Surface & Coatings Technology 206 (2012) 3981–3988

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Surface & Coatings Technology

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A 3D FE model for evaluation of peening residual stress under angledmulti-shot impacts

Taehyung Kim a, Hyungyil Lee b,⁎, Minsoo Kim c, Sunghwan Jung 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 Doctorial Course, Department of Mechanical Engineering, Sogang University, Seoul, Republic of Koread Department of Mechanical Engineering, Dankook University, JukJeon, Republic of Korea

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

0257-8972/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.surfcoat.2012.03.078

a b s t r a c t

a r t i c l e i n f o

Article history:Received 1 September 2011Accepted in revised form 27 March 2012Available online 4 April 2012

Keywords:Angled impactPeening residual stressFinite element modelMulti-shots

The finite element (FE) model for shot peening often assumes that shots impact vertically on the engineeringparts to generate compressive residual stresses. However, the shots obliquely impact on the surface in actualpeening. In this work, we propose a 3D FE model for evaluation of residual stress resulting from angled shotpeening. Using the present FE model for angled multi-shot impacts, we examine the effects of factors such asimpact angle, impact pattern and the number of shots. Plastic deformation of shot is also considered. Tovalidate the model, we then compare the FE solution with experimental results by X-ray diffraction (XRD).The model will serve as a base of 3D multi-impact FE model for various incidence angles.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

The shot peening process produces compressive residual stress byimpact of numerous shots on the surface of themetallic materials, whichtransmits the impact energy to the materials. The shot peening helps toimprove durability and reduce corrosion of the parts and is widelyadopted in the automobile, power generation and aerospace industries.Because the evaluation of the compressive residual stress by peeningis directly related to the evaluation of durability and reliability, itssignificance is increasingly stressed and thus has extensive potential fordevelopment. Generally, the experimental solution of the peeningresidual stress slightly varies with the measurement methods [1,2] andenvironment, and the measurement entails much time and cost. Therehave been attempts to project the peening residual stress solution withtheoretical approaches to solve the issue. Al-Obaid [3]made a theoreticalapproach to predict the impact energy by engaging static analysis on shotpeening for description of the dynamic behavior. Al-Hassani [4], Al-Obaid[5], Hills et al. [6] explored the theoretical correlation between shotpeening residual stress and peening parameters. However, the theoret-ical approach cannot afford to consider the effect of stress interactionfrom multi-impacts in the actual shot peening process, interactionbetween peening parameters, various material properties and surfaceshapes. To overcome this, the evaluation of residual stress by finiteelement model was introduced [7–9].

82 2 712 0799.

rights reserved.

To conduct FE analyses for shot peening residual stresses, there havebeen proposed many FE models such as 2D indentation, 2D and 3Dsingle impacts, 3Dmulti-impact and 2D and 3D angled-impacts. Amongthem, the 2D axisymmetric FE model has been most frequently used,which mainly aims to describe the single shot impact on the surface ofelasto-plastic bodies. Some studies validated the 2D FE solution bycomparing it with the Hertzian solution for spherical indentation [10],experimental results [11]. Some studies considered the deformation ofshot and friction [12,13] and strain hardening of material [14], and adent produced by a single shot [15]. Those 2D FE models were furtherbeing refined for single-angled impact [16], and used as the base for 3Dmulti-shot impacts [17–22]. Among the issues introduced above, in thepresent work we focused our concern on the 3D FE model for angledmulti-shot impacts, and experimental validation of FE solution.

Bagherifard et al. [23] proposed a multi-random shot-peeningmodel, where elastic shots are chosen and shots are introduced in aconfined surface region. They investigated the vertical impact with themodel and subsequently verified the resultswith the XRD experimentalresults. Majzoobi et al. [20] also used the 3D FE model to simulate theactual peening process. Kim et al. [24,25] suggested the FE modelinvolving the single and multi-shot for quantitative evaluation of thepeening residual stress. However, these studies are limited by the idealof FE models involving vertical shot. In actual peening processes, theincidence angle of shot varies with the surface orientation rather thanremains vertical. The impact angle of shot is a significant factor inpredicting the shot peening residual stress and largely contributes tothemagnitude and distribution of the compressive residual stress of thematerial surface [26,27]. Baek et al. [28] conducted the 3D dynamicanalysis and examined the distribution of residual stress with each

Fig. 2. Impact types with shot sequences specified.

