robson fsw symposium

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Microstructural Evolution During Friction Stir Welding of AA7449 J. D. Robson a A. Sullivan a H. R. Shercliff b G. McShane b a Manchester Materials Science Centre, Grosvenor Street, Manchester, UK b Cambridge University Engineering Department, Trumpington Street, Cambridge, UK Abstract The microstructural evolution in friction stir welded 7xxx series aluminium al- loy plate has been studied both experimentally and theoretically. Predictive models have been developed to calculate the hardness profile and precipitate distribution after welding. A coupled approach has been used, linking a thermal model to pre- dict the thermal cycle, to the microstructure and property models. Two levels of modelling have been considered. The first is a semi–empirical approach that pre- dicts hardness profiles. This simple model is demonstrated to correctly reproduce a measured profile. The second model provide a detailed prediction of the precip- itate evolution. Precipitate nucleation, growth, dissolution and coarsening are all accounted for. Model predictions have been compared with experiments for the case of friction stir welded AA7449 thick plate. 1 Introduction High strength 7xxx aluminium alloys (which contain Zn, Mg and Cu as the major alloying additions) are widely used in aerospace applications. These alloys are generally considered to be unsuitable for welding by conventional fusion processes because of the poor mechanical properties of the solidified material in the fusion zone (1). Since friction stir welding (FSW) is a solid state process, problems associated with solidification can be avoided, and thus the FSW process has attracted great interest for joining these materials (2; 3; 4; 5). Email address: [email protected] (J. D. Robson).

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Page 1: Robson Fsw Symposium

Microstructural Evolution During Friction

Stir Welding of AA7449

J. D. Robson a A. Sullivan a H. R. Shercliff b G. McShane b

aManchester Materials Science Centre, Grosvenor Street, Manchester, UK

bCambridge University Engineering Department, Trumpington Street, Cambridge,

UK

Abstract

The microstructural evolution in friction stir welded 7xxx series aluminium al-loy plate has been studied both experimentally and theoretically. Predictive modelshave been developed to calculate the hardness profile and precipitate distributionafter welding. A coupled approach has been used, linking a thermal model to pre-dict the thermal cycle, to the microstructure and property models. Two levels ofmodelling have been considered. The first is a semi–empirical approach that pre-dicts hardness profiles. This simple model is demonstrated to correctly reproducea measured profile. The second model provide a detailed prediction of the precip-itate evolution. Precipitate nucleation, growth, dissolution and coarsening are allaccounted for. Model predictions have been compared with experiments for thecase of friction stir welded AA7449 thick plate.

1 Introduction

High strength 7xxx aluminium alloys (which contain Zn, Mg and Cu as themajor alloying additions) are widely used in aerospace applications. Thesealloys are generally considered to be unsuitable for welding by conventionalfusion processes because of the poor mechanical properties of the solidifiedmaterial in the fusion zone (1). Since friction stir welding (FSW) is a solid stateprocess, problems associated with solidification can be avoided, and thus theFSW process has attracted great interest for joining these materials (2; 3; 4; 5).

Email address: [email protected] (J. D. Robson).

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Although FSW does not involve melting, the heat and deformation associ-ated with the process do lead to severe microstructural changes (3; 6). Thesechanges lead to a degradation in properties compared with the original parentmaterial. In particular, the welding process has a profound effect on the size,spacing and distribution of precipitate particles. This, in turn, has a stronginfluence on the strength, as well as other key properties such as fracturetoughness and corrosion resistance (7). A complex mixture of microstucturalprocesses can occur during the welding process. Examples of changes includeprecipitate coarsening, particle dissolution, transformation of metastable pre-cipitates and nucleation and growth of new precipitates (3; 5). Furthermore,the microstructures obtained after FSW are often highly heterogeneous. Forexample, the precipitate distribution on grain boundaries is often very differ-ent from that within grains.

