DEM-FEM coupling analysis of shot′s energy distribution and target′s residual stress of pneumatic shot peening

Pneumatic shot peening is a widely used surface strengthening method. During the peening process, shots often collide with each other, resulting in large energy loss and small compressive residual stress. In order to achieve the optimum compressive residual stress with as little energy loss as possible, firstly the collision mechanism of shots and the forming and coupling mechanism of the target’s residual stress are revealed, and then pneumatic shot peening is simulated by using DEM-FEM coupling model. Then, the effects of impact angle θ, initial shot velocity v 0, shot diameter d p, and mass flow rate r m on the percentage η of shots with different ratios of the impact velocity to initial shot velocity v m/v 0, the energy loss (EL), the energy transferred from shots to the target (ET), the residual energy (ER) and the compressive residual stress (RS) are investigated. The results show that as many random shots successively impact the target, the RS field induced by each shot couples with some adjacent RS fields induced by other shots, so that disperse RS fields are gradually transformed into a continuous RS layer with the compressive RS in the surface and the tensile RS in the subsurface. With the increase of θ and r m and with the decrease of v 0 and d p, the collision probability of shots increases, so EL also increases and η of shots with a large v m/v 0 decreases. While, ET increases with the increase of v 0 and d p, decreases with the increase of r m, and first increases and then decreases with the increase of θ. ET does not entirely determine but greatly affects the compressive RS field. So, the surface compressive RS and the maximum compressive RS first increase and then decrease with the increase of θ and r m, while the two parameters increase with the increase of v 0 and d p. The optimum parameters of shots are θ = 75°, v 0 = 60 m s−1, d p = 0.25 mm and r m = 2 kg min−1, in which ET reaches 45%, the surface compressive RS of S11 and S33 reach 512 MPa and 510 MPa respectively, and the maximum compressive RS of S11 and S33 reach 665 MPa and 746 MPa respectively.


Abstract
Pneumatic shot peening is a widely used surface strengthening method. During the peening process, shots often collide with each other, resulting in large energy loss and small compressive residual stress. In order to achieve the optimum compressive residual stress with as little energy loss as possible, firstly the collision mechanism of shots and the forming and coupling mechanism of the target's residual stress are revealed, and then pneumatic shot peening is simulated by using DEM-FEM coupling model. Then, the effects of impact angle θ, initial shot velocity v 0 , shot diameter d p , and mass flow rate r m on the percentage η of shots with different ratios of the impact velocity to initial shot velocity v m /v 0 , the energy loss (EL), the energy transferred from shots to the target (ET), the residual energy (ER) and the compressive residual stress (RS) are investigated. The results show that as many random shots successively impact the target, the RS field induced by each shot couples with some adjacent RS fields induced by other shots, so that disperse RS fields are gradually transformed into a continuous RS layer with the compressive RS in the surface and the tensile RS in the subsurface. With the increase of θ and r m and with the decrease of v 0 and d p , the collision probability of shots increases, so EL also increases and η of shots with a large v m /v 0 decreases. While, ET increases with the increase of v 0 and d p , decreases with the increase of r m , and first increases and then decreases with the increase of θ. ET does not entirely determine but greatly affects the compressive RS field. So, the surface compressive RS and the maximum compressive RS first increase and then decrease with the increase of θ and r m , while the two parameters increase with the increase of v 0 and d p . The optimum parameters of shots are θ = 75°, v 0 = 60 m s −1 , d p = 0.25 mm and r m = 2 kg min −1 , in which ET reaches 45%, the surface compressive RS of S 11 and S 33 reach 512 MPa and 510 MPa respectively, and the maximum compressive RS of S 11

