Influence of Solute Content and Solidification Parameters on Grain Refinement of Aluminum Weld Metal

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Metallurgical and MaterialsTransactions A ISSN 1073-5623Volume 44Number 7 Metall and Mat Trans A (2013)44:3198-3210DOI 10.1007/s11661-013-1649-3

Influence of Solute Content andSolidification Parameters on GrainRefinement of Aluminum Weld Metal

Philipp Schempp, Carl Edward Cross,Andreas Pittner & Michael Rethmeier

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Influence of Solute Content and Solidification Parameterson Grain Refinement of Aluminum Weld Metal

PHILIPP SCHEMPP, CARL EDWARD CROSS, ANDREAS PITTNER,and MICHAEL RETHMEIER

Grain refinement provides an important possibility to enhance the mechanical properties (e.g.,strength and ductility) and the weldability (susceptibility to solidification cracking) of aluminumweld metal. In the current study, a filler metal consisting of aluminum base metal and differentamounts of commercial grain refiner Al Ti5B1 was produced. The filler metal was thendeposited in the base metal and fused in a GTA welding process. Additions of titanium andboron reduced the weld metal mean grain size considerably and resulted in a transition fromcolumnar to equiaxed grain shape (CET). In commercial pure aluminum (Alloy 1050A), thegrain-refining efficiency was higher than that in the Al alloys 6082 and 5083. Different weldingand solidification parameters influenced the grain size response only slightly. Furthermore, theobserved grain-size reduction was analyzed by means of the undercooling parameter P and thegrowth restriction parameter Q, which revealed the influence of solute elements and nucleantparticles on grain size.

DOI: 10.1007/s11661-013-1649-3� The Minerals, Metals & Materials Society and ASM International 2013

I. INTRODUCTION

A severe problem encountered in the welding ofcertain aluminum alloys is solidification cracking. Thesecracks may form during solidification of the weld pool,depending on the alloy system and welding conditions.One important parameter that influences the suscepti-bility to solidification cracking is the weld metal grainstructure. It has been shown in several studies that a fineweld metal grain structure can be related to a lowersusceptibility to solidification cracking.[1–4] One expla-nation for this improvement is that the strain isdistributed between more grain boundaries.[5] In addi-tion to improving weldability, grain refinement can helpin enhancing the mechanical properties of the weldmetal such as strength and particularly ductility.[6–9]

One way to achieve small weld metal grains is throughthe addition of grain-refining elements to the filler wirethat is fused in the arc welding process and determinesthe weld metal chemical composition. Some commercialfiller wires contain small amounts of elements like e.g.,titanium, zirconium, or scandium that are known tohelp in the refinement of weld metal grain structure.[10]

However, it is not well understood how much of theseelements is needed to refine the microstructure com-pletely, depending on the chemical composition of thebase metal and the welding/solidification parameters.

One of the most important and most efficient alumi-num grain refiners is the master alloy Al Ti5B1 thatcontains 5 wt pct titanium and 1 wt pct boron.[11] Bothelements are present in the master alloy in the form ofparticles such as Al3Ti

[12] and TiB2[13] that act during

solidification of the weld pool as heterogeneous solid-ification nuclei for aluminum grains. The exact role ofeach particle type is still under discussion; one widelyaccepted approach suggests that the insoluble TiB2

particles are covered in the liquid aluminum by a thinAl3Ti layer (duplex nucleation theory)[14]—the subse-quent peritectic reaction Al3Ti+AlL fi AlS convertsthem into very efficient solidification nuclei.[12] Proper-ties that make such particles favorable for nucleation ofaluminum grains are their size and size distribution,[15,16]

shape, and atomic lattice.[17] Hence, sufficient additionsof grain refiners like Al Ti5B1 to liquid aluminum canprovide a greater number of active solidification nucleiand thus a fine, equiaxed grain structure in the weldmetal.Besides the availability of these solidification nuclei,

the chemical composition of the weld pool influencesstrongly nucleation and subsequent grain growth. Dur-ing equilibrium solidification of a metal, solute redistri-bution takes place according to the phase diagram andlever rule.[18] In eutectic binary alloy systems, such asAl-Si, the solubility of the alloying element (here: Si) ishigher in the liquid than in the solid phase (for Sicontents<13 wt pct). Accordingly, the liquidus slope isnegative in this region of the binary Al-Si phasediagram. As a result, the Si content of the remainingliquid increases during solidification, particularly infront of the solid–liquid interface, whereas the Si contentof the solid is low.[19] In peritectic binary alloy systemssuch as Al-Ti, the conditions are vice versa: the liquidphase has a lower solubility for Ti than the solid phase

PHILIPP SCHEMPP, Ph.D. Student, ANDREAS PITTNER,Head, and MICHAEL RETHMEIER, Head, are with the BAM,Federal Institute for Materials Research and Testing, Berlin,Germany. Contact e-mail: [email protected] CARL EDWARDCROSS, Staff Scientist, is with the LANL—Los Alamos NationalLaboratory, Los Alamos, NM.

Manuscript submitted September 13, 2012.Article published online February 23, 2013

3198—VOLUME 44A, JULY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

Author's personal copy

(for Ti contents<80 wt pct). Consequently, the liquidusslope is positive, and Ti partitions from the liquid intothe solid phase.

Solute partitioning generally changes the chemicalcomposition of the remaining liquid and decreases itsliquidus temperature. This actual liquidus temperaturefalls below the equilibrium liquidus temperature and‘‘constitutional undercooling’’ develops.[18] It has a greatimpact on the corresponding grain structure because it isnecessary to activate particles for nucleation.[20] Thelarger and the more powerful the constitutionallyundercooled zone, the more the particles are activated.The resulting growth of many grains at the same timeleads to a small final grain size. As a consequence, thegrain substructure may vary from planar or cellular (atlow undercoolings) to columnar, columnar dendritic, or(at very high undercoolings) equiaxed dendritic.[21]

The amount of constitutional undercooling and the sizeof the constitutionally undercooled zone ahead of thesolid–liquid interface depend on chemical compositionand thermal conditions. Accordingly, the undercoolingincreases with increasing alloy content; particularly,titanium provides a very high degree of constitutionalundercooling compared with other elements.[22] Thisexplains why excess solute Ti (which is not tied up inparticles) plays an important role in aluminum grainrefinement. Also, the above mentioned TiB2 and Al3Tiparticles are known to need a lower undercooling to beactivated than other particles, which is a further expla-nation for their effectiveness.[20] Furthermore, increasingcooling rates and thermal gradients provide higherdegrees of constitutional undercooling.[23] In fusionwelds, the solidification is restricted to a very short timeinterval of few seconds. This leads to a high constitutionalundercooling ahead of the solidification front oftenproducing a columnar or equiaxed grain structure.[24,25]

In the current study, weld metal grain refinement fordifferent Al wrought alloys was achieved through grainrefiner additions and analyzed by means of the und-ercooling parameter P, the growth restriction parame-ters Q and 1/Q. It is shown how these parameters canhelp in interpreting differences in grain size responsedepending on thermal conditions, solute content, andparticle concentration. P and Q have originally beendeveloped with experimental data from castings at lowcooling rates. In the current study, both P and Q areused to describe solute effects in solidification of Al weldmetal where cooling rates can reach several 100 K/s.Furthermore, it is shown what role thermal parameterssuch as cooling rate and thermal gradient play.