3982 T. Kim et al. / Surface & Coatings Technology 206 (2012) 3981–3988

respective incidence angle after the vertical and angled impacts. Miaoet al. [29] performed multi-random shots analyses and applied theanalysis result to their analyticalmodel. In themodel, the shotswere setwith rigid ball and angled at 60° and 90° measured from the surface.Furthermore, Hong et al. [16,30] investigated the residual stress afterthe angled single/multi-shot impact on the material surface of a 3D FEmodel. However, they only evaluated simulation results of the shotpeening residual stress states for various angles but excluded theexperimental verification. They also used rigid shot, ignoring thedeformation in the shot and did not account for the physical behavioralcharacteristics of the materials. It is necessary to study angled-shotimpact involving multi-shots in order to properly understand theeffects of peening. To the end,we utilized the factors of the shot peeninganalysis model from the study by Kim et al. [24,25] in order to correlatedistribution of peening residual stress with each respective incidenceangle. Moreover, in the present study the correlation between impactpattern and residual stress was integrated with the angled multi-shotimpact 3D FE model to make the present model adequately reflectactual shot peening process. In the end, the FE solution and XRDexperimental data are compared to verify the validity of the presentmodel.

2. FE model in 3D angled multi-shot impact and input properties

For the 3D angled multi-shot impact analysis, the commercial FEanalysis program called ABAQUS Version 6.7 [31] was used. TheNLGEOM (nonlinear geometry) option of the ABAQUS Explicit codewas used in the FE model to reflect the deformation of both shot andpeened material. The finite element mesh comprised of 3D 8-nodereduced integration elements (C3D8R). Fig. 1 shows the 3D angledmulti-shot-impact FE model comprised of 16 shots and materials. Theradius and height of the materials were set at 3 mm and 1 mm each,so that the effective stress after the impact fully vanishes at the backsurface of the materials. The FE material model would then readilysimulate multi-shot impact on a semi-infinite body. The plastic shotwas selected, allowing the deformation in the shot in order for the FEmodel to adequately demonstrate the actual peening process. Theshot velocity was set at v=55×103 mm/s. The spacing betweendents introduced by the shots S was fixed at the radius D/2(D=0.8 mm) to maximize stress interaction from multi-shot impact.

Fig. 1. Full view of FE model for angled multi-shot peening process.

For the boundary condition, the material bottom surface wascompletely restrained (Ux=Uy=Uz=0), and contact surface ele-ments were arranged on the surfaces of the shot ball and the materialto apply the penalty algorithm. The number of nodes is about 250,000(4 shots) to 500,000 (16 shots) and the number of elements is240,000 (4 shots) to 450,000 (6 shots) depending on the quantity ofthe plastic shot.

The material used in the present angled shot impact FE model wasAISI4340 because AISI4340 is often processed with shot peening. Thematerial was quenched from 815 °C and tempered at 230 °C for 2 h. Thetensile test provides the material properties after the heat treatment;yield strength σο=1510MPa, tensile strength στ=1860MPa, elasticmodulus E=205 GPa, Poisson's ratio ν=0.25 and density ρ=7.85×10−6 kg/m3. In this work, the power law formula (Boyce et al. [32]) forplastic strain was used, which is given as

_εp ¼ Dm

σ e _εp� �

σo−1

0@

1A

n

ð1Þ

where _εp is effective plastic strain rate; σe ( _εp) is effective stress for non-zero strain rate; σο is quasi-static yield strength. Here, the constants Dm

and n are 2.5×106 and 6 respectively [24].The properties of the shot ball for the present analysis use the ones

achieved from the tensile test on a SWRH 72Awirewith diameter equalto 3 mm, which is the material of CWRS (SCW/CW-32, SAE J441 [33]);yield strength σo=1470 MPa, tensile strength σt=1840MPa, whichbelongs in the range of in the SAE J441 standard between 1840 and2110 MPa, elastic modulus E=210 GPa, Poisson's ratio ν=0.3 andρ=7.85×10−6 kg/m3. The diameter D was set to 0.8 mm and theplastically deformable shot (PDS) was selected. The minimum size ofthe element, L, was set at 0.02 mm so that the surface and maximum

Table 1Measuring condition of residual stress [34].

