a simple but effective fe model with plastic shot for evaluation of...
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Materials Science and Engineering A 528 (2011) 5945–5954
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Materials Science and Engineering A
journa l homepage: www.e lsev ier .com/ locate /msea
simple but effective FE model with plastic shot for evaluation of peeningesidual stress and its experimental validation
aehyung Kima, Hyungyil Leeb,∗, Hong Chul Hyunb, Sunghwan Jungc
Gas Turbine Technology Service Center, KEPCO Plant Service & Engineering Co., Incheon, Republic of KoreaDepartment of Mechanical Engineering, Sogang University, Seoul, Republic of KoreaDepartment of Mechanical Engineering, Dankook University, JukJeon, Republic of Korea
r t i c l e i n f o
rticle history:eceived 22 December 2010eceived in revised form 5 April 2011ccepted 7 April 2011vailable online 14 April 2011
a b s t r a c t
We propose a practical finite element (FE) model for evaluation of peening residual stress. The model aimsto produce a solution approaching the endeavored 3D FE solution. We investigate the effect of physicalfactors including material damping, dynamic friction and strain rate. The kinematical factors includingshot diameter and impact velocity are also considered. Integrating those factors and plastic shots, weset up an effective FE model. Based on the arc height and coverage matching with the Almen saturationcurve, impact velocity needed for FE analysis is determined. The model is found to provide the solution
eywords:hot peeningesidual stress
ntegrated factoringle impact-ray diffraction
comparable with the 3D multi-impact FE solution and the experimental XRD result.© 2011 Elsevier B.V. All rights reserved.
lastic shot
. Introduction
Shot peening is widely applied in automobile, power plantnd aerospace industries to improve the fatigue life of parts byroducing compressive residual stress on the metal surface. It
s thus important to evaluate residual stress for various peeningonditions. Peening residual stress is determined by the physi-al response of material to the kinematic features of shot. Thelmen saturation curves are customarily used both for the capac-
ty calibration of peening equipment and for the measurementf peening intensity. Specifically, for example, the peening cov-rage can be determined from the impact velocity by usinglmen arc height as a mediator. Residual stress by shot peen-
ng is often measured by experimental X-ray diffraction (XRD)1–4]. However, a substantial amount of cost and time makeshe XRD prohibitive in the field. For this reason, theoretical andnalytical approaches were attempted for the evaluation of peen-ng residual stress. Numerous studies using finite element (FE)nalysis were also performed to evaluate the peening residualtress.
Regarding FE analyses for shot peening residual stresses, therere many FE models such as 2D indentation, 2D and 3D singlempact, 3D multi-impact and 2D and 3D angled-impact. Among
∗ Corresponding author. Tel.: +82 2 705 8636; fax: +82 2 712 0799.E-mail address: [email protected] (H. Lee).
921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2011.04.012
them, the 2D axisymmetric FE model has been used longest, andmainly aims to describe the single shot impact on the surface ofelasto-plastic bodies. Some studies validated the 2D FE solutionby comparing it with the Hertzian solution for spherical indenta-tion [5,6], experimental results [11]. Some studies considered thedeformation of shot and friction [7,8] and strain hardening of mate-rial [9], and a dent produced by a single shot [10]. Those 2D FEmodels were further being refined for single-angled impact [12],and used as the base for 3D multi-shot impacts [13–18]. Amongthe issues introduced above, we focused our concern on the FEmodel with kinematical factors of shot, material characteristics, andexperimental validation of FE solution.
In the early stages of FE analysis for peening, 2D single impactor indentation FE models were largely used. Follansbee and Sin-clair [19] and Sinclair et al. [20] examined residual stress field ofmaterial by FE analyses of quasi-static normal indentation with arigid sphere. Levers and Prior [21] introduced compressive resid-ual stress with thermal load. Schiffner and Helling [5] performedelasto-plastic dynamic analysis for normal impact of a single shot.Meguid et al. [22] examined the effects of size and shape of shot andthe shot velocity via 3D FE analysis to study impact of a rigid shot.Han et al. [14,23] also performed 3D dynamic analysis using com-bined finite element and discrete element (DE) for normal impact
of a single shot. Boyce et al. [24] compared FE predictions of resid-ual stress with experimental result to investigate normal impactof a rigid shot on the surface of quasi-static and dynamic mod-els. Recently, some multi-impact FE analyses were carried out to
5946 T. Kim et al. / Materials Science and Engineering A 528 (2011) 5945–5954
nd equivalent strain in a deformed shot.