II. BACKGROUND

A. Undercooling Parameters P and Q

Rutter et al.[26] were among the first who argued thatsolute elements provide constitutional undercooling duringpartitioning of the melt, which helps in the activation ofnucleant substrates and thus in the formation of fine,equiaxed grains. An analytic approach to describe theinfluence of alloying elements on the final grain size of

solidified structures was made for castings of Ni- and Al-based alloys by Tarshis et al.[27] in the early 1970s—see Eq.[1]. They developed the parameterP, which can be used forrelative grain size prediction. C0 is the concentration of analloying element, k0 is the partition coefficient (betweensolid and liquid), and mL is the slope of the liquidus line,wherebothk0 andmLare taken fromthe equilibriumbinaryphase diagram of the alloying element with aluminum.

P ¼ ð�mLÞ � 1� k0ð Þ � C0

k0½1�

Thus, high alloying contents and the presence ofelements with a high tendency to partition (such as Ti)promote high P values. Therefore, P was suggested torepresent the constitutional undercooling that is pro-vided by an alloying element during solidification.Consequently, large values of this later-called ‘‘consti-tutional undercooling parameter’’ P[28] can be related toa fine, equiaxed grain structure; small P values corre-spond to large, columnar grains.Another approach to predict relative undercooling

was proposed by Moriceau[29] and Maxwell and Hella-well.[30] They argued that the form of the phase diagramcontributes substantially to grain refinement as ex-pressed by an alloy factor (X)—see Eq. [2].[30] Theauthors stated that high values of X (i.e., low concen-tration of solute and low partitioning) correspond torapid grain growth and coarse grains. The inverse of thealloy factor (1/X) was taken as an inhibitor to growth.Hence, high values of 1/X correspond to slow growthand fine grains.

1

X¼ mL � ðk0 � 1Þ � C0 ½2�

Easton and StJohn[31] argued that the inhibition ofgrain growth at high 1/X values gives longer time forfurther nucleation events to occur. This leads to moregrains and thus a smaller final grain size. The denom-ination growth restriction factor (for 1/X) was intro-duced later[32] based on the suggestion that 1/X isinversely proportional to the growth velocity R of adendrite tip.[33–35] Furthermore, it was shown experi-mentally that grain size is proportional to R.[35–37]

Desnain et al.[38] were the first to sum the growthrestriction factors for all solute elements that are presentin an aluminum melt to apply the analytic approach onmulticomponent Al alloys:

growth restriction factor ¼Xn

i¼1mL;i � ki � 1ð Þ � C0;i ½3�

Later, the growth restriction factor has also beencoined as GRF[39] and Q[40]:

growth restriction factor ¼ GRF ¼ Q ¼ k � P ½4�

In summary, the grain-refining effect of solute ele-ments with a high GRF can be explained with the

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, JULY 2013—3199


restriction of grain growth[30] that increases constitu-tional undercooling[26] and the time for further nucle-ation events to occur.[31] The high value of GRF fortitanium (the highest of all typical alloying elements inAl alloys) helps in explaining why additions of solutetitanium usually result in a dramatic grain-size reduc-tion.[22] This cannot be explained with the parameterP.[39]

B. Physical Meaning of P and Q

Easton and StJohn[11] expressed the development ofthe constitutionally undercooled zone around a growingequiaxed grain as a function of solid fraction fS, basedon Rutter and Chalmers[26]:

DTC ¼ mL � C0 � 1� 1

1� ð1� kÞ � fS

� �½5�

Hence, a growing grain provides constitutional und-ercooling, which increases with larger solid fraction. Atone point, the constitutional undercooling (DTC)reaches the undercooling required for nucleation(DTN) of a neighboring particle. Then, nucleation of anew Al grain will occur at this particle. This in turnmeans that a grain must grow to a critical size to provideenough constitutional undercooling for the nucleationof other grains. Those authors assumed solidificationaccording to Scheil, constitutional undercooling, andnegligible thermal gradients compared with the amountof undercooling. Furthermore, they supposed a suffi-cient number of available nucleant substrates that areactivated when DTC reaches DTN. Finally, the modelprovides a physical basis for the derivation of both Pand Q and therefore an interpretation of the physicalmeaning of both parameters, which can be distinguishedas follows:

(a) P: Total constitutional undercooling that is pro-vided by a growing grain due to partitioning ofsolute elements;

! DTC at fS ¼ 1

(b) Q: Initial rate of development of constitutionalundercooling (confirmed in experiments[41]);

! dDTC=dfS at fS ¼ 0

The authors argued that Q is a suitable parameter forgrain size prediction if the potency of the particles ishigh (low DTN).

[11,42] Furthermore, they stated thatgrain refinement in alloys with high solute content (i.e.,foundry alloys) cannot be described accurately with Q,calculation of which is based on binary phase dia-grams—recall Eq. [3]. Grain refinement in wroughtalloys (low solute content), however, may be analyzedby means of parameters such as P and Q,[11] whereby thesuitability of Q is discussed in comparison.[39,42] Exper-imental data showed that the influence of solute on grainsize may be predicted better with Q than with P.[39]

Furthermore, the grain size d was found to be inverselyproportional to both P[27,28] and Q[35,39,41]:

1

P� d � 1

Q½6�

Easton and StJohn[42] studied separately the influenceof nucleant substrates and solute elements on grain size.In several experiments, they made additions of either amaster alloy (containing TiB2 particles) or solute tita-nium to Al castings. This way, they further developedEq. [6] to a semiempirical relationship, which is appli-cable for a constant set of casting/solidification condi-tions,[42,43] see Eq. [7]. q is the number density ofparticles present in the melt; f is the fraction of activeparticles that nucleate a grain; and c is a constant.

d ¼ aþ b

Q¼ 1ffiffiffiffiffiffiffiffi

q � f3p þ c � DTN

Q½7�

Hence, there exists a linear relationship between d and1/Q whereby the parameters a and b stand for theeffectiveness of a particular grain-refining master alloy;the axis intercept a represents the availability of nucle-ant substrates, and the slope b is proportional to thenucleant potency.[44] Furthermore, it was argued else-where that there is an inverse cube root relationshipbetween grain size d and the number of active TiB2

particles.[42,45]

The above analytic approaches were applied to lowcooling rates (1 to 10 K/s) and low thermal gradients inAl castings. Johnsson[36] and Chai et al.[35] found thatgrain size is related to the inverse square root of thecooling rate in the range from 0 to 5 K/s. This wasconfirmed by experimental data[44,46] for cooling ratesup to 15 K/s.

