int

zon

J. A

vance

echn

ptem

proese gzoneof thproc

volume due to temperature and pressure conditions around the pin tool. A forcing function denes the state of applied stresses

Mishra and Ma [2]. FSW has been described as a solid-

and patterns are observed in all metallic and thermo-plastic material FSW with only the volume and direc-tion of material wiping through each zone diering.

ned shear ow region forming immediately adjacent to

mally induced microstructural changes [11] typical ofthat seen in fusion weld HAZ. The ow of materialthrough these zones is highly cyclical with wipingpattern and force uctuation frequency a function ofpin tool design, material ow stress, and temperature-,strain- and process parameter-induced strain rates [12].E-mail: william.arbegast@sdsmt.edu

Available online at www.sciencedirect.com

7237state metalworking process with ow progressingthrough sequential pre-heat, initial deformation, extru-sion, forging and cool-down metallurgical processingzones [3]. Within the extrusion zone, periodic, nitewidth, wiping ow patterns form beneath the shoulderand around the probe (Fig. 1). Leading-edge initialdeformation zone material dened by the projected areaof the probe ows through the extrusion zone to con-verge and consolidate in the trailing-edge forging zone.Excess owing material is added to the initial pro-jected area of the probe within the extrusion zone basedon tool design, ow stress, temperature and processingparameters. It is interesting to note that these ow zones

the pin probe, bounded by a critical shear stress. Chenet al. [6] have shown that the ow around the pin occursin a one by one, or wiping, ow pattern. Dynamicrecrystallization (DXZ) [7], grain growth [8], and re-solution and re-precipitation of phases [9] occur withinthis DXZ region. Further away, a critical isotherm ex-ists [3] where the state of stress is less than the ow stressof the material, and this denes the boundary of thethermal-mechanically aected zone (TMAZ). Withinthe TMAZ, plastic deformation, grain growth and pre-cipitate coarsening may occur without signicant recrys-tallization [10]. The heat-aected zone (HAZ) outsidethe TMAZ experiences elastic deformation [4] and ther-which partitions the ow through these distinct zones to ll the cavity behind the pin tool. These are equated using the equationsof motion for a multi-body dynamic system. Only the concept of a ow-partitioned deformation zone model is presented in thispaper. Experimental validation of the model is in progress and the results will be made available in the future. 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Friction stir welding; Defects; Deformation zones; Flow partitioning; Mass balance

1. Introduction

Signicant advances have been made in friction stirwelding (FSW) technology over the last 15 years [1]. Anexcellent review of the state of the art has been given by

Colegrove et al. [4] have shown by numerical simula-tion that the interaction of the temperature eld, consti-tutive properties and strain rate conditions governs theextent of metal ow beneath the shoulder and adjacentto the probe. Schmidt and Hattel [5] have shown a con-Viewpo

A ow-partitioned deformationduring frictio

William

NSF Center for Friction Stir Processing, Ad

South Dakota School of Mines and T

Received 31 July 2007; revised 30 Se

AbstractA friction stir welding (FSW) metalworking model isgeometries around the pin probe and beneath the shoulder. Thstitutive properties, strain rate and pin tool geometry in thesetypes. An initial volume of material equal to the projected areaAn excess material function is presented in terms of controllable

Scripta Materialia 58 (2008) 31359-6462/$ - see front matter 2007 Acta Materialia Inc. Published by Edoi:10.1016/j.scriptamat.2007.10.031Paper

ne model for defect formationstir welding

rbegast

d Materials Processing and Joining Center,

ology, Rapid City, SD 57701, USA

ber 2007; accepted 18 October 2007

posed which partitions ow through distinct deformation zoneeometries form under the eects of the temperature eld, con-s. Inadequacies in this ow are related to specic FSW defecte pin tool probe is assumed to enter the FSW processing zone.ess parameters to describe owing material added to this initial

6

www.elsevier.com/locate/scriptamatlsevier Ltd. All rights reserved.