etreiasrewrdppipesairiepfi
fecvsawmtr
2
tM8es
Fig. 1. Plastic properties for FEA a
stimate the effects of stress interferences. Guagliano [13] derivedhe relationship between arc height of Almen strip and peeningesidual stress based on FE analyses of arbitrary multi-impacts. Kimt al. [25] tried to simulate the peening coverage by arbitrarily vary-ng the central distances between shot balls in the 3D multi-impactnalysis. Meguid et al. [26] and Majzoobi et al. [16] simulated thehot peening process with a 3D multi-impact symmetry-cell in aather methodical way. However, the prior 2D and 3D FE worksxamined the effect of an individual set of peening parameters, butere not to systematically integrate the physical response of mate-
ial and the kinematical peening factors. Moreover, those studiesid not consider the experimental Almen curve with arc height andeening coverage, which is essential in describing the real shoteening. The Almen curve is commonly used both for the capac-
ty calibration of peening equipment and for the measurement ofeening intensity of material. The meaning of curve thus reachesven the numerical approach to the evaluation of peening residualtress. Most of the above studies used only rigid or elastic shotsnd ignored the plastic deformation of shot. We will demonstraten this work that the plastic shot is essential in extracting the properesidual stress. Although providing accurate solutions, a multi-mpact 3D FE model (Kim et al. [25]), on the other hand, requiresxcessive computational time together with cumbersome pre- andost-processing, which makes the 3D approach prohibitive in theeld applications.
On this background, we propose a handy 2D impact FE modelor proper evaluation of peening residual stress. We examine theffects of material damping, dynamic friction and strain rate, andonsider kinematical factors including shot diameter and impactelocity. The role of plastic shot in the FE model is also demon-trated. We set up an operative FE model integrating those factorsnd plastic shots. Based on the arc height and coverage matchingith Almen curve, impact velocity needed for FE analysis is deter-ined. The residual stress prediction of 2D model is compared with
hat of 3D multi-impact FE model (Kim et al. [25]), and the XRDesult (Torres and Voorwald [27]).
. Finite element model for 2D single impact
In the analyses, the plastic material models were used both forhe AISI4340 material and for the cut wire rounded shot (CWRS).
aterial was tempered for 2 h at 230 ◦C after quenching from15 ◦C. Tensile test (Instron 4467) determined the following prop-rties of AISI4340 material: yield strength �o = 1510 MPa, tensiletrength �t = 1860 MPa, elastic modulus E = 205 GPa, Poisson’s ratio
Fig. 2. FE model for axisymmetric single impact.
� = 0.25 and density � = 7850 kg/m3. Tensile test of SWRH 72A wirewith diameter 3 mm, which is the material of CWRS, determinedthe properties of shot ball: yield strength �0 = 1470 MPa, tensilestrength �t = 1840 MPa, elastic modulus E = 210 GPa, Poisson’s ratio� = 0.3 and density � = 7850 kg/m3 and diameter D = 0.8 mm. Threekinds of shot ball were used for FE analyses: rigid shot (RS),elastic shot (EDS: elastically deformable shot) and elastic–plasticshot (PDS: plastically deformable shot). Both for the specimenand for the shot, the incremental plasticity theory was applied,and the material of the specimen and the shot is assumed to beisotropic elastic–plastic obeying the J2 flow theory. Fig. 1(a) is thetrue stress–strain curves normalized with their yield strengths ofAISI4340 and CWRS materials, and Fig. 1(b) shows equivalent straindistributions of plastic shot after impact.
In this analysis, we used a commercial FE analysis program,ABAQUS [28]. The true stress–strain curves in Fig. 1(a) were codedin the tabulated forms. Fig. 2 is a 2D axisymmetric FE model for sin-gle impact by using the axisymmetric four-node bilinear, reducedintegral element (CAX4R: ABAQUS [28]). In all FE simulations, wefully fixed the bottom of material model and imposed roller bound-ary conditions along axisymmetric axis. Considering the capacityof shot peening machine [29], we selected initial shot velocity as
v = 75 m/s. The penalty algorithm was applied to the contact ofmaterial and shot. The FE model consisted of approximately 3100nodes and 3000 elements.
T. Kim et al. / Materials Science and Engineering A 528 (2011) 5945–5954 5947
Fig. 3. Determination of the size of material FE model.
