ORIGINAL ARTICLENumerical modeling of friction stir welding process:a literature reviewDiogo Mariano Neto & Pedro NetoReceived: 14 February 2011 / Accepted: 9 April 2012 / Published online: 6 May 2012#Springer-Verlag London Limited 2012Abstract Thissurveypresentsaliteraturereviewonfric-tionstirwelding(FSW)modelingwithaspecial focusontheheat generationduetothecontact conditionsbetweentheFSWtool andtheworkpiece. Thephysical processisdescribed and the main process parameters that are relevanttoits modelingare highlighted. The contact conditions(sliding/sticking) are presented as well as an analytical mod-el that allows estimating the associated heat generation. Themodeling of the FSW process requires the knowledge of theheatlossmechanisms,whicharediscussedmainlyconsid-eringthemorecommonlyadoptedformulations. Differentapproachesthathavebeenusedtoinvestigatethematerialflow are presented and their advantages/drawbacks are dis-cussed. AreliableFSWprocessmodelingdependsonthefinetuningofsomeprocessandmaterialparameters.Usu-ally, these parameters are achieved with base on experimen-taldata. Thenumerical modelingoftheFSWprocesscanhelptoachievesuchparameterswithlesseffort andwitheconomic advantages.KeywordsFrictions stir welding.FSW .Modeling .Numerical simulation .Heat generation .Heat transfer .Metal flow .Review1 Introduction1.1 Friction stir welding processFrictionstir welding(FSW) isanovel solidstatejoiningprocess patented in 1991 by The Welding Institute, Cambridge,UK[1]. One of the mainadvantages of FSWover theconventional fusionjoiningtechniquesisthat nomeltingoccurs. Thus, the FSWprocess is performed at muchlower temperatures than the conventional welding. Atthe same time, FSWallows to avoid many of the environmen-tal andsafetyissuesassociatedwithconventional weldingmethods [2]. In FSW, the parts to weld are joined by forcinga rotating tool to penetrate into the joint and moving across theentire joint. Resuming, the solid-state joiningprocess ispromoted by the movement of a unconsumable tool(FSWtool) throughtheweldingjoint.FSW consists mainly in three phases, in which each onecanbedescribedasatimeperiodwheretheweldingtoolandtheworkpiecearemovedrelativetoeachother.Inthefirstphase,therotatingtoolisverticallydisplacedintothejoint line(plungeperiod). Thisperiodisfollowedbythedwell period in which the tool is held steady relative to theworkpiece but still rotating. Owing to the velocity differencebetween the rotating tool and the stationary workpiece, themechanical interaction produces heat by means of frictionalwork and material plastic deformation. This heat is dissipat-edintotheneighboringmaterial,promotinganincreaseoftemperature and consequent material softening.After thesetwo initial phases, the welding operation can be initiated bymovingeither thetool or theworkpiecerelativetoeachother alongthejoint line. Figure1illustratesaschematicrepresentation of the FSW setup [3].TheFSWtool consistsofarotatingprobe(alsocalledpin) connectedtoashoulder piece, as showninFig. 2.Duringtheweldingoperation,thetoolismovedalongthebuttingsurfacesof thetworigidlyclampedplates(work-piece),whicharenormallyplacedonabackingplate.Theverticaldisplacementofthetooliscontrolledtoguaranteethattheshoulderkeepscontactwiththetopsurfaceoftheworkpiece. Theheat generatedbythefrictioneffect andplasticdeformationsoftens thematerial beingwelded. AD. M. Neto (*):P. NetoDepartment of Mechanical Engineering (CEMUC)-POLO II,University of Coimbra,3030-788 Coimbra, Portugale-mail: diogo.neto@dem.uc.ptInt J Adv Manuf Technol (2013) 65:115126DOI 10.1007/s00170-012-4154-8severeplasticdeformationandflowof plasticizedmetaloccurs when the tool is translated along the weldingdirection. In this way, the material is transported fromthe front of the tool to the trailing edge (where it is forgedinto a joint) [4].The half-plate in which the direction of the tool rotationis the same as the welding direction is called the advancingside, whiletheotherisdesignatedasretreatingside. Thisdifferencecanleadtoasymmetryinheattransfer,materialflow, and