C. G/R and CET

The development of constitutional undercooling alsodepends on the local temperature gradient G. In fusionwelds: the heat extraction is small at the weld centerlineand high at the fusion line. G is thus minimum at thecenterline and maximum at the fusion line, whereas R ismaximum at the centerline and minimum at the fusionline.[47] The large variations of both G and R along thepool boundary are often expressed as G/R[48] and have asignificant influence on nucleation and grain size: HighG/R values can be related to low constitutional und-ercooling ahead of the solid–liquid interface[49] andfavors columnar grain growth.[21] Low G/R values,however, result in a large zone of constitutional und-ercooling,[49] which favors equiaxed grain growth.[21]

Thus, in fusion welds, the Columnar to EquiaxedTransition (CET) from columnar growth at the fusionline to equiaxed growth at the centerline is oftenobserved,[25,50–52] depending on chemical compositionand welding conditions. Hunt developed a more rigor-ous model for directional solidification in cast structure,which predicts the CET for critical values of G, R,and the number and efficiency of added nucleants.[33]



Applying Hunt’s approach, the limitations of using G/Rin welding were demonstrated by Grong and Cross[53]

who showed that equiaxed grains may also form at thefusion line where the growth rate approaches zero. Thisphenomenon is observed when welding base metalscontaining Al3Zr dispersoid particles (e.g., 7xxx andAl-Li alloys) that serve to nucleate equiaxed grains inthe partially mixed zone (PMZ) when released duringmelting.[54–56]

III. EXPERIMENTAL

Thewrought basemetals used in the current studywerecommercial pure aluminumAlloy 1050A (Al 99.5, temperH14);Alloy 6082 (Al Si1MgMn, temperT6) that is knownfor applications in automotive industry and plant con-struction; andAlloy 5083 (AlMg4.5Mn0.7, temperH111)that is frequently used in shipbuilding or as vesselmaterial. Plate thickness was 3 mm for each alloy. AlTi5B1 was used as commercial grain refiner in the form ofrods (diameter, 9.5 mm). The chemical composition of allalloys was measured using an Optical Emission Spec-trometer (ICP-OES) and is given in Table I.

In order to vary the weld metal’s content of grain-refining elements, Ti and B, ingots were cast consistingof the corresponding base metal plus additions of AlTi5B1. Fading (the dissolution of particles in the melt)was avoided in the casting process because of a lowcontact time of the grain refiner in the Al melt [about5 minutes at 1003 K (730 �C)]. A detailed description ofthe casting process is given in Reference 57. Each castingot was then machined into several small inserts (140mm 9 2 mm 9 1.5 mm). A groove was milled into thebottom surface of weld coupons (140 mm 9 60 mm 9 3mm) consisting of wrought metal plates. Afterward,

both inserts and coupons were cleaned by degreasingand etching for 15 minutes with an etchant consisting of869 mL H2O, 125 mL 65 pct HNO3, and 6.25 mL 48 pctHF. Each insert was placed into the groove of a couponand fixed with a hammer and punch. Then, the weldcoupon was clamped in a fixture with the cast insertlocated on the bottom-side. The cast insert was fusedcompletely in a single pass—full penetration gas tung-sten arc (GTA) weld with the parameters listed inTable II. A backing plate made of copper was used toavoid unwanted root drop-through.In order to insure similar weld bead sizes and dilution

of the insert, the arc current was set slightly higher whenwelding with Alloy 1050A because of its higher thermalconductivity compared with the other two alloys—seeTable III.[58] In the case of Alloys 1050A and 6082, thetorch speed was varied from 2 to 6 mm/s to study theinfluence of solidification parameters on grain sizeresponse. Accordingly, the weld current was adjustedslightly to allow a constant weld bead size. More detailsabout casting and welding processes are given inReference 57. Temperature measurements were accom-plished in the middle of each weld (mid-length, width,and depth) with Type-K thermocouples (wire diameter0.13 mm), which were mounted from below into adrilled hole in the weld coupon.Metallographic samples were prepared from the

middle of each weld to get a cross-sectional view ofthe weld metal. Each sample was ground, polishedmechanically, and etched anodically with a solutioncontaining 2 pct HBF4 and 98 pct H2O. Micrographswere made using a microscope equipped with polarizedlight, which helped in differentiating the grains. Grainsize measurements were carried out in not less than fourdifferent positions on each weld metal cross sectionthrough a circular intercept procedure according to the

Table I. Chemical Composition of Three Base Metals and the Grain Refiner (Al Ti5B1) as Measured by Optical EmissionSpectrometer (ICP-OES)

Alloy

Chemical Composition in wt pct

Si Fe Cu Mn Mg Cr Ni Zn Ti B V Zr Al

1050A (Al 99.5) 0.09 0.24 0.01 0.004 0.001 0.001 0.004 0.01 0.008 0.0003 0.01 0.001 bal.6082 (Al Si1MgMn) 0.86 0.42 0.09 0.43 0.75 0.06 0.01 0.07 0.032 0.0001 0.01 0.003 bal.5083 (Al Mg4.5Mn0.7) 0.25 0.40 0.07 0.58 4.57 0.09 0.01 0.07 0.027 0.002 0.006 0.002 bal.Al Ti5B1 0.06 0.11 — — — — — — 4.98 0.99 0.02 — bal.

Table II. GTA Welding Parameters Used to Weld Cast Inserts into Base Metal

Parameter1050A (Al 99.5) 6082 (Al Si1MgMn) 5083 (Al Mg4.5Mn0.7)

Torch Speed in mm s�1 2.0 4.17 6.0 2.0 4.17 6.0 4.17Current in A 174 180 187 170 175 181 175Voltage in V (±0.2 V) 11.5 11.3 11.6 10.7 11.2 11.2 11.3Polarity AC (80 pct negative, 20 pct positive)Frequency 50 HzElectrode W+2 pct CeO2, diameter 3.2 mm, point angle 30�Shielding Gas 50 pct Ar, 50 pct HeFlow Rate 26 L min�1

Distance Electrode—Coupon 3 mm



standard,[59] and an average value for each weld metalwas calculated. The chemical composition of pieces cutfrom the welds was determined by an Optical EmissionSpectrometer (ICP-OES). Wavelength dispersive X-rayspectroscopy (WDS) was used to investigate the weldmetal microstructure of some metallographic samples.

