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Journal of Materials Processing Technology 235 (2016) 143–148 Contents lists available at ScienceDirect Journal of Materials Processing Technology jo ur nal ho me page: www.elsevier.com/locate/jmatprotec Measuring shot peening media velocity by indent size comparison E. Nordin a,b,, B. Alfredsson b a Scania CV AB, Sweden b Royal Institute of Technology, KTH, Department of Solid Mechanics, 100 44 Stockholm, Sweden a r t i c l e i n f o Article history: Received 9 December 2014 Received in revised form 20 February 2016 Accepted 9 April 2016 Available online 16 April 2016 Keywords: Shot peening Media velocity Almen intensity Impact Indentation a b s t r a c t Shot peening is a manufacturing method that makes indentations on a components surface by impacting it with small steel balls (media). In a production environment the shot peening process is usually controlled by defining media size, coverage and Almen intensity. For simulating shot peening, the media velocity is needed and therefore it must be measured or correlated to the Almen intensity. This paper details a method to record indentations on a test plate and then compare them to single shot indentations with measured velocities. For small media sizes the results are in reasonable agreement with other published results but at larger sizes there is a larger spread in published results. It is therefore recommended that the media velocity is either measured directly or that the indents are analysed as presented in this paper. © 2016 Elsevier B.V. All rights reserved. 1. Introduction Shot peening is a manufacturing method that in the automo- tive industry mostly is used to increase bending fatigue strength. The process involves covering relevant surfaces with small indents. The plastic deformation causing these indents will try to stretch the near surface material but the material deeper into the part will resist the expansion. Equilibrium gives that the surface layer will have residual compressive stresses while the deeper material will have tensile stresses. Because the near surface layer induced by shot peening is relatively thin compared to the size of most components, e.g. gears or springs, the internal tensile stresses will be small in magnitude and thus not cause any major adverse effects for fatigue (Menig et al., 2001). The indents are usually created by having small hard metallic balls, called media, impact the surface at velocities that will create the intended effects. In a production environment the shot peening process is usually controlled by defining media size, coverage and Almen intensity. Coverage is the percent of the surface area that has been hit by an indent and is usually estimated visually through a loupe or by removal of fluorescent paint. Almen intensity is measured by exposing standardized Almen strips to the shot stream for different amounts of time. The strips will bend due to compressive stresses being generated at the shot peened surface and the arc height of the Almen strip is a measure of the indenta- Corresponding author at: Royal Institute of Technology, KTH, Department of Solid Mechanics, 100 44 Stockholm, Sweden. E-mail address: [email protected] (E. Nordin). tion ability of the shot stream (Kirk, 2007). For a given media the Almen intensity is mostly dependent on the media velocity but also on impact angle, media hardness or the Almen strips properties. Although the Almen strips are standardized there is a tolerance on its parameters. The Almen strip hardness and thickness variations are reported to give measureable deviations according to (Bailey and Champaigne, 2005). The hardness is allowed to vary between HRC 44–50 according to (SAE Standard J442, 2008). Kirk (2009) also discusses the influence of variations in elastic modulus and measures values from 195 GPa to 205 GPa. Industrial shot peening is done with two different type of machines; centrifugal wheel machines or compressed air machines. In the first type the media is accelerated by a centrifugal wheel and the velocity of the particles can be controlled by the rotational speed, RPM, of the wheel. In the compressed air type machines the media is accelerated by an air stream. With a given machine config- uration the media velocity is then mainly controlled by changing the air pressure (although the amount of media fed into the air stream will also influence the final velocity). Therefore, the actual velocity of the media is seldom reported or even known for a shot peening process. This is not a problem for practical evaluation of shot peening but for shot peening simulations knowledge of the velocity is necessary. There exist some experimental correlations between Almen intensity and media velocity in the literature. The different results are compiled into Fig. 1. The dashed results denominated “Empir- ical” are from (Shotpeener, 2014a). The results are probably from centrifugal wheel machine shot peening but unfortunately there is no source of origin or test set-up associated with the results. http://dx.doi.org/10.1016/j.jmatprotec.2016.04.012 0924-0136/© 2016 Elsevier B.V. All rights reserved.