0.0 0.2 0.4 0.6
σx /σ
o
-2
-1
0
1
0.010.020.030.04
D=0.8mm, v=75m/s, PDS
L (mm)
0.04mm
3
Ftytnsc3tbtmdiiswtdo(pW
d (mm)
Fig. 4. Convergence of residual stresses for L.
. Verification of finite element model
From Fig. 3, we determined the proper radius r and height h of 2DE model in Fig. 2. The abscissa x is the distance from the impact cen-er axis into the radial direction along the surface, and the ordinate(=d) is the distance from the surface into depth direction along
he impact center axis. The ordinate of Fig. 3 is equivalent stressormalized with material yield strength (�o = 1510 MPa). As thetress by the impact vanishes at ∼2 mm of distance from the contactenter in both radial and vertical directions, the radius, r is set tomm and the height, h is set to 3 mm. The FE material model would
hen be able to simulate the single shot impact on a semi-infiniteody. Most residual stresses formed by shot peening remain onhe surface and in the sub-surface. In the FE model, we placed fine
esh near surface and center axis, and coarse mesh elsewhere. Toetermine the minimum element size L near the surface region, we
nvestigated the stress distributions in the impact region as shownn Figs. 4 and 5 engaging a plastic shot. This is the preliminary analy-is to reduce the error of FE solution near impact region. The stressesere normalized again by material yield strength. Considering both
he test error in XRD approach and the error in FE analysis due toynamic contact, we evaluated surface residual stress at the depth
f y = 0.04 mm as depicted in Fig. 4, which is of 5% of shot diameterd/D = 0.04/0.8 = 0.05). This was motivated by the surface etchingreceding the measurement of residual stress by XRD equipment.hen the element size gets smaller, the surface residual stressFig. 5. Determination of the element minimum size L.
changes from (−) to (+). Kobayashi et al. [30] also showed the (+)surface residual stress from the single impact experiment. Fig. 5shows that surface and maximum residual stresses converge whenL/D is less than 1/40. The minimum element size was thus selectedas L = 0.02 mm for the FE model. We note that our work focuseson the validity of analytical approach which provides the FE solu-tion well matching the experimental results rather than detailedcontact mechanics in the single impact.
4. Finite element analysis for single impact
4.1. Effects of material damping
In a dynamics system, energy is dissipated by frictions or othertypes of resistance, including damping, which always plays. Damp-ing includes material damping with energy dissipation in inner partof material, structural damping involving dissipation on boundarysurface, and fluid damping involving dissipation when the energypasses into the fluid [31,32]. In shot peening, where a shot impactsthe material, stress waves propagate within the material. The stresswaves gradually diminish with time as impact energy dissipates,and eventually disappear. In this study, the global material damp-ing is taken into account to allow the impact energy to dissipate ina shorter computational time. We note, however, that the globalmaterial damping bears no specific physical meaning. Rayleighdamping [26,31] with a mass proportional coefficient ˛ and a stiff-ness proportional coefficient ˇ was used in the form of Eq. (1). Thereare viscous and hysteretic damping models for material dampingfound in literature. Complex loading history and hysteresis depen-dency often limit the numerical expression of hysteretic damping[32]. On the contrary, material damping model adopts a simpleand linear numerical expression, thereupon it satisfies rheologi-cal analytic method and superposition principle to be used [31].This model is also easily described since it consists of rheologicalelements such as nonlinear spring and dash-pot [32]. Based on this,we selected the viscous damping model given as:
C = ˛M + ˇK (1)
C = 2ω◦�M (2)
ωo = �
2h
√E
�(3)
where C is the damping matrix, M is the mass matrix, K is the stiff-ness matrix, ωo is the initial frequency, � is the damping ratio (� < 1),and h is the height of FE model (Fig. 2). Again, E is the elastic mod-ulus and � is the density of material. Fig. 6 shows distribution of
5948 T. Kim et al. / Materials Science and Engineering A 528 (2011) 5945–5954
tewtiswsd0awoi[
.5X10-6 1X10-5 1.5X10-5 2X10-5
frictional force with time. For multi-shot-impacts, measuring fric-
Fig. 6. Material damping effects.
