New approach to estimate coverage parameter in 3D FEM shot peening simulation

Abstract

Shot peening is a surface cold working process used to enhance the fatigue life of metallic parts or members. Coverage is a major parameter of shot peening process, which is defined as the percentage of the sum of peened area over the total area on the surface of the specimen. In this paper, a new method is proposed to estimate the full coverage for simulation of the shot peening process. A dynamic plastic model of the shot peening process with the aid of Matlab™ code is also presented using the finite element method (FEM). The numerical results show that the coverage, shot velocity and radius significantly affect the residual stress distribution of the target material, AISI 4340 steel. In addition, a double-shot peening process is also studied in simulation to consider its effect on compressive residual stress distribution.

Keywords

FEM random residual stress shot peening double-shot peening

Introduction

Shot peening is a cold working process, which is used to enhance the surface properties of materials, especially fatigue life since it induces large compressive residual stresses in the material sub-surface [1 -4]. Nowadays, the shot peening process is widely used in industries ranging from aerospace, automotive to construction [1 -4]. In the shot peening process, thousands of balls impact the surface of target material, which causes plastic deformation and subsequently induces compressive stresses in the sub-surface [1 -4]. After being shot peened, the surface layers of the target material become harder and rougher than its surrounding unaffected surface area [5 -7].

The computational modelling has been widely used for a number of manufacturing processes, including shot peening, in order to avoid the time and cost associated with the trial-and-error approach [8,9]. Many published papers studied the numerical simulation of shot peening process in different approaches of coverage [10 -15]. From the published works [10 -15], it is observed that three-dimensional multiple-impact models did not concentrate on the coverage parameter, but on the development of stress state during the impact process. In these researches [10 -15], the multiple-shot peening simulations studied uniformly distributed positions and prearranged sequences. The details of these impact patterns have been discussed in a review paper by Bagherifard et al. [16]. The use of symmetry patterns can help to reduce computational costs. Nevertheless, this assumption cannot totally define the random nature of practical shot peening process [16]. Therefore, these patterns often fail to simulate a full coverage condition for the actual shot peening [16].

A random impact model was developed by Miao et al. [17], where the centre of shot coordinates was generated by Equation (1). (1)

where rand(1,1) is a uniform pseudo-random number generator in the interval [0,1] and N is the number of impacts.

Bagherifard et al. [18] developed a multiple random impact simulation model to predict the generation of the nanostructured surface layer. In this research, to obtain the coverage parameter, the Kirk and Abyaneh model [19] given as the Avrami equation (Equation 2) was applied. (2)

where N is the number of shot, d is the diameter of a dimple caused by a single shot, D is the diameter of impact region of the target material. In experimental shot peening process, a coverage of 98% can still be assessed visually [1]. Therefore, the coverage of 98% is usually considered as a full coverage. To obtain 98% coverage, Ar value is equal to 4.

It is also worth to note that the high shot intensity obtained with large shots at a high velocity is effective to induce high magnitude of compressive stress in the target material [1]. However, the surface roughness of the shot-peened target material is relatively high [1]. To improve the surface finish of shot-peened components at high intensity, the use of a lower shot intensity obtained with smaller shots at a lower velocity would reduce the surface roughness of shot-peened components. This process is called double-shot peening. The experimental results of the double-shot peening process have been reported [20,21], but there is the lack of modelling and simulation knowledge.

In this paper, a new method is introduced to estimate the number of shots and their arrangements required to achieve full coverage of the target material. A multiple-impact model, developed using a commercial FE analysis programme LSDYNA, was used to investigate the effects of different shot peening parameters on the compressive residual stress distribution of the material. In addition, the effect of double-shot peening on the residual stress distribution of the material was studied in the simulation.