X-ray diffraction ConditionX-ray source (target) Cr-Kα radiationGeometer ψ goniometerRegistration {221} diffraction linesAccuracy (Δσ) ±20 MPa

3983T. Kim et al. / Surface & Coatings Technology 206 (2012) 3981–3988

compressive residual stress solution is consistent. Besides, the dynamicfriction coefficient μ=0.3 was used, however rate independency (RI)was assumed so that the deformation speed was not considered [27].

Especially, in shot peening,when a shot impacts on thematerial, stresswaves propagate across thematerial. The stresswaves gradually diminishin amplitude with time as impact energy dissipates, and eventuallydisappear. In this study, the globalmaterial damping is taken into accountto allow the impact energy to dissipate in a shorter computational time. Inour 2D study [24], without damping, ξ=0, surface residual stress wasfound unstable with all shots, leading to longer computation time(tCPU=3.86×103 s) in PDS FE model. On the other hand, when

Cycles

-2

-1

0

1

1234

Multi, D=0.8mm, L=0.02mm, S=(D/2)mm=60 , v=55x103mm/s, RI, PDS, Case 1°

XRD

(a) Case 1

Cycles

-2

-1

0

1

1234

Case 2

σ x /σ

oσ x

/σo

XRD

(b) Case 2

Cycles

-2

-1

0

1

1234

Case 3

σ x /σ

o

XRD

(c) Case 3

Cycles

0.0 0.2 0.4 0.6-2

-1

0

1

1234

Case 4

σ x /σ

o

z / D

XRD

(d) Case 4

α

Fig. 3. Residual stresses with impact cycles at α=60°.

0.1≤ξ≤0.5, surface residual stresses become stable in the middle ofgiven time step. When ξ increases from 0.1 to 0.5, computation time isshorter. When ξ=0.5, the computation time is the shortest (tCPU=30 s).The value of ξ=0.5, giving the converged solution in a shorter time, isused in this analysis.

3. FE analyses for angled multi-shot impacts

3.1. Residual stress based on cycle and impact pattern

The cycle-repetition can be categorized into 1 (4 shots), 2 (8shots), 3 (12 shots) and 4 (16 shots) (the impact involving 4 shots istermed 1 cycle). From this the convergence of the peening residualstress with impact cycle can be determined. The impact locations ofshots are fixed all same. There are 4 impact patterns, as illustrated ingray arrows in Case 1–4 as shown in Fig. 2. The impact angle was setat α=60°, and the effect of the impact cycle was examined with theshot quantity. Here, the FE solution means the area-averaged solutionand well agrees with the experimental data. In this work, thecompressive residual stress induced by shot peening was measuredby the X-ray diffraction (XRD) method, using the Raystress equip-ment [34]. The surface layer of material was removed by electrolyticpolishing with a non-acid solution. Table 1 shows the conditions formeasuring the residual stress. Fig. 2 shows 4 impact patterns of themulti-shot. The impact patterns were categorized into 4 as were inCase 1–4, and the path of the order was marked in light coloredarrows. The impact order of 1-3-2-4 was marked in the black arrow,which is close to the one of the random impact from the multi-impactpeening residual stress analysis by Kim et al. [24,25]; the order of 1-3-2-4 results in the best convergence with the equi-biaxial residualstress state; the equi-biaxial residual stress state with the order alsobest matches the experimental data.

Fig. 3 demonstrates that the distribution of residual stress for eachimpact pattern evolves with cycle with α=60°. The distributions ofall the given patterns merge to one line after 2 cycles. Particularly, thedistribution for Cases 1 and 4 where all of the shots of each cycle are

Fig. 4. Impact types with shot sequences specified.

