Surface & Coatings Technology 206 (2012) 3125–3136

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A 3D FE model with plastic shot for evaluation of equi-biaxial peening residual stressdue to multi-impacts

Taehyung Kim a, Hyungyil Lee b,⁎, Sunghwan Jung c, Jin Haeng Lee d

a Gas Turbine Technology Service Center, KEPCO Plant Service & Engineering Co., Incheon, Republic of Koreab Department of Mechanical Engineering, Sogang University, Seoul, Republic of Koreac Department of Mechanical Engineering, Dankook University, JukJeon, Republic of Koread Division for Research Reactor, Korea Atomic Energy Research Institute, Daejeon, Republic of Korea

⁎ Corresponding author. Tel.: +82 2 705 8636; fax: +E-mail address: hylee@sogang.ac.kr (H. Lee).

0257-8972/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.surfcoat.2011.12.042

a b s t r a c t

a r t i c l e i n f o

Article history:Received 13 May 2011Accepted in revised form 28 December 2011Available online 4 January 2012

Keywords:Symmetry-cellMulti-impactEqui-biaxial stressShot peeningResidual stress

A 3D multi-impact finite element (FE) model for evaluation of peening residual stress is presented. Combinedpeening factors by Kim et al. are applied to the 3D symmetry-cell originally contrived by Meguid et al. Todescribe the feature of multi-impacts, concepts such as FE peening coverage, impact sequence and cycle-repetition are introduced. We successfully extracted the equi-biaxial stress from the simulations of diversesingle-cycle and multi-cycle impacts. At four impact locations of FE symmetry-cell, surface and maximumresidual stresses converge to equi-biaxial stress, and convergence improves with the number of repetitionsof cycle. Impact velocity needed for comparing the FE solution with the XRD result is determined from theAlmen arc height and coverage. It is further found that the simulation set with plastic shot produces residualstress consistent with the experimental XRD result.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Shot peening technique is widely used to improve the fatigue lifeof mechanical parts producing compressive residual stress on thesurface. It is thus significant to evaluate the peening residual stresses,and achieve the intended durability. Key information on peeningresidual stress consists of surface residual stress,maximum compressiveresidual stress and deformed depth, all of which are largely determinedby peening conditions such as shot type and diameter, impact angle,exposure time, and peening coverage [3,4]. Peening residual stress isoften measured by experimental X-ray diffraction (XRD) [5–8].However, a substantial amount of cost and timemakes the XRD applica-tion troublesome in the field. For this reason, theoretical and analyticalapproaches were attempted in the evaluation of peening residualstress. Numerous studies using finite element (FE) analysis were alsoperformed to evaluate the peening residual stress. Al-Hassani [9], Hillset al. [10], and Al-Obaid [11] theoretically suggested the relationshipbetween shot peening parameters and residual stress. However, it isalmost prohibitive to theoretically predict the stress interference frommulti-impacts, and interaction among the peening parameters, variousmaterial properties and surface morphology. This leads the finiteelement (FE) analysis to be an advantageous tool in the evaluation ofpeening residual stress.

82 2 712 0799.

rights reserved.

Regarding FE analyses for shot peening residual stresses, there aremany FE models such as 2D indentation, 2D and 3D single impact, 3Dmulti-impact and 2D and 3D angled-impact. Among them, the 2Daxisymmetric FE model has been used longest, and mainly aims todescribe the single shot impact on the surface of elasto-plastic bodies.Some studies validated the 2D FE solution by comparing it with theHertzian solution for spherical indentation [12,13], experimentalresults [14]. Some studies considered the deformation of shot andfriction [15,16] and strain hardening of material [17], and a dentproduced by a single shot [18]. Those 2D FE models were furtherbeing refined for single-angled impact [19], and used as the base for3D multi-shot impacts [20–25]. Among the issues above, we focusedour concern on the FEmodel with kinematical factors of shot, materialcharacteristics, and experimental validation of FE solution.

In the early stages of FE analysis for peening, 2D single impact orindentation FE models were largely used. Follansbee et al. [26] andSinclair et al. [27] examined residual stress field of the host materialbased on FE analyses for quasi-static normal indentation with arigid sphere. Levers et al. [28] introduced compressive residual stresswith thermal load. Al-Obaid [29], and Schiffner and Helling [12]performed elasto-plastic dynamic analysis for normal impact of a singleshot. Meguid et al. [30] examined the effects of size and shape of shotand the shot velocity for impact of a rigid shot via 3D FE analysis. Hanet al. [31] performed 3D dynamic analysis combining finite elementand discrete element (DE) for normal impact of a single shot. Thoseprior FE approaches presumed the single-shot-impact to be 100%peening coverage on the peened surface, and accordingly, stress inter-ference by multi-shot-impacts was excluded.

Fig. 1. Impact positions of 7 shots and position (P1) for stress evaluation in a basic FE model.