Materials and methods

In this research, a new approach method is introduced to estimate the coverage of target material using a simulation model. This model is based on the assumption of the Kirk and Abyaneh model [19]. The assumption is that during shot peening process, a simplified model is considered, in which a fixed diameter of circular impression is created by uniformly sized spheres impacting a flat surface. A new approach method can provide the number of required shots for the coverage of 98%, the arrangement of shots and the dependence of the degree of coverage on the number of shots. To estimate the level of coverage parameter, a Matlab™ code is applied to the flowchart shown in Figure 1.

Figure 1

A sequence of multiple impacts shot peening process with the aid of Matlab™.

The first step of this flowchart is the calculation of the diameter of a dimple on target material surface caused by a single impact. Figure 2(a) presents the original region of a target area which is divided into several small cells. The value of each node of the cell is set equal to 1 at the beginning of the process. Value ‘1’ means that the node is not peened. The first ball, which has the radius ‘R’, randomly impacts a target (the centre of the ball is located inside the target area) to generate an indentation with radius ‘r’ on the target surface. Therefore, the values of all nodes, which are located inside the circle, change from ‘1’ to ‘0’, and value ‘0’ remains unchanged (Figure 2(b)). Value ‘0’ means that the node is peened. After each shot, the degree of coverage is calculated by Equation (3). If this ratio is less than 98%, an additional ball will impact the region area (Figure 2(c)) until this ratio is larger than 98%, so that the programme will stop and provide coordinates of all impacted balls and the final coverage of the process. (3)

Figure 2

A sequence of a new method: (a) an original target surface, and shot-peened surfaces after (b) first impact, and (c) first two impacts.

To validate the result of this newly introduced method to estimate the coverage of the shot peening process, a multiple-impact finite element method (FEM) model using a commercial FE analysis programme LSDYNA was developed. The target material in this research was set up as kinematic plastic with the mass of density ρ = 7800 kg/m³, a young modulus of elasticity E = 210 GPa and the initial yield stress σ_o = 1500 MPa. The shots used were assumed as rigid with two radii of 0.15 and 0.3 mm. The dimensions of the target material were 2 mm × 2 mm × 1.5 mm, and the shot-peened target area was 1 mm × 1 mm. The target material and the shots were meshed using an eight-node brick element with an element size of 0.04 mm. The dynamic coefficient between the shots and target is fixed at f = 0.1 [10]. In this research, the Cowper–Symonds law was employed to express the effect of strain rate on deformation process. The Cowper–Symonds law is shown in Equation (4). (4) in which σ_o is the static yield stress, C and p are constant parameters of material in the Cowper–Symonds relation. The values C and p of steel in this study are set at 2.1e + 11 and 3.3, respectively [10].

The boundary conditions imposed on the research model were as follows: fully constrained work piece bottom surface and freely constrained work piece surrounding and atop surface. This research focuses on the target material, so the shot was assumed to be a rigid body. It means that the effects of the plastic and elastic deformation were not considered for the shots in this research. The rigidity of shots was based on the fact that the yield strength and hardness of typical steel shots are required to be significantly higher than those of the target material [22]. In addition, the interaction between shots was ignored. It was also assumed in this study that the shots in the simulation have a perfectly spherical shape and the same velocity. The velocity was carried out from 30 m/s to 50 m/s.

Results and discussion

Figure 3 presents an example result of the introduced method, i.e. an indentation with r = 0.064 mm caused by the impact between a shot with R = 0.15 mm and target material of 1 mm × 1 mm at a velocity of 40 m/s. Figure 3(a) provides the result of locations of all shots and the coverage of 98.11% after peened with 311 shots. Figure 3(b) presents the coverage of target surface as a function of the number of shots. The curve is close to the Avrami curve when the single dimple area (πd²/4) is very small compared with the shot-peened target area (πD²/4). The ratio of the area, (d²/D²), is small; it means that the value of N is large.

Figure 3

(a) Coordinates of impact shots employed to obtain a coverage of 98%, and (b) dependence of degree of coverage on number of shots.