he converged residual stress for 0 ≤ � ≤ 0.5 from three shot mod-ls. Non-friction (� = 0) and strain rate independent (RI) conditionsere applied. Rigid shot [Fig. 6(a)] shows similar residual stress dis-
ributions when 0.3 ≤ � ≤ 0.5. Elastic shot [Fig. 6(b)] shows almostdentical distribution of residual stress when 0.1 ≤ � ≤ 0.5. Plastichot [Fig. 6(c)] merge to a curve for all damping ratios. From this,e selected damping ratio � = 0.5 for our FE model. Fig. 7 shows the
tabilization of surface residual stress at the impact center nodeuring the time period of 2 × 10 −5 s for three shot models for � = 0,.5. Without damping, � = 0, surface residual stress is unstable withll shots, leading to longer computation time. On the other hand,hen � = 0.5, surface residual stress becomes stable in the middle
f given time step. The value � = 0.5, giving the converged solutionn a shorter time, is used in 3D multi-impact FE analysis (Kim et al.25]), where computation time is crucial.
Fig. 7. Stabilization of surface residual stresses in FE shot models.
4.2. Effects of dynamic friction
Generally, coulomb friction coefficient varies with con-tact material types and lubrication condition. Naboulsi andNicholas [33] considered coulomb friction in the fretting FEmodel. Johansson [34] developed a numerical algorithm foranalysis of frictional impact of rigid bodies against rigidobstacles. He experimentally observed the difference betweenstatic and dynamic frictions, and demonstrated that both thealgorithm and experiment provided the similar variation of
tion coefficient is quite difficult and complex. In this study,measurement of dynamic friction coefficient is performed as fol-low.
T. Kim et al. / Materials Science and Engineering A 528 (2011) 5945–5954 5949
-2
-1
0
1
0.00.10.20.30.40.5
D=0.8mm, v=75m/s, L=0.02mm, =0.5, RIRS
µ
(a)
-2
-1
0
1
0.00.10.20.30.40.5
EDS
µ
(b)
d (mm)0.0 0.2 0.4 0.6
σσ/ x
oσ
σ/ xo
σσ/ x
o
-2
-1
0
1
0.00.10.20.30.40.5
PDS
µ
(c)
cma0d�fsvfstc
1.0 1.2 1.4 1.6 1.8 2.0
(sec
-1)
0.0
4.0e+5
8.0e+5
1.2e+6
Premack & DouglasRegression
AISI4340x106
x105
x105ε p
σ/σο
Fig. 9. Calculation of parameter values for strain rate effect.
p
ξ
Fig. 10. Time history of equivalent plastic strain-rate.
d (mm)0.0 0.1 0.2 0.3 0.4 0.5
0.0
0.1
0.2
0.3
RIRD
D=0.8mm, v=75m/s, L=0.02mm, =0.5µ=0.2
RS
EDS
PDS
ξ
p
Fig. 8. Dynamic frictional effects.
Fig. 8shows distribution of converged residual stress for theoulomb friction coefficient � between 0 and 0.5 in three shotodels. The value � = 0.5 was chosen as stated above. In rigid
nd elastic shots, the discrepancy of solutions is significant for≤ � ≤ 0.2. Especially, in non-friction condition, both shots pro-uce compressive residual stresses in the surface. Note that, as
increases, the surface residual stress approaches zero due torictional effect between shot and peened surface in this singlehot impact. In plastic shot, residual stress distributions con-
erge to a curve regardless of �. When � ≥ 0.2, the curvesor all shots converge to a curve. Thus the value � = 0.2 iselected as another physical factor. It should be noted thathe value is within the range (0.1–0.4) of the coulomb frictionoefficient between general metal surfaces. Obviously, the 2DFig. 11. Comparison of equivalent plastic strain versus depth curves obtained fromRI and RD analyses.
FE model including dynamic friction gets closer to actual shotpeening.
4.3. Effects of strain rate on plastic deformation behavior of
materialWhen the shot ball impacts on material surface, the materialinstantly deforms with high speed, showing high strain rate depen-
5950 T. Kim et al. / Materials Science and Engineering A 528 (2011) 5945–5954
x
-2
-1
0
1D=0.8mm, v=75m/s, L=0.02mm, =0.5µ=0.2, RS
RI
RD
(a)
-2
-1
0
1EDS
RI
RD
(b)
d (mm)0.0 0.2 0.4 0.6
-2
-1
0
1PDS
RD
RI
(c)
xx
ξ
dpf
ε
wnDcEst(Fs
Fig. 13. Experimental Almen saturation curves for estimation of peening intensity.
