A numerical model of severe shot peening (SSP) to predict the generation of a nanostructured surface layer of material

A numerical model of severe shot peening (SSP) to predict the generation of a nanostructured surface layer of material
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  A numerical model of severe shot peening (SSP) to predict the generation of ananostructured surface layer of material S. Bagherifard, R. Ghelichi, M. Guagliano ⁎ Politecnico di Milano, Department of Mechanical Engineering, Via La Masa, 34 20156 Milano, Italy a b s t r a c ta r t i c l e i n f o  Article history: Received 21 October 2009Accepted in revised form 20 May 2010Available online 4 June 2010 Keywords: Severe shot peening (SSP)Nanocrystalline structureFinite elementResidual stressesEquivalent plastic strainSevere plastic deformation Generation of a surface layer of material characterized by grains with dimensions up to 100 nm by means of severe plastic deformation is one of the most interesting methods to improve the mechanical behaviour of materials and structural elements. Among the ways to obtain a surface layer with this characteristic, shotpeening is one of the most promising processes, since it is applicable to very general geometries and to allmetals and metal alloys without high-tech equipments. Notwithstanding the fact that the ability of shotpeening to obtain nanostructured surfaces by using particular process parameters (mainly high impactenergy and long exposure time) is proved, deep knowledge of the correct choice of quantitative values of process parameters and their relation to the grain size and the thickness and uniformity of thenanostructured layer is still lacking.In this paper a  fi nite element model of severe shot peening (SSP) is developed with the aim of predicting thetreatment conditions that lead to surface nanocrystallization. After having assessed the accuracy of themodel as regards mesh parameters and constitutive law of the material, the results are discussed andinterpreted in terms of induced residual stresses and surface work hardening. A method to assess theformation of nanostructured layer of materials based on the value of the equivalent plastic strain isdeveloped.The comparison with experimental results allow to af  fi rm that the model is a useful tool to predict thegeneration of a nanostructured surface layer by shot peening and to relate the peening parameters with thetreated surface layer in terms of residual stresses, work hardening, and depth of the nanostructured layer.© 2010 Elsevier B.V. All rights reserved. 1. Introduction Shot peening (SP) is a well-known mechanical surface treatmentgenerally applied to improve fatigue behaviour of metallic compo-nents. During the process small spherical peening media which areaccelerated in peening devices of various kinds impact the surface of work piece with energy able to cause surface plastic deformation. Theprocess is aimed to create compressive residual stresses and workhardenthenear surface layerof material.Theseeffects areveryusefulinordertototallypreventorgreatlydelayfailureofthepartbyfatigue[1 – 6].In recent years special methods of SP have been recognized to bebene fi cial in creating  fi ne grained layers of material on surface of treated components in order to improve service life time and globalbehaviour. This improvement is due to the fact that most cases of material failure such as fatigue fracture, fretting fatigue, wear andcorrosion srcinate from the exterior layers of the work piece. Thesephenomenaareallextremelysensitivetothestructureandpropertiesof the surface material. Since most of fatigue cracks initiate from thesurface and propagate to the interior, a component with a nanos-tructuredsurfacelayerandcoarse-grainedinteriorisexpectedtohavehighlyimprovedfatigueproperties.Sincebothfatigue-crackinitiationand propagation are inhibited by  fi ne grains near the surface andcoarse grains in the interior, respectively. Moreover, the residualcompressive stresses introduced during the process can effectivelystop or delay the initiation and propagation of fatigue cracks [7].Among the alternative SP methods aimed at surface nanocrystalliza-tion, we can recall ultrasonic shot peening (USSP) [8], surfacenanocrystallization and hardening (SNH) [8] and high-energy shotpeening (HESP) [8]. The mentioned processes are somehow differentfrom the conventional SP process both for the needed technologicalfacilities and for the mechanics of the treatment. The common aspectis to use special combinations of