nandan 10 07corr:layout 1 9/5/07 12:43 pm page 313 improving … · 2007. 11. 26. · nandan 10...

WELDING RESEARCH

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ABSTRACT. The temperature fields,cooling rates, torque on the tool, stir zonegeometry, and the magnesium concentra-tion profiles were examined experimen-tally and theoretically for the friction stirwelding (FSW) of AA 1200 and AA 6061dissimilar aluminum alloys. The thermalcycles, torque on the tool, and the magne-sium concentration profiles were experi-mentally determined for various weldingconditions. A heat, momentum, andsolute transport model based on a rectan-gular fixed grid finite difference methodwas developed. Four important parame-ters, friction coefficient, the extent ofsticking, heat transfer coefficient at thebottom surface, and the extent of viscousdissipation converted to heat significantlyaffected both the temperature fields andthe torque on the tool. The reliability ofthe model predictions was improved byoptimizing these four parameters thatcannot be prescribed either from the weld-ing conditions or from fundamental prin-ciples, using a genetic algorithm and mea-sured thermal cycles and torques fordifferent welding conditions. The magne-sium concentration profiles showed thatthe plasticized materials moved in layerswithout significant diffusive interlayermixing. The computed results showed thatthe extent of viscous dissipation convertedto heat was fairly low consistent with lim-ited atomic mixing. The optimized valuesof the extent of slip between the tool andthe workpiece indicated extensive stickingfor various welding conditions. The ap-proach to determine values of uncertain

parameters led to reliable model predic-tions as evidenced by good agreement be-tween both the experimentally measuredand computed torque values and thermalcycles.

Introduction

In recent years, numerical models haveprovided significant quantitative under-standing of the welding processes andwelded materials that could not have beenpossible otherwise. Apart from the calcu-lation of temperature and velocity fields,these models have been used to calculatevarious important features of welding.These include the weld pool shape andsize (Refs. 1, 2), solidified surface profiles(Ref. 1), cooling rates (Ref. 1), solidifica-tion characteristics (Ref. 2), grain struc-ture (Refs. 3–5) and topology (Ref. 6),phase transformation kinetics (Refs. 7–9),inclusion structure (Ref. 10), weld metalcomposition change owing to both theevaporation of alloying elements (Refs.11–15) and the dissolution of gases (Refs.16, 17), and for the prevention of severaltypes of weld defects (Refs. 18, 19).

Although, these modeling capabilitieshave been demonstrated in several stud-ies, the models have not been widely used,specially in the industry. An important dif-ficulty is that the model predictions do not

always agree with the experimental resultsbecause most phenomenological modelslack any built-in component to safeguardthe reliability of the model outputs. Forexample, the computed temperatures donot always agree with the correspondingmeasured values.

For fusion welding processes, this diffi-culty has been recognized in the literature.For example, it has been demonstrated(Refs. 20–23) that the reliability of the re-sults obtained from the heat transfer andfluid flow models of fusion weldingprocesses can be enhanced by optimizingvalues of several uncertain input parame-ters using a limited volume of experimen-tal data. No similar effort has been re-ported for the modeling of FSW.

The numerical model of FSW embod-ies the equations of conservation of mass,momentum, and energy, and the appro-priate boundary conditions. The lack ofreliability in phenomenological modelsoriginates mainly from the other compo-nents of the model, i.e., incomplete knowl-edge and uncertainties in the specificationof some of the parameters that describethe friction coefficient between the tooland the workpiece, the extent of slip be-tween the tool and the workpiece, the heattransfer coefficient between the work-piece and the backing plate, and the extentof heat generated by viscous dissipation. Ifthese uncertain welding parameters affectthe output significantly, inaccuracy oftheir values will adversely affect the modelresults. In other words, if important weld-ing features such as the peak temperature,thermal cycles, and the torque are sensi-tive to the values of several welding para-meters whose values cannot be ascer-tained accurately, the uncertainty in thevalues of these parameters would ad-versely affect the modeling results.