Fig. 14. Variation of constant A with impact velocity v.
Fig. 12. Effects of strain-rate sensitivity on residual stress.
ence. Strain rate should therefore be considered as an additionalhysical factor. We used the power law formula (Boyce et al. [24])or strain rate sensitivity as
˙ p = Dm
(�e(εp)
�o− 1
)n
(4)
here εp is effective plastic strain rate; �e (εp) is effective stress foron-zero strain rate; �o is quasi-static yield strength. We obtainedm = 2.5 × 106 and n = 6 by regressing the experimental data (openircles in Fig. 9) of AISI4340 steel (Premack and Douglas [34]) withq. (4) (=the solid line passing the open circles in Fig. 9). Fig. 10hows the evolution of plastic strain rate with FE computational
ime at the depth where deformation speed is the highest for rigidd = 0.1 mm), elastic (d = 0.08 mm) and plastic shot (d = 0.07 mm; seeig. 11). Plastic strain rate increases rapidly in the initial impacttage, and reaches the maximum value at the impact time ofFig. 15. Variation of arc height H with peening coverage C for various values of v.
(1.3–1.6) × 10−6 s. At this moment, shot velocity becomes zero.
After that, during shot rebound, plastic strain rate decreases imme-diately, and becomes zero. Plastic strain rate of plastic shot is lowerthan those of rigid and elastic shot FE models. Energy transferred
T. Kim et al. / Materials Science and Engineering A 528 (2011) 5945–5954 5951
F
tpsftFsmtstNtT
5
ttwtfsSabcrettifsAts3Qe
H
Tf
ig. 16. Variation of shot impact velocity v with arc height H for various values of C.
o material is smaller in plastic shot, since the impact energy isartially consumed for deformation of plastic shot. Fig. 11 demon-trates curves of the equivalent plastic strain versus depth obtainedrom rate independent (RI) and rate dependent (RD) analyses ofhree shots. Effective plastic strain in RD is smaller than that of RI.ig. 12 shows distributions of residual stress of RI and RD analy-es for three shots. For rigid and elastic shots, the magnitudes ofaximum compressive residual stress of the RD case are larger
han those of RI case. For plastic shot in RI case, surface residualtress solution gives rather positive residual stress value, whereashe residual stress value was found negative in the experiment.ote that FE residual stress is based on single shot impact, while
he actual peening residual stress involves numerous shot impacts.his issue is discussed in the work of Kim et al. [25].
. Experimental verification of FE solution
We produced the experimental Almen saturation curves withhe peening machine (Model: PMI-0608) [29] as shown in Fig. 13o estimate the peening intensity on the AISI4340 surface by CWRSith D = 0.08 mm. The abscissa t is the shot peening time, and
he ordinate H is the arc height. After shot peening on the sur-ace of A type Almen strip, we measure the curved height of benttrip. We represent mmA (A-type) as unit of arc height obeyingAE J442 Standard [36]. Peening residual stress depends on therea fraction of dent (equivalent to peening coverage C) formedy multi-shot-impacts. About 100% area fraction is called full-overage (SAE J442 standard [36]). The reference XRD experimentalesult was obtained from the specimen with the resulting cov-rage of 200% and arc height of 0.36 mmA achieved by a nozzleype peening machine (Torres and Voorwald [35]). We just refero the magnitudes of H and C obtained. To determine the inputmpact velocities v corresponding to C = 200% and H = 0.36 mmAor FE analyses, we derived the following Eqs. (5)–(7) from theaturation curves in Fig. 13. Fig. 14 shows that the coefficient
in Eq. (5) varies linearly with impact velocity v. Consideringhe capacity of peening equipment (PMI-0680 [19]) used for thistudy, we set limits on t (min), v (m/s) and C (%): as 1 ≤ t ≤ 16,0 ≤ v ≤ 80, C ≥ 100, respectively. Here, we set the flow rate of shotsto 42 kgf/min. Arc height as a function of shot peening time is
xpressed as Eq. (5):
= A(1 − e−0.65t0.65) (5)
able 1 shows the numerical values of variables and coefficientsor Eq. (5). Fig. 15 shows arc height H vs. shot peening coverage C
Fig. 17. Comparison of FE solutions of repeated impacts with XRD solution for (a)three shots in 2D model and (b) PDS in 2D and 3D FE models.