in the mechanical properties of the weld.1.1.1 Process parametersThe welding traverse speed (Vtrans), the tool rotational speed(),thedownward force(F),thetiltangleofthetool,andthe tool design are the main variables usually used to controltheFSWprocess [4]. Therotationof thetool results instirring of material around the tool probe while the transla-tion of the tool moves the stirred material from the front tothe back of the probe. Axial pressure on the tool also affectsthequalityoftheweld. It meansthat veryhighpressureslead to overheating and thinning of the joint, whereas verylow pressures lead to insufficient heating and voids. The tiltangleofthetool, measuredwithrespect totheworkpiecesurface, isalsoanimportant parameter, especiallytohelpproducing welds with smooth tool shoulders [5].As mentionedbefore, tool design influences heat gener-ation, plastic flow, the power required to perform FSW, andthe uniformityof the weldedjoint. Generally, twotoolsurfaces are neededtoperformthe heatingandjoiningprocessesinFSW. Theshouldersurfaceistheareawherethe majority of the heat by friction is generated. This is validfor relatively thin plates; otherwise, the probe surface is theareawherethemajorityoftheheat isgenerated. Figure3presents a schematic example of an FSW tool with conicalshoulderandthreadedprobe. Inthiscase, theconicaltoolshoulder helps to establish a pressure under the shoulder, butalso operates as an escape volume for the material displacedby the probe due to the plunge action. As the probe tip mustnot penetrate the workpiece or damage the backing plate, inall tool designs the probe height is limited by the workpiecethickness [3].1.1.2 Weld microstructureFSWinvolvescomplexinteractionsbetweensimultaneousthermomechanical processes. Theseinteractionsaffect theheatingandcoolingrates, plasticdeformationandflow,dynamicrecrystallizationphenomena, andthemechanicalintegrityof thejoint [4]. Thethermomechanical processinvolvedunderthetool resultsindifferent microstructuralregions (see Fig. 4). Some microstructural regions are com-montoallformsofwelding,whileothersareexclusiveofFSW [5].& The stir zone (alsocalled nugget) is a region of deeplydeformed material that corresponds approximately to thelocation of the probe during welding. The grains withinthe nugget are often an order of magnitude smaller thanthe grains in the base material.& The thermomechanicallyaffected zone(TMAZ) occurson either side of the stir zone. The strain and temperaturelevels attained are lower and the effect of welding on thematerial microstructure is negligible.& The heat-affected zone (HAZ) is common to all weldingprocesses. This region is subjected to a thermal cycle butit is not deformed during welding.1.2 Numerical modelingSeveralaspectsoftheFSWprocessarestillpoorlyunder-stoodandrequirefurtherstudy. Manyexperimentalinves-tigations have already been conducted to adjust input FSWparameters(toolspeed,feedrate,and tooldepth),contraryFig. 1 Friction stir welding setup [3]Fig. 2 Schematic illustration of the FSW process [4] Fig. 3 FSW tool with a conical shoulder and threaded probe [3]116 Int J Adv Manuf Technol (2013) 65:115126to numerical investigations, which have been scarcely used forthese purposes. Computational tools could be helpful to betterunderstand and visualize the influence of input parameters onFSW process. Visualization and analysis of the material flow,temperaturefield, stresses, andstrainsinvolvedduringtheFSW process can be easily obtained using simulation resultsthan using experimental ones. Therefore, in order to attain thebest weld properties, simulations can help to adjust and opti-mize the process parameters and tool design [5].One of the main research topics in FSW is the evaluationof the temperature field[6]. Althoughthe temperaturesinvolvedintheprocessarelowerthanthemeltingpointsof theweldmaterials, theyarehighenoughtopromotephasetransformations. Thus, it isveryimportant toknowthetimetemperaturehistoryof thewelds. Usually, FSWtemperature