In this method, the random function was used to generate the position of shots including the number of shots and their locations and the degree of coverage varied with different repeated runs. For example, R = 0.15, v = 40 m/s, the number of shots required to get the coverage of 98.11%, 98.05%, 98.03%, 98.12% and 98.01% in five consecutive repeated runs are 311, 309, 315, 314 and 310, respectively. It is worth to note that the difference in the number of shots required to obtain a coverage of 98% in different consecutive repeated runs becomes more significant with the large ratio of (d/D)².

A practical shot peening process is a random process; thus, the number of shots used to achieve the full coverage in one unit of the surface target area is a random number followed by the standard normal distribution. Hence, it is a missing in the Kirk and Abyaneh's model e.g. Equation (2) provides only one result. Therefore, the result of Equation (2) becomes accurate only when N is sufficiently large. In that case, the value of N is approximately equal to the mean value μ of the standard normal distribution. It can be seen that if the number of shots N is sufficiently large, the Kirk and Abyaneh's model based on the Avrami's equation is approximately equal to the mean value μ of the standard normal distribution, so there is an agreement in the Kirk and Abyaneh's model with the result of this proposed method. Figure 3 shows this comparison.

However, in the case of the number of shots N is small, the Kirk and Abyaneh's model is not accurate. For example, a shot with a diameter of 1.2 mm was employed to impact the material at a velocity of 115 m/s. The single indentation was formed on the surface of the material with a diameter of 0.58 mm. Equation (2) provides the result of N = 15 impacts to achieve the full coverage of 98% in the unit of 1 mm². It can be concluded that this result is not accurate. Figure 4(a–f) displays the number of shots and their coordinates to obtain the full coverage of 98% in six consecutive repeated runs using this proposed method. It shows that 23, 24, 20, 14, 17 and 26 impacts were employed to achieve coverage of 100%, 98.30%, 99.98%, 99.24%, 98.82% and 99.89%, respectively. The comparison presents that there is a large difference in six consecutive repeated runs due to the random function of the shot peening process. Figure 4(g) illustrates a dependence of coverage on the number of shots of the Kirk and Abyaneh's model and six consecutive repeated runs of the proposed method. The figure presents the coverage of target surface as a function of the number of shots. Increasing the number of shots results in the increment of shot-peened coverage. However, the proposed curves are the same trend but not close to the Avrami curve.

Figure 4

(a–f) Coordinates of impact shots employed to obtain a coverage of 98% in six consecutive repeated runs (a–f), and (g) dependence of degree of coverage on number of shots.

To investigate the effect of full coverage of shot peening process, the result of the new proposed method was applied in the multiple-impact model. In the random multiple-impact model presented in Figure 5, multiple shots were impacted onto the surface of a kinematic plastic model. The effects of coverage, shot velocity and shot radius on the distribution of residual stress and surface roughness of target material under different process conditions were investigated.

Figure 5

Finite element model of multiple-shot impacts.

The effects of the coverage on residual stress of target material were examined and displayed in Figure 6. Multiple shots with radius R of 0.3 mm impacted the target material at a velocity of 50 m/s. Figure 6(a–c) display that, on the plane y = 0, the compressive zone becomes slightly deeper, when the coverage increases from 100% to 300%. The number of shots employed to obtain coverage of 100%, 200% and 300% was 69, 137 and 208, respectively. Figure 6(d) presents the distribution of the average residual stress along z direction on the target peened area. The maximum value of compressive residual stress in case of a coverage of 100% is −1.15 GPa which is smaller than −1.40 GPa achieved in case of a coverage of 300% (Figure 6(d)). Moreover, the compressive stress zone enhances clearly with the improvement of coverage. The simulation results in this research present that increasing the coverage is an effective approach to obtain a higher compressive residual stress in the target material [23].