for various shot impact velocities. We determined C with an opticalmicroscopic image. Let tp be the peening process time for C = 100%.Then 2tp is the peening process time for C = 200%, and 3tp is thetime for C = 300%. From this, we obtained the relationship betweenH and C in the form of Eq. (6). Table 2 shows the numerical valuesof variables and coefficients of Eq. (6). Note that the experimentaldata in Fig. 15 suggest the second order polynomial relationshipbetween H and C:
H = B1C2 + B2C + B3 (6)
Fig. 16 shows the linear relationship of impact velocity with archeights for various values of C, and the relation can be expressedas Eq. (7). The slope of C–H curve decreases with increasing C inFig. 15, and H converges to a certain value. This feature is alsoobserved in Fig. 16. Table 3 shows the numerical values of variablesand coefficients of Eq. (7):
v = C1H − C2 (7)
The experimental Almen saturation curve is obtained by measuringthe arc height of Almen strip after peening, and the area fractionof dents on the strip surface provides the coverage. The factorsthus reflect the intensity of peening. Subsequently, if the arc height
and coverage are given, the impact velocity for FE analysis canbe predicted from the experimental Almen saturation curve. Wecan calculate shot velocities using Eqs. (5)–(7), which were derivedfrom the saturation curves. In Eq. (7), when C = 200%, the numer-
5952 T. Kim et al. / Materials Science and Engineering A 528 (2011) 5945–5954
Fig. 18. Distribution of �x and FE dents on the surfaces after repeated impacts (C = 200%, H = 0.36 mmA) in (a) rigid, (b) elastic and (c) plastic shot models.
Table 1Numerical values of variables and coefficients of Eq. (5).
v (m/s) A t (min) H (mmA) Computed H (mmA) Error (%)
70 0.53
1 0.276 0.253 9.02 0.355 0.338 4.83 0.390 0.389 0.14 0.416 0.423 1.78 0.478 0.487 1.8
12 0.506 0.510 0.816 0.518 0.520 0.3
60 0.46
1 0.248 0.212 132 0.312 0.294 6.13 0.336 0.338 0.64 0.372 0.367 1.38 0.411 0.423 2.8
12 0.430 0.442 2.816 0.454 0.451 0.7
50 0.39
1 0.185 0.186 0.82 0.238 0.249 4.63 0.274 0.287 4.44 0.304 0.311 2.38 0.340 0.358 5.1
12 0.381 0.375 1.616 0.394 0.382 3.0
40 0.32
1 0.143 0.153 6.52 0.197 0.205 3.73 0.235 0.235 0.14 0.252 0.255 1.38 0.275 0.294 6.5
12 0.295 0.308 4.216 0.313 0.314 0.2
T. Kim et al. / Materials Science and Engineering A 528 (2011) 5945–5954 5953
Table 2Numerical values of variables and coefficients of Eq. (6).
v (m/s) Bi C (%) H (mmA) Computed H (mmA) Error (%)
70
B1 = −6.33 × 10−7 100 0.387 0.393 1.4B2 = 6.60 × 10−4 200 0.450 0.440 2.3B3 = 0.333 300 0.477 0.474 0.6
400 0.491 0.496 1.0500 0.500 0.505 0.9
60
B1 = −5.34 × 10−7 100 0.342 0.348 1.9B2 = 5.98 × 10−4 200 0.400 0.392 2.0B3 = 0.294 300 0.423 0.425 0.6
400 0.436 0.448 2.6500 0.444 0.460 3.4
50
B1 = −4.92 × 10−7 100 0.286 0.289 1.2B2 = 5.34 × 10−4 200 0.334 0.328 1.8B3 = 0.241 300 0.359 0.357 0.6
400 0.373 0.376 0.8500 0.381 0.385 1.0
40
B1 = −3.84 × 10−7 100 0.240 0.244 1.6B2 = 3.98 × 10−4 200 0.278 0.272 2.1B3 = 0.218 300 0.294 0.293 0.4
400 0.302 0.306 1.2500 0.307 0.311 1.3
Table 3Numerical values of variables and coefficients of Eq. (7).