peening parameters to multiply thekineticenergyoftheshotimpactsinordertogeneratealargenumberof defects, dislocations and interfaces (grain boundaries) on thesurface layer of treated part and consequently transform itsmicrostructure into nanograin size [8]. Some experimental researchhas been developed to  fi nd the relationship between the processmechanisms and the characteristics of the generated  fi ne grainedlayer but there are still many aspects to be studied. Surface & Coatings Technology 204 (2010) 4081 – 4090 ⁎  Corresponding author. Tel.: +39 02 23998206; fax: +39 02 23998202. E-mail address: (M. Guagliano).0257-8972/$  –  see front matter © 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.surfcoat.2010.05.035 Contents lists available at ScienceDirect Surface & Coatings Technology  journal homepage:  It is well-known that numerical simulation can be considerablyhelpful to limit the costly and time consuming experiments. Theiref  fi cacy is moreappreciable in cases of attempt to obtain nanocrystalswith SP. Since these processes necessitate performing many experi-ments with different combinations of peening parameters in order toincrease the kinetic energy of process for generation of nanocrystals.In the present paper, SSP refers to an SP process applied byconventional air blast shot peening device but using severe para-meters which include high shot velocity and long exposure time.These parameters are basically different from those generally appliedinindustrytoshotpeenthesamematerial.Theaimofintensifyingthepeening parameters is to increase the kinetic energy of the processand eventually obtain surface nanocrystallization.Several approaches have been suggested in the literature fornumerical simulations of SP but there are very few studies dealingwith simulation of SSP that leads to surface nanocrystallization. Dai etal. performed impact simulation of surface nanocrystallization andhardening process (SNH) and compared the results in terms of roughness, residual stress and effective plastic strain [9,10]. Ma et al.developed a routine using  fi nite element method to perform amolecular dynamic simulation and calculate the dislocation densitygenerated by ultrasonic SP [11].In this study,  fi nite element simulation of air blast shot peening(ABSP) with unconventional and severe parameters is performed toprovide quantitative description of effect of peening parameters inorder to describe the distribution and magnitude of residual stressesand also the thickness of the work-hardened layer. After havingdescribed the development of the model in terms of geometry, meshparameters and the material mechanical behaviour schematization,the attention is focused on the critical assessment of the meshconvergence and the way the number of impacts can be related to thereal treatment time and consequently to the resulting coverage.In the  fi nal part of the paper the results are critically discussed interms of residual stresses and surface work hardening.Studies performed to distinguish the essential parameters forstructuralevolutionandgenerationofnanograinshaveacknowledgedlarge strains as the most important condition favorable to producenanocrystals [12,13]. There is also a criterion set on the accumulatedequivalent plastic strain (PEEQ) value proposed to assess theformation of nanograins [12,13]. In this paper a method based onthe mentioned criterion is proposed for the estimation of thetreatment parameters needed to obtain nanostructured surfacelayer of material and to assess its depth.The comparison of the obtained numerical results with experi-mental data regarding the favorable condition for formation of nanograins allows validating the presented SSP numerical model.Someguidelinesforfutureworksaimedtore fi nethemodelare fi nallydrawn. 2. Finite element simulation development  2.1. FE model geometry A 3D model developed using commercial  fi nite element codeAbaqus/Explicit 6.7 is utilized to investigate single and multipleimpact effects. Due to symmetry only one quarter of the specimen ismodelled for studying single impact while in case of multiple impactsthe full model is analyzed to maintain the arbitrary aspect of theprocess.The target is modelled as a rectangular body (3 ⁎ 3 ⁎ 1.5 mm 3 ),suf  fi ciently large to avoid the effects of boundary conditions on theresidualstressstateintheimpactarea.Theimpactareaof(1 ⁎ 1 mm 2 )islocatedinthecentreoftherectangularface.Targetmeshissetupby513604C3D8R8-nodelinear brickelements withreducedintegrationand hourglass control. All side faces