IV. RESULTS AND DISCUSSION

A. Grain Size Response of Different Alloys

The Ti and B contents of the weld metal were variedwith the use of inserts that contained different amountsof grain refiner Al Ti5B1. The resulting weld metal grainsize could be controlled this way. Figure 1 shows forthree alloys the relationship between weld metal meangrain size and the Ti content that was measured in theweld metal (in the current study, the Ti content is usedto represent the grain refiner additions; the B contentwas approximately 1/5 of the Ti content). As one can seein Figure 1, increasing grain refiner addition levels led toa significant decrease in grain size. This has also beenreported by other authors for grain refinement throughinoculation in aluminum weld metal.[3,60,61] The grain-size reduction depended strongly on the base metal; thesmallest grain sizes were observed when grain refinerwas added to commercial pure aluminum (1050A),whereby the grain size was reduced from 112 lm (datapoint not in the diagram) to 16 lm. Welds made withAlloy 5083 showed larger grain sizes than Alloy 1050A,with Alloy 6082 in between. Figure 2 reveals thesedifferences, comparing the maximum decrease in grainsize.

The observed grain refinement can be explained by (1)a higher number of active solidification nuclei such asTiB2

[44] and Al3Ti[20] that were present in the weld pool

during solidification; and (2) a higher degree of consti-tutional undercooling, particularly provided by solutetitanium.[22] It is known from other studies that com-

mercial Al Ti5B1grain refiners contain both insolubleTiB2 and soluble Al3Ti particles.

[62] Some of the TiB2

particles present have likely nucleated grains in thesolidifying weld pool.[13,40,44,63] With respect to Al3Ti, itis not known how much Al3Ti was dissolved duringwelding. Some amount of Al3Ti is expected to dissolveduring welding and to provide solute Ti, depending onwelding conditions. It is notable that the Ti content ofmost welds was below the Ti concentration above whichAl3Ti may form (0.15 wt pct) according to the equilib-rium binary phase diagram for Al-Ti.[22] Al3Ti agglom-erates with a thickness up to 15 lm were observed in aWDS analysis of metallographic specimens of weldmetal with high grain refiner content. Furthermore,Al3Ti agglomerates were also observed by otherresearchers in similar experiments with GTA weld metalthat was inoculated by an Al3Ti-bearing grain refiner.[60]

Thus, it is unlikely that Al3Ti particles dissolved

Table III. Thermal Conductivity (After[58]), Thermal Parameters, and Grain Size Depending on Base Metal and Torch Speed

(GTA Welding; Middle of Weld Metal)

Parameter 1050A (Al 99.5) 6082 (Al Si1MgMn)

5083 (AlMg4.5Mn0.7)

ThermalConductivityin W (m K)�1

210 170 110

Torch speedin mm s�1

2.0 4.17 6.0 2.0 4.17 6.0 4.17

Heat Inputin J mm�1

996 (+104pct) 489 362 (�26 pct) 912 (+94 pct) 470 337 (�28 pct) 474

Cooling Ratein K s�1

219 (�43 pct) 384 466 (+21 pct) 200 (�42 pct) 343 369 (+8 pct) 290

Therm. Grad.G in K mm�1

110 (+20 pct) 92 78 (�15 pct) 100 (+22 pct) 82 62 (�24 pct) 70

Ratio G/Rin (KÆs) mm�2

55 (+150 pct) 22 13 (�41 pct) 50 (+150 pct) 20 10 (�50 pct) 17

Ti Contentin wt pct

0.01 0.06 0.01 0.06 0.01 0.06 0.02 0.16 0.02 0.14 0.02 0.14 0.03 0.17

Mean GrainSize in lm

140 20 112 16 119 19 70 21 69 21 52 21 39 22

Fig. 1—weld metal mean grain size depending on weld metal Ti con-tent and base metal. GTA welding, plate thickness 3 mm, torchspeed 4.17 mm/s, and mean heat input 478 J/mm.



completely in the weld metal because of the very fastfusion and solidification of the weld metal (within fewseconds). Moreover, some of these Al3Ti particles mayhave caused agglomeration through collision at highparticle concentrations.

Above a certain grain refiner addition level, saturationof grain size was observed, which is known fromgrain refinement in both aluminum castings andwelds.[3,30,46,60] In the case of Alloys, 1050A and 5083,

even a slight increase in grain size was measured at Ticontents>0.2 wt pct.[57] One explanation for saturationmay be recalescense, i.e., the time period during solid-ification in which the heat evolved from grain growthcounteracts the undercooling DTN necessary for activa-tion of nucleant substrates.[30] This is one reason whyonly at most 1 pct of potential particles finally becomesactive and nucleate an aluminum grain.[44,64]

The grain refinement effect is further illustrated inFigure 3 containing six micrographs showing weld metalgrain structure depending on base metal. One can findon the left-side weld metals with maximum grain sizewith no grain refiner additions (Figures 3(a), (c), and(e)); the right side shows the minimum grain size whenthe Ti/B contents of the weld metal is high enoughleading to a fine, equiaxed microstructure (Figures 3(b),(d), and (f)). Refinement of the microstructure preventedthe formation of centerline solidification cracks thatformed in unrefined Alloy 6082 weld metal—see Fig-ures 3(c) and (d). This reduction in the susceptibility tosolidification cracking by grain refinement is describedand discussed in Reference 4. While welding Alloy 5083,the appearance of feather grains (twinned crystals) thatcan impair the mechanical properties of the grainstructure[65] was avoided by the use of grain refine-ment[57]; see Figures 3(e) and (f).Figure 3 also reveals that the minimum weld metal

grain size was larger (Alloy 5083) or clearly smaller(Alloys 1050A and 6082) than the grain size of the cold-rolled base metal plates (Alloy 5083: 14 lm, Alloy

Fig. 2—Maximum decrease in grain size depending on weld metal Ticontent and base metal. GTA welding, plate thickness 3 mm, torchspeed 4.17 mm/s, and mean heat input 478 J/mm.

Fig. 3—GTA weld metal with low (a, c, and e) and high (b, d, and f) Ti/B content. Plate thickness 3 mm, torch speed 4.17 mm/s, and mean heatinput 478 J/mm.