C (%) Ci H (mmA) v (m/s) Computed v (m/s) Error (%)
100
C1 = 179.4 0.240 40 42.5 5.9C2 = 0.57 0.274 50 48.6 2.9
0.342 60 60.8 1.30.387 70 68.9 1.7
200
C1 = 153.4 0.278 40 41.8 4.4C2 = 0.82 0.334 50 50.4 0.8
0.400 60 60.5 0.90.450 70 68.2 2.6
300
C1 = 144.6 0.294 40 41.6 3.9C2 = 0.87 0.360 50 51.2 2.3
0.423 60 60.3 0.50.477 70 68.1 2.8
C1 = 140.2 0.302 40 42.8 6.5
iv5oCwsiIscsts
cttvFtrti
400C2 = 0.89 0.373
0.4360.491
cal coefficients C1 and C2 are 153.4 and 0.82 respectively. Then= 55 m/s with H = 0.36 mmA in Eq. (7). Our FE analysis adopts5 m/s from with v. Since we assume that a single shot impactn the surface of material produces C = 100% in this analysis for= 200%, we ran 2 cycle impacts (1 shot × 2 cycles = 2 shots). Then,e compared the 2D FE solution with the 3D FE solution for the
ame impact cycles. For the 3D FE solution, we used a 3D multi-mpact symmetry-cell FE model as suggested by Kim et al. [25,37].n the symmetry-cell, to increase the effect of multi-impacts ontress interference, we set the space between shots (or a side of aross-section of symmetry-cell) to the shot radius (=0.4 mm). Weet L to 0.02 mm; the material damping coefficient � to 0.5; andhe dynamic friction coefficient � to 0.2 in the cell. The height ofymmetry-cell was set to h = 1.5 mm.
Fig. 17(a) compares the 2D FE solution with the XRD result for 2ycle impacts with v = 55 m/s. The FE solutions with rigid and elas-ic shots differ from experimental result significantly. It is notablehat blending of the surface value from rigid shot and the maximumalue from plastic shot would be consistent with the XRD result.ig. 17(b) shows that the 2D FE solution with plastic shot is almost
he same with 3D FE solution, and both FE results are close to XRDesult. The magnitude of maximum compressive residual stress inhe FE solution is smaller than the XRD result for 2D 2-cycle multi-mpact as shown in Fig. 17. Here, assuming that the coverage from50 53.1 5.860 62.2 3.570 70.1 0.2
a shot is 100%, we performed two shots to achieve 200% of peen-ing coverage. Hence, the 200% FE peening coverage of differs fromthe actual 200% peening coverage produced by numerous shots.Since the 2D solution is obtained along the axis of impact center,it differs from the solution averaged over certain area involvingmulti-impacts. Fig. 18 shows the distribution of �x and FE dents onthe surfaces after repeated impacts in (a) rigid, (b) elastic and (c)plastic shot models. Dents by rigid and elastic shots are apparent,while dent of plastic shot is barely noticeable.
We note that the 2D FE model requires two orders of magnitudeless computational time and substantially less effort in pre and postprocessing than the 3D model. This would make the 2D approachfairly competitive in the field applications.
6. Summary
We proposed an operative 2D impact FE model for evaluation ofpeening residual stress. Physical factors of material and kinematicalfactors of shot were integrated along with the plastic shot into theFE model. For minimum element sized less than 1/40 of shot diam-
eter and for friction coefficient larger than 0.2, the FE residual stressdistribution converged into a single curve. Deformation depth andmagnitude of maximum residual stress in a rate dependent mate-rial were a bit smaller than those of a rate independent material.
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sing the arc height and coverage fit on the Almen saturation curve,e determined the impact velocity needed for FE analysis. In all
spects, the 2D model was found to provide the solution consis-ent with the 3D multi-impact FE solution and the experimentalRD result. Especially, the 2D FE solution form 2 cycle-impacts (=2hots) matched well with the 3D FE solution. Since the 2D approachakes two orders of magnitude less computational time than the 3D
odel, it can be competitive in the field applications.
cknowledgement
The authors are grateful for the support provided by a grant fromhe Korea Research Foundation (Grant No. KRF-2006-511-D00009).
eferences
[1] P.S. Song, C.C. Wen, Eng. Fract. Mech. 63 (1999) 295–304.[2] R.M. Menig, L. Pintschovius, V. Schulze, O. Vöhringer, Scr. Mater. 45 (2001)
977–983.[3] W. Luan, C. Jiang, V. Ji, Y. Chen, H. Wang, Mater. Sci. Eng. A 497 (2008) 374–377.[4] I.F. Pariente, M. Guagliano, Surf. Coat. Technol. 202 (2008) 3072–3080.[5] K. Schiffner, C. Helling, Comput. Struct. 72 (1999) 329–340.[6] S. Baragetti, Int. J. Comput. Appl. Technol. 14 (1–3) (2001) 51–63.[7] E. Rouhaud, D. Deslaef, Mater. Sci. Forum 404–407 (2002) 153–158.[8] H.L. Zion, W.S. Johnson, Am. Inst. Aero. Astro. J. 44 (9) (2006)
1973–1982.[9] E. Rouhaud, A. Ouakka, C. Ould, J.L. Chaboche, M. Francois, Proc. of the 9th Int.