3126 T. Kim et al. / Surface & Coatings Technology 206 (2012) 3125–3136

Hence, somemulti-impact FE analyseswere carried out to simulatethe peening process in a more actual manner including the effect ofstress interference. Guagliano [20] derived the relationship betweenarc height of Almen strip and peening residual stress via FE analysesfor arbitrary multi-impacts. Han et al. [21] extended their singleimpact analysis to multi-impact analysis for peen-forming processwith combined finite and discrete elements. Kim et al. [32] set thepeening coverage as central distances between shot balls in the 3Dmulti-impact analysis. Those FE analyses for arbitrary multi-impacts,however, could not provide homogeneous equi-biaxial residual stresson the peened surface. Meguid et al. [2] and Majzoobi et al. [23]contrived a 3D symmetry-cell FE model for multi-impacts to achievelocation free residual stress. They used rigid or elastic shots in thesimulation, but they excluded plastic deformation of shot ball, whichis however crucial in extracting the proper residual stress. Further,they neither checked the convergency to equi-biaxial stress norcompared it with experimental result. Overall, the prior 2D and 3D FEworks examined the effect of an individual set of peening parameterswithout any systematic integration of the physical response of materialand the kinematical peening factors.

Recently, FE peening analyses have been widely studied for multi-random impact. Miao et al. included additional computation in theirmulti-random shots analyses and applied the analysis result to theiranalytical model [33]. In the model of Miao et al., the shots set withrigid ball and angled at 60o and 90o, respectively involved a limitedsurface area. However, the model has not been experimentallyverified. Bagherifard et al. [34] proposed a multi-random shot-peeningmodel, where elastic shots are chosen and shots are introduced in a

Fig. 2. Deformed shapes of dents with var

confined surface region, and they investigated the vertical impactwith the model and subsequently verified the results with the XRDexperimental results. However, in all of the previous works the impactregions were confined so that randomness in multi-shots was onlylimitedly achieved. Thus, randomness in multi-shot simulationsremained yet to be properly addressed. To the end, previously weaddressed randomness in conjunction with various possible impactsequences instead of actually expanding the impact area in the simulationset-up.We proposed to construct a 3D FEmodel (named Symmetry-cell)bounded by four symmetry planes enabling the simulation of large-surface peening. Various possible impact sequences were studied usingthe FE model and the optimal impact sequence to best match theexperimental data was found based on the FE results. In addition, the FEmodel was assumed elastic–plastic material to realistically behave atthe impact (whereas the previous works used elastic shots). Using theFE model tuned with the optimal impact sequence and the shot ballmaterial characteristic, the accuracy of the shot peening predictions waslargely improved in comparison with those from the previous works.

In this study, we propose a 3D FE model (Symmetry-cell) forevaluation of peening residual stress resulting from multi-impacts.The integrated peening factors are applied to the 3D symmetry-cellcontrived by Meguid et al. [2]. To describe the feature of multi-impacts, concepts such as FE peening coverage, impact sequence andcycle-repetition are introduced. The role of plastic shot is alsodiscussed. We then obtain the homogeneous equi-biaxial stress withdiverse single-cycle and multi-cycle impacts. In the end, the residualstress solution of the 3D FEmodel (setwith the impact velocity achievedby using the Almen curve) is compared with the XRD result [35].

ious S and shot diameter D=0.8 mm.

Fig. 3. Comparison of residual stresses for various values of S after 7 multi-shot-impacts.

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2. Preliminary 3D FE analysis for multi-impact

2.1. FE modeling of multi-impact

We used the commercial FE analysis program ABAQUS Ver.6.5(2004) [36]. Fig. 1(a) shows a 3D FE model for preliminary multi-impact simulation, meshed with the 3D 8-node bilinear, reducedintegral element (C3D8R, ABAQUS Library). In shot peening, dentsare generated on material surface by continuous impacts, and thesub-surface region undergoes large deformation. To analyze largedeformation of elasto-plastic material, we adopted the NLGEOMoption in the ABAQUS Explicit code. The FE model consisted ofabout 169,000 nodes and 164,000 elements, and we fixed the bottomof the circular plate. We placed contact surfaces elements on contactareas of material and shot (Contact surfaces, ABAQUS Ver.6.5 (2004)[36]) and applied the penalty algorithm designed for dynamic contact/impact FE analyses [37–39]. Considering the capacity of shot peeningmachine [40], we set the initial shot velocity v to 75×103 mm/s.

Since shot peening process is commonly used to improve thesurface property of AISI4340, AISI4340 was chosen as the material

Fig. 4. Deformed shapes of dents

for the single impact FE model. The material was tempered for 2 hat 230 °C after quenching from 815 °C. Tensile test provided thematerial properties; yield strength σo=1510 MPa, tensile strengthσt=1860 MPa, elastic modulus E=205 GPa, Poisson's ratio ν=0.25and density ρ=7850 kg/m3. In this work, the power law formula[24] for plastic strain was used as

_εp ¼ Dm

σe _εp� �σo

− 1

0@

1A

n

ð1Þ

where _εp is effective plastic strain rate; σe( _εp) is effective stress fornon-zero strain rate; and σo is quasi-static yield strength. Here, theconstants Dm and n are 2.5×106 and 6 respectively [1].