In order for a FSW model output to be

KEYWORDS

Aluminum Welding Numerical ModelsFriction Stir WeldingPlastic FlowThermal CyclesConcentration Profile

Improving Reliability of Heat Transfer and Materials Flow Calculations

during Friction Stir Welding of Dissimilar Aluminum Alloys

Friction, slip between the tool and the workpiece, heat transfer at the bottom surface, and internal heat generation were studied for

their effects on model reliability

BY R. NANDAN, B. PRABU, A. DE, AND T. DEBROY

R. NANDAN and T. DEBROY are with Depart-ment of Materials Science and Engineering, ThePennsylvania State University, University Park, Pa.B. PRABU and A. DE are with Department ofMechanical Engineering, Indian Institute of Tech-nology Bombay, Powai, Mumbai, India.

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WELDING RESEARCH

OCTOBER 2007, VOL. 86-s314

as close to the experimental results as pos-sible, the model must have a mechanism todetermine the optimized values of theseuncertain input parameters within theframework of the phenomenological laws.In the fusion welding processes, a globaloptimization methodology using a geneticalgorithm has been demonstrated to workwell for the determination of uncertainwelding parameters (Ref. 24).

Here we report the results of a sensi-tivity study aimed at understanding theroles of friction coefficient, the extent ofsticking, heat transfer coefficient at thebottom surface, and the extent of internal

heat generation by viscous dissipation onthe model output such as the peak tem-perature, thermal cycles, and the torque.It is shown that all four of these variablessignificantly affect the FSW model outputresults. Therefore the values of these pa-rameters are optimized by a genetic algo-rithm using a limited volume of measuredtemperatures at several monitoring loca-tions during FSW of dissimilar aluminumalloys AA 1200 and AA 6061. Using theoptimized values of the parameters, thecomputed values of the peak tempera-tures and the time spans at the base of thethermal cycles at several monitoring loca-

tions are compared with the correspond-ing experimentally measured values.

Aluminum Alloy AA 6061 contains0.85 wt-% Mg while AA 1200 containstrace amounts of alloying elements.Hence, a study of FSW of these two alloysprovides an excellent way to determine thenature of solute transport, which in turn isrelated to the plastic flow. Comparison ofcalculated and experimentally determinedconcentration profiles of Mg across theweld provides important insight about thenature of plastic flow and mixing of mag-nesium between the two alloys. The mate-rials flow, temperature fields, coolingrates, torque on the tool, stir zone geome-try, and the magnesium concentrationprofiles are examined for the FSW of AA1200 and AA 6061 dissimilar aluminum alloys.

Mathematical Model

A schematic diagram of the FSWprocess is shown in Fig. 1. Friction stirwelding of AA 6061 and AA 1200 alu-minum alloys was modeled. The dimen-sions of the plate and the tool used and thethermophysical properties of the work-piece and the tool material (Ref. 25) aregiven in Table 1. The same thermophysicalproperties were used for both aluminumalloys. The constitutive equation for flowwas the same for the alloys; however, thevalues of the constants were different.

The plastic flow in three-dimensionalCartesian coordinate system is repre-sented by the momentum conservationequation in index notation, with i = 1, 2,and 3 representing x, y, and z directions,respectively (Refs. 26–29).

A B

Fig. 1 — A — Schematic diagram of the FSW system considered in the model. B — top view of the rotating tool moving in the negative x-direction. θ = 0 cor-responds to plane y = 0, x < 0.

Table 1 — Data Used in the FSW Calculations

Property/Weld parameter Value

Workpiece length (x-direction) 0.45 mWorkpiece half-width (y-direction) 0.07 mWorkpiece thickness 10.0 mmShoulder radius 10.0 mmPin radius 5.0 mmPin length 9.0 mmPitch of the thread 1.0 mmWeld speed 1.05 mm/sRotational speed 700–1400 rpmAxial pressure 18.0 MPaTilt angle 0°Density 2700 kg/m3

Workpiece materials AA 1200, AA 6061Specific heat capacity, (Ref. 34) Cp

929.3 –0.627 T + 1.48 × 10–3 T2 –4.33 × 10–8 T–3 J/kg–KThermal conductivity, (Ref. 34) k

25.2 + 0.398 T + 7.36 × 10–2 T6–2.52 × 10−7 T–3 W/m–KToolDensity 7860–kg/m3

Specific heat capacity, (Ref. 34) Cp468.3 –8.5 T + 3.0 × 10-4 T2 + 1.8 × 10-7 T3 J/kg-K

Thermal conductivity, (Ref. 34) k3.8 + 9.2 × 10-2T -1.8 × 10-4 T2 + 7.8 × 10-8 T3 W/m-K


WELDING RESEARCH


(1)where ρ is the density, μ is the non-New-tonian viscosity, U1 is the welding velocity,and p is the pressure. Viscosity can be de-termined from flow stress and effectivestrain rate as follows (Ref. 30).

