A combined DEM–FEM numerical method for Shot Peening parameter optimisation

Advances in Engineering Software 79 (2015) 13–26

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Advances in Engineering Software

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A combined DEM–FEM numerical method for Shot Peening parameteroptimisation

http://dx.doi.org/10.1016/j.advengsoft.2014.09.0010965-9978/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +44 (0) 1865 613452, mobile: +44 (0) 7837975376.E-mail address: [email protected] (K. Murugaratnam).

Kovthaman Murugaratnam a,⇑, Stefano Utili a,b, Nik Petrinic a

a Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdomb School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 January 2014Received in revised form 6 August 2014Accepted 7 September 2014

Keywords:Shot PeeningResidual stressesDiscrete Element MethodFinite Element MethodOptimisationNumerical simulation

A numerical modelling approach capable of simulating Shot Peening (SP) processes of industrial interestwas developed by combining the Discrete Element Method (DEM) with the Finite Element Method (FEM).

In this approach, shot–shot and shot–target interactions as well as the overall shot flow were simulatedefficiently using rigid body dynamics. A new algorithm to dynamically adapt the coefficient of restitution(CoR) for repeated impacts of shots on the same spot was implemented in the DEM code to take intoaccount the effect of material hardening. Then, a parametric study was conducted using the Finite Ele-ment Method (FEM) to investigate the influence of the SP parameters on the development of residualstresses.

Finally, a two-step coupling method is presented to combine the output of DEM simulation with FEManalyses to retrieve the Compressive Residual Stresses (CRS) after multiple impacts with the aim to eval-uate the minimum area required to be modelled to realistically capture the field of residual stresses. Aseries of such coupled analyses were performed to determine the effect of peening angle and the combi-nation of initial velocity and mass flow rate on CRS.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Shot Peening (SP) is common industrial cold working processthat is applied to induce a field of Compressive Residual Stresses(CRS) on the surface of a metallic component [1]. Compressivestresses are beneficial in increasing resistance to fatigue failures,corrosion fatigue, fretting, wear, etc. In the process, a huge numberof tiny spherical particles impact the treated surface. The overallprocess is ruled by multiple parameters, which need to be con-trolled and monitored in order to induce an appropriate CRS distri-bution providing additional resistance to the treated component[2]. The treatment surface is impacted by a large amount of roundmetallic particles, the so called ‘shots’, at high velocities. Each shotacts as a tiny peen hammer, causing the surface to yield in plasticdeformation and leaving a concave depression, termed dimple, onthe surface of the target component. The stress field of the depres-sion is similar to the field of a flat bar being bent. The concave sideof the bar is in compression and the convex side is in tension. Thenormal stress along the cross section of the bar varies from a max-imum compressive stress on the concave surface, to zero stress at

the neutral axis up to a maximum tensile stress on the convexsurface.

Several parameters have a direct influence on the CRS. The mostimportant ones are: shot density, shot shape and material, impactangle, air pressure (shot velocity), nozzle geometry (diameter,peening angle and distance to the treated surface), and exposuretime. Fig. 1 provides a succinct conceptual visualisation of howthe peening parameters affect the peening quality.

Currently section of the optimal SP parameters is carried outempirically by performing several peening tests. The currentempirical procedures are time – consuming and very expensive.An efficient numerical method for the simulation of SP processesis needed to provide a faster procedure for the selection of the opti-mal parameters for SP requiring the use of far less experimentaltests which would be employed as validation of the numericalmethod rather than as a tool to search for the optimal values ofthe parameters. Moreover, an efficient numerical model can alsohelp improve quality control and increase confidence in the SPprocess.

In this paper a novel combined DEM–FEM numerical approachwas developed to simulate the SP process. Modelling SP processesis very complex since it involves the interaction of a metallic sur-face with an enormous number of shots. Experimental studiesare normally extremely costly, especially when aiming to optimise

Fig. 1. Parameters affecting the peening process.

14 K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26

the set of peening parameters. Numerical simulations allow for theunderstanding of the influence of the individual peening parame-ters on the field of residual stresses to be improved and for a pre-scribed peening target to be achieved. SP parameters arecustomarily chosen on the basis of either empirical laws or pastpractice. The relationship between the desired peening effect, par-ticularly the residual stress distribution of the treated surface, andthe peening parameters is still unknown and needs to be investi-gated. In fact, different values of peening parameters may give riseto very different fields of residual stress distribution.

Single and multiple shot impacts have been analysed byAl-Hassani [3], Deslaef et al. [4], Majzoobi et al. [5], Meguid et al.[6], Han et al. [7], Hong et al. [8], and Bhuvaraghan et al. [9].Al-Hassani et al. [3] investigated the single shot impacts at variousangles. Deslaef et al. [4] examined the effect of rigid and deform-able shots. Majzoobi et al. [5] conducted a three dimensionalnumerical study where multiple shots impact on a target surfaceat different velocities. They concluded that the obtained residualstress distribution highly depends on impact velocity and numberof impacts and that the maximum CRS rises as the velocityincreases only up to a point and thereafter it begins to decline.Meguid et al. [6] performed dynamic finite element analyses of sin-gle shot impacts investigating the effects of shot velocity, size andshape and target characteristics on CRS concluding that the effectsof shot parameters were more significant than the strain-hardening rate of the target material.