The complex interactions of the pin tool design,material properties and process parameter eects on

processing window with parameters that are considered

(listed in terms of increasing forge force). It is postulatedthat the optimum processing conditions to prevent ow-

Figure 1. Flow-partitioned deformation zone geometries forming within the extrusion zone [3].

W. J. Arbegast / Scripta Materialia 58 (2008) 372376 373either too hot or too cold. Under hot processing withstick conditions, excessive material ow results withash formation, surface galling and nugget collapse.Under cold processing with slip conditions, insucientowing material results in surface lack of ll, wormhole,or lack of consolidation defects on the advancing sidedefect formation are important. To date, existing CFDow models do not address defect formation. In thispaper, a simple partitioned mass balance ow model isproposed which relates defect formation to the volume(mass) and direction of material owing through spe-cic, and distinct, ow zones within the FSW.

2. Relationship of ow zone formation to defect formation

Several characteristic defects (Fig. 2) are seen to oc-cur within the FSW and are identied as either ow orgeometric related [13]. The geometric lack of penetra-tion/fusion defect occurs due to improper pin toolpenetration depth or improper seam tracking. Theow-related defects occur outside the acceptableFigure 2. Characteristic defect types in friction stir welds [13].related defects occur at a temperature where stickslipwiping ow occurs and material owing from the regionahead of the pin tool is exactly balanced with that ow-ing back into the vacated region behind the tool.

Advancing (Zone I) and a retreating (Zone II) defor-mation zone geometries form around the pin probe withdierent volume, velocity and ow directions. Materialpassing through Zone II moves downward and aroundthe probe and converges with the material in Zone I.Material passing through Zone II may move far enoughdownward to enter Zone IV beneath the probe tip andagain rise to merge with the materials within Zone I.The Zone III material originating on the retreating sideis dragged across the top toward the advancing side.This retreating side Zone III material is interleavedwith the Zone III material originating on the advancingside and forced (pumped) downward to ll Zone I fromthe top. Excess ow of Zone III material into Zone I re-sults in nugget collapse. Loss of material from Zones II,III or IV due to ash, a raised crown, sheet lifting orsheet separation results in insucient material enteringZone I and a surface lack of ll, wormhole or lack ofconsolidation (microvoid/scalloping) volumetric defect

depending on the level of forging force. Inadequatedepth of material owing in Zone IV beneath the probetip contributes to the lack of penetration defect whileexcessive material owing into Zone IV results in theroot ow (over-penetration) defect. A fth ow zone(Zone V) has been observed under very hot conditionswhere the downward ow is reversed upwards into arecirculation pattern. In lap joints, this contributes tosheet thinning, or hooking, defect formation.

3. Processing parameter eects on ow zone formation

Debate exists about whether material passes aroundthe pin on both the advancing side (Zone I) and retreat-ing sides (Zone II), or only around the retreating side. Inthis model (which assumes a typical low-angle convexshoulder, cylindrical, left-hand, ne-thread pitch pin

passing around the pin probe on the retreating side isgreater than the advancing side V R1 > V A1 . The criticalshear deformation boundary forms adjacent to theprobe and a strain discontinuity occurs to dene thewidth of the advancing W A1 and retreating W R1 sideextrusion zones. (Note: In FSW of dissimilar alloys,the material constitutive properties may dier for eachside.) This pin rotation also results in a greater volumeof material passing around the probe tip V P1 > V P0 asevidenced by a greater depth of penetration.

In case (c), the rotation speed again increases(x2 x0) with more heat generated beneath the shoul-der with an increase in the owing volume V S2 > V S1.Likewise, the higher rotation speed results in more mate-rial passing around the retreating side than the advanc-ing side V R2 V A2 . Stickslip conditions occur. Thehigher local temperatures result in smaller critical shearextrusion zone widths W R2 < W R1 and the addition of

