** and **(d)**). Because one part of the kinetic energy is transferred to the deformation energy during SP, while increasing shot velocity, much more kinetic energy can be transferred to the deformation energy, which can result in the surface deformation more

In order to set up 3D SP model for inhomogeneous materials, the morphology of reinforcements were observed by scanning electron microscope (SEM, Hitachi S-3400 N, Japan) under 15 kV, 70 μA. Before SEM observation, the samples were ground by abrasive papers, and then by the diamond papers and the aluminum oxide suspensions in order. For acquiring clear morphology of reinforcements, the sample was etched using Kroll's solution (HF: HNO<sup>3</sup>

O = 3:5:100 (vol)) for 2–6 s after polishing. All experiments were performed at room temperature. The SEM images of reinforcements in (TiB+TiC)/Ti-Al-4V after etching on surface with different percentage have been shown in **Figure 11** [36, 43]. It is indicated that the reinforcements are distributed uniformly in the composite. The reinforcements like short sticks are TiB, while the equiaxed or near equiaxed particles are TiC. In the following work, the 3D SP model for inhomogeneous materials is based on the microstructure of reinforcements in 8% (TiB+TiC)/Ti-6Al-4V. Based on the simulated results from homogeneous model, the inhomogeneous SP model containing the reinforcements is built in this part and the residual stress distribution in and around the reinforcements are obtained and analyzed. In this model, the parameters of *v* = 100 m/s, *r* = 0.3 mm and coverage = 200% are chosen as the initial parameters. The 3D SP model for inhomogeneous materials is shown in **Figure 12** [36] based on the microstructure observation of reinforcements. In the figure, the green part represents the matrix, the

29.50 × *p* \_\_\_\_\_\_\_\_\_ 0.598 × *d* + *p*

Finite Element Dynamic Analysis on Residual Stress Distribution of Titanium Alloy and Titanium…

+ 4.83 × *p* (5)

http://dx.doi.org/10.5772/intechopen.73120

37

:

**Figure 10.** Residual stress distribution in depth with different shot velocities, (a) *r* = 0.15 mm, coverage = 100%; (b) *r* = 0.15 mm, coverage = 200%; (c) *r* = 0.3 mm, coverage = 100%; (d) *r* = 0.3 mm, coverage = 200%; (e) *r* = 0.6 mm, coverage = 100%; (f) *r* = 0.6 mm, coverage = 200%.

in which, the shot velocity on surface is almost the same as initial velocity. Moreover, the direction of peening nozzle is perpendicular to the surface, which can keep the shot velocity perpendicular to the surface and transfer most of kinetic energy to the deformation energy.

In order to simulate the practical process of SP better, the actual shot velocity is estimated by the semi-experiential formula introduced by Dr. Klemenz [42], which is shown in Eq. (5).

Finite Element Dynamic Analysis on Residual Stress Distribution of Titanium Alloy and Titanium… http://dx.doi.org/10.5772/intechopen.73120 37

$$v = \frac{16.35 \times p}{1.53 \times m + p} + \frac{29.50 \times p}{0.598 \times d + p} + 4.83 \times p \tag{5}$$

*m*, *p*, and *d* represent the flux of shot balls (kg/min), the jet pressure (bar), and the diameter of shot balls (mm), respectively. In current experiment, the value of *m* is 0.5 kg/min. The different SP parameters are shown: (1) 0.15 mmA (SP intensity), 4 bar (air pressure), 0.5 min (SP time); (2) 0.3 mmA, 10 bar, 0.5 min. The average radius of shot balls *r* = 0.3 mm. Based on above parameters, the approximate shot velocities are estimated as 57 and 92 m/s, corresponding to SP intensities of 0.15 and 0.3 mmA respectively. Thus, the shot velocities of 50 and 100 m/s are considered in this work.

During simulation, the initial shot velocity represents SP intensity. The larger velocity means the higher SP intensity. **Figure 10** indicates the residual stress distribution in depth with different initial velocities. In these figures, the variation trends are similar. While increasing velocity, both the surface and max CRS significantly increase and the depth of deformation layer is also improved. At *v* = 100 m/s, the max depth of CRS in the material reaches 600 μm with *r* = 0.6 mm and coverage = 200% (in **Figure 10(f)**). The surface residual stress is less affected by the shot velocity while *r* = 0.3 and the surface residual stress is around −100 to −200 MPa (in **Figure 10(c)** and **(d)**). Because one part of the kinetic energy is transferred to the deformation energy during SP, while increasing shot velocity, much more kinetic energy can be transferred to the deformation energy, which can result in the surface deformation more severely and the deeper deformation layer can be obtained.