Most of the SP studies performed in the literature do not modelthe shot–shot interaction occurring during the travel from the noz-zle to the target surface and the shot rebounds from the target sur-face. Discrete element models were proposed by Han et al. [7],Hong et al. [8] and Bhuvaraghan et al. [9] to analyse the shot–shotand shot–target interaction in more detail, assuming both shot andtarget surface being rigid bodies. Later on, Bhuvaraghan et al. [9]coupled the DEM with FEM. However, the relationship betweenthe peening parameters employed as input data in the DEM andthe resulting CRS in FEM has not been established.

Cao et al. [10] proposed an approximate model able to relateAlmen intensity to shot velocity, however the relationship withthe residual stresses in the shot peened object was not investi-gated. Many approaches recorded in published research deal withthe prediction of residual stresses due to SP but do not relate themwith Almen intensity and are therefore of limited practical interest.In contrast, Guagliano [11] employed the FEM to predict theresidual stresses induced by SP on a metal target surface and

related these stresses to Almen intensity simulating the impactof a few shots on a flat plate.

An explicit dynamic algorithm for modelling up to 1000 impactswas described by Wang et al. [12] who showed that the FEM is ableto investigate macroscopic effects (e.g. curvature) of SP as well asmicroscopic effects (e.g. local plasticity and residual stresses).The study, however, did not include any shot–shot interaction.

On the other hand, this paper focuses on the development of anappropriate numerical model that can be used to optimise thepeening process and the in turn the material response. In the fol-lowing section, first the peening process is expounded. The pro-posed SP numerical model for the analysis of the shot stream inDEM and single shot impact analysis run by FEM are discussednext. A section describing the obtained results is followed byconclusions.

2. Shot Peening numerical model

2.1. Discrete element modelling of a shot stream

The Discrete Element Method (DEM) records the motion of eachsingle particle and its interaction with other particles and surfacesusing Newton’s laws of motion. The state of the system is updatedincrementally, at short time intervals using explicit time integrationbased on a leap-frog central difference scheme. At every time step,particle accelerations, velocities and positions are calculated. Con-tact mechanics laws relate the inter-particle elastic force with theparticle deformation through the physical and geometrical proper-ties of the particles. Damping is employed at contacts in order toaccount for the loss of kinetic energy during shot interaction.

2.1.1. The contact lawShots are modelled as elastic isotropic bodies. The Hertz–Mind-

lin non-slip contact law was employed to model the shot–shotinteraction and the shot–target surface interaction. The model isbased on the work of Mindlin [13].

In the normal direction, the exact analytical solution for the pres-sure and therefore the force upon the contact is given by the Hertzlaw. According to this law, the normal force–displacement (N–d)relationship is non-linear. Considering a collision between 2 parti-cles with elastic modulus E, Poisson’s ratio m and radii R1 and R2

Fn ¼43

E�ffiffiffiffiffiR�p

d32n ð1Þ

Table 1CoR for shot interaction after Bhuvaraghan et al. [9].

Impact No Input velocity m/s Rebound velocity m/s CoR

1 100 39.60 0.3962 100 54.04 0.5403 100 58.28 0.5834 100 76.31 0.763

K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26 15

where the equivalent Young’s Modulus E⁄, the equivalent radius R⁄

are defined as

1E�¼ ð1� v2

i ÞEi

þð1� v2

j ÞEj

ð2Þ

1R�¼ 1

Riþ 1

Rjð3Þ

with Ei, vi, Ri and Ej, vj, Rj being the Young’s Modulus, Poisson ratioand radius of each sphere in contact. Additionally there is a damp-ing force, Fd

n, given by:

Fdn ¼ �2

ffiffiffi56

rbffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiSnm�vn

pð4Þ

where m� ¼ 1miþ 1

mj

� ��1is the equivalent mass, vn is the normal

component of the relative velocity, the parameter b and Sn (the nor-mal stiffness) are given by:

b ¼ ln effiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiln2eþ p2

p ð5Þ

Sn ¼ 2E�ffiffiffiffiffiffiffiffiffiffiR�dn

pð6Þ

where e is the CoR.

2.1.2. Tangential forcesThe tangential force, Ft, depends on the tangential overlap dt and

the tangential stiffness St.

Ft ¼ �Stdt ð7Þ

with

St ¼ 8G�ffiffiffiffiffiffiffiffiffiffiR�dn

pð8Þ

with G⁄ being the equivalent shear modulus.

1G�¼ ð1� v2

i ÞGi

þð1� v2

j ÞGj

ð9Þ

Additionally, tangential damping is given by:

Fdt ¼ �2

ffiffiffi56

rbffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiStm�v t

pð10Þ

where vt is the relative tangential velocity.As in the normal direction, we assume that the plastic dissipa-

tion can be expressed by a CoR. However, it is important to notethat dissipation can also occur due to friction. Therefore, unlikethe normal case, the contact law is made by a linear spring, a dash-pot and a slider. The CoR will be assumed equal to the normal case:et = en. In the same way the tangential damping force will be calcu-lated according to Eqs. (3) and (4).