The tensile test of SWRH 72A wire with diameter 3 mm, which isthe material of CWRS (SCW/CW-32, SAE J441 [41]), provides theproperties of shot ball; yield strength σo=1470 MPa, tensile strengthσt=1840 MPa, which is also included in the SAE J441 standard from1840 to 2110 MPa, elastic modulus E=210 GPa, Poisson's ratioν=0.3, density ρ=7850 kg/m3 and diameter D=0.8 mm. Three

with various impact cycles.

Fig. 5. Comparison of residual stresses for various impact cycles after 7 multi-shot-impacts.

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types of shot ball were used for the present FE analysis which arerigid shot (RS), elastic shot (EDS: elastic deformable shot) andelastic–plastic shot (PDS: plastic deformable shot) whereas onlyPDS was used in the preliminary analysis. For both the specimenand the shot, the incremental plasticity theory was applied in theanalysis, and the material was modeled as an isotropic elastic–plasticmaterial obeying J2 flow theory [42,43]. The friction coefficient μ=0.2and material damping coefficient ξ=0.5, which were suggested andused in our prior 2D work [1], were also applied to the present 3DFE model.

Fig. 6. FE symmetry-cell model for

2.2. Peening residual stress under multi-impacts for a single cycle andrepeated cycles

In the preliminary FE model (Fig. 1(a)), dents after 7 consecutiveshot-impacts are illustrated in Fig. 1(b), when S=0.4 mm for thegiven shot diameter D=0.8 mm. We denote the center shot bynumber 1,meaningfirst impact on the surface of specimen.Weevaluatethe residual stress distribution along with the vertical depth from thecenter impact location P1. Knowing that the residual stress from actualshot peening is in equi-biaxial stress state (σx=σz), we selected the

simulating multi-shot-impacts.

Fig. 7. Normalized equivalent stress distribution in FE symmetry-cell model.

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impact sequences of a single cycle as (1) 1–2–3–5–6–4–7 (assumed asrandom sequence) and (2) 1–2–3–4–5–6–7.

Fig. 2 illustrates that, for S=0.6, 0.5, and 0.4 mm, and Fig. 3 showsdistributions of residual stress σx for various values of S withsequences (1) and (2). In Fig. 3 d represents depth from surface,and “single” means the single shot. With S, surface and maximumcompressive residual stresses change clearly. Smaller S increases thestress interference between dents, producing residual stress muchgreater than that of the previous single impact.

Let one-cycle represent the 7 shot-impacts as shown in Fig. 1.Thereby n-cycle implies 7n impacts. Fig. 4 shows the shapes ofdents with various repeated impacts of 1–4 cycles for S=0.4 mmwith shot diameter D=0.8 mm. For one-cycle impact, dents areclear from one another. From 2 to 3 cycles, the dents graduallygrow, and then for 4-cycles, the size and shape of dent change dueto interference. As the impact energy is further transferred to thematerial surface, plastic deformation occurs to enlarge the dent.Fig. 5 shows the distributions of residual stress with depth from theP1 position at each cycle-repetition with sequence (1) and (2). Forboth sequences, the stress distributions are similar, but surface stres-ses are rather different. Residual stress distributions for 3 and 4 cyclesare almost identical. As the impact energy of each shot is transferredto the material surface, energy dissipation (= plastic deformation)capacity of material seems to get smaller and finally disappear.Those concepts of area fraction of dent (It is called FE peening

Fig. 8. Definition of FE coverages for g

coverage), impact sequence and cycle repetition are applied in thesymmetry-cell model described below.

3. 3D finite element analysis using symmetry-cell model

3.1. Symmetry-cell model

Fig. 6 shows a 3D FE model for multi-shot-impact peening analysis[2]. The left side simulates the shot peening where numerous shots,depicted by four rows, impact on the material surface. The gapbetween rows is equal, and each row remains horizontal. Shots offour rows impact on the material surface consecutively. The secondrow is set apart from the first row by the shot radius of R inx-direction. The third row is set apart in x and z-directions by R, andthe fourth row is set in z-direction by R, respectively. Such an arrange-ment provides the smallest gap between the shots without bumpinginvolved, achieving evenly spaced impacts. After impacts of fourrows, FE peening coverage C reaches 78% at any part of the materialsurface. With this observation, we extracted the smallest unit cellon which the symmetry-cell FE model is composed as shown in theright side of Fig. 6. The symmetry-cell FE model may serve as thewhole body being shot-peened.

The FE model was meshed with 3D eight-node reduced integralelements (C3D8R, ABAQUS Library) [36]. We fixed the bottom of thesymmetry-cell completely, and imposed symmetric displacementconditions on the four sides (Ux=0 or Uz=0). In shot peening,depending on the capacity of the peening machine, the shot velocityvaries from 20 to 100×103 mm/s [44,45]. Considering the capacityof shot peeningmachine used in [40], we set the initial impact velocity,v to 75×103 mm/s. The number of nodes and elements of the FEmodelwere about 16,000 and 14,000 for rigid shot. For elastic and plasticshots, the number of nodes is about 85,000 (4shots) to 100,000(16shots) and the number of elements is about 80,000 (4shots) to96,000 (16shots) depending on the quantity of shot. We used dynamicfriction coefficient μ=0.2 and material damping coefficient ξ=0.5,which were determined from the 2D single impact analysis [1].Especially, in shot peening, where a shot impacts the material, stresswaves propagate within the material. The stress waves graduallydiminish with time as impact energy dissipates, and eventuallydisappear. In this study, the global material damping is taken intoaccount to allow the impact energy to dissipate in a shorter computationaltime. In our 2D study, without damping, ξ=0, surface residual stress isunstable with all shots, leading to longer computation time. On the

iven shot diameter D=0.8 mm.

