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

#### **3.1. Establishment of inhomogeneous SP model**

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

**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,

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).

to the surface and transfer most of kinetic energy to the deformation energy.

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

coverage = 100%; (f) *r* = 0.6 mm, coverage = 200%.

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> : H2 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

**Figure 11.** SEM images of reinforcements in (TiB+TiC)/Ti-Al-4V after etching on surface with different percentage; (a) 8% (TiB+TiC) [36]; (b) 5% (TiB+TiC) [43].

**Figure 12.** 3D SP model for inhomogeneous materials [36].

blue parts with disjunction distribution represent the reinforcements TiB and TiC, and the red and 1/4 spherical object is the shot ball. Because the mechanic parameters of these two reinforcements are similar, one kind of mesh is used in this model to simplify the calculation. Moreover, the whole mesh number reaches 320,000. In addition, a combination of two kinds of materials is built, one is the matrix Ti-6Al-4V, and the other is the average parameters of TiB and TiC.Wherein the relatively large area of plastic deformation, actually the directly impact area, the quite fine mesh is introduced. In this inhomogeneous model, the volume percentage of reinforcement is set as 8% based on the microstructure of material. The 1/4 symmetry model is set up and the nonreflecting boundary conditions on flank of model are applied. The symmetric boundary conditions are also applied on the symmetry plane in order to avoid the effect of stress wave.

−1511 MPa and the max tensile residual stress is +1155 MPa. Moreover, the CRS exist in the matrix, but there are tensile residual stresses in the reinforcements, which reveal that the reinforcements withstand the tensile stresses, and this stress distribution indicates the higher yield strength of reinforcements. The stress distribution indicates the effect of reinforcements, keeping the adverse tensile stresses in reinforcements and retarding the damage to matrix. The different residual stress distributions between the matrix and reinforcements are resulted from the different mechanical properties, consisting with the desired results after SP treatments.

**Figure 13.** Residual stress distribution in depth simulated from inhomogeneous SP model (σ*xx* direction); (a) 3D result;

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(b) 2D result; (c) magnification of 2D result.

The simulation results of residual stress field of SP (σxx) on the whole surface are shown in **Figure 14**. The similar stress distribution as **Figure 13** has been shown, in and around the reinforcement. Tensile residual stress appears and the stress concentration exists, but between the reinforcements, there are CRS and the distribution of CRS is uniform below the subsurface (in

#### **3.2. Residual stress distribution**

The residual stress distribution (σxx) of plastic deformation area is shown in **Figure 13** after SP. In the plastic deformation zone, there are both CRS and tensile stresses, the max CRS is Finite Element Dynamic Analysis on Residual Stress Distribution of Titanium Alloy and Titanium… http://dx.doi.org/10.5772/intechopen.73120 39

**Figure 13.** Residual stress distribution in depth simulated from inhomogeneous SP model (σ*xx* direction); (a) 3D result; (b) 2D result; (c) magnification of 2D result.

blue parts with disjunction distribution represent the reinforcements TiB and TiC, and the red and 1/4 spherical object is the shot ball. Because the mechanic parameters of these two reinforcements are similar, one kind of mesh is used in this model to simplify the calculation. Moreover, the whole mesh number reaches 320,000. In addition, a combination of two kinds of materials is built, one is the matrix Ti-6Al-4V, and the other is the average parameters of TiB and TiC.Wherein the relatively large area of plastic deformation, actually the directly impact area, the quite fine mesh is introduced. In this inhomogeneous model, the volume percentage of reinforcement is set as 8% based on the microstructure of material. The 1/4 symmetry model is set up and the nonreflecting boundary conditions on flank of model are applied. The symmetric boundary conditions

**Figure 11.** SEM images of reinforcements in (TiB+TiC)/Ti-Al-4V after etching on surface with different percentage; (a)

The residual stress distribution (σxx) of plastic deformation area is shown in **Figure 13** after SP. In the plastic deformation zone, there are both CRS and tensile stresses, the max CRS is

are also applied on the symmetry plane in order to avoid the effect of stress wave.

**3.2. Residual stress distribution**

**Figure 12.** 3D SP model for inhomogeneous materials [36].

8% (TiB+TiC) [36]; (b) 5% (TiB+TiC) [43].

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

−1511 MPa and the max tensile residual stress is +1155 MPa. Moreover, the CRS exist in the matrix, but there are tensile residual stresses in the reinforcements, which reveal that the reinforcements withstand the tensile stresses, and this stress distribution indicates the higher yield strength of reinforcements. The stress distribution indicates the effect of reinforcements, keeping the adverse tensile stresses in reinforcements and retarding the damage to matrix. The different residual stress distributions between the matrix and reinforcements are resulted from the different mechanical properties, consisting with the desired results after SP treatments.

The simulation results of residual stress field of SP (σxx) on the whole surface are shown in **Figure 14**. The similar stress distribution as **Figure 13** has been shown, in and around the reinforcement. Tensile residual stress appears and the stress concentration exists, but between the reinforcements, there are CRS and the distribution of CRS is uniform below the subsurface (in

there is still high compressive stress in the plastic deformation zone even though the elastic recovery occurs. Meanwhile, the elastic recovery of matrix is limited by the reinforcement,

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During SP process, the matrix material in the composite undergoes the severe plastic deformation and the compressive stress is introduced. The tensile stress in whisker reinforcements is produced with a symmetrical distribution due to the bending deformation. In the top region where the whisker is strengthened, also the compressive stress is produced, but it is significantly less than the stress between the whisker reinforcements. After SP, the material will spontaneously show the elastic recovery and both the compressive and tensile stress are reduced. While the elastic recovery is completed, the compressive stress region is obtained in the matrix between the whisker reinforcements and the tensile stress is retained in the reinforcements (in **Figure 14**). Since the tensile stresses in reinforcement are much lower than the strength of reinforcement, it is reasonable to believe that these tensile stresses have no detrimental influences on the fatigue properties of shot peened composites. In order to verify the simulated results obtained by 3D finite element dynamic analysis, the experimental investigation on residual stress distribution

of Ti-6Al-4V and 8% (TiB+TiC)/Ti-6Al-4V after SP are carried out via XRD method.

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 measure-

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.

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

*ψ* method [44] and

**4. Experimental validation on residual stress distribution**

ments and then the residual stresses were determined according to the sin2

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

**4.1. Experimental process**

which also makes the CRS in matrix further improved.

**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.

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

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, there is still high compressive stress in the plastic deformation zone even though the elastic recovery occurs. Meanwhile, the elastic recovery of matrix is limited by the reinforcement, which also makes the CRS in matrix further improved.

During SP process, the matrix material in the composite undergoes the severe plastic deformation and the compressive stress is introduced. The tensile stress in whisker reinforcements is produced with a symmetrical distribution due to the bending deformation. In the top region where the whisker is strengthened, also the compressive stress is produced, but it is significantly less than the stress between the whisker reinforcements. After SP, the material will spontaneously show the elastic recovery and both the compressive and tensile stress are reduced. While the elastic recovery is completed, the compressive stress region is obtained in the matrix between the whisker reinforcements and the tensile stress is retained in the reinforcements (in **Figure 14**). Since the tensile stresses in reinforcement are much lower than the strength of reinforcement, it is reasonable to believe that these tensile stresses have no detrimental influences on the fatigue properties of shot peened composites. In order to verify the simulated results obtained by 3D finite element dynamic analysis, the experimental investigation on residual stress distribution of Ti-6Al-4V and 8% (TiB+TiC)/Ti-6Al-4V after SP are carried out via XRD method.