Introduction
Pneumatic shot peening, as a mechanical surface strengthening method [1][2][3][4][5][6][7], can introduce compressive residual stress (RS) in the surface layer, so as to improve target's performance including fatigue life [8][9][10] and wear resistance [4,[11][12][13][14][15][16]. Hence, it has been widely used in aviation, aerospace, automobile, and other fields.  [22] investigated the effects of v 0 and the mass flow rate r m on the compressive RS by DEM-FEM coupling method. The results showed that v 0 has a greater effect on the compressive RS than r m , and a large v 0 can induce a deep compressive RS field. Compared with the experimental method, DEM-FEM coupling method can help us to observe the forming process of the RS field clearly. However, most of the above references mainly focus on target's RS and rarely concern the forming and coupling mechanism of the RS field, and few references analyze the energy distribution of shots, which is unfavorable to optimization of the shot parameters and improvement of the compressive RS. Only Murugaratnam et al [23] and Marini et al [24]respectively studied the changing trend of the velocity of shots by using DEM-FEM coupling method. However, no energy loss, energy transfer and residual energy of shots have been reported so far. Hence, in order to achieve the optimum compressive RS with as little energy loss as possible, firstly the collision mechanism of the shots and the forming mechanism of the target's RS are revealed, and then pneumatic shot peening is simulated by using DEM-FEM coupling model. Then, the effects of θ, v 0 , d p , and r m on the percentage η of shots with different ratios of the impact velocity to initial shot velocity v m /v 0 , the energy loss (EL), the energy transferred from shots to the target (ET), residual energy (ER) and compressive residual stress (RS) are investigated.
2. Mechanism of pneumatic shot peening 2.1. Process of pneumatic shot peening The process of pneumatic shot peening is shown in figure 1. Many random shots eject from the nozzle and impact the target with the impact angle θ and the initial shot velocity v 0 . Meanwhile, the nozzle moves in the x-direction and shots will follow the nozzle, then a banded strengthened area is obtained. Next, the nozzle moves in the z-direction to a new area and repeats the above steps to get a new banded strengthened area. After multipass pneumatic shot peening, the entire target surface is finally strengthened. Figure 2 shows the collisions of shots at different parameters. As shown in figure 2(a), when the incident angles θ is large, the overlap area (pink shaded area) between the incident path and the rebound path is large, resulting in large collision probability between the incident shots and the rebound shots and large energy loss. On the contrary, when θ is small, the overlap area (pink shaded area) between the incident path and the rebound path is small, leading to small collision probability and little energy loss. However, when θ is small, the energy transferred to the target is also little because the normal velocity is small. As shown in figure 2(b), when the initial shot velocity v 0 is small, the spatial distribution of the shots is dense and the distance between adjacent shots is small, resulting in large collision probability and large energy loss. On the contrary, when v 0 is large, the spatial distribution of shots is sparse and the distance between adjacent shots is large, leading to small collision probability and little energy loss. As shown in figure 2(c), when the shot diameter d p is small, the number of shots is large at the equal mass flow rate and the spatial distribution of shots is dense, resulting in large collision probability and large energy loss. On the contrary, when d p is large, the number of shots is small at the equal mass flow rate and the spatial distribution of shots is sparse, leading to small collision probability and little energy loss. As shown in figure 2(d), when the mass flow rate r m is small, the spatial distribution of shots is sparse, resulting in large collision probability and large energy loss. On the contrary, when r m is large, the spatial distribution of shots is dense, resulting in large collision probability and large energy loss. Figure 3 shows the forming and coupling mechanism of the RS field. At one moment, five random shots sequentially move downward to impact the target. The black shot 1 first impacts the target and then rebounds away, and a hemispherical RS field of internal compressive stress and external tensile stress is formed. Then, the green shot 2 and the yellow shot 3 sequentially impact the target, and two independent hemispherical RS fields  are formed, as shown in figures 3(b) and (c). When the red shot 4 impact the region between the two shots 1 and 2, the RS field induced by shot 4 will couple with the two RS fields induced by two shots 1 and 2, as shown in figure 3(d). If the tensile stress field overlaps with the previous tensile stress field, the previous tensile RS in the tensile-tensile overlap region will be enhanced. If the tensile stress field overlaps with the previous compressive stress field, the previous compressive stress in the tensile-compressive overlap region will be weakened. If the compressive stress field overlaps with the previous compressive stress field, the previous compressive stress in the compressive-compressive overlap region will be enhanced [25]. Similarly, the blue shot 5 impacts the region between the two shots 2 and 3, and the residual stresses will also couple with adjacent RS fields. After all five shots impact the target, a continuous RS field is formed, as shown in figure 3(e). If more shots impact the target until 100% coverage is achieved, a compressive RS layer will be obtained in the surface, while the tensile RS only exists in the subsurface, as shown in figure 3(f).