Fig. 9. Impact types with similar impact sequences in FE multi-impact symmetry-cell.

3130 T. Kim et al. / Surface & Coatings Technology 206 (2012) 3125–3136

other hand, when ξ=0.5, surface residual stress becomes stable in themiddle of given time step. The value of ξ=0.5, giving the convergedsolution in a shorter time, is used in this analysis.

We also determined the height h of symmetry-cell FE model fromFig. 7. The abscissa is the depth measured from the surface of

Fig. 10. Distribution of residual stresses

symmetry-cell, and the ordinate is equivalent stress normalized bythe yield strength of σo=1510 MPa. The letters A–D denote fournodal locations impacted by the shots on the surface of symmetry-cellas shown in Fig. 8. Since the stress vanishes at ~1 mm of distancefrom the surface, we set the height of FE model h to 1.5 mm.

for 4 impact sequences in Case 1.

Fig. 11. Identity of peening residual stresses for similar impact types of unit cycle.

Table 1Impact sequences with single/multi cycles.

Case Cycles (shots) Impact sequence

1

1 (04) (1–2–3–4), (2–1–4–3), (3–4–1–2), (4–3–2–1)4 (16) (1–2–3–4/2–1–4–3/3–4–1–2/4–3–2–1)×18 (32) (1–2–3–4/2–1–4–3/3–4–1–2/4–3–2–1)×216 (64) (1–2–3–4/2–1–4–3/3–4–1–2/4–3–2–1)×4

2

1 (04) (1–2–4–3), (2–1–3–4), (3–4–2–1), (4–3–1–2)4 (16) (1–2–4–3/2–1–3–4/3–4–2–1/4–3–1–2)×18 (32) (1–2–4–3/2–1–3–4/3–4–2–1/4–3–1–2)×216 (64) (1–2–4–3/2–1–3–4/3–4–2–1/4–3–1–2)×4

31 (04) (1–3–2–4), (2–4–1–3), (3–1–4–2), (4–2–3–1)4 (16) (1–3–2–4/2–4-1–3/3–1–4–2/4–2–3–1)×18 (32) (1–3–2–4/2–4–1–3/3–1–4–2/4–2–3–1)×216 (64) (1–3–2–4/2–4–1–3/3–1–4–2/4–2–3–1)×4

3131T. Kim et al. / Surface & Coatings Technology 206 (2012) 3125–3136

Generally, peening residual stresses are built on the surface andsub-surface. In the FE model, we placed fine mesh near the surfaceand center axis, and coarse mesh elsewhere. We then set theminimum element size L to 0.02 mm based on the prior study [1].Considering both the test error in XRD approach and the error inthe FE analysis involving dynamic contact, we evaluated stressconvergency at d=0.04 mm, which is 5% of the shot diameter (=d/D=0.04/0.8=0.05). Solutions of surface and maximum residual stressconverged for L/D less than 1/40 (see [1] for details).

3.2. Definition of FE peening coverage

Peening residual stress depends on the area fraction of dentformed by multi-shot-impacts. The area fraction of dent is termedpeening coverage C, and about 100% of peening coverage C is called

Fig. 12. Convergence to equi-biaxial str

“full coverage”. The peening coverage generally exceeds 100% inshot peening application. Most prior FE studies overlooked the peeningcoverage, or represented it simply with central distance between dents.Disregard of peening coverage left the prior FE solutions far apart fromthe actual one. Peening coverage of more than 100% is expressed withmultiples of full coverage. For example, 200% of peening coveragemeans the case where full coverage is repeated twice including thedent overlap. Here we only define FE peening coverage in symmetry-cell for example as shown in Fig. 8 to obtain a realistic stress solutionfor multi-impacts. Fig. 8(a) is regarded as the case with 55% peeningcoverage resulting from consecutive impacts by 4 shots. Fig. 8(b)corresponds to C=75% resulting from 12 shots (4 shots×3 cycles),(c) corresponds to C=85% from 16 shots (4 shots×4 cycles), and(d) corresponds to C=98% from 24 shots (4 shots×6 cycles). In theinitial state of impacts, the circular dents are apart from each other.However, they overlap soon after subsequent impacts are executed,resulting in gradually changing in their shape and size. The residualstress changes with the degree of dent overlap, which is explained inthe concept of peening coverage. To obtain the proper FE peeningsolution, the concept of FE peening coverage should be taken as themain factor in the FE model.