2.1.3. The coefficient of restitutionMetal spheres do not behave elastically but undergo permanent

deformations during collisions at high speed, when the contacttractions exceed their elastic limits. This means that the particlekinetic energy is dissipated by the occurrence of plastic strains, heattransfer and elastic wave propagation. According to the study byWu et al. [14], the latter phenomenon is negligible in comparisonwith the energy dissipated via plastic deformations and heat trans-fer. To use a contact law characterised by an elasto-visco-plasticmodel such as those typical of continuum mechanics would beoverly complex and unaffordable from a computational point ofview. As a result, the adopted model simulates the shots interactionby approximating the energy and momentum lost by the collidingshot by means of the so-called coefficient of restitution.

Hertz–Mindlin law applies to purely elastic bodies whereas CoRwas derived from experiments on elasto-plastic. The approxima-tion introduced by our law is to separate out the elastic and plasticdeformations. The relationships among the CoR, the incomingvelocity, the collision time and the contact force/displacement,were discussed in [15] and the FE analysis agreed closely withthe results produced by applying the Hertz theory. The coefficientexpresses the total amount of energy dissipated and momentumloss during an impact without calculating the permanent localdeformations undergone by the interacting surfaces. It is definedas:

e ¼ v r

v ið11Þ

with vr and vi the rebound and impact velocities respectively.The CoR is likely to affect significantly the final CRS, therefore it

should be determined as accurately as possible for the varioustypes of interactions. The CoR depends on both the impact velocity,and the impact angle hi. Therefore, ideally values of en and et shouldbe experimentally determined for a set of values of Vi initial veloc-ity and hi the angle of impingement. The CoR for the shot–surfaceinteraction will substantially vary depending on the history of pre-vious collisions on the shot and plastic deformation occurred bythe component. In Table 1, experimental data about the values ofthe CoR for shot–surface interaction for successive hits arereported. Keeping track of the location of each impact on the targetsurface over time, it is possible to implement values of CoR in theDEM code which change over time as a function of the number ofprevious impacts at the same location. In this way, it is possible toassess the effect of an impact dependent CoR on the obtained CRSand whether a value of the CoR averaged out of the number of col-lisions per spot could be applied instead.

The CoR for sphere–sphere interaction, es–s is different from thesphere–flat plate interaction es–p. In the absence of experimentaldata, es–p = 0.4 was assumed for both normal and tangential direc-tion independent of the angle of impact and of the relative velocitybetween colliding shots.

To assign a prescribed a viscous damping force, Fd, was appliedto the two shots involved in the collision:

Fd ¼ �gv ð12Þ

with g being the damping coefficient and v the relative velocitybetween the two colliding particles. The relationship here employedto work out the damping coefficient corresponding to the desiredCoR is from Tsuji et al. [16]. They numerically integrated the differ-ential equation of motion (single degree of freedom system) for var-ious values of the viscous coefficients, then evaluated the CoR asratio between initial and final velocity to obtain the relationshipof CoR vs. viscous coefficient.

g ¼ affiffiffiffiffiffiffiffiffiffiffimKH

pd

14 with a ¼

ffiffiffi54

r2 lnðeÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ððlnðeÞÞ2 þ p2Þq ð13Þ

2.1.4. Model setup3D DEM analyses were performed using the commercial dis-

crete element code EDEM [17]. The input data for the simulations

16 K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26

consists of: the nozzle inner diameter dn and the distance d,between nozzle and target surface, the angle between nozzle andtreated surface, the so-called angle of attack h. Spherical shots ofequal size were randomly generated at the nozzle cross sectionusing the Particle Factory function in EDEM. The number of shotsdelivered from the nozzle in a given time period is a function ofthe presented mass flow rate used in the peening process. The ini-tial velocity of the shots, Vi, is a function of the air pressure of thepeening system. In this simulation a variation of 5% around the ini-tial velocity was applied. SP quality is determined by the generatedCRS pattern within the target component derived by the energytransfer and plastic deformation. The impact energy can be easilyextracted from the DE simulation. One way to evaluate the impactenergy is to determine the velocity of the shot just before impact.In the DEM simulation, the shots impacting on the target were con-tinuously monitored and recorded along with time of impact,impact position and the components of this velocity along threecoordinates are Vox, Voy and Voz respectively.

2.1.5. Coefficient of restitution for repeated impacts2.1.5.1. Algorithm and implementation. An algorithm to change theCoR for repeated impacts for the same location was implementedusing the User Defined Library (UDL) in EDEM. The EDEM applica-tion triggers the UDL module for every shot–shot and shot–targetcollision. Once a shot–target collision is detected, the contact loca-tion of the target surface is retrieved and for every new contact thefacets falling within the predefined impact diameter is recorded.The corresponding CoR data for the impact number is thenretrieved from Table 1 and applied to compute the contact forces.Fig. 2 shows the process flow diagram. The results depend on themesh size, the number of impacts per geometry face and the valuesof the CoR data. The shot–shot, shot–target interaction includingthe resulting CRS were compared and analysed for the constantCoR case and for the case of variable CoR which progressivelyincreases with number of impacts.