DEM-FEM coupled model
A nozzle with a diameter of 2 mm and a distance of 20 mm is adopted, and a 18CrNiMo7-6 plate with a dimension of 4.8 mm × 3.6 mm × 1.5 mm is employed as the target, as shown in figure 4. In EDEM software, the material parameters of shots and target are set according to table 1 [23]. Then, a shot plant is established, and the interaction coefficients of shot-shot and shot-target are set according to table 2. Next, the solver module is configurated with the coupling switch turned on. In ABAQUS software, the target is divided by hexahedral mesh [24]. The bottom surface is fixed. Reflection-free boundary conditions are imposed on the four sides and the bottom surface. In the process of pneumatic shot peening, many shots eject from the nozzle and then impact the target. Then, the effects of θ, v 0 , d p and r m are investigated.     Figure 6 shows the velocity distribution and energy distribution of shots at different θ. With the increase of θ, the overlap area between the incident path and the rebound path gradually increases, resulting in large collision probability between the incident shots and the rebound shots, so that the percentage η of shots with a large v m /v 0 decreases and the energy loss EL increases. When θ increases from 30°to 90°, η of shots whose v m /v 0 > 0.7 rapidly decreases from 80% to 16% and EL rapidly increases from 8% to 62%. While, the energy transferred from shots to the target ET first increases and then decreases with the increase of θ. When θ increases from 30°to 75°, ET increases from 22% to 41% due to the increased normal impact velocity of shots; when θ increases from 75°to 90°, ET decreases from 41% to 37% due to the collisions among shots. Meanwhile, the residual energy ER rapidly decreases with the increase of θ, indicating the increase of both ET and EL. When θ increases from 30°to 90°, ER decreases from 70% to 1%. For achieving as much ET as possible, θ in the range of 60°−75°is the optimum. Figure 7 shows the cloud atlas and curves of RS at different θ. When θ is small, the compressive RS layer is small in area, shallow in depth and even scattered in distribution. As θ increases, the compressive RS layer becomes larger in area, thicker in depth and more continuous in distribution, as shown in figures 7(a) and (b). As shown in figures 7(c) and (d), when θ = 30°, the RS first decreases from the surface compressive RS to zero, then changes to a tensile RS, and eventually slowly tends to zero. When θ = 45°, 60°, 75°and 90°, the RS first increases from the surface compressive RS to the maximum compressive RS, then rapidly decreases to zero and changes to a tensile RS, and eventually slowly tends to zero. Whether S 11 or S 33 , the surface compressive RS, the maximum compressive RS, the depth of the maximum compressive RS and the depth of the compressive RS field first increase when θ increases from 30°to 75°, and then decrease when θ increases from 75°to 90°, which is consistent with the changing trend of ET.

Effect of shot parameters 4.2.1. Effect of shot impact angle θ
For achieving the optimum compressive RS with as little energy loss as possible, θ = 75°is considered to be the optimum in this study. When θ = 75°, the surface compressive RS of S 11 and S 33 reach 282 MPa and 271 MPa respectively, the maximum compressive RS of S 11 and S 33 reach 489 MPa and 457 MPa respectively, the depth of the maximum compressive RS of S 11 and S 33 reach 0.028 mm and 0.027 mm respectively, and the depth of the compressive RS field of S 11 and S 33 reach 0.082 mm and 0.081 mm respectively. Figure 8 shows the velocity distribution and energy distribution of shots at different v 0 . With the increases of v 0 , the distance between adjacent shots increases and shots become difficult to collide with each other, resulting in small collision probability between shots, so that η of shots with a large v m /v 0 increases and EL decreases. When v 0 = 20 m s −1 , v m /v 0 for most shots is in the range of 0.1-0.7, and η of shots whose v m /v 0 > 0.7 is only 19%.