3984 T. Kim et al. / Surface & Coatings Technology 206 (2012) 3981–3988

directed toward the center of the material agrees best with the XRDexperimental data. The maximum compressive residual stress σmax

for Cases 1 and 4 matches the experimental data better than those ofCases 2 and 3. The depth zmax of σmax is also almost similar to theexperimental data. However, in overall the FE solution of the residualstress in the surface layer of material σsur is smaller than the XRDexperimental data. For the discrepancy with the surface residualstress to be resolved, the residual stress distribution of the analyticalmodel involving 4 cycles was examined with each pattern inconjunction with the multi-cycle angled impact orders, and theevolution of the stress solution of the residual stress on the surfacewas then predicted.

Case

-2

-1

0

α

α

α

α

1

1234

Multi, D=0.8mm, L=0.02mm, S=(D/2)mm=45 , v=55x103mm/s, RI, PDS, 4-Cycle °

XRD

1324/2413/3142/4231

(a) = 45°

Case

-2

-1

0

1

1234

=60°

σ x /σ

oσ x

/σo

XRD

(b) = 60°

Case

-2

-1

0

1

1234

=75°

σ x /σ

o

XRD

(c) = 75°

0.0 0.2 0.4 0.6-2

-1

0

1

XRDα = 90

=90°

σx /σ

o

z / D

°

(d) = 90°

α

α

α

α

Fig. 5. Residual stresses with the impact pattern of 1324/2413/3142/4231 for various cases.

3.2. Effect of incidence angle

The incidence angle was defined with respect to the materialsurface. The smaller incident angles (αb45°), at which the effect ofpeening is weak, was excluded and instead, α=45°, 60°, 75° and 90°(vertical impact) were considered. Also, four impact patterns wereselected to study evolution of the peening residual stress distributionbased on impact pattern. Fig. 4 shows redundancy with the impactorders, which can be eliminated. If 4 shots of impact is 1 cycle, then 16shotsmake up 4 cycles. The shots were introducedwith the order of thecycles designed in 1324/2413/3142/4231. The area-averaged residualstress solution after the impact was calculated, which engages the areaof (D/2)2 mm2, and verified with the experimental data.

Fig. 5 shows the residual stress distribution for the angledmulti-shotimpact of the given order of the impact patterns after 4 cycles areexecuted. At αb60°, most FE solutions were found to be different fromthe experimental solutions. At α≥60°, however, the FE solutions bettermatch the experimental data. This is due to the fact thatwith increasingα, the vertical component of the shot velocity increases, introducinggreater transmitted shot energy and thereby greater compressiveresidual stress at the impact. In such case, the FE solutions of Cases 1

A (mm2)

-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

Multi, D=0.8mm, L=0.02mm, 4Cycles =45 , v=55x103mm/s, RI, PDS, Case 1°

z / D

z / D

z / D

XRD

1324/2413/3142/4231

(a) = 45°

A (mm2)

0.0 0.2 0.4 0.6

0.0 0.2 0.4 0.6-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

=60°

XRD

(b) = 60°

A (mm2)

0.0 0.2 0.4 0.6-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

=75°

XRD

(c) = 75°

σ x /σ

oσ x

/σo

σ x /σ

o

α

α

α

α

α

α

Fig. 6. FE solutions and XRD solution for Case 1.

3985T. Kim et al. / Surface & Coatings Technology 206 (2012) 3981–3988

and 4 of the impact patterns are relatively similar to the experimentalsolutions, and the residual stress in surface layer of material σsur isalmost close to the experimental solutions. At α≥75° particularly, theFE solutions of Case 1 were closest to the experimental solution. On theother hand, Cases 2 and 3 of the impact patterns indicated that the FEsolution of the residual stress was closer to the experimental solution atα≥75°, but was yet quite different from the FE solutions of Cases 1 and4. Fig. 5(d) demonstrates that the analytical solutions of Case 1–4 of theresidual stress distribution for the vertical impact (α=90°) merge intoa single curve. In Fig. 5(c), it can be seen that the experimental data issimilar to all of the FE solution for α=75°. In conclusion, for Cases 1 and4 in the range of α ≥75°, with increasing incidence angle the peeningcompressive residual stress on the material surface increases to becloser to the experimental data.