Modelling offers a promising tool to help understand the effect of key weldingvariables (such as heat input, deformation, and alloy composition) on the finalmicrostructure and properties. Models can be developed at different levels ofcomplexity, and the most appropriate level will depend on the intended ap-plication of the model. In general, more complex models aim to capture moreaccurately the underlying physics controlling microstructural and propertyevolution, whereas the simpler models tend to be semi-empirical. A successfulsemi-empirical approach that allows prediction of hardness profiles after weld-ing has been developed by Myhr and Grong (8) and adapted for 7xxx alloysby Shercliff et al. (9; 10). The key features of this model are summarized insection 2. Once calibrated for a given alloy composition and initial heat treat-ment condition, this model can be used to predict the hardness for any giventhermal profile. When coupled to a thermal model (e.g. (11; 12)), this allowsprediction of cross weld hardness profiles for a given set of welding conditions.

To understand how the microstructure itself evolves during the welding cy-cle, it is necessary to develop a more complex model that explicitly calcu-lates how each of the possible precipitate phases evolve, and how they aredistributed. This level of microstructural detail is also required for modelsthat predict more complex properties such as fracture toughness (13). In thispaper, a physical model is described to predict the evolution of precipitatephases in 7xxx aluminium alloys subject to FSW. This model is based on awell established numerical framework (the Kampmann and Wagner Numerical(KWN) model (14)). This framework has been successfully applied to predictmicrostructural evolution under non–isothermal conditions in 6xxx alloys (15).The model has been calibrated using isothermal heat treatments, before beingtested for thermal cycles encountered in FSW.

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Mg Zn Cu Si Fe Mn Cr Ti+Zr Al

2.2 8.2 1.7 0.12 0.15 0.2 0.05 0.25 Bal

Table 1Nominal composition of AA7449 as used in this study

2 Experimental

Experimental studies were performed on both as–welded and isothermallyheat treated specimens. The purpose of the isothermal heat treatments wasto provide data with which to calibrate the microstructural model.

The material studied in all cases was AA7449 supplied by Alcan in an ini-tially overaged (T7) condition. The nominal chemical composition of this al-loy is shown in Table 1. Friction stir welding was carried out by Airbus UK.Half thickness welds (20mm in depth) were produced in 40mm thick plate.Isothermal heat treatments were carried out on unwelded material for modelcalibration. To obtain data on the kinetics of precipitation from the super-saturated state, an initial solution treatment was first carried out at 482◦Cfollowed by a water quench to dissolve the soluble alloying elements. Followingsolution treatment, isothermal heat treatments were carried out at two tem-peratures, 350◦C and 400◦C, with hold times of 1 min, 10 mins, 1 h and 5 h,after which the specimens were quenched and prepared for examination in aPhilips XL30 Field Emission Gun Scanning Electron Microscope (FEGSEM).Preparation consisted of mechanical grinding and polishing.

Specimens traversing the weld, from the weld line out to unaffected parentplate, were also prepared for examination in the FEGSEM. Following this ex-amination, selected positions were chosen from which specimens were preparedfor Transmission Electron Microscopy (TEM) in a Philips CM200 operated at200kV. The positions chosen for examination were 13mm, 19mm, 25mm and34mm from the weld line. TEM sample preparation consisted of spark erosionof 3mm discs and subsequent grinding to 80 µm thickness. Electro-polishingfollowed, using a Struers Tenupol-3 operating at 12 V, in a 70% Methanol,30% Nitric acid solution at a temperature of -30C. Microhardness measure-ments were performed across the weld using an Instron Wilson Tukon 2100with a Vickers indenter loaded with a 1kg weight.

2.1 Experimental Results

2.1.1 Isothermal Heat Treatments

Micrographs showing the evolution of the microstructure at 350◦C are pre-sented in Figure 1. It can be seen that even after 1 minute of heat treatment,

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copious precipitation occurred both within the grains and on grain bound-aries. The precipitates rapidly coarsened at this relatively high temperature,eventually leading to a structure characterized by coarse precipitates, withwide precipitate free zones, as shown in Figure 1(d).

The microstructural evolution at 400◦C was observed to be similar to thatat 350◦C. Image analysis was used to determine the mean particle size andnumber per area for each temperature and time. Particles on grain boundariesand those within the grains were measured separately. These results are shownin Figure 2.