3 3 3predominate. This perturbates the interleaving of

374 W. J. Arbegast / Scripta Materialia 58 (2008) 372376tool under clockwise rotation) both cases are allowed(Fig. 3). Case (a) assumes a zero pin rotation speed(x = 0) and a positive forward travel speed (m > 0).The volume of material processed in the shoulder zoneequals zero (VS = 0) with the volume passing throughthe advancing side equal to the volume passing aroundthe retreating side (VR = VA). This material must owequally through a non-zero extrusion zone width (W)on the advancing and retreating sides (WA =WR). Thewidth of these extrusion zones on each side are governedby the temperature eld, constitutive properties, strainrate conditions and pin tool geometry as suggested byColegrove. The overall height of the pin probe is lessthan the material thickness and some material passes be-neath the probe tip (Zone IV) from the front to the back(VP > 0). Metallurgical conrmation of these trends inow zone formation based on optically observable owpattern features, dissimilar alloy FSW and forced graingrowth studies in aluminum alloy FSW are shown inFigure 4.

In case (b), the rotation speed increases slightly(x1 > x0) while the travel speed remains constant(m1 = m0). Slip conditions predominate. Material beginsto rotate beneath the shoulder V S1 > 0. The volumeFigure 3. Processing parameter eects on deformation ow zone geometry aadvancing and retreating side shoulder zone materialwith the excess (VXS) diving downward to ll Zone I.The high temperatures form a localized shear disconti-nuity very close to the pin probe resulting in much smal-ler advancing V A3 and retreating side V R3 ow zones.The increased downward motion of the retreating sideow V R3 causes an increase in the volume owingbeneath the pin tip V P3 > V P2 .

4. Mass balance and ow partitioning model for defectformation

A critical total mass ux of material M crT must movefrom the front leading-edge to the trailing-edge throughthe extrusion zone cross-sectional area per revolution toexcess owing material V XSI , V XSII , V XS V A XSIII V R XSIII , V

XSIV dened and bounded by the critical

isotherm associated with each zone.Case (d) represents excessively high rotation speeds

(x3o x0) with the volume of material owing throughthe shoulder V S3 V XS much greater than through theother zones V AnV R V S V XS. Stick conditionst constant travel speed.

and th

MaterFigure 4. Eect of rotation speed and travel speed on ow partitioning

W. J. Arbegast / Scriptamaintain mass balance and prevent volumetric (void)formation. Eq. (1) is proposed to equate this criticalmass ux per revolution for typical xed pin geometryin terms of the pin probe shape factor a (mm1), pinshoulder shape factor b (mm2) and processing para-meters / = x/m (mm1) as originally dened in Ref. [3]

M crT qa b /21: 1From the above, the total critical mass ux through

the extrusion zone area can be represented by Eq. (2)where qi is the density, vi is the forward travel speedand xi is the rotation speed at each specic location (i)within the extrusion zone

M crT X

qi a b ximi

2 !1: 2

M iT is dened as the mass of the control volume enter-ing the initial deformation zone (Eq. (3)),M eT as the totalmass processed within the extrusion zone (Eq. (4)), andM fT as the total mass entering the nal forging zone (Eq.(5)). Within the extrusion zone (M eT, excess materialMXST is added to the initial control volume M iT. Theamount of this excess material is determined by aboundary condition factor (Wj) dened by the criticalisotherm, ow stress and pressure distributions aroundthe pin tool and beneath the shoulder (Fig. 5):

M iT M iI M iII M iIII M iIV XIVjI

M ij; 3

FSW of an aluminum alloy.

e volume of material owing through the distinct zones formed during

ialia 58 (2008) 372376 375M eT M iT MXST XIVjI

M ij XIVjI

MXSj ; 4

M fT M fI M fII M fIII M fIV XIVjI

M fj: 5

For balanced ow and conservation of mass,M fT M crT . For unbalanced ow and volumetric defectformation M fT < M

crT such that M

fT M eT MwhT where

MwhT > 0 is the wormhole mass deciency in the nalforging zone. Eq. (6) denes this mass deciency as thedierence between the critical mass M crT , the initial con-trol volume M iT and the excess material factor (Wj (a,b, /2)) which denes the extra owing material intro-duced within the extrusion zone. Eq. (7) denes a masspartitioning function (MPF) and is the forcing functionwhich causes material to ow from one zone (j) into an-other zone (k) under the combined applied rotational,translational and forging forces (Hjk):