4. Experimental verification of finite element solution

4.1. Area averaged peening residual stress solution

Generally, XRD provides the stress averages over the area, whichvaries in shape and size, inspected by X-ray. Boo et al. [35] achieved the

A (mm2)

-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

Multi, D=0.8mm, L=0.02mm, 4-Cycle =45 , v=55x103mm/s, RI, PDS, Case 2°

XRD

1324/2413/3142/4231

(a) = 45°

A (mm2)

-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

=60°

XRD

(b) = 60°

A (mm2)

0.0 0.2 0.4 0.6

0.0 0.2 0.4 0.6

0.0 0.2 0.4 0.6-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

=75°

XRD

(c) = 75°

z / D

z / D

z / D

α

α

α

α

α

α

σ x /σ

oσ x

/σo

σ x /σ

o

Fig. 7. FE solutions and XRD solution for Case 2.

XRDdata from the circular area ofmetalwith the diameter of 0.4 mmandHong et al. [36] achieved the XRD data from the area of 2 mm×7mm.Prevey and Cammett [37] characterized the relationship between shotpeening coverage and the area-averaged XRD data from the area of5 mm×5mm. Kirk and Hollyoak [38] achieved the area-averaged XRDdata of residual surface stress from the areas of 4 mm×4mm, 12 mm×1mm and 4 mm×1mm, respectively. The area-average concept used inXRD measurement was adopted in this study for consistency ofcomparison with the XRD data. The FE area-averaged peening residualstress solution refers to the averaged values of stresses from the nodesthat comprise a finite area. In this study, the averaged residual stresssolution was achieved with various areas and the relationship ofaveraged residual stress distribution with area engaged for the stressaveraging was examined.

Figs. 6–9 show the distributions of the FE solutions of the averagedresidual stress for various areas and various angles. The areas engagedfor the stress averaging were (D/4)2, (D/2)2 and (3D/4)2 mm2. The FEsolutions from (D/2)2 and (3D/4)2 mm2 showed similar residual stressdistribution, but the FE solutions from (D/4)2 mm2 is rather different.Furthermore, the FE solutions from (D/2)2 and (3D/4)2 mm2 at everyimpact pattern agrees better with the XRD experimental data than

A (mm2)

-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

Multi, D=0.8mm, L=0.02mm, 4Cycles =45 , v=55x103mm/s, RI, PDS, Case 3°

z / D

z / D

z / D

XRD

1324/2413/3142/4231

(a) = 45°

A (mm2)

-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

=60°

XRD

(b) = 60°

A (mm2)

0.0 0.2 0.4 0.6

0.0 0.2 0.4 0.6

0.0 0.2 0.4 0.6-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

=75°

XRD

(c) = 75°

σ x /σ

oσ x

/σo

σ x /σ

o

α

α

α

α

α

α

Fig. 8. FE solutions and XRD solution for Case 3.

3986 T. Kim et al. / Surface & Coatings Technology 206 (2012) 3981–3988

those from (D/4)2 mm2. Computation time to calculate the average ofthe node solutions varies with area engaged for averaging. In otherwords, (D/2)2 mm2 has fewer nodes than (3D/4)2 mm2 and thereforesolution averaging with (D/2)2 mm2 requires less time, suggesting thatsmaller areas are preferred for time saving. Of the given 4 impactpatterns, Case 1 agrees best with the experimental data. For time savingand the best consistency with the experimental data, the Case 1 impactpattern and the (D/2)2 mm2 area was chosen for the angled multi-shotimpact FEmodel. Fig. 10 shows the residual stress distribution for variousS (spacing between dents by the shots) with angled multi-shot impact.The FE analysis was conducted for S=D/2 and 3D/4 mm respectivelywith α=75°. After the analysis, the (D/2)2 mm2 area-averaged solutionswere compared with the experimental data. The (D/2)2 mm2 area-averaged solutions for S=D/2 mm were found much closer to the XRDexperimental solutions than for S=3D/4 mm. Based on the above-mentioned analysis, this study concludes that the analytical model withα=75°, S=D/2 mm, Case 1 and (D/2)2 mm2 area simulates shotpeening process in the most realistic manner. Thereby, we adopted theFE evaluation area of (D/2)2 mm2 area for our present analysis. Here,the area irradiated by X-ray and the area of (D/2)2 mm2 are notidentical. It is not easy to evaluate the impact behavior owing to

A (mm2)