(2)The calculation of viscosity requires localvalues of strain rate and temperature. Theviscosity was calculated based on the fol-lowing formulation of flow stress, σe, pro-posed by Sheppard and Wright (Ref. 31)

(3)where A, α, and n are material constantand Z is the Zener-Hollomon parameter.The values of constants A, α, and n aregiven in Table 2 for AA 6061 and AA 1200alloys. The Zener-Hollomon parameter,Z, that represents the temperature-com-pensated effective strain rate is given by

(4)Here Q is the temperature-independentactivation energy, R is gas constant, and εis the effective strain rate given by

(5)where εij is the strain rate tensor, definedas

(6)This flow-stress model does not have anystrain dependency because flow stress isnot very sensitive to strain at high temper-atures (Ref. 32). Finally, viscosity can bedetermined from flow stress and effectivestrain rate from Equation 2. The pressurefield was obtained by solving the continu-ity equation for incompressible single-phase flow simultaneously with the mo-mentum equation

(7)where u is the velocity of plastic flow. Thesteady single phase momentum conserva-tion equations with reference to a coordi-nate system attached to the heat source inindex form may be represented as (Refs.

εij i

j

j

i

ux

ux

=∂∂

+∂∂

⎛

⎝⎜

⎞

⎠⎟

12

�ε ε ε= ⎛⎝⎜

⎞⎠⎟

23

1 2

ij ij

/

Z QRT

= ⎛⎝⎜

⎞⎠⎟

�ε exp

σαe

nZA= ⎛

⎝⎜⎞⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

−1 11

sinh/

μ σε

= e3 �

ρ

μ μ

∂∂

= − ∂∂

+ ∂∂

∂∂

+∂∂

⎛

⎝⎜

⎞

⎠⎟ −

u ux

px x

ux

ux

i ji j i

ji

ij

ρρU uxj

11

∂∂

∂∂

=uxi

i0

Fig. 2 — Computed dimensionless values of peak temperature, time span at the base of the thermal cycle, and the torque with change in (A) slip, (B) heat trans-fer coefficient at the bottom, (C) friction coefficient, and (D) multiplicand for viscous dissipation term. In each case, when one of the parameters is varied, otherparameters were kept constant. The welding velocity was 0.42 mm/s, and the rotational speed was 450 rev/min.

A B

C D

.

Nandan 10 07corr:Layout 1 9/5/07 12:37 PM 15

T. DebRoy

Text Box

1/

WELDING RESEARCH


26–28).

(8)where Cp is the specific heat and k is thethermal conductivity of theworkpiece/tool. The term Sin representsthe source term due to interfacial heatgeneration rate per unit volume at the toolpin-workpiece interface, and Sb is the heatgeneration rate due to plastic deformationin the workpiece away from the interface.The heat generated at the interface be-tween vertical and horizontal surface ofthe tool pin and the workpiece, Sin, may bedefined as (Refs. 26–28)

(9)where Ar is any small area on the tool pin-workpiece interface, r is the radial dis-tance of the center of the area from thetool axis, V is the control-volume enclos-ing the area Ar, τ is the maximum shearstress at yielding, and θ is the angle withthe negative x-axis in the counterclockwisedirection, η is the mechanical efficiency,i.e., the amount of mechanical energy con-verted to heat energy, δ denotes the spa-tially variable fractional slip between thetool and the workpiece interface, μf is thespatially variable coefficient of friction,and ω is the angular velocity. Full stickingis indicated by δ = 0. The velocity (ωr–U1,sincθ) represents the local velocity of a

point on the tool sur-face with the originfixed at the tool-axis.The symbol P is equalto PU acting on thefront half of the cylin-drical surface of thepin, and P is equal toPZ acting on the hori-zontal surfaces of thetool including boththe tool shoulder andpin. The pressure onthe tool shoulder andthe tool bottom, PZ,has been assumed tobe the same at allpoints. The pressureon the front half of

the cylindrical pin, PU, is much smallerthan PZ, and has been assumed to be zero.