MwhT M crT XIVjI

M ij XIVjI

Wja; b;/2; 6

MPF XIVj;kI

Hjka; b;/2: 7

The wiping ow through each of the processing zonescan be represented by a multi-body coupled dynamicsystem where the motion of one body aects the motionof an adjacent body. The position (qp and velocity ( _qpstate variables, mass matrix ([M]) and forcing function

ne, formation of excess owing material and formation of volumetric void

ater([MPF]) are expressed through the equations of motion:M q MPF. The forcing function contains theinstantaneous rotational, translational and forgingforces at specic coordinate system locations andgoverns the material ow direction through each zone.

Figure 5. Schematic showing initial material entering FSW extrusion zofrom insucient ow and ll of Zone I.376 W. J. Arbegast / Scripta MThe mass matrix includes the initial material owinginto, and the excess material formed within, each pro-cessing zone. From these, the following can be shownfor balanced ow (Eq. (8)) and unbalanced ow (Eq.(9)):

XIVjI

M ijXIVjI

Wja;b;/2 !

qp XIVj;kI

Hjka;b;/2; 8

MwhT XIVjI

M ijXIVjI

Wja;b;/2 !

qp

XIVj;kI

Hjka;b;/2: 9

5. Summary

A ow-partitioned deformation zone model has beenproposed to describe the conditions under which volu-metric defects will, or will not, form during wiping owin a FSW. The model assumes a critical mass of materialM crT necessary to maintain balanced ow and preventvolumetric wormhole formation. A mass deciencyfactor MwhT is introduced to represent the volumetricdefect. An excess material factor (W) describes theowing material added to the incoming control volumedue to the temperature eld, constitutive propertiesand strain rate conditions beneath the shoulder andaround the pin. A ow partitioning function (H) is pre-sented which describes the ow of material from onezone (j) into another (k) under the applied rotational,translational and forging forces. These are equatedialia 58 (2008) 372376using the equations of motion for a multi-body dynamicsystem.

References

[1] W.J. Arbegast, Weld. J. 85 (3) (2006) 2835.[2] R.S. Mishra, Z.Y. Ma, Mater. Sci. Eng. 50 (2005) 178.[3] W.J. Arbegast, Hot Deformation of Aluminum Alloys III,

TMS, Warrendale, PA, 2003, pp. 313327.[4] P.A. Colegrove, H.R. Shercli, R. Zettler, Sci. Technol.

Weld. Join. 12 (4) (2007) 284.[5] H. Schmidt, J. Hattel, Friction Stir Welding and Process-

ing III, TMS, Warrendale, PA, 2005, p. 205.[6] Z.W. Chen, T. Pasang, Y. Qi, R. Perris, In: 6th Interna-

tional FSW Symposium, TWI Ltd., Cambridge, 2006.[7] R.W. Fonda, J. Wert, A. Reynolds, W. Tang, Sci.

Technol. Weld. Join. 12 (4) (2007) 304.[8] Y.S. Sato, H. Watanabe, H. Kokawa, Sci. Technol. Weld.

Join. 12 (4) (2007) 318.[9] V. Dixit, R.S. Mishra, R.J. Lederich, R. Talwar, Sci.

Technol. Weld. Join. 12 (4) (2007) 334.[10] Z. Feng, X.L. Wang, S.A. David, P.S. Sklad, Sci. Technol.

Weld. Join. 12 (4) (2007) 348.[11] M.M. Attallah, C.L. Davis, M. Strangwood, Sci. Technol.

Weld. Join. 12 (4) (2007) 361.[12] W.J. Arbegast, Friction Stir Welding and Processing III,

TMS, Warrendale, PA, 2005.[13] W.J. Arbegast, Friction Stir Welding and Processing,

ASM International, Materials Park, OH, 2007, ISBN-13978-0-87170-840-3, (Chapter 13).

A flow-partitioned deformation zone model for defect formation during friction stir weldingIntroductionRelationship of flow zone formation to defect formationProcessing parameter effects on flow zone formationMass balance and flow partitioning model for defect formationSummaryReferences