Role of Plastic Deformation on Elevated Temperature Tribological Behavior of an Al-Mg Alloy...

Role of Plastic Deformation on Elevated TemperatureTribological Behavior of an Al-Mg Alloy (AA5083): A FrictionMapping Approach

S. DAS, A.T. MORALES, A.R. RIAHI, X. MENG-BURANY, and A.T. ALPAS

Friction maps have been developed to explain the behavior of aluminum alloys under dynamictribological conditions generated by the simultaneous effects of temperature and strain rate. Aspecially designed tribometer was used to measure the coefficient of friction (COF) of AA5083strips subjected to sliding with a simultaneous application of tensile strain in the temperaturerange of 693 K to 818 K (420 �C to 545 �C) and strain rates between 5 9 10�3 s�1 and4 9 10�2 s�1. The mechanisms of plastic deformation, namely, diffusional flow, grain boundarysliding (GBS), and solute drag (SD), and their operation ranges were identified. Relationshipsbetween the bulk deformation mechanism and COF were represented in a unified map bysuperimposing the regions of dominant deformation mechanisms on the COF map. The changein COF (from 1.0 at 693 K (420 �C) and 1 9 10�2 s�1 to 2.1 at 818 K (545 �C) and4 9 10�2 s�1) was found to be largest in the temperature–strain rate region, where GBS was thedominant deformation mechanism, as a result of increased surface roughness. The role of bulkdeformation mechanisms on the evolution of the surface oxide layer damage was also examined.

DOI: 10.1007/s11661-011-0649-4� The Minerals, Metals & Materials Society and ASM International 2011

I. INTRODUCTION

WHEN aluminum blanks come into contact withforming tools, a tribological system is created thatdetermines the tool life and the surface quality of thefinal product. Superplastic forming (SPF) is a techniquethat takes advantage of superplasticity of fine-grainedalloys such asAA5083[1–4] and uses gas pressure to force aheated aluminum blank to stretch into conformance witha die surface. An important improvement over SPF is thequick plastic forming (QPF) process that deformsAA5083 aluminum-magnesium (Al-Mg) alloy in thestrain rate and temperature regimes of 1 9 10�4

to 5 9 10�3 s�1 and T = 723 K to 818 K (450 �C to545 �C), respectively.[5] A number of vital improvementsin the heating/cooling and automated handling systemsenable much faster forming cycles than were convention-ally achieved by the SPF process.[5] QPF or, more spe-cifically, the hot air blow forming process can be used toproduce automotive body in white components withcomplex shapes such as present in liftgates and fenders.[6]

The future advancement in aluminum hot and warmforming operations is intimately related to the controland improvement of the tribological conditions between

the aluminum blanks and the forming tool. The tribo-logical problems that occur during these processes tendto be numerous and include metallic particle transfer tothe tool, which leads to adhesion and surface damage toboth the die and the workpiece.[7]

The use of solid lubricants reduces adhesion ofaluminum to the die surface.[8] The most commonlyused lubricants in the SPF and QPF processes are boronnitride (BN) and graphite.[9] While graphite providesexcellent lubricity at low cost, it decreases the efficiencyof the subsequent sheet welding process, and so must beremoved from the surface after forming. The use ofcoatings, including PVD and plasma-assisted CVDcoatings based on TiAlN,[10,11] thermal spray coatingsbased on Cr compounds, and electroless nickel-basedcoatings have also been considered[12] to reduce the die-sticking problem. Although improvements in achievinglow friction at temperatures above 673 K (400 �C) havebeen observed in laboratory tests, these coatings usuallyfall short of eliminating the industrial problems.Fundamental research aimed at understanding the

factors that control friction and aluminum adhesion isessential to developing an effective lubricant or coatingfor improving the viability of the hot forming processthat is sustainable in automotive volumes. The approachtaken in this study is to systematically examine themicrostructural basis of the tribological behavior ofaluminum at elevated temperatures, and to understandhow bulk deformation mechanisms influence the surfaceconditions and the coefficient of friction (COF). A briefreview of high-temperature deformation mechanismsthat occur in Al-Mg alloys is given in Section I–A,followed by a review of the surface oxide microstructurethat forms at these elevated temperatures.