including target's base aresurrounded by so called half in fi nite elements that provide quietboundaries by minimizing the re fl ection of dilatational and shearwavesbackin totheregionofinterest [14].The shapeandorientationof this element are similar to C3D8R element excluding that theelement must be attached such that the in fi nite end faces away fromthe model. In fi nite elements are allowed only with linear elasticbehaviour, so they must be positioned suf  fi ciently distant from thenon-linear interaction region to ensure accuracy [15].Steel shots with a diameter of 0.6 mm similar to the shots used inexperiment (commercial grade S230) are modelled as sphericalbodies consisting of tetrahedral C3D4 elements with an isotropicelastic behaviour. Velocity in the z-direction was de fi ned as initialcondition to all the shots, regarding an impact angle=90° as it istypical for ABSP.General contact was used as the criteria of contact with anisotropic Coulomb friction coef  fi cient equal to  μ  =0.2 [16]. Thescheme of full model is presented in Fig. 1.It is to be underlined that thermal effects have been neglected inthe developed simulation.  2.2. Material model Since strain rate dependency of target material will have notableeffects on stress pro fi le and the extent of surface hardening, it isrecommended to use a material model able to describe the nearsurface high strain rate response due to the high-energy successiveimpacts [17]. In this study non-linear kinematic Chaboche hardeningmodel [18] and also Johnson – Cook equation [19], which are bothconstitutive models representing effect of strain rate on materialhardening, were initially chosen to describe target material'sbehaviour. The results for both material models were comparedwith experimental results and  fi nally combined isotropic kinematicmodel was chosen for the rest of analysis due to better consistencywithexperimentalresults.Johnson – Cookmodelhighlyoverestimatedsurface residual stress and also the maximum residual stress belowthe surface.The material used in this study is steel (39NiCrMo3, according totheItaliannomenclature)withthechemicalcompositionpresentedinTable 1. Static tension tests were carried out according to ASTM E8M[20] in order to obtain monotonic properties of the material. ThespecimenswerepreparedfollowingtheinstructionsofASTMA370-05[21]. Obtained results are reported in Table 2. For characterization of  plastic behaviour of material a set of cyclic tension compressionexperiments were performed to obtain the properties needed for theChaboche hardening model. The adopted model consists of acombined isotropic kinematic hardening formulation  fi rstly intro-duced by Armstrong and Fredrick [22], and subsequently modi fi ed byChaboche [18,23 – 25]. The detailed description of its formulation isprovided in [26].Low-cycle fatigue tests up to the stabilized cycle were performedat different deformation intervals ( ∆ ε  =0.012,  ∆ ε  =0.014, ∆ ε  =0.016), all symmetric with respect to zero, using cylindricalspecimens following instructions of ASTM E606 [27]. Fig. 2 shows the monotonic tension and stabilized cyclic tension compression curvesobtained from tests. The results represent that the material issubjected to cyclic softening.The results obtained for different deformation intervals wereelaborated to de fi ne parameters of hardening model [18]. Forsimpli fi cation it was supposed that the isotropic component can beexcluded from hardening model taking in to account that shotpeening process provides small number of loading unloading cyclesand consequently the in fl uence of cycling softening of material aftersmall number of cycles can be negligible in this case.Determination of combined hardening parameters was performedbyAbaqus/CAEwhichprovidesaspecialfunctionfordeterminationof hardening parameters based on experimental data of a stabilized 4082  S. Bagherifard et al. / Surface & Coatings Technology 204 (2010) 4081 – 4090  cycle obtained in a deformation control condition with a symmetricstrain interval [15].The stress – strain data was extracted from the test performed at ∆ ε  =0.016. However instead of the stabilized cycle, the hysteresiscycle obtained in the beginningof the test (after 3 cycles) was used inorder to make a more realistic model by simulating low number of cycles. Also cyclic yield stress and elastic modulus were used insteadof the values obtained in monotonic tension tests. The obtainedkinematic parameter values and the  fi nal chosen properties arereported in Table 3.In order to assess the correspondence of the obtained data fromAbaqus and the experimental tests, a low cycle push – pull fatigue testwas simulated on a simple cylindrical model ( ∆ ε  =0.016). Asinusoidal deformation as shown in Fig. 3a was applied to one endof the cylinder. The model was comparatively coarsely meshed by8 node brick elements as shown in Fig. 3b.ComparisonofthenumericalandexperimentalresultsasshowninFig. 