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Page 1: Journal of Materials Processing Technology · CV AB, Sweden b Royal Institute ofTechnology, KTH, Department Solid Mechanics, 100 44 Stockholm, Sweden a r t i c l e i n f o Article

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Journal of Materials Processing Technology 235 (2016) 143–148

Contents lists available at ScienceDirect

Journal of Materials Processing Technology

jo ur nal ho me page: www.elsev ier .com/ locate / jmatprotec

easuring shot peening media velocity by indent size comparison

. Nordin a,b,∗, B. Alfredsson b

Scania CV AB, SwedenRoyal Institute of Technology, KTH, Department of Solid Mechanics, 100 44 Stockholm, Sweden

r t i c l e i n f o

rticle history:eceived 9 December 2014eceived in revised form 20 February 2016ccepted 9 April 2016vailable online 16 April 2016

a b s t r a c t

Shot peening is a manufacturing method that makes indentations on a components surface by impacting itwith small steel balls (media). In a production environment the shot peening process is usually controlledby defining media size, coverage and Almen intensity. For simulating shot peening, the media velocityis needed and therefore it must be measured or correlated to the Almen intensity. This paper details amethod to record indentations on a test plate and then compare them to single shot indentations with

eywords:hot peeningedia velocity

lmen intensitympact

measured velocities. For small media sizes the results are in reasonable agreement with other publishedresults but at larger sizes there is a larger spread in published results. It is therefore recommended thatthe media velocity is either measured directly or that the indents are analysed as presented in this paper.

© 2016 Elsevier B.V. All rights reserved.

ndentation

. Introduction

Shot peening is a manufacturing method that in the automo-ive industry mostly is used to increase bending fatigue strength.he process involves covering relevant surfaces with small indents.he plastic deformation causing these indents will try to stretchhe near surface material but the material deeper into the part willesist the expansion. Equilibrium gives that the surface layer willave residual compressive stresses while the deeper material willave tensile stresses. Because the near surface layer induced by shoteening is relatively thin compared to the size of most components,.g. gears or springs, the internal tensile stresses will be small inagnitude and thus not cause any major adverse effects for fatigue

Menig et al., 2001). The indents are usually created by having smallard metallic balls, called media, impact the surface at velocitieshat will create the intended effects. In a production environmenthe shot peening process is usually controlled by defining mediaize, coverage and Almen intensity. Coverage is the percent of theurface area that has been hit by an indent and is usually estimatedisually through a loupe or by removal of fluorescent paint. Almenntensity is measured by exposing standardized Almen strips to the

hot stream for different amounts of time. The strips will bend dueo compressive stresses being generated at the shot peened surfacend the arc height of the Almen strip is a measure of the indenta-

∗ Corresponding author at: Royal Institute of Technology, KTH, Department ofolid Mechanics, 100 44 Stockholm, Sweden.

E-mail address: [email protected] (E. Nordin).

ttp://dx.doi.org/10.1016/j.jmatprotec.2016.04.012924-0136/© 2016 Elsevier B.V. All rights reserved.

tion ability of the shot stream (Kirk, 2007). For a given media theAlmen intensity is mostly dependent on the media velocity but alsoon impact angle, media hardness or the Almen strips properties.Although the Almen strips are standardized there is a tolerance onits parameters. The Almen strip hardness and thickness variationsare reported to give measureable deviations according to (Baileyand Champaigne, 2005). The hardness is allowed to vary betweenHRC 44–50 according to (SAE Standard J442, 2008). Kirk (2009)also discusses the influence of variations in elastic modulus andmeasures values from 195 GPa to 205 GPa.

Industrial shot peening is done with two different type ofmachines; centrifugal wheel machines or compressed air machines.In the first type the media is accelerated by a centrifugal wheeland the velocity of the particles can be controlled by the rotationalspeed, RPM, of the wheel. In the compressed air type machines themedia is accelerated by an air stream. With a given machine config-uration the media velocity is then mainly controlled by changingthe air pressure (although the amount of media fed into the airstream will also influence the final velocity). Therefore, the actualvelocity of the media is seldom reported or even known for a shotpeening process. This is not a problem for practical evaluation ofshot peening but for shot peening simulations knowledge of thevelocity is necessary.