An estimate of the viscous dissipationof momentum per unit volume, Sb, hasbeen calculated as fmμφ where φ is given by (Ref. 33)

(10)

and fm is an arbitrary constant that indi-cates the extent of molecular friction inthe system. The value of fm may tend to 1for a well-mixed system in molecular scale.In systems where the grains remain largelyintact, the value of fm may be very small.Here, we try to optimize the value of thisparameter so that a good agreement canbe obtained between the output of themodel and physical experiment, thus im-proving the reliability and usability of themodel.

Since the alloys being welded containdifferent concentrations of Mg, thechanges in the concentration of Mg in thetwo plates due to welding are examined.Apart from 0.85 wt-% Mg AA 6061 alloyalso contains other alloying elements.However, for simplicity, it is treated as abinary alloy for modeling purposes. Simi-larly, AA 1200 is considered to be purealuminum. We assume no diffusion takes

place into the tool. The equation of con-servation of mass of any alloying elementpresent at low concentration is given by

(11)Here, D denotes temperature-dependentchemical-diffusivity given by

(12)The pre-exponent and activation energyvalues were obtained from Table 13.4 fromSmithells Metals Reference book for binaryalloy containing 99 at-% Al and 1 at-% Mg(Ref. 34).

The total heat generated at the shoul-der/workpiece interface has been parti-tioned between the workpiece and the toolin the ratio given below (Ref. 35).

(13)where the subscripts W and T denote theworkpiece and the tool, respectively. Theanalytical expression is based on steady-state one-dimensional heat transfer frompoint heat source located at the interfaceof dissimilar metals. The heat flux into theworkpiece is estimated to be 90% of thetotal heat generated. This relation hasbeen examined experimentally by Lienertet al. (Ref. 25) and found to be reliable.

A heat flux continuity at the shouldermatrix interface yields

(14)

RP and RS represent the tool pin andshoulder radius, respectively, and q1 rep-resents the total rate of heat generation atthe shoulder-workpiece interface. It isgiven by

(15)At the bottom surface, there is a backingplate and the heat transfer coefficientfrom the bottom of the workpiece is notthe same as for free convection. The valueof the heat transfer coefficient is deter-mined by optimization.

q P r Uf T1 11= −( ) +⎡⎣ ⎤⎦ −( )η δ τ δμ ω θsin

k Tz

JJ +J

q

in the range R r Rtop

w

w T

p s

∂∂

=

≤ ≤

1

f= JJ

k C

k CW

T

p W

p T

=( )( )

ρ

ρ

D expRT

cm s= −⎛⎝⎜

⎞⎠⎟0 49 124000 2. /

∂ ( )∂

= −∂∂

+ ∂∂

∂∂

⎛

⎝⎜

⎞

⎠⎟

u C

xU C

x xD C

xj i

j

i

i j

i

j1

ρ ρCu Tx

C U Tx

xk T

xS

p p

i i

∂ ( )∂

= − ∂∂

+ ∂∂

∂∂

⎛⎝⎜

⎞⎠⎟

+

ii

11

iin bS+

S P

r U AV

in f

r

= −( ) +⎡⎣ ⎤⎦

−( )

1

1

δ ητ δμ

ω θsin

Φ =∂∂

⎛⎝⎜

⎞⎠⎟

+∂∂

⎛⎝⎜

⎞⎠⎟

+∂∂

⎛⎝⎜

⎞⎠⎟

2 1

1

22

2

23

3

ux

ux

ux

22

1

2

2

1

21

3

3

⎛

⎝⎜⎜

⎞

⎠⎟⎟

+∂∂

+∂∂

⎛⎝⎜

⎞⎠⎟

+∂∂

+∂∂

ux

ux

ux

uxx

ux

ux

1

2

3

2

2

3

2

⎛⎝⎜

⎞⎠⎟

+∂∂

+∂∂

⎛⎝⎜

⎞⎠⎟

Fig. 3 — Objective function value decreases with iteration. The symbols in-dicate the objective function values for individual sets of variables, and theline indicates the change in average value of all individuals with successiveiterations.