3.3. Dependency on the impact sequence

To apply the FE peening coverage to the 3D symmetry-cell FEmodel in Fig. 8, we set S to 0.4 mm (= shot radius R) in the followinganalyses. This is because the symmetries of cell and shot require S≥R,and the stress interference is at its maximum when S=R. Fig. 9illustrates six basic impact types. Each type is divided into four sub-types with respect to the position of first impact each unit cycle. Cases1 and 6 are the same since x and z axes are equivalent in equi-biaxial

ess in for 4-cycles with rigid shot.

Fig. 13. Convergence to equi-biaxial stress in for 4 cycles with elastic shot.

Fig. 14. Convergence to equi-biaxial stress in for 4 cycles with plastic shot.

3132 T. Kim et al. / Surface & Coatings Technology 206 (2012) 3125–3136

stress state. Only by 90° clockwise rotation of Case 6, Case 1 and Case 6would coincide. Similarly, Case 2=Case 5 and Case 3=Case 4.Therefore only 3 impact types remain independent.

The study aims to systematically define a sequence of analysisprocedure and achieve the uniform biaxial residual stress field ateach of the four impact locations of the symmetry-cell. We thusexamined the residual stress and its convergency for variousimpact sequences at locations A–D. The receptive stress fields atthe four points are adopted in the following steps to achieve theequi-biaxial stress field and then achieve node-averaged FEsolution.

Fig. 15. Convergence to equi-biaxial residual stress state with numb

Fig. 10 shows the distribution of residual stress for 4 types of unitcycle in Case 1. The rigid shot FE model was used without consideringany effect of strain rate. The residual stress distributions at impactlocations A–D appear different. However, if we do not differentiatelocations A–D, Fig. 10(a)–(d) are the same. Thus we may considerthe curves in Fig. 10(a)–(d) as location-free (LF) solutions. However,residual stress by actual peening is homogeneous, implying that fourcurves must converge to a single curve regardless of A–D locations.Fig. 11(a) shows that (σx of Case 1)=(σz of Case 6). Fig. 11(b)–(c)also demonstrates that Case 2=Case 5 and Case 3=Case 4. We cannow consider only Cases 1–3 below.

er of shot ball in (a) rigid and (b) elastic and (c) plastic shots.

Fig. 16. Experimental Almen saturation curves for estimation of peening intensity.

Table 3Numerical values of variables and coefficients of Eq. (3).

v (×103 mm/s) Bi C(%)

H(mmA)

ComputedH (mmA)

Error(%)

70 B1=−6.33×10−7

B2=6.60×10−4

B3=0.333

100200300400500

0.3870.4500.4770.4910.500

0.3930.4400.4740.4960.505

1.42.30.61.00.9

60 B1=−5.34×10−7

B2=5.98×10−4

B3=0.294

100200300400500

0.3420.4000.4230.4360.444

0.3480.3920.4250.4480.460

1.92.00.62.63.4

50 B1=−4.92×10−7

B2=5.34×10−4

B3=0.241

100200300400500

0.2860.3340.3590.3730.381

0.2890.3280.3570.3760.385

1.21.80.60.81.0

40 B1=−3.84×10−7

B2=3.98×10−4

B3=0.218

100200300400500

0.2400.2780.2940.3020.307

0.2440.2720.2930.3060.311

1.62.10.41.21.3

3133T. Kim et al. / Surface & Coatings Technology 206 (2012) 3125–3136

3.4. Effects of impact cycle-repetition

Peening residual stress gradually converges to an equi-biaxialstress state not by a single-cycle impact but by repeated impacts ofnumerous shots. In this section, we therefore examined the effect ofcycle-repetition with respect to its pattern and quantity to properlysimulate multi-impacts. Table 1 summarizes the impact sequencesfor multi-cycles of Cases 1–3. We grouped them as 1 (4 shots) cycle,and 4 (16 shots), 8 (32 shots), and 16 (64 shots) cycles. Figs. 12–14show the convergence to equi-biaxial residual stress state in the FEmodels for Cases 1–3 with 4 cycle impacts. Here, the strain ratesensitivity of the material is neglected. The stress convergency withmulti-cycle impacts is superior to that with single-cycle impacts.Convergency to equi-biaxial stress state (σx=σz) is found the bestwith Case 3. In contrast to the rigid and elastic shots, plastic shotgives the best convergence. To check the convergency to equi-biaxial

Table 2Numerical values of variables and coefficients of Eq. (2).

v (×103 mm/s) A t(s)

H(mmA)

ComputedH (mmA)

Error(%)