1050A: 20 lm, 6082: 35 lm). This emphasizes that theinfluence of the solute content of each alloy on grain sizeresponse is high, which is also shown by the diagram inFigure 4. As one can see, the optimum Ti content, or theminimum Ti content needed to achieve a minimum grainsize, depends strongly on the base metal alloy. Accord-ing to this, the grain refiner efficiency was the highest incommercial pure Al (1050A), where small Al Ti5B1additions led to a large decrease in the mean grain size.This is in contrast to Alloy 5083, where large additionswere needed to achieve a grain-size reduction that wasless pronounced than with Alloy 1050A (Alloy 6082 inbetween)—recall Figure 1.

B. Effect of Solidification Parameters on Grain SizeResponse

It is of interest to note that the weld metal grainrefinement came along with a change in grain shape—seeFigure 5. The diagram illustrates the measured areafraction of equiaxed grains as percentage of the cross-sectional area of the weld metal, depending on Ti contentand base metal. Both Alloys 6082 and 5083 showed asimilar behavior; the grain refiner additions led to thereduction (and finally elimination) of columnar grainsthat formed particularly at the fusion line—recall Fig-ure 3. In comparison, even high amounts of grain-refining elements could not refine the columnar grainstructure in weld metal of Alloy 1050A (commercial pureAl); about 20 pct of the grain structure remainedcolumnar at the fusion line. It should be noted here thatthe higher amount of columnar grains has likely influ-enced the grain size measurements that represent in thecurrent study the mean grain size of equiaxed grains.Measuring the mean grain size of all weld metal grains(equiaxed+columnar) is of questionable benefit due toshape effects.[59]

It can be assumed that the cast inserts and hence thenucleant particles were diluted and distributed homoge-neously in the weld metal, except in the PMZ next to the

fusion line.[66] Thus, the presence of columnar grains atthe fusion line can be explained particularly by solidi-fication parameters such as local thermal gradient (G)and the growth rate of the solid–liquid interface (R).Table III shows the thermal conditions in the middle ofthe welds (mid-depth and width), depending on the basemetal. The cooling rate at the liquidus temperature wasdetermined with thermocouples in the middle of theweld pool. G and the ratio G/R were calculatedassuming that R is equal to torch speed. This assump-tion is usually made for the point at the trailing edge ofthe weld pool top surface where the weld centerline andmoving solid–liquid boundary intersect.[51] In the cur-rent study, the assumption was extended to the middleof the weld pool (mid-depth) where a thermocouplemeasured the temperature. In addition, it is assumedthat dendrites are oriented in the same direction as graingrowth and that grains grow normal to the solid–liquidinterface.[67] Torch speed thus provides an order ofmagnitude upper limit for R. The heat input (energyinput per unit length) was calculated with data fromTable II. No measureable influence of the grain refineraddition level on the thermal conditions was found.Thus, the thermal parameters listed in Table III areaverage values for a set of different grain refiner additionlevels. Furthermore, torch speed was varied whenwelding Alloys 1050A and 6082 to investigate theinfluence on solidification and grain size response; thevalues for the standard torch speed 4.17 mm/s are boldin Table III.The high thermal conductivity of commercial pure Al

was the reason why the welding current had to beincreased slightly to produce welds with similar size—re-call Table II. This adjustment did not change the heatinput significantly—see Table III. However, the largedifferences in the alloys thermal conductivities led tolarge differences in the solidification parameters for eachalloy. The bold values in Table III (constant torch speed4.17 mm/s) reveal that maximum values of cooling rate,G and G/R were found for 1050A weld metal andminimum values for 5083 weld metal (6082 in between).

Fig. 4—Optimum Ti content needed for maximum decrease in grainsize. GTA welding, plate thickness 3 mm, torch speed 4.17 mm/s,and mean heat input 478 J/mm.

Fig. 5—Area fraction of equiaxed grains as percentage of cross-sec-tional weld metal area. GTA welding, plate thickness 3 mm, torchspeed 4.17 mm/s, mean heat input 478 J/mm.



Low G/R values are usually related to a greater extent ofconstitutional undercooling,[49] which may activatemore of the particles present[20] and which is thereforean important requirement for the formation of fine,equiaxed grains.[21] This is one explanation why thegrain size was the highest in 1050 A weld metal (112 lm)and the smallest in 5083 weld metal (Alloy 5083 weldmetal: 39 lm; Alloy 6082 weld metal: 36 lm) when nograin refiner had been added—recall Figures 3(a), (c)and (e). Furthermore, the constitutional undercooling in5083 and 6082 weld metal was further increased byalloying elements, especially Ti, that were not present in1050A weld metal—recall Table I. The high values ofcooling rate, G, and G/R in 1050A welds also explainwhy the CET was here less pronounced than in welds ofAlloys 5083 and 6082. It can be concluded that G wastoo high at the fusion line of the Alloy 1050A welds toallow for a transition from columnar to equiaxed graingrowth.[51] The constitutionally undercooled zone andthe undercooling itself were too small to activate theparticles present, even if a high number of very efficientparticles were present in the weld pool.

In a second set of experiments, the torch speed wasvaried from 2 to 6 mm/s when welding Alloys 1050Aand 6082; the weld bead size was held constant againby adjusting the weld current slightly—recall Table II.The shape of the weld pools was elliptical with onlyslight changes from low to high torch speed. Increasingtorch speed led to significantly lower heat inputs—seeTable III. The fact that the weld bead size was constantwas facilitated by the copper backing below the weldcoupon, which extracted heat and helped maintain theweld bead size. In addition, increasing torch speed led toa clear increase in cooling rate and a decrease in both Gand G/R. The corresponding weld metal mean grain sizethat was measured for a low and a high Ti weld metalcontent, depending on alloy and torch speed, is listed inthe last two rows of Table III. The peak weld pooltemperatures at the weld centerline (mid-depth) weremeasured to be between 1073 K and 1273 K (800 �C and1000 �C).

It is of interest to observe how G/R influenced thegrain size response—see Figure 6. If no grain refiner wasadded (low Ti/B content), then the mean grain size wasstepped: high torch speeds and low G/R values produceda lower mean grain size than low torch speeds and highG/R values. There appears to exist a critical G/R valuethat is needed to activate nucleating particles, some-where between 22 and 55 Ks/mm2 (Alloy 1050A) andbetween 10 and 20 Ks/mm2 (Alloy 6082). Here, the grainsize drops from a higher to a lower level—see Figure 6.This decrease was not observed in the case of grainrefiner additions (high Ti/B content) where the meangrain size remained at a constant level around 20 lm(both alloys). The critical G/R rather lies somewhereabove 60 Ks/mm2 (outside of range, Figure 6).