-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

Multi, D=0.8mm, L=0.02mm, 4-Cycle =45 , v=55x103mm/s, RI, PDS, Case 4°

XRD

1324/2413/3142/4231

(a) = 45°

A (mm2)

-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

=60°

XRD

(b) = 60°

A (mm2)

0.0 0.2 0.4 0.6

0.0 0.2 0.4 0.6

0.0 0.2 0.4 0.6-2

-1

0

1

(D/4)2

(D/2)2

(3D/4)2

=75°

XRD

(c) = 75°

z / D

z / D

z / D

α

α

α

α

α

α

σ x /σ

oσ x

/σo

σ x /σ

o

Fig. 9. FE solutions and XRD solution for Case 4.

numerous experimental parameters in multi-impact. However, thisarea-averaging concept was successfully applied in our previous study[27] and had been recently adopted by other researchers [23,39,40].

4.2. The convergence of stress field to the equi-biaxial stress state

Generally, the peening residual stress state tends to graduallyconverge to equi-biaxial stress state, as multiple shots create multipleimpacts, producing uniform residual stress. Since the convergence tothe equi-biaxial stress indicates that the uniform compressiveresidual stress distribution is achieved, which is observed in actualpeening process, the convergence was examined in this study. In theanalysis, the aforementioned conditions (α=75°, v=55×103 mm/s,Strain rate independent (RI), PDS, 4 cycles [1324/2413/3142/4231])were set, and Cases 1 and 3 were selected as the impact patterns.In Fig. 11, it shows the residual stress created after the impact. ForCase 1, the distribution of σx and σz were very similar at 90° and closeto the perfect convergence, whereas both stresses for Case 3 weredifferent. This demonstrates that the FE model set with Case 1 wasthe most adequate for the analysis. Since the convergence to the equi-biaxial stress and the consistency with the XRD experimental data ofthe present FE model are both achieved, it is confirmed that thepresent FE model readily simulates angled multi-shot impacts.

4.3. Meaning of FE peening coverage in angled multi-shot impact

We apply the FE peening coverage for our present model. Theconcept of FE peening coverage was defined in our previous impactanalysis [24] where symmetry-cell was used and the effectiveness wasconfirmed by FE solutions. Peening residual stress depends on the areafraction of dent formed by multi-shot-impacts. The area fraction of dentis termed peening coverage denoted as C, and 100% of peening coverageC is called “full coverage”. The peening coverage generally exceeds 100%in shot peening application. Most prior FE studies overlooked thepeening coverage, or represented it simply with distance between

S (mm)

-2

-1

0

1

D/23D/4

Multi, D=0.8mm, L=0.02mm, =75o, PDS, v=55x103mm/s, RI, Case 1, 4-CycleA=(D/2)2mm2

°

z / D

XRD

1324/2413/3142/4231

S (mm)

0.0 0.2 0.4 0.6

0.0 0.2 0.4 0.6-2

-1

0

1

D/23D/4

A=(3D/4)2mm2

z / D

XRD

(b) A=(3D/4)2 mm2

(a) A=(D/2)2 mm2

σ x /σ

oσ x

/σo

α

Fig. 10. Residual stress distributions with shot spacing.

σx (MPa)+678

+228

-222

-673

-1123

-1573 x

z

σz (MPa)+658

+213

-233

-678

-1123

-1568 x

z

(a) Case 1

σx (MPa)+607

+189

-227

-644

-1061

-1478 x

z

σz (MPa)+715

+201

-313

-827

-1341

-1855 x

z

(b) Case 3

Fig. 11. Distribution of residual stresses σx and σz in (a) Case 1 and (b) Case 3.

3987T. Kim et al. / Surface & Coatings Technology 206 (2012) 3981–3988

centers of dents. Disregard of peening coverage left the prior FEsolutions far apart from the actual one. Peening coverage of morethan 100% represents multiples of full coverage. For example, 200% ofpeening coveragemeans the casewhere full coverage is repeated twice.

