**4.2. Residual stress distribution of Ti-6Al-4V**

The CRS distribution of Ti-6Al-4V under three different SP intensities is shown in **Figure 16(a)**. The residual stresses are compressive stresses and the values increase to max and then decrease, close to the simulated results by the homogeneous SP model. When the SP intensity increases from 0.15 to 0.45 mmA, the depths of max CRS are located at 50, 50, and 75 μm, corresponding to the intensity of 0.15, 0.30, and 0.45 mmA, respectively. The surface deformation layers are 275, 325, and 400 μm depth, which show that the deformation layer depth increases gradually with increasing SP intensity. In addition, with the increase of SP intensity, the CRS of surface is enhanced from

At the same depth, the higher of SP intensity, the values of CRS are bigger. These variation trends of residual stresses are similar to **Figure 16(a)**, and the depths of max CRS are located at 25 μm, which are shallower than the matrix's under the same SP intensity. The CRS of surface is enhanced from −545 to −724 MPa and the max CRS varies from −655 to −819 MPa. Contrasting the results from experiment and simulation, the ranges of residual stress measured via experiments are good agreement with the simulated results by 3D finite element dynamic analysis shown in **Figure 13**. The difference between simulation and experiment are inevitable, because the irradiation area of X-ray is larger than the dimension of reinforcement, and the tested residual stresses show the average values of the matrix and reinforcements. Based on all results, analysis and discussion, 3D finite element dynamic analysis is an effective method to simulate the residual stress distribution of metal matrix composite after SP treatment, especially to obtain the residual stress distribution in and around the reinforcements in the composite.

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

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

43

In order to study the effect of various parameters on the residual stress distribution after SP, LS/DYNA analysis module in ANSYS is utilized to establish the finite element model for Ti-6Al-4V and (TiB+TiC)/Ti-6Al-4V, and both 3D homogeneous and inhomogeneous models are set up. The influence of coverage rate, shot radius, and shot velocity on residual stress distribution is studied using the multi-layer shot balls to simulate the actual SP process. The

**1.** The influence of different coverage rates on residual stress distribution is investigated. With increasing coverage rate, the number of craters on the surface is increased obviously, and the uniformity of surface residual stresses is improved a lot. Comparing the results under coverage rate of 200 and 300%, the increment of surface residual stresses are not obvious, since the surface of almost all covered by craters and the stress field reaches saturation.

**2.** The influence of cast steel shot balls with different radius on the residual stress distribution is simulated when the shot velocity is 100 m/s. The CRS induced by smaller shot balls is higher, but the depth of residual stress layer is smaller and decreases rapidly. While increasing radius, the surface and max CRS are smaller, while the depth of residual stress layer decreases slowly.

**3.** The simulation results of different shot velocities show that the higher CRS and the deeper residual stress layer can be obtained under higher velocity. At 100 m/s, the max depth of CRS reaches 600 μm with *r* = 0.6 mm and coverage = 200%. The surface residual stress is less affected by shot velocity, while the radius of shot balls is 0.3 mm and the surface re-

**4.** The residual stress distribution in the plastic deformation zone, and in and around the reinforcements are obtained. Due to the different mechanic properties between the reinforcement and matrix, the elastic deformation of the reinforcement is mainly caused by SP, and a large tensile residual stress is formed in the body of reinforcement. Meanwhile, the plastic deformation of the matrix occurs and CRS are formed. After the elastic recovery,

sidual stress under two kinds of velocities is around −100 to −200 MPa.

there is still high CRS remained in the matrix.

**5. Conclusions**

main results are concluded as the following:

**Figure 15.** (a) Schematic figure of residual stress measurement coordinate; (b) photo of the residual stress measurement using X-ray stress analyzer.

**Figure 16.** Depth distribution of CRS on the matrix and composite under three different SP intensities [36], (a) Ti-6Al-4V; (b) 8% (TiB+TiC)/Ti-6Al-4V.

−517 to −605 MPa, which is improved by 17%. The max CRS varies from −684 to −794 MPa and the increase rate is about 16%. It is mainly due to the improved shot velocity after increasing SP intensity, which can cause more severe plastic deformation on surface, the deeper surface deformation layer and the larger CRS. Comparing the results by simulation and experiment, it reveals that the variation trends of residual stress by simulation are similar with the results from experiment.

#### **4.3. Residual stress distribution of 8% (TiB+TiC)/Ti-6Al-4V**

**Figure 16(b)** shows the experimental results of residual stress distribution on the composite 8% (TiB+TiC)/Ti-6Al-4V. From the figure, the depths of surface deformation layer are 200, 250, and 300 μm corresponding to 0.15, 0.30, and 0.45 mmA, which are shallower than the matrix's. The difference is resulted from the existence of reinforcements' resistance to the deformation of surface. Moreover, SP intensity has direct relation to the shot velocity. The larger impact velocity, the higher impact kinetic energy, and the depths of surface deformation layer are deeper. At the same depth, the higher of SP intensity, the values of CRS are bigger. These variation trends of residual stresses are similar to **Figure 16(a)**, and the depths of max CRS are located at 25 μm, which are shallower than the matrix's under the same SP intensity. The CRS of surface is enhanced from −545 to −724 MPa and the max CRS varies from −655 to −819 MPa. Contrasting the results from experiment and simulation, the ranges of residual stress measured via experiments are good agreement with the simulated results by 3D finite element dynamic analysis shown in **Figure 13**. The difference between simulation and experiment are inevitable, because the irradiation area of X-ray is larger than the dimension of reinforcement, and the tested residual stresses show the average values of the matrix and reinforcements. Based on all results, analysis and discussion, 3D finite element dynamic analysis is an effective method to simulate the residual stress distribution of metal matrix composite after SP treatment, especially to obtain the residual stress distribution in and around the reinforcements in the composite.