The heterogeneous nature of the microstructures means that the experimentalmeasurements are subject to considerable error. Interpretation of the results isfurther complicated because AA7449 contains a number of different phases. Inparticular, the grain boundaries contain insoluble iron containing constituentparticles, in addition to the soluble precipitate phases of interest here. Al-though attempts were made to exclude these particles from the experimentalanalysis, it is possible that the measurements were influenced by their pres-ence. Despite these limitations, useful information regarding the precipitationkinetics can be extracted from these results.

It can be seen that the average particle size on the grain boundaries is, ingeneral, approximately four times larger than that within the grains. In ad-dition, it is clear that as the heat treatment time increases, the mean radiusincreases and the particle number decreases. This corresponds to the expectedbehaviour during particle coarsening. Therefore, after only 1 minute the earlystages of precipitation are complete, and coarsening is dominant.

2.1.2 Weld Microstructures

Figure 3 shows FEGSEM and TEM images taken at a depth of 5 mm belowthe top surface of the plate at a range of distances from the weld line. At themaximum distance from the weld line (35 mm), the microstructural observa-tions and hardness measurements (see Figure 5(c)) suggest that the parentplate has been unaffected by the welding process.

The observed transition in microstructure as the distance from the weld lineincreases is consistent with previous observations of other 7xxx alloys (3; 6).At 5 mm from the weld line, the temperatures reached are sufficiently highto dissolve the fine precipitates within the grains, and greatly coarsen thelarger particles, which are situated predominantly on grain boundaries. At13 mm, the precipitates remain largely undissolved within the grains, butcoarsen greatly. As the distance from the weld line is increased, and the peaktemperature decreases, the amount of coarsening reduces, as does the width ofthe precipitate free zone at grain boundaries. These complex microstructural

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(a) (b)

(c) (d)

2µm

Fig. 1. FEGSEM images after solution treatment and isothermal heat treatment at350◦C for (a) 1 min, (b) 10 mins, (c) 1 h and (d) 5 h.

101 102 103 104 1050

0.05

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icro

n

400 gb350 gb400 interior350 interior

10-1

100

101

102

101 102 103 104 105

Time / s

Num

ber

density / m

icro

n2

Fig. 2. Measured mean equivalent radius and number per area for grain boundaryand grain interior particles as a function of isothermal heat treatment time

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(a) (b) (c)

(

(d) (e) (f)

(g) (h) (i)

Fig. 3. (a–e) FEGSEM images at a depth of 5mm across the weld at (a) 5mm, (b)13mm, (c) 19mm, (d) 25mm, (e) 35mm from weld line. (f–i) TEM images at thesame depth, (f) 13mm, (g) 19mm, (h) 25mm, (i) 35mm from weld line.

changes are responsible for the large property variations that are observedacross the weld.

3 Semi-Empirical Hardness Modelling

3.1 Model Description and Calibration

The semi–empirical hardness model is based on an extension of the approachdeveloped by Myhr and Grong (8), originally applied to welding of AA6082 (8).This model was then extended and applied to 7xxx alloys by Shercliff and

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Hyoe (10; 16). It is based on physical principles, but requires calibrating foreach alloy and starting heat treatment. The model is based on the assumptionthat the dominant process that leads to strength loss in after welding is areduction in the hardening precipitate volume fraction. This is clearly an oversimplification of the true microstructural changes. However, the calibrationprocess in part compensates for this simplifying assumption. The full detailsof the model are given elsewhere (16), but the key points are summarized here.

It is assumed that the time taken for complete precipitate dissolution can berelated to a reference time and temperature by:

t∗1

= tr1 exp[

Qeff

R

(

1

T−

1

Tr

)]

(1)

where t∗1 is the time for complete dissolution at temperature T and tr1 is thetime for complete dissolution at the reference temperature Tr. Qeff is the effec-tive activation energy for the dissolution process. The activation energy andreference time for complete dissolution at the reference temperature consti-tute calibration parameters in the model, found by fitting experimental data.Assuming dissolution can be adequately modelled as a 1–Dimensional diffu-sion process, the normalized precipitate volume fraction remaining undissolvedafter an isothermal treatment can be related to the dissolution time by:

f

f0

= 1 −

(

t

t∗1

)1

2

(2)

where f is the precipitate volume fraction and f0 is the precipitate volumefraction prior to dissolution. Finally, it is assumed that the precipitate volumefraction and hardness are proportionally related, in which case:

f

f0

=HV − HVmin

HVmax − HVmin

(3)

where HV is the measured Vickers hardness at a precipitate fraction f , HVmin

is the minimum Vickers hardness after full dissolution and HVmax is the max-imum Vickers hardness (precipitates fully undissolved).