Table 2 — Constants Used in Constitutive Equation for Plastic Flow(Ref. 43)

Alloy A, s-1 α, (MPa)-1 n6061 2.409 × 108 0.045 3.551200 3.902 × 109 0.037 3.84


WELDING RESEARCH


(16)

At the top surface, heat transfer is due toboth convection and radiation and is givenby

(17)Velocities at the tool pin periphery havebeen defined in terms of tool translationvelocity and the tool pin angular velocity

(18)where κ denotes the pitch of the threadson the cylindrical tool. The value of weldpitch was taken as 1 mm. Similarly, at theshoulder contact, velocity condition maybe written as

(19)

At all other surfaces, temperatures are setto ambient and the velocities are set tozero.

The boundary conditions used for cal-culation of concentration are straightfor-ward. No flux condition is used for the topand bottom surfaces of the weld plate. Thevalue of concentration is fixed at all otherboundaries.

The differential equations of continu-ity and transport were solved using SIM-PLE algorithm (Ref. 36) based solutionprocedure, capable of calculating three- dimensional heat transfer and fluid flowwith a stationary or moving heat source,with a free or flat surface, and well tested

k Tz

h T-Tbottom

b a∂∂

= ( )

u r U

v r

in t

= −( ) −( )= −( )

⎫⎬⎪

⎭⎪

1

11δ ω θ

δ ω θsin

coshhe range R r Rp s≤ ≤

u R U

v R

w R

p

p

p

= −( ) −( )= −( )

=

1

1

2

1δ ω θ

δ ω θ

κ ωπ

sin

cos

k Tz

h T–T T –Ttop

b a4

a4∂

∂= ( )+ ( )σ

Fig. 4 — Comparison between experimental and calculated time-tempera-ture profile at a point 13 mm away from the centerline on the advancingside. The welding velocity was 1.05 mm/s, and the rotational speed was (A)710 and (B) 1400 rev/min.

Fig. 5 — Stream-lines in a horizontal plane (A) 3.66 mm and (B) 7 mm belowthe top surface, showing plastic flow during FSW. Material flows along the re-treating side around the pin, and a stagnant zone forms in the advancing side.The welding velocity was 1.05 mm/s and the rotational speed was 710rev/min.

A

B B

A


WELDING RESEARCH


and used for several welding processes. The trend of the reported data on ex-

tent of slip during cross-wedge rolling canbe expressed by the following relation(Ref. 37)

(20)

where δ denotes the fraction-slip, and δ0 isa constant. The above equation was usedfor all interfaces, with r denoting the dis-tance of the center of the grid-area from

the tool axis. It varies from 0 to RP for thetool pin’s bottom surface, is constant at RPfor the vertical surface of the pin, andvaries from RP to RS for the tool shoulder-workpiece interface. The value of δ0 wasoptimized from a limited volume of ex-perimental data. This equation embodiesthe physical picture of the extent of slip in-creasing with increase in relative velocitybetween the tool and the workpiece.

Values of friction coefficient were cal-culated considering the relative velocitybetween the tool and the workpiece

guided by previous work in the field of fric-tion welding of steel bars (Refs. 38, 39).The relative velocity increases from zeroat the axis of rotation (static condition) toωRS at the periphery of the tool shoulder(dynamic condition). Experimental evi-dence in Refs. 37 and 38 suggest that μ hasthe following form:

(21)where δ is the extent of sticking expressedas a fraction and r is the radial distancefrom the tool axis for the point in consid-

δ δ ωω

= − −⎛⎝⎜

⎞⎠⎟

1 00

exp rRs

μ μ δωf r= −( )0 exp

Fig. 6 — Concentration profile at depths of 1, 3, and 5 mm from the top surface, across the weld centerline for AA 6061 (advancing) and AA 1200 (retreatingside) weld at 710 rev/min and a weld velocity of 1.05 mm/s. A — Computed; B — measured.

Fig. 7 — Concentration profile at depths of 1, 3, and 5 mm from the top surface, across the weld centerline for AA 1200 (advancing) and AA 6061 (retreatingside) weld at 710 rev/min and a weld velocity of 1.05 mm/s. A — Computed; B — measured.

A

A B

B


WELDING RESEARCH

-sWELDING JOURNAL

eration. This equation implies that thefriction coefficient decreases with de-crease in the relative velocity between thetool and the workpiece.