70 0.53 60120180240480720960

0.2760.3550.3900.4160.4780.5060.518

0.2530.3380.3890.4230.4870.5100.520

9.04.80.11.71.80.80.3

60 0.46 60120180240480720960

0.2480.3120.3360.3720.4110.4300.454

0.2120.2940.3380.3670.4230.4420.451

136.10.61.32.82.80.7

50 0.39 60120180240480720960

0.1850.2380.2740.3040.3400.3810.394

0.1860.2490.2870.3110.3580.3750.382

0.84.64.42.35.11.63.0

40 0.32 60120180240480720960

0.1430.1970.2350.2520.2750.2950.313

0.1530.2050.2350.2550.2940.3080.314

6.53.70.11.36.54.20.2

stress states in further detail, we involved 4, 8, and 16 cycles. Inother words, we set cycle-repetitions such as (4 cycles=16 shots),(8 cycles=32 shots) and (16 cycles=64 shots). Fig. 15 shows conver-gence of the residual stresses with the number of cycles for 3 types ofshots. As the cycle is repeated, the stress state converges toequi-biaxial state. The results achieved from shot peening tests withAISI4340 are likely inconsistent with the FE solutions of shot peeningfor a rigid or elastic shot. For 200% of the shot peening coverage whereenergy transfer to the material at the impact is considerable, discrep-ancy between the experimental data and the FE solutions withAISI4340 is more likely to appear. Since the plastic shotmodel demon-strates the best convergency, we selected Case 3 as the basic FEmodel.Note that here convergence to equi-biaxial stress state is used toassess the validity of randomly sequenced multi-impacts in the FEmodel. Strictly speaking, perfectly random multi-impact could not berealized using symmetry-cell because the shot-ball symmetry condi-tions would have to be met for the case where the shot balls impactthe top surface at the lines where the four symmetry sides intersectthe top surface of Symmetry-cell. However, whereas randomness isnot fully realized in the present analysis, improved consistency ofthe FE solution with the experimental data was achieved by tuning

Table 4Numerical values of variables and coefficients of Eq. (4).

C(%)

Ci H(mmA)

v(×103 mm/s)

Computedv (m/s)

Error(%)

100 C1=179.4C2=0.57

0.2400.2740.3420.387

40506070

42.548.660.868.9

5.92.91.31.7

200 C1 =153.4C2=0.82

0.2780.3340.4000.450

40506070

41.850.460.568.2

4.40.80.92.6

300 C1 =144.6C2=0.87

0.2940.3600.4230.477

40506070

41.651.260.368.1

3.92.30.52.8

400 C1=140.2C2=0.89

0.3020.3730.4360.491

40506070

42.853.162.270.1

6.55.83.50.2

Fig. 17. Variation of arc height H with peening with coverage C for various values of v.

Fig. 18. Variation of shot impact velocity v arc heights H for various values of C.

3134 T. Kim et al. / Surface & Coatings Technology 206 (2012) 3125–3136

the random sequence in multi-impacts and the number of cycles ofshots.

4. Experimental verification of finite element solution

We have introduced the concepts such as FE peening coverage,impact sequence and cycle-repetition in the FE model. Deformationof shot ball has been additionally considered. Fig. 16 shows themodified experimental Almen saturation curves by Kim et al. [1] forcalibration of peening intensity on the AISI4340 surface for the shotball of D=0.08 mm. The abscissa t represents the shot peening

Fig. 19. Residual stresses with 3 types o

time, and the ordinate H represents the arc height. After shot-peening on A-type Almen strip, we measured the curved height ofthe bent strip-A meeting the SAE J442 standard [46]. In our priorstudy [1], we derived Eqs. (2)–(4) from the experimental Almencurves to calculate the shot velocities. In the present study, theunits of the parameters in Eqs. (2) and (3) are corrected to be consis-tent, and Figs. 17-19 and Tables 2-4 from [1] are also corrected ac-cordingly.

Ht ¼ A 1−e−0:0454t0:65� �

ð2Þ

HC ¼ B1C2 þ B2C þ B3 ð3Þ

vH ¼ C1H−C2 ð4Þ

where A, B1, B2, B3, C1, and C2 are fitting coefficients [1]. Consideringthe capacity of peening equipment (Model: PMI-0608) [40] used inthis work, we set the limits of t (s), v (mm/s), and C (%), as0≤ t≤1000, 30000≤v≤80000 and C≥100 respectively. The XRD ex-perimental result was obtained from the specimen with coverage of200% and arc height of 0.36 mmA [35] to be used as the reference.In Eq. (4), for C=200%, the numerical coefficients C1 and C2 are153.4 and 0.82 respectively. Then, v is 55×103 mm/s by Eq. (3) setwith H=0.36 mmA. We input this value into our FE analysis, strainrate effect is ignored in the analysis. Fig. 19 shows convergency of sur-face and maximum compressive residual stresses for 3 types of shotswith Case 3. After the multi-impacts with four cycles, at the locationsof A–D in the symmetry-cell, surface and maximum compressive re-sidual stresses converge to equi-biaxial stress state. Especially, thebest convergence was achieved with plastic shot. Fig. 20(a) illustratesthat the plastic shot model agrees well with the XRD result in terms ofdistribution of residual stress. Here, the analytical solutions representthe average values of the results from the four nodal points of A–D.The difference between plastic shot FE solution and XRD result wasfully discussed in [47]. The convergence to equi-biaxial stress statein plastic shot is well demonstrated in Fig. 20(b). Relative deforma-tion rate and sensitivity at the impact varies among rigid, elastic,and plastic shot balls, all of which adopt the material properties ofAISI4340. Therefore, it can be argued that the resulting residual stressfield after the impact also varies on type of shot ball. The impact withthe plastic shot ball type produces the least deformation rate amongthe three types, which is due to the fact that the transferred energyto material is reduced by the amount of the kinetic energy consumedby the plastic deformation of the shot ball. In comparison with theXRD experimental data, the FE model using the plastic shot ball wasfound the most consistent, which demonstrates the validity of usingthe plastic shot ball for the present FE model.

f shot vs. cycle repetition in Case 3.