Conf. on Shot Peening, 2005, pp. 107–112.10] N. Hirai, K. Tosha, E. Rouhaud, Proc. of the 9th Int. Conf. on Shot Peening, 2005,
pp. 82–87.11] C. Ould, E. Rouhaud, M. Francois, J.L. Chaboche, Mater. Sci. Forum 524–525
(2006) 16–166.12] T. Hong, J.Y. Ooi, B. Shaw, Eng. Fail. Anal. 15 (8) (2008) 1097–1110.13] M. Guagliano, J. Mater. Process Technol. 110 (2001) 227–286.
[
[
ineering A 528 (2011) 5945–5954
14] K. Han, D. Owen, D. Peric, Eng. Comput. 19 (2002) 92–118.15] M.S. Eltobgy, M.A. Elbestawi, Proc. IME B: J. Eng. Manuf. 218 (11) (2004)
1471–1481.16] G.H. Majzoobi, R. Azizi, N.A. Alavi, J. Mater. Process Technol. 164–165 (2005)
1226–1234.17] S.A. Meguid, G. Shagal, J.C. Stranart, J. Eng. Mater. Technol. 129 (2) (2007)
271–283.18] M. Zimmermann, V. Schulze, H.U. Baron, D. Löhe, Proc. of the 10th Int. Conf. on
Shot peening, 2008, pp. 63–68.19] P.S. Follansbee, G.B. Sinclair, Int. J. Solid Struct. 20 (1) (1984) 81–91.20] G.B. Sinclair, P.S. Follansbee, K.L. Johnson, Int. J. Solid Struct. 21 (8) (1985)
865–888.21] A. Levers, D. Prior, Multi-axial fatigue: Analysis and experiments, Society of
Automotive Engineers, Inc., Warrendale, 1989, pp. 16–17.22] S.A. Meguid, G. Shagal, J.C. Stranart, J. Daly, Finite Elem. Anal. Des. 31 (1999)
179–191.23] K. Han, D. Peric, D.R.J. Owen, J. Yu, Eng. Comput. 17 (6) (2000) 680–702.24] B.L. Boyce, X. Chen, J.W. Hutchinson, R.O. Ritchie, Mech. Mater. 33 (2001)
441–454.25] T. Kim, H. Lee, S. Jung, J.H. Lee, A 3D FE model with plastic shot for evaluation of
equi-biaxial peening residual stress due to multi-impacts, Surf. Coat. Technol.,submitted for publication.
26] S.A. Meguid, G. Shagal, J.C. Stranart, Int. J. Impact Eng. 27 (2002) 119–134.27] M.A.S. Torres, H.J.C. Voorwald, Int. J. Fatigue 24 (2002) 877–886.28] ABAQUS User’s Manual, Version 6.5, Hibbitt. Karlsson and Sorensen, Inc., Paw-
tucket, RI, 2004.29] Rotation table type impeller peening machine (PMI-0608) User’s Manual, Sae-
myung Shot Machinery, Inc., 2004.30] M. Kobayashi, T. Matsui, Y. Murakami, Int. J. Fatigue 20 (5) (1998) 351–357.31] C.W. De Silva, Vibration, CRC Press, New York, 1994, pp. 349–398.32] A.J.L. Crook, D.R.J. Owen, Eng. Comput. 17 (5) (2000) 593–619.33] S. Naboulsi, T. Nicholas, Int. J. Solids Struct. 40 (23) (2003) 6497–6512.34] L. Johansson, Comput. Methods Appl. Mech. Eng. 191 (2001) 239–254.
2812.36] SAE J442, Test Strip, Holder and Gage for Shot Peening, Society of Automotive
Engineers, Inc., 2004.37] T. Kim, J.H. Lee, H. Lee, S.K. Cheong, Mater. Des. 24 (2010) 877–886.