2.2. DEM/FEM coupling

The DEM is unable to model the plastic deformations and resid-ual stresses induced on the treated surface. Hence, a FE analysis isneeded to determine the compressive residual stresses of the sur-faces. In our system a User Defined Library (UDL) is created withinthe EDEM application to log locations and impact velocities. Thisinformation is then used to create the Abaqus input files.

Fig. 2. Description of the process for chan

Depending on the target geometry size and number of impacts,the input file can become very large. Since running a set of pro-grams to generate a computable FE input from the DEM outputcan be very time consuming, we implemented an algorithm to gen-erate the Abaqus input files within the DEM code.

In the simulation, the DEM application uses a coarse meshwhile the FEM analyses require a finer mesh to capture the CRS.This would require the coupling algorithm to match the meshesin DEM and FEM according to the impact location. Previously,Bhuvaraghan et al. [9] coupled DEM and FEM by recording theforces, location and indentation information to apply the equiva-lent pressure to retrieve the CRS. They retrieved the indentationinformation from simulations of single shot impacts. The circularpressure zone was modelled as an octagonal zone to follow themesh pattern. However, in this study shots were assumed toimpact the target surface in the normal direction only. Hence, thismethod is unable to replicate the different indentations producedby shots impacting the treated surface at different angles. More-over, the subsequent shots impacting the intended area willrebound differently.

In our approach instead, the shots are modelled in FEM as rigidparticles and placed right above the location recorded in DEM. Anew step is created with initial conditions using the shot impactvelocity from DEM. In the next step, the impact is performed andexcluded in future steps. In this way, we retrieve the exact inden-tation for different shots sizes impacting at various angles andvelocities. The advantage of the proposed method lies in the factthat there is no need to employ the same mesh for the DEM andFEM analyses. Fig. 3 illustrates the algorithm via a flow diagramdetailing the coupling between the DEM code EDEM and the FEMcode Abaqus [16,17]. The coupling can be outlined in the followingsteps:

1. The ⁄.stl geometry file is loaded into Abaqus and the mate-rial properties are selected. The input file is created and sep-arated into dynamic and static parts. These are parts of themain input file that need to be populated and parts of thefile that will remain unchanged regardless of the numberof impacts, location, etc. The main input file is divided intofour separate files. The dynamic parts are discarded andthe static parts are saved to be used later in step 6.

2. The same ⁄.stl file is loaded into the commercial EDEM pro-gram along with a file containing the geometry surface datafrom FEM.

ging the CoR for subsequent impacts.

Fig. 3. The diagram shows the DEM–FEM coupling process.

Fig. 4. Effect of impact number for the reference case (mass flow rate rm = 13 kg/min, initial velocity vimp = 50 m/s, angle of attack h = 67.5�, distance d = 20 mm and shotdiameter dshot = 0.58 mm).

Fig. 5. Number of shot–shot and shot–target collisions for different Nozzle distance d.

K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26 17

Fig. 6. Total energy loss of shot–shot and shot–target collisions for different Nozzle distance d.

Table 2Different parameter values for different mass flow rates and velocities and their corresponding after Hong et al. [8].

No 1 2 3 4 5 6 7 8 9

e 3.154 2.244 2.103 1.577 1.496 1.334 1.122 0.890 0.667rm kg/min 13 9.25 13 13 9.25 5.5 9.25 5.5 5.5vo m/s 50 50 75 100 75 50 100 75 100

Fig. 7. Shows the number of shot–shot and shot–target interactions at different initial velocities.

Fig. 8. Shows percentage of shot retaining their normalised initial velocity higher than 90% for different mass flow rate and initial velocity.

18 K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26

Fig. 9. Showing the energy loss doe to shot–target collisions.

Fig. 10. Effect of angle of attack on the percentage of particles maintaining theirinitial velocity at impact.

Fig. 11. Effect of angle of attack on the percentage of particles remaining at normalimpact velocity.

Fig. 12. Number of shots delivered per second vs. shot diameter.

K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26 19

3. The SP model is set up with the individual peeningparameters.

4. The DEM SP simulation is run, applying the CoR forrepeated impacts. For each new shot–target contact theimpact location and velocity are recorded.

5. When the simulation ends, two separate files are createdcontaining the ⁄Nset, ⁄Step and ⁄Loads parts of the Abaqusfile. Impacts that are further away from each other aregrouped together and are computed simultaneously inthe same time step. This reduces the computation timeand the output size of the file.

6. The two output files created from the EDEM simulationsare then merged together with the two files from stepone to generate the main Abaqus input file.