Figure 6

Residual stress distribution: (a) on plane y = 0 at a coverage of 100%, (b) on plane y = 0 at a coverage of 200%, (c) on plane y = 0 at a coverage of 300% and (d) average residual stress along z direction on the target area at different coverage degrees.

The effect of the velocity of shots with R of 0.3 mm was examined in the multiple-impact model using velocities of 30, 40 and 50 m/s. The dimension of the indentation caused by each single-shot increases with the increase of shot velocity; therefore, shots 82, 73 and 69 need to be used to achieve the required coverage of 98% in the velocities. Figure 7(a–c) illustrate that the increase of velocity increases the compressive residual stress region. Figure 7(d) shows that the largest value of compressive residual stress caused at a velocity of 50 m/s would be higher than that of the one caused by a velocity of 30 m/s. In addition, the compressive stress zone increases from 0.125 mm to 0.200 mm when the velocity of shot increases from 30 m/s to 50 m/s. Therefore, the result illustrates that increasing the velocity of shots is an effective approach to obtain deeper compressive stress zone in the target material. Comparing this result with the research of Meguid et al. [22,24] and Majzoobi et al. [10], a good agreement of the effect of velocity on the distribution of residual stress on the shot-peened material is achieved.

Figure 7

Residual stress distribution: (a) on plane y = 0 at a velocity of 30 m/s, (b) on plane y = 0 at a velocity of 40 m/s, (c) on plane y = 0 at a velocity of 50 m/s and (d) average residual stress along z direction on the target area at different velocities.

The effect of the size of shots was studied by applying two different radii of shots of 0.15 mm and 0.3 mm. In this section, the velocity of the shot was 50 m/s. The size of the dimple formed by each single impact increased when the size of shots was increased; therefore, the number of shots employed to obtain a full coverage were 311 and 69 for the shot radii of 0.15 and 0.3 mm, respectively. The compressive residual stress region after shot peening is wider and deeper for the larger shot radius due to the higher impact energy of the shots (Figure 8). The result suggests that increasing the shot size is an effective approach to obtaining a higher compressive residual stress and deeper compressive residual stress zone in the target material [24].

Figure 8

Residual stress distribution: (a) on plane y = 0 at a shot radius of 0.15 mm, (b) on plane y = 0 at a shot radius of 0.3 mm and (c) average residual stress along z direction on the target area at a velocity of 50 m/s.

The above results also suggest that a larger shot size can induce higher compressive stress in the sub-surface of the target material. However, it has been previously mentioned that a smaller shot size can result in a more uniform compressive residual stress distribution and a smoother target surface finish. Therefore, it is possible to use two different sizes of shots for double-shot peening to obtain their combined effects. The target material after shot peening with large shots of 0.3 mm in radius at a velocity of 50 m/s for 100% coverage was shot peened using smaller shots of 0.15 mm in radius at a velocity of 30 m/s (DP1) and 50 m/s (DP2) for 100% coverage. Figure 9 shows that consecutive second-shot peening with the smaller shots of 0.15 mm in radius slightly lowers the maximum value of the compressive residual stress, but does not affect the depth of compressive zone obtained after first shot peening of the target material with the larger shots of 0.3 mm in radius. However, the compressive residual stress becomes more uniform and the surface profile looks smoother after the double-shot peening process [20,21].

Figure 9

Residual stress distribution on plane y = 0:(a) shot peening with shots of 0.3 mm in radius, (b) double-shot peening with a velocity of second shot of 30 m/s, (c) double-shot peening with a velocity of second shot of 50 m/s and (d) average residual stress along z direction on the target area.