The key to explain this different behavior is in the typeof nucleant particles present: in the case of no grainrefiner additions, one can assume that nucleation occurson inclusions or some other unknown particles. Theseparticles, however, likely need a much higher criticalundercooling to become activated (DTN) than particles

such as TiB2 or Al3Ti that are present when grain refineris added.[20] Hence, the addition of efficient nucleantparticles results not only in a significant decrease ingrain size, but also in an increase in the critical G/R thatis needed to activate the particles present. In otherwords, if no potent particles are present, the torch speedand the corresponding G/R influence the grain sizeconsiderably. This influence is reduced if efficientsolidification nuclei are present. These observationswere confirmed by a more detailed analysis for Alloy6082, where grain size was almost constant at differenttorch speeds and constant grain refiner additions.[4]

The results of the current study were compared withgrain refinement in laser beam welds.[68] The grain sizeof the laser beam weld metal was found to be generallyhigher than that in GTA weld metal (same base metals)despite higher torch speeds (17 times), cooling rates (3times), and thermal gradients (2 times) than those inGTA welds. In addition, laser beam weld metal con-tained, at a constant grain refiner addition level, muchmore columnar grains than GTA weld metal.[68] Thisconfirms Hunt’s approach[33] that decreasing thermalgradients can enhance the formation of small, equiaxedgrains. Indeed, several authors have shown that theformation of equiaxed grains can be enhanced byincreasing torch speed and/or welding power withoutadding grain refiner.[25,51,69,70] In the current study,however, the influence on grain size by grain refiner andsolute content seems to be much higher than theinfluence of torch speed and solidification parameterssuch as cooling rate and thermal gradient.

C. Effect of Solute and Nucleant Substrateson Grain Size Response

The effect of the solute content of each alloy on thecorresponding grain size response was studied by meansof the undercooling parameter P and the growthrestriction factor Q. P and Q were calculated for eachalloy according to Eqs. [1] and [3], from the chemicalcomposition C0 (recall Table I) and from values of mL,i

Fig. 6—Weld metal mean grain size depending on G/R. GTA weld-ing and plate thickness 3 mm.



and ki which were taken from several studies[22,42,71]; seeTable IV. The P values were therefore calculated foreach alloy by summing the single P values of eachalloying element, similar to what has been done with Q.In the case of grain refiner additions, it was assumedaccording to References 36, 42 that all of the addedboron was tied up in TiB2 particles that originate fromthe master alloy since TiB2 is one of the most stableborides.[72,73] Excess Ti, which was not in the form ofTiB2, was assumed to be present as solute Ti, whichrestricts grain growth and contributes to constitutionalundercooling. For purposes of calculation, it wasassumed that Al3Ti originating from the grain refinerwas dissolved completely in the weld pool. Thisassumption was made elsewhere also for grain refine-ment in Al castings[42] and is understood to be not validfor Al weld metal, where considerable amounts of Al3Tiare known to exist (recall Section IV–A). Nevertheless,this assumption allows for the use of an upper limit ofsolutal Ti for determining P and Q.

Table IV clearly shows that titanium is by far theelement that influences most the values of P and Q. Thehigh values of mL and k for Ti come from the Al-richend of the binary (peritectic) system Al-Ti[22] and makethe titanium content of each alloy the most importantcontrol variable for P and Q. This is why solute Ti isbelieved to restrict growth[30] and thus provide consti-tutional undercooling,[39] eventually promoting grainrefinement. Figure 7 shows the calculated values of P(right columns) and Q (left columns) for the three base

metals without any grain refiner addition. Here, it isunderstood that the ki values taken from binary Alalloys and used for the calculation of P and Q, likely donot reflect exactly the values for multicomponent alloys.Owing to their higher alloying content, P and Q of bothAlloys 6082 and 5083 are clearly higher than values forcommercial pure aluminum (1050A). All P values arehigher than Q due to the equilibrium partition coeffi-cient ki that is <1 for most binary systems—seeTable IV. It is notable that in the case of the Alloys6082 and 5083, P is almost equal, whereas Q is verydifferent. Q predicts the trend in mean grain size ofunrefined weld metal (no Al Ti5B1 additions/low Ticontent), which decreased in the order: 1050A (112 lm),6082 (69 lm) and 5083 (39 lm), from Figure 1. Asdemonstrated in Section IV–B (recall Table III), thethermal conditions such as cooling rate and thermalgradient generally showed only a step-wise effect ongrain size response. Consequently, it appears that themain reason for the different grain size response to basemetal composition is the solute content of each alloy.[42]

The greater the amount of alloying elements, the higherwill be the undercooling and the greater the number ofactivated particles resulting in grain-size reduction.[20]

It is important to point out that solidification underthe current welding conditions is restricted to a veryshort time period in comparison with Al castings. Thevery high cooling rates of the welds dictate that theconstitutional undercooling needed for the activation ofnucleant substrates has to be supplied rapidly at theinitial part of the solidification of each new grain. Thisin turn emphasizes the importance of the initial rate ofdevelopment of constitutional undercooling as repre-sented by Q.[11] Hence, as per Easton and StJohn,[11] itmay be concluded for the given parameters of thecurrent study that Q is more appropriate for grain sizeprediction than P. Similar results were observed in grainrefinement analysis in castings of Al wrought alloyswhere alloys with low Q (1050A, 3003 and 6060) showeda higher tendency for grain refinement than alloys withhigh Q (2014, 5083, 7075).[42] From the current study, itappears that grain size prediction by means of Q alsoapplies to Al weld metal.When Al Ti5B1 is added to the cast inserts to raise the

Ti/B weld metal content and to reduce grain size, thecalculated P and Q values develop differently—seeFigure 8. Q (continuous lines) increases and P (dashedlines) stays almost constant as grain refiner is added.Furthermore, the constant slope of each line reveals

Table IV. Parameters from Equilibrium Binary Phase Diagrams of Aluminum with Alloying Elements After[22,42]

(Data for Titanium) and[71] (Data for Zinc)

Parameter

Binary system

Al-Si Al-Fe Al-Cu Al-Mn Al-Mg Al-Cr Al-Ni Al-Zn Al-Ti Al-V Al-Zr

Liquidus Slope mL,i in K wt pct�1 �6.6 �3.0 –3.4 –1.6 –6.2 3.5 �3.3 �1.6 33.3 10 4.5Partition Coefficient ki 0.11 0.02 0.17 0.94 0.51 2.0 0.007 0.4 7.8 4.0 2.5mL,i (ki � 1) in K wt pct�1 5.9 2.9 2.8 0.1 3.0 3.5 3.3 1.0 220 30 6.8