7. The input file is then loaded into Abaqus to obtain theresidual compressive stresses.

3. Results

3.1. Discrete element modelling of shot stream

3.1.1. Effect of peening parametersFirst, the number of impacts after which the system reaches a

steady sate was investigated. Impact velocities just before theshot–target collision were recorded and analysed. Fig. 4 showsthe distribution of normalised impact velocities for the consid-ered reference case: mass flow rate rm = 9.25 m/s, initial velocityvimp = 75 m/s, angle of attack h = 67.5�, distance d = 20 mm andshot diameter dshot = 0.58 mm. These parameters were adoptedfrom Hong et al. [8]. It emerges that in the first 50 impacts about64% of shots hitting the target surface with a velocity within 10%from the initial velocity (vimp = 0.9vo � 1.0vo). This indicates thatthese shots had only little or no interaction with other shotsbefore hitting the target surface. The remaining 36% of shots(18 shots) had energy dissipation due to interaction with othersshots. Steady state is reached after an initial period of 4000impacts, with 33.65% of impacts hitting the surface with initialvelocity. The longest transient state occurs with the highest massflow rate of 13 kg/min and lowest initial velocity 50 m/s andangle of attack h = 90� and distance d = 20 mm. Since the steadystate is reached after 4000 impacts, the impact number of10,000 can be taken as the steady state for all combination ofparameters used in this study.

Fig. 13. Number shot–shot and shot–target interaction for different shot diameters.

Table 3Shows the results for indentation radius dshot.

Constant CoR Variable CoR with indentation radius 0.29 mm

Shot–shot collision 6485 5912Shot–target collision 13,959 15,615Total energy loss through shot–target collision in J 21.99 13.1993Average velocity at impact in m/s 78.29 79.3572Average normal velocity at impact in m/s 62.38 63.7258

20 K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26

3.1.2. Effect of nozzle distanceNext, the effect of the distance between the nozzle and target

surface was investigated. Distances ranging from 5 mm to 30 mmwere investigated. Fig. 5 shows the total number of interactionsfor different distances d. Fig. 6 shows the total energy loss fordifferent distances d. The effect of distance on the peening qualitywas not found to be significant when d greater than 20 mm isemployed and shot diameter is 0.58 mm and therefore 20 mmwas chosen as the peening distance between nozzle andcomponent.

3.1.3. Effect of mass flow and initial velocityA matrix simulation covering various mass flow rates and initial

velocities was carried out next. Table 2 shows the different param-eters for different mass flow rates. For simplicity a dimensionlessflow rate parameter e is introduced:

Fig. 14. Showing the energy dissipation for shot–target with a constant CoR 0.4 andthe energy dissipation for shot–target interaction with changing the CoR for thecase with indentation radius 0.58 mm.

rm � d50

vo �mshot:

where rm is the mass flow rate of the nozzle, d50 the averageparticle diameter, vo initial velocity and mshot the shot mass.

Fig. 7 shows the number of shot–shot and shot–target interac-tions for the different initial velocities. It can be concluded thatthe number of shot–shot and shot–target interaction increaseswith lower initial velocity. Compared to the shot–target collisions,the shot–shot interactions nearly doubles from 75 m/s to 200 m/s.

The effect of mass flow rate and initial velocity on the distribu-tion of normalised impact velocity for h = 90� and h = 62.5� wasinvestigated next. Fig. 8 shows the percentage of shot retainingtheir normalised initial velocity higher than 90% for different massflow rate and initial velocity for =62.5�. It can be seen that theparameter e is significant.

Fig. 15. Show the peening process of turbine rotor.

Fig. 16. Shows the peening process of a flat surface using a dynamic nozzle.

Fig. 17. Stress–stress behaviour of the linear – strain hardening plastic material.

K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26 21

For a lower e value, more shots hit the surface with initial veloc-ity than in the simulation with a higher value. The key parametersrm = 5.5, h = 62.5� and vo = 100 m/s corresponds to the lowest valueof e = 0.667 where at which point about 56% of impacts maintainedtheir initial velocity at impact (vimp = 0.9vo � 1.0vo). This indicatesthat the shots had little or no energy dissipation from the nozzle

Fig. 18. The three-dimensional fin

to the surface. Fig. 9 confirms that for a lowest value of e, caseH9, the energy loss due to shot–target interaction is the lowest.

The lowest percentage of normalised impact velocity wasencountered with the highest value e = 3.154, corresponding tocase H1 with the mass flow rate rm = 13 and vo = 50 m/s where only3.89% of shots maintained their initial velocity.

Highest energy loss was encountered in case H7, correspondingto rm = 9.25 and vo = 100 m/s. The second highest was H4 withparameters s rm = 13 and vo = 100 m/s. This indicates that velocityis an important factor for shot–target energy dissipation.

In can be concluded that with a higher mass flow rate rm theenergy dissipation increases due to the large number of shot–shotinteractions. A lower mass is therefore more suitable for the peen-ing process with smaller shot–shot interactions associated withlower energy dissipation. With a lower initial velocity the shotsdo not move quickly enough and the likelihood of interactions withrebounding shots increases. With a much higher initial velocity theshots move quicker and the probability of interactions between theshots decreases. Lower mass flow rate implies less energy dissipa-tion for shot interaction but also less transferred energy. Howeverthis could be countered by longer peening time. The optimal com-bination depends on the cost of peening time and how the industrychooses this parameter.

Looking at results from h = 90� and h = 62.5� it can be concludedthat the angle of attack has a significant influence on the outcome.Hence, the angle of attack needs to be investigated next.