In conclusion, the shot peening process can significantly enhance the fatigue life of the metallic parts due to the introduction of the compressive stress into the sub-surface of the material [5]. The compressive stress can prevent the initiation crack as well as a simultaneous crack growth [25]. Shot peening process has been widely used in industries ranging from aerospace to construction with up to 75% of components in aeroplane engines being subjected to shot peening [26,27]. Bagherifard et al. [28] indicated that the shot peening process can improve the fatigue life for the treated samples but also create the high surface roughness of the material surface. The roughness has a negative effect which reduces the fatigue life of the material. Therefore, the increase of shot peening velocity (by applying a higher shot peening pressure), media size or shot peening time can increase the residual compressive stress in the treated material which results in the increment of the fatigue life. However, this increased trend of these operating parameters also causes a negative effect on the treated material. The rougher surface becomes the preferable conditions for the initiation of the micro-cracks on the surface of the material so it reduces the fatigue life of the shot-peened samples. As a result, to maximise the benefits of the shot peening process, the operating parameters need to be investigated and selected wisely.

Conclusion

A new approach was introduced to estimate the number of shots and their arrangements in order to obtain the desired coverage. This method could provide the number of shots, and their coordinate positions required to obtain full coverage. Based on the new approach, multiple-impact model of the shot peening process was studied using a finite element simulation. The simulation results suggested that increasing the coverage, shot velocity and shot size were effective approaches to obtain a higher level of compressive residual stress and deeper compressive stress zone in the target material. In addition, the simulation results also suggested that it was possible to apply the smaller shots after peening the target material with the large shots. The double-shot peening simulation results showed that the smaller shots reduced slightly the compressive residual stress previously induced by the larger shots but did not affect the depth of the compressive stress zone. The second-shot peening process could be used in small intensity, in that case, double-shot peening was considered as a low-cost simple method for improving the surface finish of the shot-peened components.

Footnotes

Disclosure statement

No potential conflict of interest was reported by the authors.

References

Baiker

Shot peening: a dynamic application and its future. 4th ed. Metal Finishing News; 2014. Available from: http://www.mfn.li/books/

Elias

, Lima

JHC

, Da Silva

, Titanium dental implants with different morphologies. Surf Eng. 2002;18(1):46–49. doi: 10.1179/026708401225001200

Kaysser

Surface modifications in aerospace applications. Surf Eng. 2001;17(4):305–312. doi: 10.1179/026708401101517926

Zhan

, Xie

, Jiang

, Thermostability of S30432 shot peened surface layer. Surf Eng. 2013;29(1):61–64. doi: 10.1179/1743294412Y.0000000070

Bagheri

, Guagliano

Review of shot peening processes to obtain nanocrystalline surfaces in metal alloys. Surf Eng. 2009;25(1):3–14. doi: 10.1179/026708408X334087

Závodská

, Guagliano

, Bokuvka

, Effect of shot peening on the fatigue properties of 40NiCrMo7 steel. Manuf Technol. 2016;16(1):295–299.

Trško

, Guagliano

, Lukáč

, Effects of severe shot peening on the surface state of AW 7075 Al alloy. Kovove Mater. 2015;53(4):239–243.

Murugaratnam

, Utili

, Petrinic

A combined DEM-FEM numerical method for Shot Peening parameter optimisation. Adv Eng Softw. 2015;79:13–26. doi: 10.1016/j.advengsoft.2014.09.001

Ghasemi

, Hassani-Gangaraj

, Mahmoudi

, Shot peening coverage effect on residual stress profile by FE random impact analysis. Surf Eng. 2016;32(11):1–10. doi: 10.1080/02670844.2016.1192336

10.

Majzoobi

, Azizi

, Nia A

Alavi.

A three-dimensional simulation of shot peening process using multiple shot impacts. J Mater Process Technol. 2005;164–165:1226–1234. doi: 10.1016/j.jmatprotec.2005.02.139

11.

Schiffner

, Droste

, Helling

Simulation of residual stresses by shot peening. Comput Struct. 1999;72(1):329–340. doi: 10.1016/S0045-7949(99)00012-7

12.

Klemenz

, Schulze

, Rohr

, Application of the FEM for the prediction of the surface layer characteristics after shot peening. J Mater Process Technol. 2009;209(8):4093–4102. doi: 10.1016/j.jmatprotec.2008.10.001

13.