Fig. 7—Q and P of base metals.



again how dramatically the Ti content influences thecalculation of P and Q—recall Table IV. The largedifference between P of commercial pure aluminum(1050A) and P of the two other alloys, which have verysimilar P values independent of the Ti content, isnoteworthy. This trend is very similar to the transitionfrom columnar to equiaxed grain structure (CET) inFigure 5. There, Alloys 6082 and 5083 behave almostidentically, and Alloy 1050A is very distinct. One mayinterpret from this similarity that P can be used forthe prediction of the CET effect. Earlier study byKarantzalis and Kennedy[74] has shown that the CETmay also be described by Q. Easton and StJohn,[11]

however, argued that columnar growth can be avoided ifthe total constitutional undercooling (P after[11]) exceedsthe undercooling needed for activation of nucleatingparticles (DTN). This was the author’s explanation whyin experiments with Al castings a certain amount ofsolute is usually required for the CET to occur.[11] Thiscritical amount is reduced if efficient nucleant substrateswith low DTN are added (e.g., in the form of Al Ti5B1additions).[11] Experimental data from Al castings[39]

and the above results from weld metal grain refinementsupport the relationship between P and the CET effect.

As an additional evaluation, the relationship betweengrain size and the reciprocal value of Q (i.e., 1/Q) wasinvestigated per Eq. [7] for constant welding parameters.In this regard, it is important to emphasize that in thecurrent study, additions of the grain refiner Al Ti5B1 ledto an increase in both nucleant particles (TiB2 and Al3Ti)and solute Ti. The addition of such a master alloy iscommon practice in both casting and filler wire industry,whereby Al Ti5B1 is most frequently used.[44] Separateeffects of either particles or soluteTi on grain size have notbeen studied here, but were examined by Easton andStJohn[42] who made separate additions of TiB2 particles(in the formof anAlTi3B1master alloy) or of solute Ti (inthe form of an Al Ti2 master alloy). These authors con-firmed a linear dependency of grain size on 1/Q—recallEq. [7]. Their experimental data achieved a linear fit,following Eq. [7] and the schematic in Figure 9.[42] One

important result was the suggestion of how nucleantparticles influence this linear relationship. It was con-cluded that the slope b of each line decreases if the potencyof the nucleant particles increases (Figure 9(a)).[42,44,46]

Furthermore, it was argued that a higher number of activeparticles reduces the intercept of the line at the verticalgrain size axis a—see Figure 9(b).[42,44,46]

The relationship between d and 1/Q for the currentstudy is shown in Figure 10. As mentioned above, thedata represent additions of both nucleant particles andsolute Ti; each single data point of Figure 10 representsa particular combination of number of active particlesand amount of solute Ti. For a better understanding, thediagram can be divided into different ranges.

1. base metal composition (no Al Ti5B1 additions)The three data points that represent base metal

composition (no Al Ti5B1 additions) are shown as opensymbols in Figure 10. According to Figure 1, they lie,depending on the alloy, at higher grain sizes than theother data points of the corresponding alloy.

2. First addition of small amounts of Al Ti5B1An addition of small amounts of Al Ti5B1 grain

refiner led to a decrease in grain size that dependedstrongly on alloy composition—see the last data point onthe right end of each continuous line in Figure 10. Whilecommercial pure Al (1050A) showed a very high grain-size reduction, Alloy 5083 showed almost no decrease(Alloy 6082 in between—recall Section IV–A), althoughthe amounts of added particles and solute Ti in thisfirst addition step were similar for all the three alloys.Interestingly, the grain size that was achieved by this firstgrain refiner addition was very similar for all three alloys(about 40 lm) despite very different 1/Q values of eachalloy at these data points. This phenomenon suggeststhat the addition of solute Ti might only play a minorrole in this first grain-size reduction. Furthermore, thegrain refiner addition to 1050A weld metal was obviouslymuch more effective than an addition to the other twoalloys.

3. Further additions of Al Ti5B1If further grain refiner is added, then the decrease in

grain size is less pronounced. Interestingly, these datapoints for each alloy can quite well be fitted linearly onthe basis of Figure 9,[42] as demonstrated by the threecontinuous lines in Figure 10. All data points (except forweld metal without Al Ti5B1 additions—see opensymbols in Figure 10) were considered in each linearfit, which was calculated according to Eq. [7] (first part)by the method of least squares. Table V contains thelinear parameters a (vertical axis intercept) and b1(slope) of these continuous lines. The most accuratelinear fit could be achieved with Alloy 6082 wherenonlinearity in the data is very low; data for the Alloys1050A and 5083 reveal a higher data variation. Fur-thermore, the lowest grain size of Alloy 1050A wasachieved at a much higher 1/Q value (0.11 1/K) than forAlloy 6082 (0.04 1/K) and Alloy 5083 (0.03 1/K). A verysimilar trend for the same alloys was observed in grainrefinement experiments with aluminum castings.[46]

Fig. 8—Q and P depending on weld metal Ti content (continuouslines: Q, dashed lines: P). GTA welding, plate thickness 3 mm, torchspeed 4.17 mm/s, mean heat input 478 J/mm.



According to Figure 9(b), further Al Ti5B1 additionsincrease the number of particles, but not their potency.Hence, these grain refiner additions should result foreach alloy in several parallel lines with different verticalaxis intercepts, which though is not the case in Fig-ure 10. One may conclude carefully that after the firstaddition, further Al Ti5B1 additions do not providesignificantly more active nucleant particles. This issupported by observations in Al castings, where addi-tions of only TiB2 particles (no additional solute Ti) led

first to a large and then to a moderate decrease in grainsize.[42] A further argument is that only a very small partof added particles (0.1 pct[75] to 1.0 pct[44,64]) actuallynucleate a grain,[76] being controlled particularly by theparticle size and size distribution.[15,16,75] The freegrowth model[15] suggests that the undercooling neededto activate particles present is inversely proportional toparticle size, whereby particles with mean diameters ‡2 lm require a low undercooling £ 0.3 K. An investi-gation of the particle size distribution in commercialgrain refiners revealed that a large number of theparticles are not activated because they are too small.[16]

Size and distribution of the nucleating particles were notinvestigated in the current study but by Tronche et al.who reported for an Al Ti5B1 grain refiner that at most1 pct of the particles become active. For a constant axisintercept a and assuming that the fraction of activeparticles f is 1 pct, one can calculate using Eq. [7] thenumber density of particles q—see Table V.For comparison, dashed lines were put into Figure 10,

which connect the data points that represent no grainrefiner additions (open symbols in Figure 10) with theaxis intercepts of the continuous lines. It is of note thatfor each alloy the slope of the dashed line (b2) is muchgreater than the slope of the corresponding continuousline (b1)—see Table V. This emphasizes in accordancewith Figure 9(a) that even small grain refiner additionscan increase the number of the nucleating particlesconsiderably,[42] which is indicated by arrows in Fig-ure 10. Consequently, TiB2 and Al3Ti particles are morepotent than other particles that nucleate grains inuntreated Al alloys.