Optimization of Uncertain FSW Parameters

Among the necessary input variables inthe FSW model, there are four uncertaininput parameters that affect the reliabilityof the model output. These parametersare the heat transfer coefficient from thebottom of the workpiece (h), the spatiallyvariable slip between the tool and theworkpiece interface (δ), the spatially vari-able coefficient of friction (μf), and the ex-tent of the viscous dissipation term (fm),which indicates the extent of internal fric-tion in the system. In order to optimize thevalues of these parameters from a limitedvolume of experimental data, the follow-ing objective function is minimized:

(22)Subscript i denotes different rotationalspeeds and the subscripts a and r refer tothe advancing and the retreating sides, re-spectively. Two different thermal cycles(at locations 13 mm from the weld center-line on advancing and retreating sides) foreach experiment done at 710, 1000, and1400 rev/min were used to calculate theobjective function, i.e., six different ther-mal cycles were used. The temperatureand time span were nondimensionalizedusing the simple formulas given below

(23)where T is the peak temperature in theworkpiece at a monitoring location 13 mmaway from the weld centerline on eitheradvancing or retreating side, and L is thetime span on the thermal cycle starting

when the temperaturereaches 523 K duringheating and finishingwhen the temperaturereaches 523 K duringcooling at the monitor-ing location. The nor-malization of the calcu-lated value is done bythe experimental valueat the same monitoringlocation for the samewelding condition. Thesubscripts cal and exprefer to calculated andexperimental values, re-spectively. The objec-tive function value de-pends on the choice ofthe four uncertain parameters.

(24)Differential Evolu-

tion (DE), a popula-tion-based optimizationtechnique (Refs. 40,41), was used to optimize the uncertainparameters for FSW.

Results and Discussion

The sensitivities of the computed val-ues of torque on the tool, and peak tem-perature and cooling time on the four un-certain parameters, identified previously,are examined in Fig. 2A–D. Figure 2Ashows that when δ0 indecreases and moresticking takes place, torque increases asthe tool now moves a larger volume of ma-terial during its rotation. Torque is in-cluded in the calculations because it af-fects material flow. Temperatures arehigher and the thermal cycles are strongerbecause of more intense deformationalheating consistent with the reduction infrictional heating. Higher temperatureleads to longer cooling time.

Figure 2B shows that as the heat trans-fer coefficient increases, more heat is lostfrom the workpiece and, therefore, thepeak temperature at a distance of 13 mmaway from the weld centerline in the ad-vancing side and the time span in the ther-mal cycle at 523 K decreases. When theheat transfer coefficient is high, lowertemperatures result in harder materialand higher torque.

Figure 2C shows that the peak temper-ature and the time span at the base of thethermal cycle increase with increase infriction coefficient due to more intensefrictional heating. As the friction betweenthe tool and the workpiece increases, thetorque also increases. It offsets the de-crease in torque that has been anticipateddue to the softening of material with in-crease in temperature.

Figure 2D shows increase in tempera-ture and cooling time with increase in vis-

O = f h fm, , ,μ δ0 0( )

OTa Tr

La Lr

i*

i*

i*

i*

=−( ) + −( )

+ −( ) + −( )

⎧

⎨1 1

1 1

2 2

2 2⎪⎪

⎩⎪

⎫

⎬⎪

⎭⎪=

∑i 1

3

T = TT

L LL

* cal

exp

cal

exp; ∗ =

319

Fig. 8 — Computed concentration profile for magnesium (wt-%) near thetool for AA 1200 (retreating) and AA 6061 (advancing side) weld in hor-izontal planes corresponding to depths of (A) 1, (B) 3, and (C) 5 mm fromthe top surface. The rotational speed was 710 rev/min and a welding ve-locity of 1.05 mm/s.

A B

C


cous generation of heat that is propor-tional to fm. More intense heating resultsin higher temperatures and softer mater-ial, resulting in lower torque.

The results in Fig. 2A–D show that allthree output variables, peak temperature,time span at the base of the thermal cycle,and the torque are sensitive to variationsin all the four uncertain input variables.Therefore, it is appropriate that all theseuncertain input parameters need to be op-timized to enhance the reliability of thevalues of the output variables from themodel.