Effect of initial shot velocity v 0
When v 0 increases from 20 m s −1 to 80 m s −1 , η of shots whose v m /v 0 > 0.7 increases from 19% to 39% and EL decreases from 69% to 38%. Due to the decreased EL, ET increases with the increase of v 0 . When v 0 increases from 20 m s −1 to 80 m s −1 , ET increases from 24% to 45%. In addition, ER remains below 17%. For achieving as much ET as possible, v 0 should be as large as possible.    Figure 9 shows the cloud atlas and curves of RS at different v 0 . When v 0 is small, the compressive RS layer is small in area, shallow in depth and even scattered in distribution. As v 0 increases, the compressive RS layer becomes larger in area, thicker in depth and more continuous in distribution, as shown in figure 9(a) and figure 9(b). As shown in figures 9(c) and (d), when v 0 = 20 m s −1 the RS first decreases from the surface compressive RS to zero, then changes to a tensile RS, and eventually slowly tends to zero. When v 0 = 40 m s −1 , 60 m s −1 and 80 m s −1 , the RS first increases from the surface compressive RS to the maximum compressive RS, then rapidly decreases to zero and changes to a tensile RS, and eventually slowly tends to zero. Whether S 11 or S 33 , the surface compressive RS, the maximum compressive RS, the depth of the maximum compressive RS and the depth of the compressive RS field first increase rapidly when v 0 increases from 20 m s −1 to 60 m s −1 and then increase slowly when v 0 increases from 60 m s −1 to 80 m s −1 , which is consistent with the changing trend of ET.
For achieving the optimum compressive RS with as little energy loss as possible, v 0 = 60 m s −1 is considered to be the optimum in this study. When v 0 = 60 m s −1 , the surface compressive RS of S 11 and S 33 reach 282 MPa and 271 MPa respectively, the maximum compressive RS of S 11 and S 33 reach 490 MPa and 457 MPa respectively, the depth of the maximum compressive RS of S 11 and S 33 reach 0.028 mm and 0.027 mm respectively, and the depth of the compressive RS field of S 11 and S 33 reach 0.078 mm and 0.080 mm respectively. Figure 10 shows the velocity distribution and energy distribution of shots at different d p . With the increase of d p , the number of shots decreases at the equal-mass flow rate r m . Shots will become sparsely distributed and difficult to collide with each other, so that η of shots with a large v m /v 0 increases and EL decreases. When d p increases from 0.1 mm to 0.25 mm, η of shots whose v m /v 0 > 0.7 increases from 39% to 46% and EL decreases from 46% to 25%. While, ET increases slowly with the increase of d p . When d p increases from 0.1 mm to 0.25 mm, ET increases from 41% to 45%. Because the EL decrement is larger than the ET increment, ER also increases with the increase of d p based on the energy conservation law. When d p increases from 0.1 mm to 0.25 mm, ER increases from 13% to 30%. For achieving as much ET as possible, d p should be as large as possible. Figure 11 shows cloud atlas and curves of RS at different d p . When d p is small, the compressive RS layer is small in area, shallow in depth and even scattered in distribution. As d p increases, the compressive RS layer becomes larger in area, thicker in depth and more continuous in distribution, as shown in figures 11(a) and (b). As shown in figures 11(c) and (d), the RS first increases from the surface compressive RS to the maximum compressive RS, then rapidly decreases to zero and changes to a tensile RS, and eventually slowly tends to zero. Whether S 11 or S 33 , the surface compressive RS, the maximum compressive RS, the depth of the maximum compressive RS and the depth of the compressive RS field increase with the increase of d p , which is consistent with the changing trend of ET. However, the compressive RS increment is much larger than ET increment, indicating that ET does not entirely determine the RS field.  For achieving the optimum compressive RS with as little energy loss as possible, d p = 0.25 mm is considered to be the optimum in this study. When d p = 0.25 mm, the surface compressive RS of S 11 and S 33 reach 512 MPa and 510 MPa respectively, the maximum compressive RS of S 11 and S 33 reach 665 MPa and 746 MPa respectively, the depth of the maximum compressive RS of S 11 and S 33 reach 0.045 mm and 0.047 mm respectively, and the depth of the compressive RS field of S 11 and S 33 reach 0.13 mm and 0.12 mm respectively. Figure 12 shows the velocity distribution and energy distribution of shots at different r m . With the increase of r m , shots become densely distributed and easy to collide with each other, so that η of shots with a large v m /v 0 decreases and EL increases. When r m = 1 kg min −1 , v m /v 0 for most shots is in the range of 0.4-1.0, and η of shots whose v m /v 0 > 0.7 is 44%. When r m increases from 1 kg min −1 to 4 kg min −1 , η of shots whose v m /v 0 > 0.7 rapidly decreases from 44% to 21% and EL rapidly increases from 30% to 71%. Due to the rapidly increased EL, both ET and ER decrease with the increase of r m , especially ET. When r m increases from 1 kg min −1 to 4 kg min −1 , ET rapidly decreases from 42% to 11% and ER decreases from 28% to 18%. For achieving as much ET as possible, r m should be as small as possible. Figure 13 shows the cloud atlas and curves of RS at different r m . When r m is small, the compressive RS layer is small in area. As r m increases, the number of shots increases, so the compressive RS becomes larger in area, as shown in figures 13(a) and (b). As shown in figures 13(c) and (d), the RS first increases from the surface compressive RS to the maximum compressive RS, then rapidly decreases to zero and changes to a tensile RS, and eventually slowly tends to zero. Whether S 11 or S 33 , the surface compressive RS, the maximum compressive RS, the depth of the maximum compressive RS and the depth of the compressive RS field first increase when r m increases from 1 kg min −1 to 2 kg min −1 due to the increased number of shots and then decrease when r m increases from 2 kg min −1 to 4 kg min −1 due to the decreased ET.