4 represent a good level of correspondence in the reconstructionof simulated load cycle if the values in the  fi rst plastic loading phaseare excluded. This difference is due to the fact that the numericalmodel is not able to describe the  “ plateau ”  for yield stress in the  fi rstbranch of plastic load as already demonstrated by Broggiato et al.[26,28].Moreover, regarding the fact that it is not possible to predict thelevelofstrainthatthematerialwillundergoduringSPprocess,asetof simulations are performed to check model transferability. Thesimulation has been repeated applying different symmetric straincycles ( ε  max =0.006 and  ε  max =0.007) while in both cases thehardening parameters obtained from  ε  max =0.008 test were used forcharacterization of material. In both simulations the comparison withnumerical data was in agreement with the experimental results. ThenumericalresultscomparedwithexperimentaldataasshowninFig.5for  ε  max =0.007, show the independence of the results from the inputdata that is  ε  max =0.008 experimental results.  2.3. Assessment of mesh convergence Fora3Dmodelwithmultipleimpacts,themostchallengingaspectof simulation is the solution time; since in explicit FE simulation sizeof smallest element determines total solution time, setting theminimum element size would be of great importance.In all SP simulations available in literature fi ne mesh is used in theimpact area and coarser elements in the area far from impact region.Whereas the size of elements utilized in these simulations aredifferent and the authors did not manage to make out a clear justi fi cation about the chosen element sizes. Moreover all the fewmesh convergence studies have focused on obtaining good resolution just in terms of residual stress distribution under impact area. Frija etal. simpli fi ed the case and carried out a sensitivity study to optimizedimensions of the elements in re fi ned zone, comparing stress resultswith the elastic Hertz contact problem [29].Zimmerman et al. used an element size equal to 1/15th of thedimple diameter produced by a single shot impact for the modelledshot diameter and velocity for which convergence was obtained interms of stresses [30]. Klemenz et al. also used Hertz analyticalsolution for a purely elastic material behaviour to examine theaccuracy of FE mesh in the cases of single and double impact model Fig. 1.  3D model used for multiple impact simulation.  Table 2 Monotonic mechanical characteristic of the material. σ  y  734 MPa σ  u  908 MPaE 210.522 GPaA% 14.8  Table 1 Chemical composition of steel in mass density.C (wt.%) Si (wt.%) max Mn (wt.%) P wt(wt.%) max S (wt.%) max Cr (wt.%) Mo (wt.%) Ni (wt.%)0.35 – 0.43±0.02 0.40±0.03 0.5 – 0.8±0.04 0.025+0.005 .035±0.005 0.60 – 1.00±0.05 0.15 – 0.25±0.03 0.70 – 1.00±0.054083 S. Bagherifard et al. / Surface & Coatings Technology 204 (2010) 4081 – 4090  and for multiple impacts they chose the size of elements equal to 1/10th of dimple size [31].In this study the effect of element size not only on stress state butalsoonthestrains,particularlyintermsofPEEQisexamined,sincetheaccumulated strain is a key parameter to be applied in assessment of favourable conditions for formation of nanograins.A single shot impact was simulated in order to estimate thedimensions of plastic indentation generated on target surface. Theindentation diameter i.e. the diameter of the concaved surface due tothe single shot impact was measured to be 0.2439 mm. Thenconvergence evaluation was performed changing element size inimpact zone of the target as a ratio of this dimple diameter. Resultsindicate that with  fi ne mesh convergence can be reached in terms of residual stresses in the impact zone but even with very minute size of elements it is not possible to  fi nd absolute convergent results in thecase of PEEQ.ALE (Arbitrary Lagrangian – Eulerian) adaptive meshing was alsoused to take bene fi t from adaptive meshing options due to severedeformations generated in impact zone. ALE adaptive meshing canoften maintain a suf  fi ciently re fi ned mesh under severe materialdeformation by allowing the mesh to move independently of theunderlying