is measured using thermocouples [7, 8]. How-ever, the process of measuring temperature variations in thenugget zone using the technique mentioned above is a verydifficult task. Numerical methods can be very efficient andconvenient for this studyandinfact, alongthelast fewyears, theyhavebeenusedinthefieldofFSW[9]. Riahiand Nazari present numerical results indicating that the highgradient intemperature(for analuminumalloy) isintheregion under the shoulder [10].In the process modeling, it is essential to keep the goalsof the model in view and at the same time it is also importanttoadopt anappropriatelevel ofcomplexity. Inthissense,bothanalyticalandnumericalmethodshavearoletoplay[11]. Usually, two types of process modeling techniques areadopted: fluiddynamics(simulationof material flowandtemperature distribution) and solid mechanics (simulation oftemperaturedistribution,stress,andstrain).Bothsolidandfluidmodelingtechniques involvenonlinear phenomenabelonging to the three classic types: geometric, material, orcontact nonlinearity.Thesimulationof material flowduringFSWhasbeenmodeled using computational fluid dynamics (CFD) formu-lations. In this scenario, the material is analyzed as a viscousfluid flowing across an Eulerian mesh and interacting with arotatingtool [12]. Other authors havealsousedaCFDapproachtodevelopaglobal thermal model inwhichtheheat flowmodel includes parameters related with theshear material andfrictionphenomenon[13]. Oneof themajor disadvantages of CFDmodels has todowiththedefinition of the material properties (residual stressescannot bepredicted) [7].Solidmechanicsmodelsrequiretheuseof Lagrangianformulationduetothehighdeformationlevels. However,the high gradient values of the state variables near to the probeand the thermomechanical coupling imply a large number ofdegrees of freedomin FSWmodeling, which is costly in termsof CPUtime[14]. Recent researchdemonstratedthat thecomputational timecanbereducedbyrecurringtohigh-performance computing techniques [15]. Nevertheless, in or-der tofacethelongcomputational timesassociatedtothesimulationof theFSWprocess, theadaptivearbitraryLa-grangian Eulerian (ALE) formulation has been implementedbysomeauthors[16, 17]. VanderStelt et al. useanALEformulationtosimulatethematerial flowaroundthepinduring FSWprocess[16].Thesemodelsoftheprocesscanpredict the role played by the tool plunge depth on the forma-tion of flashes, voids, or tunnel defects and the influence ofthreads on the material flow, temperature field, and weldingforces [14]. Lagrangian, Eulerian, and ALE approaches havebeenusedtonumericallysimulatetheFSWprocess, usingsoftware such as FORGE3 and THERCAST [18], ABAQUS[10], DiekA [16], WELDSIM [19], and SAMCEF [20].2 Heat generationThe heat generated during the welding process is equivalenttothepower input introducedintotheweldbythetoolminussomelossesdue tomicrostructural effects[21].Theperipheralspeedoftheshoulderandprobeismuchhigherthan the translational speed (the tool rotates at high speeds).FSWprimarilyuses viscousdissipationintheworkpiecematerial, driven by high shear stresses at the tool/workpieceinterface.Therefore,theheatgenerationmodelingrequiressome representation of the behavior of the contact interface,together with the viscous dissipation behavior of the mate-rial. However, the boundary conditions in FSWare complextodefine. Material at theinterfacemayeithersticktothetool (it has the same local velocity as the tool) or it may slip(thevelocitymaybelower)[11]. Ananalytical model forheatgenerationinFSWbasedondifferentassumptionsinterms of contact condition between the rotating tool surfaceand the weld piece was developed by Schmidt et al. [3]. Thismodel will be discussed in the following sections.2.1 Contact conditionWhen modeling the FSW process, the contact condition is acritical part of the numerical model [22]. Usually, the Cou-lombfrictionlawis appliedtodescribetheshear forcesFig.4 Differentmicrostructuralregionsinatransversecross-sectionof FSW [5]Int J Adv Manuf