3.1.4. Effect of angle of attackThe effect of angle of attack was investigated with the following

parameters; mass flow rate rm = 9.25 m/s, initial velocityvo = 100 m/s, distance d = 20 mm and shot diameter dshot = 0.58 -mm. Fig. 10 shows the percentage of shots retaining their initialvelocity for different angles of attack, where impact velocity is90–100% of initial velocity. Analysing the velocity at impact, forh = 35�, about 74% of shot retained their initial velocity and hadfewer interactions between shots. Shot–shot interactions increasedsignificantly when h = 90� and only 50% of shots retained their ini-tial velocity. This is explained by the large number of reboundingshots coinciding with incoming shots. The percentage of shotsretaining their initial velocity decreases with the angle of attackincreasing. To measure CRS, the normal impact velocity is moresignificant than the tangential component. Fig. 11 shows the effect

ite element mesh in Abaqus.

Fig. 19. Validation of single shot impact with Meguid et al. [6].

Fig. 20. The three dimensional finite element numerical simulation model of themulti shot impact in Abaqus.

22 K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26

of angle of attack on the percentage of particles retraining theirnormal impact velocity (vo = 100 m/s). Looking at the normalimpact velocity it can be shown that h = 62.5� provides the highestpercentage of shots retaining initial velocity at impact (62.83%). Noshots retraining their normal impact velocity when h < 45�. This isa useful information for the industry providing the target inclina-tion for the process.

3.1.5. Effect of shot diametersThe distribution of impact velocities for differ shot diameters

was examined. Specially, five different shot diameters dshot = 0.4,0.58, 0.75, 1.0 and 1.5 mm with the process parameters rm = 9.25kg/min, vo = 75 m/s, h = 62.5� and d = 20 mm were studied. Thetotal mass and mass flow rate are kept constant such that whenthe shot size is decreased, the overall peening time is increased.Fig. 12 shows the number of shots per second delivered from thenozzle for the different shot diameters. For dshot = 0.4 mm a highnumber of shots (590, 000) are delivered from the nozzle com-pared to 11, 200 shots for dshot = 1.5 mm. The shot–shot collisiondecreased almost linearly for dshot = 0.4 mm (18, 057) towardsdshot = 1.5 mm (2, 174). Fig. 13 shows the shot–shot and shot–target interaction numbers for the different shot diameters.

3.1.6. Effect of changing the CoR for subsequent impactsCoR and the energy dissipation for shot–target interaction with

changing CoR. In practice the region of influence will depend onthe impact velocity, angle of impact and the shot size. The inden-tation area is affected by shot size, the impact velocity (the higher

the velocity the larger the dimple) and the angle of impingement(an oblique angle generates an elliptical dimple). For simplicity,the region of influence was chosen as the average shot diameter(0.58 mm). When applying the CoR dynamically the energy dissi-pation decreases with the increase of indentation radius. Table 3shows the results for constant and variable CoR for 10,000 impacts.A target location that is being hit for the first time has a low CoR,resulting in high energy dissipation. The next shot hitting a loca-tion that was hit previously and plastically deformed the targetsurface has a higher CoR, resulting in lower energy dissipation.Subsequent shots hitting the target surface will rebound with ahigher velocity than the first shot and retaining more of theirkinetic energy. Fig. 14 shows the energy dissipation for shot–targetwith a constant CoR 0.4 and the energy dissipation for shot–targetinteraction with changing the CoR for the case with indentationradius 0.58 mm.

Results show that shot–shot interaction decreases and shot–target interaction number increases. More importantly the averagenormal velocity at impact increases, which is important for thegeneration of compressive residual stress. Changing the CoR forrepeated impacts will result in a more intense compressiveresidual stress distribution.

3.1.7. CoverageCoverage is defined as the percentage of a given surface that is

obliterated by dents or dimples. Coverage beyond 100% is referredto as full coverage or multiples of time to achieve 100% coverage.However, in practice, the size of impressions will vary due to theshot size variation, shot velocity, impact angle and peened materialproperties. The current model only considers the shot size. Otherrelevant parameters can be assigned as a function taking intoaccount a more realistic size of indentation.

The imported target geometries consist of a triangular mesh. TheUDL implemented within the DE application counts the number ofimpacts for every single mesh element, providing a rapid way to ana-lyse the individual peening parameters and peening quality. Visual-ising the impact location in the DE simulation can give a goodindication of the peening coverage. Figs. 15 and 16 show the shotimpact location in DEM. Surface location coloured in brown showsthe concentration of the number of impacts. The number of impactsfor a particular location can be extracted and analysed in moredetail. This allows analysing SP processes with multiple nozzlesand complex geometries to comprehend more complex conditions.

3.2. FEM analysis

3.2.1. Single shot analysisThe three-dimensional FE model was developed to investigate

single shot impacts on the circular plate. A comparison was made

Fig. 21. Show the minimum area 3 � d and the midpoint at which the CRS is measured.

Fig. 22. Shows the CRS resulting from analysing different area from the same simulation for peening angle 90�.

Fig. 23. Shows the CRS resulting from analysing different area from the same simulation for peening angle 35�.