There exist some experimental correlations between Almenintensity and media velocity in the literature. The different results

are compiled into Fig. 1. The dashed results denominated “Empir-ical” are from (Shotpeener, 2014a). The results are probably fromcentrifugal wheel machine shot peening but unfortunately thereis no source of origin or test set-up associated with the results.
Page 2: Journal of Materials Processing Technology · CV AB, Sweden b Royal Institute ofTechnology, KTH, Department Solid Mechanics, 100 44 Stockholm, Sweden a r t i c l e i n f o Article

144 E. Nordin, B. Alfredsson / Journal of Materials Pr

Fd

TSbsbSssm“o

fimpaitoaidBucsemcm

TC

ig. 1. Comparison of relations between Almen intensity and shot velocity fromifferent sources. Numbers in the legend refer to average media diameter.

he curves are shown for different media sizes according to SAEtandard J444 (2005). The average media size can be approximatedy the indicated average diameter in (Shotpeener, 2014b) and arehown in Table 1. Roughly similar results can also be calculatedy fitting a normal distribution to the sieve sizes defined in SAEtandard J444 (2005). Some researchers prefer to use the nominalhot diameter instead of the average. The nominal diameter corre-ponds to the nominal sieve opening where approximately 85% orore of the mass of shots will stay. The “S” in the SAE nr stands for

Shot” and the number is the nominal test sieve in ten thousandthsf inches (SAE Standard J444, 2005).

Könitzer and Polanetzki (2011) use a compressed air machinetted with an optical velocity measurement system. The peeningedia used was S110 and results for intensity versus velocity are

resented for an impact angle of 70◦. The relation is linear withn increase in intensity of 0.01 mm A for a 5 m/s increase in veloc-ty. Könitzer and Polanetzki (2011) also draw the conclusion thathe same intensity-velocity relationship is achieved irrespectivef machine type, nozzle size or shot flow rate. Tufft (1999) usesn electro-magnetic velocity sensor to measure the media veloc-ty. At an impact angle of 85◦ three results for a media with meaniameter 0.81 mm are reported and four results for 0.36 mm media.oth show an approximate linear relationship. Cao et al. (1995)sed experimental data obtained with a commercial optical systemalled TRAVEL (Lecoffre et al., 1993). The data was obtained by per-onal communication and no further details are presented. Barker

t al. (2005) uses another commercial system for media velocityeasurements, ShotMeter from http://www.progressivesurface.

om. Results are presented for S110 and S550. The S550, with aean diameter of 1.68 mm, results are not included here however

able 1ommon SAE media sizes.

SAE Nr Average diameter [mm] Nominal diameter [mm]

S70 0.297 0.178S110 0.353 0.279S130 0.419 0.330S170 0.500 0.432S190 0.594 0.483S230 0.706 0.584S280 0.841 0.711S330 1.001 0.838S390 1.191 0.991S460 1.410 1.168

ocessing Technology 235 (2016) 143–148

since it is so far from the other reported media sizes. Additionallythese results were measured on Almen C strips and an approxi-mate translation would have to be done to Almen A strips. TheS110 results of Barker agree well with both Könitzer’s and Tufft’sresults. The experimental results used by Cao for S110 agree at lowvelocities but show higher intensities with large scatter at veloci-ties above 50 m/s. The 0.5 mm media presented by Cao agrees wellwith the empirical results for S170. Some sort of limit in velocitymeasurement seems to be reached at 80 m/s for both media types.Zinn and Scholtes (2005) measure the shot velocity with the sys-tem developed by Linnemann et al. (1996). Zinn and Scholtes (2005)present results for a large number of tests for S110, S170 and S230media sizes. A fitted mean line is used here. The results for S110deviate much from the other sources. Similar trends can be seen forthe results for S170 and S230 also. A source of these discrepancies isattributed to the fact that there is a distribution of velocities comingfrom the nozzle of a compressed air machine. Differences in howa mean velocity should be calculated might give these deviations.The results from Linnemann et al. (1996) match Zinn and Scholtes(2005) results at the same media size. Kim et al. (2012) presentsthe times and arc heights from Almen saturation measurements atfour velocities, 40, 50, 60 and 70 m/s. The Almen intensity is calcu-lated by the program developed by Kirk (2005) and with the 2PFformula. The result shows a linear relation and fit quite well to theempirical S230 curve which however has a smaller average diam-eter of 0.7 mm. The inconsistent results at especially larger mediasizes show that there is a need to measure the media velocity if theresults should be used to compare with FEM-simulations.

This paper presents a method for comparing the indent size ofa low coverage shot peening process to indent sizes of single shotswith the purpose to determine the shot velocity at the peening pro-cess. Since the velocity distribution in the production shot streamvary the velocity determined here will be an equivalent velocitythat creates on average the same indent size. The present resultswere compared to those of other researchers.