The values of the four uncertain inputparameters were optimized using differ-ential evolution (DE) technique. For DE,a population of ten individual sets of fourvariables was generated. Figure 3 indi-cates that the average objective functionvalue decreased with successive iterations.

The decrease in theobjective function wasmost pronounced dur-ing the initial itera-tions. After 25 itera-tions, using a mutationfactor of 0.8 and acrossover ratio of 0.5,ten sets of optimizedparameter values wereobtained. They aregiven in Table 3. Theoptimized value of theheat transfer coeffi-cient does not varywith the individual so-lutions and is almostconstant at 0.01cal/cm2-s. For othervariables, we get arange of values de-pending on the indi-vidual solution se-lected. Since DE iselitist, i.e., the bettersolution is alwayspicked during selec-

tion, we see that diversity of the popula-tion steadily decreases.

Figure 4 shows the computed thermalcycle at a distance of 13 mm away from theweld centerline in the advancing side,which used the parametric values ob-tained through DE, in the heat transferand plastic flow model. The set of opti-mized values of the four uncertain para-meters that are used in the numerical cal-culations are given in the second row ofTable 3. A close match between the com-puted temperature-time variation and thecorresponding measured values obtainedfrom the thermocouple can be seen in Fig.4. Using the optimized values of the un-certain parameters, the computed stream-lines for the plastic flow are shown in Fig.5. Two important features of flow, mater-ial going around the pin in the retreating

side and the formation of a stagnant zonein the advancing side, can be observed.

The concentrations of Mg and Si weremeasured in a transverse cross sectionacross the weld centerline at depths of 1,3, and 5 mm from the top surface. Themeasurement was done using electronprobe microanalysis (EPMA) of polishedtransverse-cut friction stir welded sam-ples, with beam diameter of 50 μm. Themeasured and calculated values of Mgconcentration across the weld joint areshown in Figs. 6 and 7. Figure 6 representsa case with AA 6061 on the advancing sideand AA 1200 on the retreating side. Themeasured concentration distributionacross the weld joint indicates that there isvirtually no mixing and very little Mg hasdiffused from AA 6061 to AA 1200. Nu-merical results indicate a much larger dif-fusion distance although the predictedweight-percent of Mg diffusion is similarto the corresponding measured values.The increased movement of Mg from AA6061 in the advancing side toward AA1200 in the retreating side with the in-crease in depth of the workpiece is de-picted in both the EPMA measurementsand the numerical calculations. In con-trast, when AA 6061 was placed on the re-treating side, very small amounts of Mgcould be traced across the weld joint, ex-cept very near to the top surface of thespecimen, as indicated in Fig. 7. The cal-culated trends in Mg concentrationsacross the weld joint (Fig. 7A) are slightlydifferent from the corresponding mea-sured results (Fig. 7B) when Mg-contain-ing alloy (AA 6061) is on the advancingside. Although the reason for this mis-match is not clearly known, the calcula-tions assume molecular level mixing in theplasticized material whereas in the exper-iments, the grains are deformed but re-main largely intact.

Contours of concentration of Mg nearthe tool are shown in Figs. 8 and 9, at dif-

WELDING RESEARCH


Fig. 9 — Computed concentration profile for magnesium (wt-%) near thetool for AA 1200 (advancing) and AA 6061 (retreating side) weld in hori-zontal planes corresponding to depths of (A)1, (B) 3, and (C) 5 mm fromthe top surface. The rotational speed was 710 rev/min, and the weld veloc-ity was 1.05 mm/s.

A B

C


WELDING RESEARCH


ferent depths from the top surface. It isobserved from these figures that Mg isdrawn toward the direction of rotation ofthe tool, in front of the tool. Just below thetool shoulder, the plug of material flowingaround the tool is larger. Material is trans-ported from the rear of the tool to thefront in the advancing side. Hence the re-gion where plastic flow has occurred be-comes depleted in Mg and therefore thefront of the tool is rich in Mg. At the mid-dle horizontal plane, the circular plug ofmaterial around the tool is smaller andhence the high concentration region iscloser to the tool pin.