material; and it can be used as a continuous adaptivemeshing tool for problems undergoing large deformations [15].HoweverevenwithALEmeshingitwasnotpossibletoobtainentirelystabilized results in terms of PEEQ by decreasing element size even inthe order of 1/30th of dimple diameter.As a solution to describe element size effect, the  “ real ”  maximumPEEQwasworkedout bylinearextrapolationto  “ zeroelementsize ” , amethod used in similar situations in simulation of cold spray processwhichhasmanyaspectsin commonwithSP[32].Consideringthefactthat while the meshing is excessively fi ne, it is dif  fi cult to conduct thecalculation owing to the limited system capability and time, Assadi etal. andLi et al. concludedthattheextrapolationofinstable resultsto ameshing size of zero could be used to stand for the real one while asthemeshsizeis decreasedvariationsof instableparameterarealmostlinear [32,33]. In this study a similar extrapolation was performed onvalues of PEEQ in order to assess the in fl uence of mesh size onvariation of PEEQ values. Variation of maximum PEEQ in the singleshot model with respect to element size is shown in Fig. 6. As it isobserved, the variations show a clear linear trend. By extrapolating,thevalueofmaximumPEEQforelementsizeofzeroiscalculatedtobe0.611(mm/mm).SP simulations available in literature are usually performed usingrigid shots for numerical simulations [17,34 – 36]. There are fewstudies that have modelled deformable shots. In all these studies the  Table 3 Cyclic mechanical characteristic of the material. σ  y0 =359.26 MPaE=190 GPa ν =0.3C=169823 γ =501.87 Fig. 3.  a. Applied deformation function. b. Meshing of the simple model. Fig. 4.  Comparison of experimental and numerical results obtained for  ε  max =0.008(1st  fi ve cycles). Fig. 2.  Monotonic and cyclic behaviour of the material.4084  S. Bagherifard et al. / Surface & Coatings Technology 204 (2010) 4081 – 4090  sizeofshotelementhasoftenbeenchosenmuchcoarserthanthesizeof elements in the impact region [10,14,29,31,37 – 40]. In the presentwork, for mesh convergence studies the same size of elements of impact area was used for the shots.Due to computational costs as a  fi nal solution in the multipleimpacts simulation, the size of the elements on the shots was chosenas 1/10th of dimple diameter and the size of elements in the impactzone was selected 1/20th of dimple diameter. These choices result inacceptable convergence in terms of stress and PEEQ in impact zoneand also avoidextremelylong solution times common for fi ner size of elements. It is also to be mentioned that in the  fi nal stage thediscussed extrapolating process is performed on results in order toincrease the accuracy of de fi nitive PEEQ values and eliminate effect of element size.Top view of elements in the target and close view of mesh densityin impact zone are shown respectively in Fig. 7a and b.  2.4. Coverage determination To achieve a realistic model of SP process, the developed FE modelshall consist of a large number of identical shots impinging the targetwith an impact angle of 90° at random locations and in randomsequences.Surface coverage is de fi ned as the ratio of the area covered byplastic indentation to the whole surface area treated by SP expressedin percentage. It is one of the most important input variables in SPsimulation and specifying a required level of coverage is a necessarystarting point. However no comprehensive investigations on how toaccurately model coverage have been carried out yet. In fact most of the 3D multiple impact simulation models developed in recent timesdid not focus on coverage but on the general understanding of howthe stress state develops during successive impacts [41].Miao et al. suggested a method based on distribution of PEEQ toevaluate percentage of coverage [42]. In their de fi nition coverage isapproximated as the ratio of the number of nodes with PEEQ largerthan the PEEQ atthe boundaryof the indentation,to the totalnumberof nodes on the representative surface. The sensitivity of peeningcoverage with respect to this de fi nition is not investigated and is let Fig. 5.  Comparison of experimental and numerical results obtained for  ε  max =0.007(stabilized cycles). Fig. 6.  Variation of maximum PEEQ just under impact by changing element size of impact area. Fig. 7.  a. Top view of elements in the target model. b. Close view of elements in impactzone.4085 S. Bagherifard et al. / Surface & Coatings Technology 204 (2010) 4081 – 4090
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