2. Experiment

Shot peening of square test plates, 30 × 30 mm and 10 mm thick,Fig. 2a, were performed in a compressed air machine. The plateswere of case hardened SS (Swedish Standard) 92506 gear steel tem-pered to a surface hardness of 716HV1. The surfaces were groundbefore hardening (to avoid grinding burns after hardening) to a sur-face roughness comparable to that of gears, Ra 0.5 �m. In this caseit gave an Rz value around 5 �m. Two media sizes were used whichwere both cut wire rounded to G3 grade and had a nominal diam-eter of 0.7 mm and 0.35 mm. The media had an average Vickershardness of 742HV1. The 0.7 mm media is shown in Fig. 2b.

2.1. Low coverage shot peening

For the 0.7 mm media three different intensities were used;0.22 mm A, 0.34 mm A and 0.49 mm A. For the 0.35 mm mediathe intensity 0.24 mm A was used. A test plate was shot peenedwith low coverage for each intensity. The 0.7 mm media used inthe machine were sampled and the same shot media was used tomake the single indents. The average diameter of the media wasmeasured to 0.84 mm with a standard deviation of 0.1 mm.

2.2. Single indent shots

When making the single indents only larger balls were chosen to

ease both the velocity and indent measurement. The average diam-eters of balls used for single impact were 0.92 mm. However, sincethe media is not completely round the indent crater will be influ-enced by which side of the ball that contacted the surface. Therefore
Page 3: Journal of Materials Processing Technology · CV AB, Sweden b Royal Institute ofTechnology, KTH, Department Solid Mechanics, 100 44 Stockholm, Sweden a r t i c l e i n f o Article

E. Nordin, B. Alfredsson / Journal of Materials Processing Technology 235 (2016) 143–148 145

Fig. 2. Test plate and shot peening media used.

Fig. 3. (a) Single indent measured with confocal microscope. (b) Chosen indent outline and mirrored along plate surface plane to create an “island”.

the gr

ecev

Fig. 4. Surface topography of

xtra round balls were also chosen. To make the single indents, aompressed air gun was used and each ball velocity was measuredlectronically, Nordin et al. (2014). The estimated accuracy of theelocity measurements were within 1.5%.

ound plates at low coverage.

Indents were made at three different velocities, 30, 60 and90 m/s, and 30 indents were measured at each velocity. The meanand standard deviation for measured velocities and indent depth,area and volume are calculated for each group. Results for these

Page 4: Journal of Materials Processing Technology · CV AB, Sweden b Royal Institute ofTechnology, KTH, Department Solid Mechanics, 100 44 Stockholm, Sweden a r t i c l e i n f o Article

146 E. Nordin, B. Alfredsson / Journal of Materials Processing Technology 235 (2016) 143–148

F

gva

2

tscipitboe4iatc

3

abcebOfFc

FS

ig. 5. Indent depth as a function of impact velocity for media diameter 0.84 mm.

roups are called “Average”. A few extra indents were made atelocities above 90 m/s. These results are for only one indent eachnd called “Single”.

.3. Confocal microscope measurements

The indent craters from both the low coverage shot peening andhe single impacts was measured with a PL� 2300 confocal micro-cope from Sensofar (www.sensofar.com). The resulting 3D-surfaceould then be used to calculate depth, area and volume of eachndent. Depth is defined as the distance from the indents deepestoint to the plate surface. Area is the surface area of the selected

ndent outline. The outline is chosen visually as the boundary whenhe indent reaches the surrounding surface. Volume is calculatedetween a plane parallel to the surface through the highest pointn the indent outline to the surface of the indent. Fig. 3 shows anxample of a single shot indent evaluated in the software SensoMap.1. The outline of the indent is selected by hand and extracted. It

s then inverted so the indent becomes an “island”. Depth, areand volume can then be calculated from the “island”. Examples ofhe topography measured with the confocal microscope on the lowoverage plates are shown in Fig. 4.

. Result

Figs. 5–7 show the indent depth, indent area and indent volumes functions of ball velocity. Observe that there is no simple relationetween volume, area and depth. This is because of the non-linearhanges of plastic deformation between target and media at differ-nt impact depths. This is shown for equal materials on target andall in Alfredsson and Nordin (2013) and for unequal materials inlsson and Larsson (2016). Since the single shot balls were chosen

rom the larger part of the media size distribution the results inigs. 5–7 are scaled to correspond to the mean diameter of the lowoverage shot peening media. Denoting the radii’s of two different

ig. 6. Area of indent as a function of impact velocity for media diameter 0.84 mm.econd order polynom fitted to the average points.