K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26 23

with the numerical study of Meguid et al. [6] and Hong et al. [8].The circular plate was given the following geometric properties;R = 4dshot, height H = 3dshot where dshot is the shot diameter, massdensity = 7800 kg/m3, elastic modulus E = 200 GPa, initial yield

Table 4Shows the depth of the CRS zone for different impact area.

Impact area 1 R 2 R 3 R 4 R

No. of impacts 2 12 35 66Depth of CRS zone in mm 0.80 0.92 0.91 0.93

stress r = 600 MPa and linear strain hardening parameterH1 = 800 MPa. The plate was retrained against all displacementsand rotations on the bottom end and was modelled usingeight-node linear brick elements with reduced integration(C3D8R) with element size 0.05dshot � 0.05dshot � 0.05dshot. Theshot was modelled as rigid sphere with a mass positioned at itscentre. The diameter of the shot was dshot = 1 mm and massmshot = 4.085 mg. Additionally, coulomb law with friction l = 0.25was applied during the contact. The results are plotted in a norma-lised manner with the residual stress rxx normalised with ro theinitial yield stress of the component. The stresses distribution plot-ted with the normalised deformed depth along the centre line of

Fig. 24. Shows the effect of CoR in DEM on the CRS in FEM.

Table 5Shows the depth of the CRS zone for different CoR in FEM.

CoR 0.4 0.57 Variable (Table 1)

No. of impacts 35 38 29Depth of CRS zone in mm 0.896 0.922 0.882

24 K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26

the component. Fig. 17 shows the material model and Fig. 18shows three-dimensional finite element mesh. Numerical valida-tion of single shot impact with Meguid et al. [6] is shown in Fig. 19.

3.3. DEM/FEM coupled analysis

A number of coupled analyses were performed with 4000 shotsimpacting a flat surface. The plate was given the following5 mm � 5 mm � 3 mm, mass density = 7800 kg/m3, elastic modu-lus E = 200 GPa, initial yield stress r = 600 MPa and linear strainhardening parameter H1 = 800 MPa. All displacements and rota-tions of the plate bottom were restrained. The diameter of the shot

Fig. 25. Shows the impact location for peening angl

was dshot = 1 mm and mass mshot = 4.085 mg. A friction coefficientof l = 0.25 was applied during the contact. The CRS distributionover time was measured at the midpoint of the flat surface to eval-uate the saturation time. Fig. 20 the dimensional finite elementnumerical simulation model of the multi shot impact in Abaqus.

Analyses were performed to evaluate the minimum area sizerequired to be modelled to retrieve the true residual stresses. Threedifferent simulations were performed to evaluate the effect ofstandard, average and variable CoR in DEM on the resulting CRSin FEM. Further a coupled analysis was performed to access theeffect of the peening angle on the resulting CRS and the influenceof mass flow rate and velocity on CRS. Fig. 20 shows the coupledanalysis in FEM.

3.3.1. Minimum simulation domainAnalyses were performed to evaluate the size of the area

required to be modelled to retrieve the true residual stresses. Theimpact area diameter were defined as 1 � R, 2 � R, 3 � R and4 � R from the midpoint where R is the radius of the shot. Fig. 21shows the minimum area 3 � R. The CRS is measured at the

e in DEM, h = 35�,45�, 62.5�, 67.5�, 75� and 90�.

Fig. 26. Shows the effect of peening angle on the CRS.

Table 6Shows the depth of the CRS zone for different peening angle.

Angle 35� 45� 62.5� 67.5� 75� 90�

No. of impacts 20 30 36 44 40 35Depth of CRS zone in mm 0.54 0.59 0.76 0.70 1 0.9

K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26 25

midpoint and at 3 different points (midpoint (0,0,0), point1(0.1,0,0.1) and point2 (�0.1,0,�0.1) and point3 (0.1,0,�0.1)around the midpoint. The three measurement points lie withinthe distance of the smallest minimum area 1 � R. The plastic straingenerated by the high velocity impacts of the shots varies on thesurface layer. Since the surface residual compression progressivelyrelaxed with increased SP coverage condition [18], the depth of theCRS layer is consider as the suitable factor to be considered for thedifferent cases. To determine a precise CRS state of the peenedmaterial, an average CRS is determined from the four measure-ments. Figs. 22 and 23 show the CRS resulting from analysing dif-ferent area from the same simulation for peening angle h = 90� and35�. Evaluating the CRS for different area, it can be noted that thedepth of the compressive zone only changes very little whenthe peening area is greater than 3 � R. The compressive stress atthe surface layer various for the different areas. Table 4 showsthe depth of the CRS zone for different impact area.

3.3.2. Effect of CORThree different simulations were performed to evaluate the

effect of standard (0.4), average (0.57) and variable CoR in DEM

Fig. 27. Shows the influence of mas

on the resulting CRS in FEM. Only little variation of the depth ofthe compressive zone was encountered in the different simula-tions. Fig. 24 shows the effect of CoR in DEM on the CRS in FEM.Table 5 shows the depth of the CRS zone for different CoR in FEM.