Technol (2013) 65:115126 117between the tool surface and the workpiece. In general, thelaw estimates the contact shear stress as:tfriction p 1where is the friction coefficient and p is the contact pressure.Analyzing the contact condition of two infinitesimal surfacesegments in contact, Coulombs law predicts the mutual mo-tion between the two segments (whether they stick or slide).The normal interpretation of Coulombs law is based on rigidcontact pairs, without taking into account the internal stress.However, this is not sufficiently representative for the FSWprocess. Thus, three different contact states were developed atthetool/workpieceinterface, andtheycanbecategorizedaccording to the definition presented by Schmidt et al. [3].2.1.1 Sliding conditionIf the contact shear stress is smaller than the internal matrix(material to be welded) yield shear stress, the matrix segmentvolumeshearsslightlytoastationaryelasticdeformation(sliding condition).2.1.2 Sticking conditionWhen the friction shear stress exceeds the yield shear stress oftheunderlyingmatrix, thematrixsurfacewill sticktothemoving tool surface segment. In this case, the matrix segmentwill accelerate along the tool surface (receiving the tool ve-locity), until the equilibrium state is established between thecontact shear stress and the internal matrix shear stress. At thispoint, thestationaryfull-stickingconditionisfulfilled. Inconventional Coulombs friction law terms, the static frictioncoefficient relates the reactive stresses between the surfaces.2.1.3 Partial sliding/sticking conditionThelast possiblestatebetweenthestickingandslidingconditionisamixedstateofboth.Inthiscase, thematrixsegmentacceleratestoavelocitylessthanthetoolsurfacevelocity. Theequilibriumis establishedwhenthecontactshearstressequalstheinternal yieldshearstressduetoaquasi-stationaryplasticdeformationrate(partial sliding/stickingcondition).Insummary,theslidingconditionpro-motes heat generation by means of friction and the stickingconditionpromotes heat generationbymeans of plasticdeformation. Inpractice, we have these twoconditionstogether (partial sliding/sticking condition).2.1.4 Contact state variableItisconvenienttodefineacontactstatevariable, whichrelates the velocity of the contact workpiece surface with thevelocity of the tool surface. This parameter is a dimension-less slip rate defined by Schmidt et al. [3] as:d vworkpiecevtool 1 gvtool2g vtoolvworkpiece3whereVtoolisthevelocityof thetool calculatedfromr(being the angular velocity and r the radius), Vworkpiece isthelocalvelocityofthematrixpointatthetool/workpiececontact interface, andg isthesliprate. Furthermore, theassumptionthat theweldingtransversespeeddoesnot in-fluencethesliprateand/orthedeformationrate,resultsinthat all workpiece velocities can be considered tangential tothe rotation axis. It is then possible to define as:d wworkpiecewtool4where workpiece is the angular rotation speed of the contactmatrixlayerandtoolistheangularrotationspeedofthetool. Ulysse uses this relationship to prescribe a slip bound-aryconditioninhisCFDmodelsof thematerial flowinFSW[23]. Therelationshipbetweenthedifferent contactconditions is summarized in Table 1.2.2 Analytical estimation of heat generationDuring the FSW process, heat is generated close to the contactsurfaces, which can have complex geometries according to thetool geometry. However, for theanalytical model, it isas-sumed as a simplified tool design with a conical or horizontalshouldersurface, averticalcylindricalprobesurface,andahorizontal probe tip surface. The conical shoulder surface ischaracterized by the cone angle , which in the case of a flatshoulder assumes the value zero. The simplified tool design ispresentedinFig. 5, whereRshoulderis theradius of theTable 1 Definition of contactcondition, velocity/shearrelationship, and state variable(" strain rate) [24]Contact condition MatrixvelocityToolvelocityContact shear stress StatevariableSticking vmatrix0vtoolvtool0r tcontact tyield"" 01Sticking/sliding vmatrix