Fig. 7. Volume of indent as a function of impact velocity for media diameter0.84 mm.

sized balls R2 and R1 the corresponding relations between indentdepth h, indent area A and indent volume V are (see Appendix A):

h2

h1= R2

R1;A2

A1=

(R2

R1

)2;V2

V1=

(R2

R1

)3(1)

Fig. 5 shows the indentation depth. The error bars show onestandard deviation which is relatively large. The main issue here isthat the surface roughness is in a similar range as the indentationdepth. Studying the depth in this way can therefore only be doneon mirror finished surfaces. Calculating the coefficient of variation(COV) as the standard deviation divided by the mean value gives0.28, 0.22 and 0.25 for respectively 30, 60 and 90 m/s. Fig. 6 showsthe indent areas. The COV are here 0.22, 0.14 and 0.12 respectively.Fig. 7 shows the indent volume which in the same way has COV of0.4, 0.28 and 0.21. The larger scatter in volume probably has thesame cause as the scatter in depth.

Because the indent area had the lowest coefficient of variationit was used to relate velocities to indents made with shot peeningequipment and the compressed air gun. A second order polynomwas fitted through the three average points and is shown as thedashed line in Fig. 6. The extrapolation of the curve for low velocitiespasses close to origo which is expected. The curve was not forced togo through origo in the fitting to the average points. Single indentscompare well to the extrapolated curve above 90 m/s.

Relating single shot indents with shot peening indents should bedone with the same media and target and the target should prefer-ably be polished as noted before. The mean indent areas measuredon the low coverage shot peened plates are shown in Table 2. Thefitted curve to the measured indent areas in Fig. 6 are used to calcu-late the corresponding velocity. The indent area for the media withaverage size 0.36 mm is scaled with Eq. (1) before using the fittedcurve in Fig. 6. The error estimate for the velocity is calculated usingthe combined standard deviation from Fig. 6 and the area measure-

ments in Table 2. The standard deviation of the average points inFig. 6 is assumed to scale linearly with the media velocity as shownin Fig. 8.

Fig. 8. Standard deviation of area measurement.

Page 5: Journal of Materials Processing Technology · CV AB, Sweden b Royal Institute ofTechnology, KTH, Department Solid Mechanics, 100 44 Stockholm, Sweden a r t i c l e i n f o Article

E. Nordin, B. Alfredsson / Journal of Materials Processing Technology 235 (2016) 143–148 147

Table 2The four shot peening settings, the corresponding average indent area and calculated velocity.

Shot peening Intensity [mm A] Area [�m2] Media size [mm] Velocity [m/s]

iD 0.24 10506 ± 2264 0.36 ± 0.02 76 ± 16i1 0.22 15523 ± 51i2 0.34 22623 ± 65i3 0.49 33976 ± 96

F

rfsf(osactwttmnp

cKmLe00vi

4

wtas

ig. 9. Comparison of different published results with the results from this paper.

Fig. 9 compares the results in Table 2 with several published cor-elations between Almen intensity and media velocity. The resultor the media size of 0.36 mm and Almen intensity 0.24 mm A areimilar to the results by Cao. It is also close to the empirical valuesor S110. The bulk of the measurements by Könitzer and Polanetzki2011), Tufft (1999) and Barker et al. (2005) agree very well to eachther but indicate a much higher velocity for 0.24 mm A. One rea-on for the low velocity compared to Könitzer and Polanetzki, Tufftnd Barker et al. can be that there was a problem creating the lowoverage in the shot peening machine. The mass flow was set tohe same amount as for the 0.84 mm media, meaning that thereere a lot more balls shot towards the target. One revolution of the

arget table gave too high coverage. To try to reduce that coveragehe machine was started and shut down quickly to just empty the

edia in the hoses. This could mean that the media velocity hadot reached steady state and was lower than during the actual shoteening.

The results for the 0.84 mm media are similar to the empiri-al results for S280 media and are in between Tufft (1999) andim et al. (2012). There are however considerable larger disagree-ent between different researchers in this range of media sizes.

innemann et al. (1996) or Zinn and Scholtes (2005) have almostxactly the same relation between intensity and velocity as the.84 mm results in this study but for a reported media size of.5 mm. On the other hand, Zinn and Scholtes (2005) measuredelocities for 0.7 mm media that was about half of the determinedn this paper for the 0.84 mm media.