Calibration involves performing a series of isothermal heat treatments whichlead to partial dissolution of the precipitates. Hardness is measured and usedto calculate f/f0 using equation 3. A graph of log(1−f/f0) against log(t/t∗

1) is

then plotted and Qeff is adjusted until all points fall on a master curve, as ex-pected from equation 1. Note that equation 2 implies the master curve shouldbe a straight line of gradient 1/2. However, in practice, the master curvesusually deviate from this when the fraction dissolved is large, and this is a re-sult of soft impingement (overlap of the diffusion fields of adjacent dissolving

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-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-3 -2 -1 0 1 2 3 4 5 6

log(t/t1*)

log

(1-f

/f0)

200˚C250˚C300˚C350˚C400˚C480˚C

Qeff = 118kJ/molTr = 623Ktr1 = 16s

gradient=1/2

Fig. 4. Master curve showing isothermal softening data (from Mcshane (17)). Modelparameters are indicated on the plot.

particles). The master curve for AA7449–T7 (as obtained by McShane (17))is shown in Figure 4, along with the calibration parameters derived from thefitting.

To apply this model to welding it is necessary to calculate an effective equiv-alent time for the weld cycle. This can be done by considering the thermalcycle as a series of infinitesimal isothermal heat treatments. The dissolutionlaw is isokinetic (8), so that the increments in the fraction dissolved can beadded over the thermal cycle to give the total fraction dissolved. Equation 2can then be modified for non–isothermal treatment to give:

f

f0

= 1 −

(

∫ dt

t∗1

)1

2

(4)

where the integral is performed for the entire thermal cycle. entire thermalcycle. Alternatively, a best fit master curve from Figure 4 may be used di-rectly as a ‘look–up’ table to find f/f0 for the given effective t/t∗

1evaluated

in the integral. The calculated f/f0 for the weld thermal cycle is then used tocalculate the predicted hardness immediately after welding using equation 3.

There is an additional complication when considering the final hardness thatis obtained some time after welding. This is because natural ageing will occurin regions of the weld where sufficient solute has been taken into the matrixduring the thermal cycle. This process leads to some recovery of the hardness,particularly in the weld nugget where the temperatures reached are greatest,

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and the largest fraction of solute is dissolved.

In this work, a simple approach was used to predict the hardness increasedue to natural ageing, following the method of Hyoe (16). Natural ageingexperiments following isothermal softening show that, for AA7449-T7, thehardness increase can be directly related to the prior hold temperature, butdoes not depend on the hold time on the timescale of welding. The higher thepeak temperature, the more solute taken into the matrix, and the greater thehardness increase due to natural ageing.

Calibration of this hardness increase due to natural ageing against hold tem-perature was performed in AA7449 by McShane and Shercliff (17), and thisdata was used in the present study. This data shows that for peak tempera-tures below 300◦C the hardness increase due to natural ageing is negligible,but increases to ' 70 Hv when the peak temperature approaches 480◦C.

3.2 Thermal Modelling

To use the above model to calculate hardness profiles across the weld it isnecessary to predict the thermal cycle associated with welding for a series ofpositions. To do this, a thermal model is required. In this work, a well proventhermal model (TS4D (18; 19)) was used to predict thermal cycles. Details ofthe model, as applied to other welding processes, are available elsewhere (18;19). The predictions of this model have been compared with thermocouplemeasurements for the weld configuration used in this study (Figure 5(a)) andhave been shown to give a good match to the experimental data . Predictionswere made for a series of ten points 5 mm below the upper surface of the plateand spaced 3 mm apart (Figure 5(a)). This depth below the plate surfacecorresponds to the depth used for the hardness measurements.