4. Very high Al Ti5B1 addition levelsAt very high grain refiner addition levels and low 1/Q

values (very left part of Figure 10), the data showcurvature and deviates from linearity to larger grainsizes. This reveals that the grain refiner effectivenessdecreases at very high Ti/B contents and low 1/Q values,respectively. This may be explained with phenomenalike recalescense or with the agglomeration of Al3Tiparticles at high grain refiner addition levels—recallSection IV–A. Thus, the number of Al3Ti particlescapable of nucleating new grains did not necessarily

Fig. 9—Effect of changes in nucleant potency (left) and nucleant density (right) on relationship between grain size and 1/Q (after[35]).

Fig. 10—weld metal mean grain size depending on 1/Q for no (opensymbols, dashed lines) and different (full symbols, continuous lines)grain refiner additions. GTA welding, plate thickness 3 mm, torchspeed 4.17 mm/s, and mean heat input 478 J/mm.

Table V. Linear Intercept a and Slopes b1 (DifferentAlTi5B1 Additions, Continuous Lines) and b2 (no AlTi5B1

Additions, Dashed Lines) from Lines in Fig. 10

Parameter1050A

(Al 99.5)6082

(Al Si1MgMn)5083

(Al Si4.5Mn0.7)

a in lm 9 3 17b1 in lm K 77 393 332b2 in lm K 343 943 550q in lm�3 0.14 3.70 0.02



increase at high grain refiner additions. Also, thenumber of small Al3Ti particles, capable of dissolvingand increasing solute Ti for enhanced undercooling, alsolikely decreased.

An additional reason for the different grain sizeresponse of each alloy besides thermal parameters(Section IV–B) and solute content (Section IV–C) maybe interactions of the elements Ti and B with alloyingelements, particularly for Alloys 6082 and 5083. Poi-soning by silicon, which can coat TiB2 nuclei makingthem inefficient, is unlikely because the Si content of thealloys was<3 wt pct;[32] recall Table I. Indeed, chemicalreactions of B or Ti with alloying elements such as Mn,V, or Cr[11] or poisoning due to chemical reactions of Tiwith Zr[62] may be a reason for the observed differencesbetween the three alloys. If there were chemical reac-tions that consumed a part of the Ti and/or B present,then commercial pure Al (1050A) with its very lowsolute content may have been affected less than theAlloys 6082 (medium alloying content) and 5083 (highalloying content). This is also apparent in Table V,where q is found to vary with alloy content.

V. CONCLUSIONS

Experiments with additions of commercial grainrefiner Al Ti5B1 to weld metal of the aluminum alloys1050A (commercial pure Al), 6082 and 5083 haverevealed the following results:

1. Significant decrease in weld metal mean grain sizein the order 1050A (�86 pct), 6082 (�69 pct), and5083 (�44 pct)

2. Highest grain-refining efficiency in the order 1050A(mean grain size 16 lm at weld metal Ti content of0.04 wt pct), 6082 (21 lm at 0.07 wt pct Ti), and5083 (22 lm at 0.15 wt pct Ti)

3. Increase in area fraction of equiaxed grains as per-centage of cross-sectional area of weld metal up to80 pct (Alloy 1050A) and 100 pct (Alloys 6082 and5083)

Greater torch speeds (from 2 up to 6 mm/s) whenwelding the Alloys 1050A and 6082 led to a largedecrease in the heat input (max. �64 pct), a largeincrease in the cooling rate (max. +113 pct), and adecrease in the thermal gradient G (max. �38 pct). Theresulting influences on grain size response were found tobe

1. Small when no Al Ti5B1 was added (base metalcomposition) in the form of a drop in grain size ata critical G/R when torch speed increases and G/Rdecreases.

2. Negligible when Al Ti5B1 was added

The influence of solute elements (particularly Ti) andnucleant particles (TiB2 and Al3Ti) on grain size wasanalyzed by means of the undercooling parameter P andthe growth restriction factor Q. A comparison betweenthe three aluminum alloys showed that, for the givenwelding/solidification parameters

1. Q may be used to predict the weld metal meangrain size.

2. P may be used to predict the transition fromcolumnar to equiaxed grain growth (CET).

3. 1/Q may be used to analyze the grain refiner effec-tiveness and the influence of nucleant particles andsolute content on grain size response.

ACKNOWLEDGMENTS

The authors are grateful to H. Hayen (formerly fromAljo Aluminium-Bau Jonuscheit GmbH, Germany)and P. Gudde from KBM Affilips B.V., Netherlandsfor the very kind donation of plates of Alloy 5083(Alijo) and grain refiner (KBM Affilips). They alsowould like to thank W. Schneider from Hydro Alumin-ium Rolled Products GmbH, Germany for the veryfruitful discussion of the results and H. Strehlau (ICP-OES chemical analysis), G. Oder (WDS analysis) andD. Kohler (casting of ingots) for their great support atBAM. The authors are very thankful to the ResearchAssociation on Welding and Allied Processes of theDVS for their support and to the Program for Fundingof Industrial Research and Technology (IGF) of theGerman Federal Ministry of Economics and Technol-ogy for funding the research project 16.242N.

NOMENCLATURE

a Parameter that represents availability ofnucleant substrates (lm)

b, b1, b2 Parameters that represent nucleant potency(lm K)

c Constant (lm)C0 Concentration (wt pct)d Grain size (lm)fS Solid fraction (–)G Thermal gradient (local) (K mm�1)k Partition coefficient (between solid and

liquid) (–)mL Slope of liquidus line (K wt pct�1)P Undercooling parameter (K)Q Growth restriction parameter (K)q Number density of particles present (lm�3)R Growth velocity of dendrite tip (mm s�1)DTC Constitutional undercooling (K)DTN Constitutional undercooling required for

nucleation of a particle (K)X Alloy factor (K�1)GRF Growth restriction factorCET Columnar to equiaxed transition

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Influence of Solute Content and Solidification Parameters on Grain Refinement of Aluminum Weld Metal

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