Kang

, Wang

, Platts

Multiple impact modelling for shot peening and peen forming. Proc Inst Mech Eng B J Eng Manuf. 2010;224(5):689–697. doi: 10.1243/09544054JEM1672

14.

Kim

, Lee

, An area-average approach to peening residual stress under multi-impacts using a three-dimensional symmetry-cell finite element model with plastic shots. Mater Des. 2010;31(1):50–59. doi: 10.1016/j.matdes.2009.07.032

15.

Klemenz

, Hochrainer

, Delonnoy

, Similarity rules for the shot peening process based on finite element simulations. Proc Int Conf Shot Peen ICSP. 2005;ICSP-9:94–99; Doc ID: 2005057.

16.

Bagherifard

, Ghelichi

, Guagliano

On the shot peening surface coverage and its assessment by means of finite element simulation: a critical review and some original developments. Appl Surf Sci. 2012;259:186–194. doi: 10.1016/j.apsusc.2012.07.017

17.

Miao

, Larose

, Perron

, On the potential applications of a 3D random finite element model for the simulation of shot peening. Adv Eng Softw. 2009;40(10):1023–1038. doi: 10.1016/j.advengsoft.2009.03.013

18.

Bagherifard

, Ghelichi

, Guagliano

A numerical model of severe shot peening (SSP) to predict the generation of a nanostructured surface layer of material. Surf Coat Technol. 2010;204(24):4081–4090. doi: 10.1016/j.surfcoat.2010.05.035

19.

Kirk

, Abyaneh

MY.

Theoretical basis of shot peening coverage control. Shot Peen. 1995;9(2):5–7.

20.

Vielma

, Llaneza

, Belzunce

FJ.

Effect of coverage and double peening treatments on the fatigue life of a quenched and tempered structural steel. Surf Coat Technol. 2014;249:75–83. doi: 10.1016/j.surfcoat.2014.03.051

21.

Scuracchio

, de Lima

, Schön

CG.

Role of residual stresses induced by double peening on fatigue durability of automotive leaf springs. Mater Des. 2013;47:672–676. doi: 10.1016/j.matdes.2012.12.066

22.

Meguid

, Shagal

, Stranart

JC.

3D FE analysis of peening of strain-rate sensitive materials using multiple impingement model. Int J Impact Eng. 2002;27(2):119–134. doi: 10.1016/S0734-743X(01)00043-4

23.

Prevéy

, Cammett

JT.

The effect of shot peening coverage on residual stress, cold work and fatigue in a Ni-Cr-Mo low alloy steel. Proc Int Conf Shot Peen. 2002;ICSP-8; Doc ID: 2002038.

24.

Meguid

, Yang

, Zhuo

, 3D FE analysis of shot peening of strain-rate sensitive materials accounting for multiple and repeated impingement. Paper presented at: 13th International Conference on Fracture 2013, ICF 2013, 2013.

25.

Schijve

Fatigue of structures and materials. Dordrecht : Springer Netherlands; 2009.

26.

Shaw

, Tian

J-W

, Ortiz

, A direct comparison in the fatigue resistance enhanced by surface severe plastic deformation and shot peening in a C-2000 superalloy. Mater Sci Eng A. 2010;527(4–5):986–994. doi: 10.1016/j.msea.2009.10.028

27.

Gharbi

, Sghaier

, Al-Fadhalah

, Effect of ball burnishing process on the surface quality and microstructure properties of aisi 1010 steel plates. J Mater Eng Perform. 2011;20(6):903–910. doi: 10.1007/s11665-010-9701-6

28.

Bagherifard

, Guagliano

Fatigue behavior of a low-alloy steel with nanostructured surface obtained by severe shot peening. Eng Fract Mech. 2012;81:56–68. doi: 10.1016/j.engfracmech.2011.06.011