Fig. 20. (a) Comparison of stresses from FE and XRD (b) equi-biaxial stress by plastic shot.

3135T. Kim et al. / Surface & Coatings Technology 206 (2012) 3125–3136

Generally, XRD provides the stress averages over the area involvedby the X-ray inspection. Boo et al. [48] achieved the XRD data fromthe circular area of metal with the diameter of 0.4 mm and Hong etal. [49] achieved the XRD data from the area of 2 mm×7 mm. Preveyand Cammett [50] characterized the relationship between shot peen-ing coverage and the area-averaged XRD data from the area of5 mm×5 mm. Kirk and Hollyoak [51] achieved the area-averagedXRD data of residual surface stress from the areas of 4 mm×4 mm,12 mm×1 mm and 4 mm×1 mm, respectively. Since the presentXRD data are area-averaged, the nodal stress values from the presentmodel were averaged with the area accordingly and then comparedwith the XRD data. Fig. 21 illustrates the node sets of A–D and A–Iof the symmetry cell where the stress fields are computed. The stressvalues from the nodes are then averaged with the impact area. Eachof the average stress values from the model well agrees with theaverage value of the corresponding residual stress values collectedfrom the areas of I, II, and III, respectively (Fig. 21). Fig. 22 presentsthe average values involving the 4-node set and the 9-node setagainst the XRD data. The 9-node-averaged solutions better matchthe XRD data than the 4-node-averaged ones. Thus, these experimen-tal verifications demonstrate that the present symmetry cell is able toserve to realize random sequence multi-impact shot peening simula-tion: the multi-random shot peening analysis requires large impactarea to reflect the reality, but instead of actually expanding the

Fig. 21. Locations of 4 and 9 nodes for FE

impact area in the simulation set-up, the present FE model is opti-mized for random multi-shot simulation with a sequence of impactand an arrangement of the impact cycle. The present model is greatlysimplified by adopting impact sequence, yet efficiently realizes ran-dom sequence multi-impact shot peening process.

5. Concluding remarks

Using the 3D FE model designed for multi-impacts, we examinedresidual stress distributions with respect to FE peening coverage,impact sequence and cycle-repetition and integrated combinedfactors [1] with the symmetry-cell [2]. We defined FE peening cover-ages over 100% to simulate the actual peening coverage. For variouspatterns of unit impact cycle, the symmetry-cell generated the dis-similar stress distribution at the four impact locations. As the cycleis more repeated, the stress convergency to equi-biaxial stateimproves. The plastic shot FE model provided an equi-biaxial stressstate, which agrees well with the XRD experimental results [41]. Inaddition, the 9-node-averaged solutions are in better agreementwith the XRD experimental data than the 4-node based solution. Itis shown that the present symmetry-cell set with a plastic shotefficiently realizes multi-random shot peening process only with animpact area confined with the four symmetry planes.

averaged solution in symmetry-cell.

Fig. 22. Closeness to XRD solution for 4- and 9-node-averaged FE solution.

3136 T. Kim et al. / Surface & Coatings Technology 206 (2012) 3125–3136

Acknowledgment

The authors are grateful for the support provided by a grant fromthe Korea Research Foundation (Grant No. KRF-2008-D00017).

References

[1] T. Kim, H. Lee, H.C. Hyun, S. Jung, Mater. Sci. Eng., A 528 (2011) 5945.[2] S.A. Meguid, G. Shagal, J.C. Stranart, Int. J. Impact Eng. 27 (2002) 119.[3] C.M. Verport, C. Gerdes, Inst. Ind. Technol. Transfer Int., 1, 1989, p. 11.[4] R.P. Garibay, S.L. Terry, Inst. Ind. Technol. Transfer Int. 1 (1989) 227.[5] P.S. Song, C.C. Wen, Eng. Fract. Mech. 63 (1999) 295.[6] R.M. Menig, L. Pintschovius, V. Schulze, O. Vöhringer, Scr. Mater. 45 (2001) 977.[7] W. Luan, C. Jiang, V. Ji, Y. Chen, H. Wang, Mater. Sci. Eng., A 426 (2008) 374.[8] I.F. Pariente, M. Guagliano, Surf. Coat. Technol. 202 (3) (2008) 072.[9] S.T.S. Al-Hassani, Proc. of the 1st Int. Conf. on Shot Peening, 1981, p. 583.

[10] D.A. Hills, R.B. Waterhouse, B. Noble, J. Strain Anal. 18 (1983) 95.[11] Y.F. Al-Obaid, Mech. Mater. 19 (1995) 251.[12] K. Schiffner, C. Helling, Comput. Struct. 72 (1999) 329.[13] S. Baragetti, Int. J. Comput. Appl. Technol. 14 (1–3) (2001) 51.[14] C. Ould, E. Rouhaud,M. Francois, J.L. Chaboche,Mater. Sci. Forum524–525 (2006) 16.[15] E. Rouhaud, D. Deslaef, Mater. Sci. Forum 404–407 (2002) 153.[16] H.L. Zion, W.S. Johnson, Am. Inst. Aero. Astro. J. 44 (9) (2006) 1973.