The predicted thermal profiles are shown in Figure 5(b). The predicted peaktemperatures at each position are summarized in Table 2. The maximum pre-dicted peak temperature occurs closest to the weld line, as expected.

3.3 Hardness Predictions

The predicted hardness profiles with and without natural ageing are shown inFigure 5(c). The measured hardness data is also plotted. It can be seen thatthe model has correctly captured the main features of the measured hardnessprofile. A minimum in hardness is predicted 12 mm from the weld line, in goodagreement with the measurements. The predicted position of the hardnessminimum correlates well with the measured position. However, the predicted

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(a)

Toolshoulder

40

mm

We

ld d

ep

th2

0m

m

5mmxxxxxxxxxxxxxxxx xx

3 6 9 12 15 18 21 24 27 30

(b)

0 50 100 150 200 250 3000

100

200

300

400

500

Time / s

Tem

pera

ture

/ o C

3mm6mm9mm12mm15mm18mm21mm24mm27mm30mm

(c)

10 20 30 4060

80

100

120

140

160

180

200

220

Distance from weld line / mm

Har

dnes

s / V

HN

Predicted Predicted (no age)Measured

Fig. 5. (a) Schematic showing the weld configuration and the positions at whichpredictions of the thermal profile and hardness were made. (b) Predicted thermalprofiles at each position. (c) Predicted hardness variation with and without naturalageing compared with measured hardness.

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Distance/mm Peak Temp./ ◦C Distance/mm Peak Temp./ ◦C

3 420 18 273

6 399 21 248

9 369 24 228

12 367 27 212

15 293 30 199

Table 2Predicted peak temperatures during weld thermal cycles as a function of distancefrom weld centre

hardness values in the nugget and the TMAZ are approximately 20VHN belowthe measured hardness, even once natural ageing has been accounted for.This underestimate in the hardness may be due to effects associated withthe deformation structure, which are not included in the present model. Forexample, the contribution to strength from the fine substructure formed in thenugget zone can be significant. To account for this, the influence of deformationmust be included in the model.

4 Microstructural Modelling

4.1 Outline of Model

As the experimental results show, the microstructural changes that occur dur-ing welding are more complex than precipitate dissolution alone, which is theonly mechanism considered in the simple model described above. The mi-crostructural model aims to provide a full prediction of these changes.

In common with the semi–empirical hardness model, the dominant factor in-fluencing the precipitate evolution is taken as the thermal cycle the material isexposed to. The effect of deformation on the precipitate evolution is assumedto be second order in importance and is currently ignored in the model.

Figure 6 shows a flowchart of the complete model. There are three inputs tothe model; 1. the thermal cycle (as in the semi-empirical hardness model),2. the initial microstructure (precipitate size distributions) and 3. the alloycomposition. The initial microstructure depends on the alloy and heat treat-ment condition, and must be quantified by electron microscopy (as describedin section 2.1.1). At the heart of the kinetics model is a numerical precipi-tate evolution model, based on classical phase transformation theory and theKampmann and Wagner numerical method (KWN) (14). This method is de-

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Thermal cycle

From thermalmodel

From microstructuralcharacterisation

Initialmicrostructure

Alloycomposition

Update time, temperature

Evolve particle sizedistributions for allphases-Dissolution-Coarsening-Nucleation-Growth

Update sizedistributionand matrix

composition

Final timereached?

Error checkpassed?

Calculatetimestep

Y

NN

Y

ThermodynamicCalculation

Precipitate parameters-Size distribution-Mean radius-Number density-Volume fraction

Outputs

Numerical precipitateevolution model

Fig. 6. A flowchart showing the components of the microstructural evolution modeland how these are linked.

scribed in detail elsewhere (14; 20).

Two key features of the KWN method make it particularly suitable for mod-elling microstructural evolution during welding. The first is that precipitatenucleation, growth, coarsening and dissolution are all incorporated in themodel and the transition between these regimes arises naturally as the tem-perature or matrix composition changes. The second feature is that the fullparticle size distribution is tracked at all times. This means the model can ac-count for situations where bimodal or more complex particle size distributionsarise. These are commonly encountered in weld microstructures.