. Discussion

The single shot measurements and low coverage shot peening

as difficult to measure, especially at low velocities. This was due

o the surface roughness being in the same order of magnitudes the final indent depth. Only the indent area gave reasonabletable results but even for this it was a matter of judgment to

35 0.84 ± 0.1 24 ± 966 0.84 ± 0.1 34 ± 1123 0.84 ± 0.1 49 ± 14

decide how to define the outline of the indent. When measuringthe low coverage shot peened plates with a confocal microscopemany non-round indents were found. This is probably due to eitherfragmented media parts or unusual un-even balls. As can be seenin Fig. 2b some parts of a ball can be quite sharp. During evalua-tion only round and well defined indent were chosen. Thereforethe extra round balls chosen during the single indent shots shouldcorrespond with the measurements of selected round indents fromshot peening. No selection was done on diameter of the low cover-age shot peening and therefore the single indent results made withan average diameter of 0.91 mm were scaled with Eq. (1) to theaverage shot size of 0.84 mm. Polishing the plates to mirror finishwould have given much better definition of the outline and con-sistence in depth values. However, there will always be an addedscatter due to the irregular shape of the shot peening media. Sincethe same media should be used for the single shot indents as usedfor the shot peening process this cannot be avoided. Another expla-nation for indent area being the best measurement for determiningthe impact velocity is found in the elastic rebound. Elastic reboundaffects impact depth and volume compared to those at maximumimpact load but leaves the impact diameter more or less unaffected(Tabor, 1951).

The high scatter and differences between sources correlatingAlmen intensity and media velocity adds to the uncertainty indetermining the media velocity. One reason can be how the mediavelocity is measured and how the average is calculated. Otherreasons can be differences in media hardness, Almen strips used,centrifugal wheel or compressed air machines, impact angles oruncertainties about nominal and average media diameters.

5. Conclusions

The velocity of the shot peening media can be estimated bycomparing indents on shot peening targets with a low coverageto single indents with the same media using a compressed air gun.By measuring the velocity in the single indent setup and compar-ing the indent areas the velocity in the shot peening setup can bedetermined. If the ball size differs between single shots for velocitymeasurements and that at low coverage production shot peening,Eq. (1) can be used to scale the results. However, the target platesshould be polished to decrease scatter. The method is useful as asimple way to “record” the average velocity used in a specific shotpeening setup or when equipment to measure the media velocityis not available.

Acknowledgement

The authors gratefully acknowledge the financial support fromScania CV AB.

Appendix A.

The radius a of a plastic indent is approximately (Johnson,

1985)(p.362)

a = Num ×(�shot

�Y

)1/4√vR (A1)

Page 6: Journal of Materials Processing Technology · CV AB, Sweden b Royal Institute ofTechnology, KTH, Department Solid Mechanics, 100 44 Stockholm, Sweden a r t i c l e i n f o Article

1 ials Pr

wtpkti

w

e

h

s

a(isrg

ot

wdb

48 E. Nordin, B. Alfredsson / Journal of Mater

here Num is a constant, �shot is the density of the media, �Y ishe yield strength of the target and v is the media velocity. Com-aring the indent radius of two different sized balls, R1 and R2,eeping velocity, density and yield strength the same it is seen thathe indent radius is proportional to the ball radius. Comparing thendent area, A, of two different ball sizes thus becomes

A2

A1= �a2

2

�a21

= (· · ·)R22

(· · ·)R21

=(R2

R1

)2(A2)

here the (· · ·) contains the common values.The indent depth h is correlated to the area parameter c2 (Hill

t al., 1989) as

= a2

2Rc2(A3)

The area parameter c2 evolves as a function of the representativetrain (Johnson, 1985) (p.176)

= aE∗

R�Y(A4)

For two indents with different ball radii’s R1,R2 the indent radii’s1, a2 are related with the same proportional factor, see equationA1). The representative strain will therefore have the same valuen both cases which gives that the area parameter will have theame value. Comparing two indent depths made with different balladii’s, keeping all other parameters equal and using equation (A1)ives

h2

h1= a2

2

2R2c2

2R1c2

a21

= R22R2

R1

R21

= R2

R1(A5)

Since the shape of the deformation will be the same for a smallr large ball and the area and depth scales as equation (A2) and (A5)he volumes will be related as

V2 = f h2 A2 =(R2

)3(A6)

V1 f h1 A1 R1

here f is a correction factor for the plastic deformations which isependent on the velocity and material parameters of target andall.

ocessing Technology 235 (2016) 143–148

References

Alfredsson, B., Nordin, E., 2013. An elastic-plastic model for single shot-peeningimpacts. Tribol. Lett. 52, 231–251.