3.3.3. Peening angleCoupled analyses were performed to investigate the effect of

peening angle on CRS. Simulations were performed with the peen-ing angle h = 90�, 75�, 67.5�, 62.5�, 45� and 35�. The peening angle hhas an effect of the coverage. A lower penning angle will cover alarger area than peening the component at angle h = 90�. Fig. 25shows the impact location for different peening angles in DEM.CRS results in Fig. 26 show that the CRS zone is large when theangle h = 75� and 90�. Table 6 shows the depth of the CRS zonefor different peening angle.

3.3.4. Influence of mass flow rate and velocity on CRSThe DEM analyses have shown that for a lower value of e more

shots retain their initial velocity. For the circular area 3 � R, a lowervalue of e results in a lower number of shot–target interactions andthe number of impacts increases when e increases. When peeningwith a lower mass flow rate and lower initial velocity, the shotsare delivery more precisely onto the surface. The resulting CRS areanalysed for the nine different cases and shown in Fig. 27. Analysingthe resulting CRS graphs for the nine different cases show that for thecase where e is small the CRS zone is the largest and the CRS zone issmall when e is large. Results also show that when using a higher ini-tial velocity like in cases H4, H7 and H9 the CRS zone is deeper thanin cases where a lower initial velocity is applied such as in case H1,

s flow rate and velocity on CRS.

Table 7Number of impacts for area 3 � R for different values of e adopted from Table 2 and corresponding depth of CRS zone.

No 1 2 3 4 5 6 7 8 9

e 3.154 2.244 2.103 1.577 1.496 1.334 1.122 0.890 0.667rm kg/min 13 9.25 13 13 9.25 5.5 9.25 5.5 5.5vo m/s 50 50 75 100 75 50 100 75 100Impacts 48 49 48 37 40 35 31 29 33Depth of CRS zone in mm 0.54 0.59 1.05 1.14 0.95 0.56 1.05 0.92 1.2

26 K. Murugaratnam et al. / Advances in Engineering Software 79 (2015) 13–26

H2 and H6. Table 7 shows the number of impacts for area 3 � R fordifferent values of e adopted from Table 2 and corresponding depthof CRS zone.

4. Conclusions

A new computational framework for SP processes based on boththe discrete element and the Finite Element Methods has been pre-sented. The introduced framework allowed to run an extensiveparametric analysis of the influence of the several mechanicalparameters involved in the SP process. Visualising the shot impactlocations in DEM can help to investigate the coverage build-upwhen peening a mechanical component of complex geometry withvery little computational effort: for instance a simulation with10,000 impacts can be simulated in only a few minutes on a singlecomputer with an Intel i7 870 processor (4 cores) with 8 MB cacheand 16 GB of memory running Linux CentOS.

The current model can be used to analyse the shot flow andassist in improving current nozzle designs and develop new ones.In the DEM simulations, the shot flow reached steady state after4000 impacts with the parameters used in this study. From theparametric analyses it emerged that the air pressure in the nozzle(vo) is the most important factor, followed by the mass flow rate rm

and the duration of the peening process.The new DEM–FEM coupling proposed in this paper provides a

convenient way to couple the commercial DEM and FEM applica-tions. A routine manages the interface between EDEM and Abaqus.The EDEM application generates an Abaqus input file, which is thenused to analyse the treatment surface and resulting CRS. Analyseswere performed to evaluate the minimum size of the area requiredto be modelled to retrieve the true residual stresses, which wasfound to be 3 � R where R is the radius of the shot.

Investigating the angle of attack and the normal impact veloc-ity, it emerged that the normal impact velocity can be quite largeand in some cases up to 60% of the initial velocity. For the casesconsidered in this study, the optimal angle of attack in DEM wasfound to be h = 62.5�. However analysing the peening angle inthe combined analysis showed that the depth of the CRS zone islargest when h = 70� followed by h = 90�.

A novel algorithm was implemented to change the CoR forrepeated impacts accounting for work hardening and the impactarea. Results showed that changing the CoR decreases the numberof shot–shot collisions and increases shot–target collisions. Theaverage impact velocity increases compared to the case wherethe CoR of first impact or the average of the CoRs of successiveimpacts is employed. Instead only a very small variation in CRSwas encountered in the different cases. A higher number ofimpacts resulted in a deeper CRS zone.

Energy transfer per unit time is a significant factor that has to beevaluated. Similar amounts of energy can be transferred onto thetarget surface using different peening parameters in short time.It was found that for a higher mass flow rate and lower initialvelocity fewer shots retain their initial velocity at impact but the

number of impacts is larger. Results from the coupled analysisshowed that the initial velocity is more important than the massflow rate and that when the initial velocity is high (100 m/s) theCRS depth zone is deeper than in the cases where a lower velocitywas used. However, a relation between CRS and mass flow ratecould not be established.

The existing computational SP model can be adopted such thatAlmen strips can be virtually placed onto the peening component.Future work will investigate the peening of more complex geome-tries with curved surfaces and edges, where Almen strips cannot beused during the peening process. Using the proposed computa-tional model it will be then possible to predict the percentage ofcoverage and Almen intensity reducing the need for expensiveexperimental testing.

Acknowledgements

The authors would like to acknowledge the funding provided byan Industrial CASE EPSRC award, Rolls Royce and DEM Solutions.

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