As illustrated in Figure 6 the evolution of the precipitates is considered overa series of small timesteps. The duration of each step is automatically ad-justed to assure numerical accuracy using a Runge-Kutta numerical integra-tion scheme (21). The key assumptions used in the KWN model as imple-mented here are:

(1) The continuous size distribution of the particles is discretized into a largenumber of size classes.

(2) The number of new particles in each time step is calculated using clas-sical nucleation theory. The exchange of particles between size classes iscalculated assuming solute diffusion is the rate limiting process and theapproximation of a spherical growth morphology. The Gibbs Thomsonrelationship is used to calculate the modified interfacial compositions foreach size class at each time step.

(3) The change in matrix solute level due to precipitate formation or disso-lution is calculated at each timestep using the mean field approximation.

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The resultant model is capable of predicting nucleation, growth, coarseningand dissolution without artificial constraints, whether these processes occurconcommitantly or sequentially.

The Kampmann and Wagner model was originally developed for simple bi-nary alloy systems. The method has recently been extended to properly predictgrowth, coarsening and dissolution in ternary systems (22). However, each ad-ditional alloying element adds an extra degree of freedom in the model, whichgreatly increases the model run time. Another widely used approach is toreduce complex multicomponent alloys to an appropriate pseudo–binary sys-tem (23). This approach is used here. A full multicomponent thermodynamiccalculation is used to calculate the equilibrium solute levels in the matrix, butnucleation, growth and coarsening are modelled by considering that a singleelement is rate limiting.

The phase of most importance in controlling the strength in high strength7xxx alloys is M (or η) phase and its metastable variants. The compositionof this phase can be approximated by the ideal, stoichiometric compositionMgZn2. Magnesium is assumed to be the rate limiting element that controlsits evolution, since it diffuses approximately 20 times slower than zinc in alu-minium at the temperatures of most interest for FSW (24).

It is possible to extend the KWN method to model the precipitation of themetastable and equilibrium phases by considering explicitly each phase. How-ever, this requires calibration data (interfacial energies and nucleation sitedensities) for each phase. In this work, calibration data was only collected forthe equilibrium M–phase. Therefore, only one phase is included in the model,and this is assumed to have a composition corresponding to the equilibriumM–phase. In the case of an initially overaged structure, as investigated here,this is a reasonable approximation. To apply the model to other cases (forexample, underaged or peak aged starting material) calibration data would berequired for the metastable phases.

The method used to calculate the nucleation and growth rates for the particlesis based on classical nucleation and diffusion controlled growth theory. Detailsare given elsewhere (20). There are two unknown parameters which have astrong effect on the nucleation and growth rates. These are the interfacialenergy and the nucleation site density (for particles that nucleate heteroge-neously). These parameters are fitted by matching predictions to experimentaldata during the model calibration process.

4.1.1 Grain Boundary Precipitation

The KWN framework described above has previously been used to predict theevolution of a single precipitate phase nucleating homogeneously. In this work

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100 200 300 400 5000

0.5

1

1.5

2

2.5

3

3.5

4

Temperature / oC

Ato

mic

% in F

CC

CuMgZn

100 200 300 400 5000

1

2

3

4

5

6

7

Temperature /oC

Mole

fra

ction o

f phase / %

Al7Cu

2Fe

Mg2Si

S-phaseM-phase

(b)(a)

Fig. 7. (a) Predicted precipitate phase fractions in AA7449 that leads to minimiza-tion of Gibbs free energy equilibrium phases. (b) Equilibrium matrix concentrationof the major alloying elements (Cu, Mg, Zn).

the model was extended to consider two distinct precipitation sites, grainboundaries and grain interiors. To model grain boundary precipitation, thefollowing modifications were made:

(1) The energy barrier for nucleation is reduced by multiplying it by a shapefactor that is less than one. The shape factor is fitted during model cali-bration.

(2) The number density of nucleation sites is reduced in proportion to thefraction of atoms that lie on grain boundary sites (25).

(3) The effective diffusion coefficient is increased by a constant factor torepresent enhanced grain boundary diffusion and the collector plate effect.The factor is found by comparing predicted and measured particle sizesduring model calibration. In future, a physical model will be developedto calculate this factor directly.