Fig. 12. Definition of FE coverages fo

Fig. 12(a) is regarded as the casewith 55% of peening coverage resultingfrom consecutive impacts by 4 shots. Fig. 12(b) corresponds to C=75%resulting from 12 shots (4 shots×3 cycle), (c) corresponds to C=85%from 16 shots (4 shots×4 cycle), and (d) corresponds to C=98% from24 shots (4 shots×6 cycle). In the initial state of impacts, the circulardents are apart from each other. But they overlap soon after subsequentimpacts are executed, resulting in gradual change in their shape andsize. The state of residual stress changeswith the degree of dent overlap,which is presented with peening coverage, which indicates that the FEpeening coverage should be taken as the main factor in the FE model.

4.4. Model verification with multi-shot peening materials

This section is dedicated to explore the validity of our FEmodelwiththe choice of peeningmaterial. Thematerials chosen included AISI4340,which was used in the previous analysis [27], AISI4140 and SPS8.AISI4140 was tempered for 2 h at 450 °C after being quenched from850 °C. The resulting material properties of AISI4140 after the heattreatment were as follows: yield strength at σο=1390MPa; tensilestrength at σt=1700 MPa; modulus of elasticity at E=210 GPa;Poisson's ratio at ν=0.28; and density at ρ=7.85×10−6 kg/m3. SPS8went through the vacuum-heat treatment after machining to preventoxidation and decarburization. It was quenched from 910 °C andtempered at 420 °C for 90 min. The material properties of SP8 afterthe heat treatment were as follows: yield strength at σο=1630 MPa;tensile strength atσt=1920MPa; modulus of elasticity at E=210 GPa;Poisson's ratio at ν=0.3; and density at ρ=7.85×10−6 kg/m3. Thepeening factors used the values obtained from the existing FE models[27] (set with Material: AISI 4340) except for the shot velocity v. TheXRD result of AISI4340 was measured with the arc height ofH=0.33 mm A and coverage of C=200% [34], which were achievedafter machining, while the experimental data of AISI4140 and SPS8were achieved after machining with H=0.26 mm A and C=100% [41],and H=0.37 mm A and C=85% [42] respectively. Generally, if theexperimental coverage is between 85≤C≤98%, it is considered as thetotal coveragemeaning that C is set to 100% for the FEmodel. Therefore, Cwas 100% for SPS8. v of AISI4140 and SPS8 models were 40×103 mm/sand61×103 mm/s respectively based on the equation of v=C1H–C2 [25].Fig. 13 indicates that the area-averaged solutions for all the chosenmaterials well agree with the XRD experimental data. For SPS8 inparticular, the FE solutions and the XRD experimental data were nearlyidentical with respect to the maximum compressive residual stress.

5. Concluding remarks

This study proposed the 3D angled multi-shot FE model. Theconvergence of the residual stress solution was demonstrated withshot quantity, impact angle and impact cycle. The evolution of theresidual stress solutions was explored with various impact patterns

r angled multi-impact analyses.

-2

-1

0

1

XRDArea averaged

AISI4140, D=0.8mm, L=0.02mm, =75=0.5, =0.3, RI, PDS, Case1

v=40x103mm/s

°

1324/2413/1423/4231

z / D

(H=0.26mmA, C=100%)

(a)

-2

-1

0

1

XRDArea averaged

AISI4340v=55x103mm/s

z / D

(H=0.36mmA, C=200%)

(b)

0.0 0.2 0.4 0.6

0.0 0.2 0.4 0.6

0.0 0.2 0.4 0.6-2

-1

0

1

XRDArea averaged

SPS8v=61x103mm/s

z / D

(H=0.37mmA, C=100%)

(c)

σ x /σ

oσ x

/σo

σ x /σ

oα

ξ μ

Fig. 13. FE solutions and XRD solution for (a) AISI4140 (b) AISI4340 and (c) SPSmaterials.

3988 T. Kim et al. / Surface & Coatings Technology 206 (2012) 3981–3988

and shot intervals. Base on the residual stress solutions, the optimalimpact angle and pattern were chosen which provides the equi-biaxial peening residual stress state. The area-averaged solution for(D/2)2 mm2 is best consistent with the XRD experimental data interms of the maximum compressive residual stress and the deforma-tion depth. It was also found that the area-average FE solutions were

well consistent with the experimental data for AISI4340, AISI4140and SPS8, supporting that the proposed FE model is insensitive to thechoice of material and thereby reflects actual shot peening process.

Acknowledgments

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

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