Effect of mass flow rate r m
For achieving the optimum compressive RS with as little energy loss as possible, r m = 2 kg min −1 is considered to be the optimum in this study. When r m = 2 kg min −1 , the surface compressive RS of S 11 and S 33 reach 474 MPa and 473 MPa respectively, the maximum compressive RS of S 11 and S 33 reach 614 MPa and 702 MPa respectively, the depth of the maximum compressive RS of S 11 and S 33 reach 0.046 mm and 0.044 mm respectively, and the depth of the compressive RS field of S 11 and S 33 reach 0.127 mm and 0.126 mm respectively.

Model comparison and verification
For ensuring the accuracy of this model, the results in this study are compared with those in the two references [26,27], as shown in figure 14. The simulation curve in this study has the same change trend as the curves in the two references. All three curves first increase and then decrease with the increase of the depth from the surface. Moreover, the maximum compressive RS, the depth of the maximum compressive RS and the depth of the compressive RS field in this study are all close to those in the two references. Especially for the maximum compressive RS, the value in this study has only 0.23% and 1.81% differences from those in the two references, respectively. Hence, this DEM-FEM coupling model is considered to be accurate and can be used to simulate pneumatic shot peening.

Conclusions
(1) As many random shots successively impact the target, the RS field induced by each shot couples with some adjacent RS fields induced by other shots, so that disperse RS fields are gradually transformed into a continuous RS layer with the compressive RS in the surface and the tensile RS in the subsurface.