4.2 Microstructure Model Predictions

4.2.1 Thermodynamic Calculations

An essential input to the kinetic model for precipitate evolution is the ther-modynamic information for M–phase precipitation. The required informationis the matrix composition in equilibrium with the phase, and the solvus tem-perature. Figure 7 shows (a) the calculated mole fraction of the equilibriumprecipitate phases and (b) the equilibrium matrix composition of the main al-loying elements, Cu, Mg, and Zn, that leads to minimization of the Gibbs freeenergy for AA7449. These calculations were performed using JMatPro (26).As expected, the dominant precipitate phase is M–phase.

It can be seen that in this alloy, the M–phase solvus temperature is predicted

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Parameter Value

Interfacial Energy 0.1 Jm−2

Nucleation site factor (in grain) 1

Nucleation site factor (GBs) 1×10−5

Shape factor 0.05

Diffusion enhancement factor 20

Table 3Best fit set of calibration parameters for the microstructure model. Note that anucleation site factor of 1 corresponds to the case when every solute atom is apotential nucleation site (homogeneous nucleation) (27).

to be at 439◦C. With reference to Table 2 it can be seen that the peak tem-perature reached, even only 3 mm from the weld line, is below the predictedM–phase solvus. Therefore, welding is not expected to fully dissolve the Mphase, even close to the weld line. This is consistent with the microstructuralobservations, and confirms that the large particles observed in the weld aremost probably greatly coarsened M–phase particles, present originally in thestarting plate.

4.3 Model Calibration

The unknown parameters in the model are the site density factor and inter-facial energy for nucleation, and the shape factor and diffusion enhancementfactor for grain boundary precipitation. These were found by adjusting theseparameters to give the best fit between model predictions and measurementfor isothermal heat treatments. For example, a comparison of the predictedparticle and measured radius evolution at 350◦C is shown in Figure 8. Reason-able agreement between experiment and measurement can be obtained usinga set of calibration parameters that are physically sensible (shown in Table 3).Note that this set of calibration parameters is not necessarily unique. Theremay be another set of parameters that provide equal, or even better, fit tothe data. Further calibration experiments are required to fully optimize thesefitted constants.

4.4 Microstructural Evolution during Welding

To predict the microstructural evolution during welding, it was first necessaryto initialise the model by inputting the particle size distribution in the T7condition, corresponding to the starting plate.

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10−2

100

102

104

0

0.5

1

1.5

2

2.5

3x 10

−7

Time / s

Rad

ius

/ m

GB predictedGB measuredInterior predictedInterior measured

Fig. 8. A comparison of the predicted and measured equivalent particle radius afterisothermal treatment at 350◦C

As a first approximation, it was assumed that the initial particle size dis-tribution followed the log–normal distribution predicted by coarsening the-ory (28; 29). The mean particle sizes in the as received (T7) condition weredetermined by calculating the mean equivalent particle radii from TEM mi-crographs for both the grain interior and grain boundaries (see Figure 9(b)for values). The volume fraction was assumed to be that given by the ther-modynamic calculations, assuming the equilibrium M-phase fraction has beenreached in the T7 condition. From these values, the initial particle numberdensities on grain boundaries and within grains were estimated.

Microstructural predictions were performed for three positions across the weld;3 mm from the weld line, 12 mm (the approximate position of the hardnessminimum) and 30mm (a point towards the outer edge of the heat affectedzone). Figure 9 shows the predicted evolution of the precipitate volume fractionand equivalent radius of the largest particle during welding at each position.

It can be seen that close to the weld line (3mm) it is predicted that most ofthe original M–phase dissolves during the heat up to the peak temperature.This is accompanied by a sharp increase in the maximum particle size bothwithin the grains and on grain boundaries. During post weld cooling, it ispredicted that reprecipitation occurs. At the grain boundaries, full reprecipi-tation is expected, restoring the equilibrium fraction of M–phase. Within thegrains, the kinetics are predicted to be too slow for full reprecipitation, andsome excess solute will remain in the matrix. This solute will be available fornatural ageing. The precipitation during cooling is accompanied by a furtherincrease in the maximum particle size, which is predicted to finish approxi-mately three times larger than the original size for both grain boundary andinterior precipitates.