[17] E. Rouhaud, A. Ouakka, C. Ould, J.L. Chaboche, M. Francois, Proc. of the 9th Int.Conf. on Shot Peening, 2005, p. 107.

[18] N. Hirai, K. Tosha, E. Rouhaud, Proc. of the 9th Int. Conf. on Shot Peening, 2005,p. 82.

[19] T. Hong, J.Y. Ooi, B. Shaw, Eng. Fail. Anal. 15 (8) (2008) 1097.[20] M. Guagliano, J. Mater. Process. Technol. 110 (2001) 227.[21] K. Han, D. Owen, D. Perić, Eng. Comput. 19 (2002) 92.[22] M.S. Eltobgy, M.A. Elbestawi, Proc. IME B J. Eng. Manufact. 218 (11) (2004) 1471.[23] G.H. Majzoobi, R. Azizi, N.A. Alavi, J. Mater. Process. Technol. 164–165 (2005)

1226.[24] S.A. Meguid, G. Shagal, J.C. Stranart, J. Eng. Mater. Technol. 129 (2) (2007) 271.[25] M. Zimmermann, V. Schulze, H.U. Baron, D. Löhe, Proc. of the 10th Int. Conf. on

Shot peening, 2008, p. 63.[26] P.S. Follansbee, G.B. Sinclair, Int. J. Solids Struct. 20 (1) (1983) 81.[27] G.B. Sinclair, P.S. Follansbee, K.L. Johnson, Int. J. Solids Struct. 21 (8) (1985) 865.[28] A. Levers, A. Prior, D. Socie, Multi-axial fatigue: Analysis and experiments, Society

of Automotive Engineers Inc., Warrendale, 1989, p. 16.[29] Y.F. Al-Obaid, Comput. Struct. 36 (1990) 681.[30] S.A. Meguid, G. Shagal, J.C. Stranart, J. Daly, Finite Elem. Anal. Des. 31 (1999) 179.[31] K. Han, D. Peric, D.R.J. Owen, J. Yu, Eng. Comput. 17 (6) (2000) 680.[32] T.J. Kim, N.S. Kim, S.C. Park, W.W. Jeong, Korea Soc. Mech. Eng. A 26 (12) (2002)

2656.[33] H.Y. Miao, S. Larose, C. Perron, M. Lévesque, Adv. Eng. Softw. 40 (10) (2009) 1023.[34] S. Bagherifard, R. Ghelichi, M. Guagliano, Surf. Coat. Technol. 204 (24) (2010)

4081.[35] M.A.S. Torres, H.J.C. Voorwald, Int. J. Fatigue 24 (2002) 877.[36] ABAQUS User's Manual, Version 6.5, Hibbitt, Karlsson and Sorensen, Inc., Paw-

tucket, RI, 2004.[37] F. Armero, E. Petocz, Comput. Meth. Appl. Mech. Eng. 158 (1998) 69.[38] D.R.J. Owen, E.A. De Souza Neto, S.Y. Zhao, D. Peric, J.G. Loughran, Comput. Meth.

Appl. Mech. Eng. 151 (1998) 479.[39] D.R.J. Owen, Y.T. Feng, E.A. De Souza Neto, M.G. Cottrell, F. Wang, F.M. Andrade

Pires, J. Yu, Int. J. Numer. Methods Eng. 60 (2004) 317.[40] Rotation Table Type Impeller Peening Machine (PMI-0608) User's Manual, Sae-

myung Shot Machinery Co., Inc., 2004[41] SAE J441, Cut wire shot, Society of Automotive Engineers, Inc., 2001[42] R. Hill, The mathematical theory of plasticity, Oxford University Press, London,

1998.[43] J. Davis, M. Ramulu, Proc. of 11th Int. Conf. Shot Peening, 2011.[44] W. Cao, R. Fathallah, L. Castex, Mater. Sci. Technol. 11 (9) (1995) 967.[45] R. Fathallah, G. Inglebert, L. Castex, 6st Int. Conf. on Shot peening, 1996, p. 464.[46] SAE J442, Test Strip, Holder and Gage for Shot Peening, Society of Automotive En-

gineers, Inc., 2004[47] T. Kim, J.H. Lee, H. Lee, S.K. Cheong, Mater. Des. 24 (2010) 877.[48] M.H. Boo, S.W. Oh, Y.C. Park, Y. Hirose, Study Ocean Technol. 8 (2) (1994) 105.[49] S.H. Hong, D.W. Lee, S.S. Cho, W.S. Joo, Int. J. Automot. Technol. 10 (6) (2002) 150.[50] P.S. Prevey, J.T. Cammett, Proc. of 8th Int. Conf. Shot Peening, 2002, p. 295.[51] D. Kirk, R.C. Hollyoak, Proc. of 9th Int. Conf. Shot Peening, 2005, p. 373.