The concentration profiles, with Mg onthe advancing side, are qualitatively simi-lar to experimental results for Ti-markerflow in FS-welded AA 2024, studied byZettler et al. (Ref. 42) using high-resolu-tion (20 μm) computer microtomography.The tomographic volume data are shownin Fig. 10. Zettler et al. also observed thatwhen the marker was placed in the ad-vancing side, it redistributed as fine par-ticulates, while the marker placed on theretreating side appeared as much largerclumps. This could be the reason for theconcentration calculations, with Mg onthe retreating side, not reconciling withthe corresponding experimental results.

Summary and Conclusions

Heat transfer, materials flow, mixingand energy necessary for the friction stirwelding of dissimilar aluminum Alloys AA1200 and AA 6061 were studied both ex-perimentally and theoretically. The spe-cial features of the work and the mainfindings of this investigation are the following:

1) A numerical model embodying theequations of conservation of mass, mo-mentum, and energy was used to examine

the sensitivity of four important parame-ters, which are friction coefficient, the ex-tent of slip between the tool and the work-piece, the heat transfer coefficient at thebottom of the workpiece, and the extent ofviscous dissipation converted to heat onthe computed temperature fields andtorque on the tool. These parameters can-not be prescribed either from the weldingconditions or from fundamental princi-ples. All four parameters were found tosignificantly affect both the temperaturefields and the torque on the tool.

2) When the values of these four un-certain parameters were optimized using asmall volume of experimental data, thecomputed peak temperature, thermal

cycle, and the torque on the tool agreedvery well with the corresponding experi-mental data.

3) The transport and mixing of magne-sium from Mg-rich AA 6061 alloy intovery low alloy containing AA 1200 wereexamined both experimentally by EPMAand numerically in the entire volume ofthe three-dimensional specimens. Themeasured concentration profiles showedthat the mixing of magnesium did notoccur in the atomic level and the spatialvariation of concentration distributionshowed a step profile between the twoplates. The computed magnesium concen-tration profile based on its transport byconvection and diffusion showed a grad-ual decrease from 0.85% Mg in AA 6061to very small concentration in AA 1200.The comparison of the experimental andcomputed concentration profiles showedimperfect mixing of the plasticized alloysduring FSW where the materials seem tomove in layers without significant diffu-sive interlayer mixing.

4) For the conditions of experimentsreported here, the cooling rates were ofthe order of about 5 K/s in the 700 to 500K temperature range. The relatively lowcooling rate is consistent with fairly highenergy input per unit length.

5) The small value of the extent of slipbetween the tool and the workpiece ob-tained by optimization procedure indi-cates close to sticking condition, even atthe outer periphery of the tool shoulder.

6) The optimized extent of viscous dis-sipation converted to heat is small consis-tent with the fact that the grains in the

Table 3 — Optimized Sets of Uncertain Parameters after 25 Iterations and the Corresponding Objective Functions

Friction Fractional Heat Transfer Efficiency ObjectiveCoefficient Slip Coefficient of Mixing Function

μ0 δ0 h (cal/cm2-s) fm O

0.488 0.022 0.010 0.036 0.1490.487 0.014 0.010 0.03 0.1480.484 0.014 0.010 0.028 0.1480.482 0.017 0.011 0.034 0.1490.479 0.016 0.011 0.033 0.1480.489 0.012 0.010 0.029 0.1500.49 0.015 0.010 0.032 0.1480.492 0.012 0.012 0.033 0.1500.499 0.010 0.012 0.031 0.1490.499 0.017 0.010 0.031 0.149

Fig. 10 — Tomographic volume data depicting Ti-marker flow in AA 2024 T351 alloy with two differenttool pins: 1. conical and threaded; and 2. conical, threaded with flats. The markers were placed in bothA) advancing and R) retreating sides (Ref. 42).


WELDING RESEARCH


workpiece are deformed but largely retaintheir identity after welding.

7) The torque values and the interfacialheat generation rate were computed fromshear stress. Therefore, the close agree-ment between the experimentally mea-sured and the calculated thermal cyclesand torque values indicates that the com-puted shear stress at the tool-workpieceinterface is accurate and the optimizationof uncertain parameters provide reliablecomputed results.

Acknowledgment

This research was supported by a grantfrom the American Welding Society andthe Materials Division, Office of NavalResearch, Julie A. Christodoulou, Pro-gram Officer.

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