Further from the weld line (12mm) where the temperature excursion during

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0

0.02

0.04

0.06

0.08

0 100 200 3000

2

4

6

8x 10-8

0

0.02

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0.08

0 100 200 3000

2

4

6

8x 10-8

0

0.02

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0.06

0.08

0

2

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8x 10-8

0 100 200 300

0 100 200 300

0 100 200 300

0 100 200 300

Time / s

Vo

lum

e F

ractio

n

Ma

x.

Ra

diu

s /

m

GBInterior 3mm 3mm

12mm

12mm

30mm

30mm

(a) (b)

(c) (d)

(e) (f)

rinitial GB=15nm

rinitial interior=2nm_

_

Fig. 9. Predicted evolution of M–phase volume fraction and maximum particle radiusduring FSW at (a–b) 3mm (c–d) 12mm (e–f) 30mm from the weld line

welding is less severe, the fraction of dissolution and the amount of coarseningare predicted to be less. Again, reprecipitation during cooling is predicted to goto completion on the grain boundaries but not within the grains. At 30mm, aposition where the hardness is unaffected by the weld cycle, it can be seen thatalmost no change in volume fraction is predicted. The only microstructuralchange expected according to the model is a slight increase in the size of thelargest particles on grain boundaries.

The model also allows the full particle distribution to be calculated. As anexample, Figure 10 shows the predicted size distribution of particles at aposition 12 mm from the weld line before and after welding. It can be seenthat after welding, it is predicted that a bimodal size distribution will begenerated. The upper peak in this size distribution corresponds to particlesfrom the original parent material that were large enough to survive the weldingprocess, and have coarsened. The lower peak corresponds to new particleswhich are predicted to have nucleated during post–weld cooling. They arevery small, and in practice the metastable phases may nucleate in preference

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0 1 2 3 4 50

0.5

1

1.5

2

2.5

3x 10

5

Radius / nm

Num

ber

Den

sity

/ µm

After weldingBefore welding

Original particles

New particles

Fig. 10. Predicted particle size distribution of M–phase particles within grains afterwelding (12mm from weld line). The assumed starting size distribution in the parentplate is also shown.

to the equilibrium M–phase. Since these phases are not explicitly included inthe model, the size and position of the lower peak is likely to be unreliable.Nevertheless, the model suggests that fine precipitates may form during postweld cooling, leading to partial artificial re-ageing of the weld, before the onsetof post-weld natural aging. By controlling the post–weld cooling rate, it shouldbe possible to optimize this precipitation.

5 Conclusions

The microstructural variation across a friction stir weld in AA7449 plate hasbeen studied and models have been developed to predict the resultant hardnessprofile and the microstructural evolution during the welding process.

The hardness model is based on a semi–empirical method that requires cali-bration with data from isothermal heat treatments. A thermal model is usedto predict the temperature evolution during the welding process. The modelhas been shown to give a good prediction of the observed hardness profile, cor-rectly predicting the position of the hardness minimum. The model slightlyunderestimates the hardness in the nugget zone, and this is attributed to ne-glecting the effects of deformation strengthening.

The microstructural model is based on the numerical framework of Kampmannand Wagner. Given the temperature profile and initial precipitate parameters,this model predicts how the precipitates evolve.

It has been shown that bimodal particle size distributions are predicted toevolve during welding, resulting from the mixture of coarsened particles from

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the original parent material and new particles formed on post weld cooling.The model suggests that it may be possible to form particles during coolingthat are small enough to lead to artificial re-ageing of the weld.

The microstructural model presented here is still in its early stages of de-velopment. However, it already shows promise as a tool to design improvedwelding practices. Future developments will include properly accounting forthe metastable precipitates and accounting for the influence of deformationon the precipitate evolution.

6 Acknowledgements

The authors are grateful to Alcan and the EPSRC for providing financialsupport for this work. Airbus UK are thanked for the provision of the AA7449friction stir welds used in this study and for supplying the thermal model.

7 References

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