Bailey, P., Champaigne, J., 2005. Factors That Influence Almen Strip Arc Height. In:Schulze, V. (Ed.). Int. Conf. on Shot Peening 9 (ICSP-9), Marne la Vallee, France.

Barker, B., Young, K., Poulio, L., 2005. Particle Velocity Sensor for Improving ShotPeening Process Control. In: Schulze, V. (Ed.). Int. Conf. on Shot Peening 9(ICSP-9), Marne la Vallee, France.

Cao, W., Fathallah, R., Castex, L., 1995. Correlation of Almen arc height withresidual stresses in shot peening process. Mater. Sci. Technol. 11 (9), 967–973.

Hill, R., Storåkers, B., Zdunek, A.B., 1989. A theoretical study of the Brinell hardnesstest. Proc. R. Soc. Lond. Ser. A: Math. Phys. Sci. 423 (1865), 301–330.

Johnson, K.L., 1985. Contact Mechanics. Cambridge University Press, Cambridge,UK.

Könitzer, A.M., Polanetzki, H., 2011. Implementation of Velocity Measurement asIntensity Verification in Production. In: Champaigne, J. (Ed.). Int. Conf. on ShotPeening 11 (ICSP-11), South Bend, IN, USA.

Kim, T., Lee, H., Jung, S., Lee, J.H., 2012. A 3D FE model with plastic shot forevaluation of equi-biaxial peening residual stress due to multi-impacts. Surf.Coat. Technol. 206, 3125–3136.

Kirk, D., 2005. Computer-based saturation curve analysis. Shot Peener Mag. 19 (4).Kirk, D., 2007. Peening intensity curves. Shot Peener 21 (3), 24–30.Kirk, D., 2009. Strip factors influencing Almen arc height. Shot Peener 23 (4), 26–32.Lecoffre, Y., Bonazzi, X., Jouet, F., Huet, D., 1993. A real time particle velocity

measuring system for use in shot peening. Shot Peener Mag. 7 (2).Linnemann, W., Kopp, R., Kittel, S., Wüstefeld, F., 1996. Shot Velocity Measurement.

In: Champaigne, J. (Ed.). Int. Conf. on Shot Peening 6 (ICSP-6), San Francisco,CA, USA.

Menig, R., Pintschovius, L., Schulze, V., Vöhringer, O., 2001. Depth profiles of macroresidual stresses in thin shot peened steel plates determined by X-ray andneutron diffraction. Scr. Mater. 45 (8), 977–983.

Nordin, E., Ekström, K., Alfredsson, B., 2014. Experimental investigation of thestrain rate dependence of the SS 2506 gear steel, Int. Conf. on Shot Peening 12(ICSP-12), Goslar, Germany.

Olsson, E., Larsson, P.L., 2016. A unified model for the contact behaviour betweenequal and dissimilar elastic-plastic spherical bodies. Int. J. Solids Struct. 81,23–32.

SAE Standard J444, 2005. Cast shot and grit size specifications for peening andcleaning, http://www.sae.org/.

SAE Standard J442, 2008. Test strip, Holder, and Gage for Shot Peening, http://www.sae.org/.

Shotpeener, 2014a. http://www.shotpeener.com/learning/velocity size intensity.pdf, (2015-10-26).

Shotpeener, 2014b. http://www.shotpeener.com/learning/csvscwsizes.pdf,(2015-10-26).

Tabor, D., 1951. The Hardness of Metals. Oxford University Press, London, UK.Tufft, M., 1999. Shot Peen Impact on Life, Part 3: Development of a Fracture

Mechanics/threshold Behavior Predictive Model. In: Nakonieczny, A. (Ed.). Int.Conf. on Shot Peening 7 (ICSP-7), Warsaw, Poland.

Zinn, W., Scholtes, B., 2005. Influence of Shot Velocity and Shot Size on AlmenIntensity and Residual Stress Depth Distributions. In: Schulze, V. (Ed.). Int.Conf. on Shot Peening 9 (ICSP-9), Marne la Vallee, France.