S. DAS, PhD Student, A.R. RIAHI, Assistant Professor, X.MENG-BURANY, Research Associate, and A.T. ALPAS, Professorand NSERC/General Motors of Canada Industrial Research Chair,are with the Department of Mechanical, Automotive and MaterialsEngineering, University of Windsor, Windsor, ON N9B 3P4, Canada.Contact e-mail: [email protected] A.T. MORALES, Staff ResearchScientist, is with the Chemical Science & Materials System Lab,General Motors Global Research and Development, Warren, MI48090.

Manuscript submitted August 7, 2010.Article published online March 29, 2011

2384—VOLUME 42A, AUGUST 2011 METALLURGICAL AND MATERIALS TRANSACTIONS A

A. High-Temperature Deformation Mechanisms in Al-Mg Alloys

Details of an Al-Mg alloy’s elevated temperaturedeformation mechanisms depend on the alloy’s solutecontent and grain size, but the general trends governingtemperature, strain, and strain rate dependence of thesealloys’ deformation behavior are well known. At tem-peratures near the melting point (T> 0.8Tm) of thealloy, and very low stresses (r/E = 4 9 10�5), creepnormally occurs as a result of vacancy diffusion, aphenomenon that causes strain accumulation by grainelongation. This mechanism is known as Nabarro–Herring creep[13] and is characterized by lattice diffusionthat occurs at the grain interiors, while Coble creep, forwhich the grain boundaries are the preferential diffusionpaths, is normally observed at T<0.8Tm. A dependenceon the third power of the grain size is characteristic ofCobble creep. In both cases, the steady-state strain(creep) rate increases linearly with the applied stress,producing a stress exponent, n = 1. Another creepmechanism that operates at high temperatures, but atvery low stresses (with a resulting stress exponent ofn = 1), is the Harper–Dorn linear viscous creep,[14]

which accounts for deformation rates much higher thanthose achieved by diffusional flow. One possible mech-anism proposed for Harper–Dorn creep is climb-con-trolled deformation, in which the dislocation density isnot changed with stress.[15,16] Harper–Dorn creep isindependent of grain size[17] and is unlikely to occur infine-grained materials such as AA5083.[16,18] Dislocationcreep controls plastic deformation at midrange homol-ogous temperatures (T> 0.5Tm) and moderate stresses(r/E> 5 9 10�5), at which point a diffusion-controlledclimb mechanism becomes responsible for strain accu-mulation. Dislocation creep results in a power-lawrelationship, where the creep rate shows sensitivity tothe applied stress with a typical exponent of n ~ 5.[19]

The Appendix presents generic constitutive equationsthat describe the deformation (creep) rates as a functionof applied stress and temperature.

The superplasticity of aluminum alloys, particularlywith small grain sizes and low solute contents, has beenassociated with grain boundary sliding (GBS).[4,20–22]

Large total strains exceeding 300 pct occur at a givencombination of temperature and strain rate within therange of T = 723 K to 818 K (450 �C to 545 �C) andde/dt = 10�4 to 5 9 10�3 s�1.[1–4] GBS is generallycharacterized by an activation energy that is equal tothe activation energy for either GB diffusion or latticeself-diffusion and a stress exponent of n = 2 (Appen-dix). Proposed models of GBS include boundary slidingaccommodated by diffusional flow, akin to Coble creep(Ashby–Verrall model[23]), and GBS that occurs in amantlelike region at the grain boundaries.[24] GBS isfavored in alloys with equiaxed grains <10 lm and thepresence of second-phase particles that inhibit graingrowth.

A solid solution may influence diffusional flow bychanging the rate of diffusion.[13] Additionally, the solidsolution can impose a drag on dislocations to slow therate of creep. Their redistribution can also lead to creep

transients. Taleff et al.,[25] using the concept of the solutedrag (SD) creep mechanism, discussed the mechanismsof superplasticity in coarse-grained Al-Mg alloys inwhich a large lattice misfit strain is introduced whenmagnesium is in the aluminum lattice, causing a largelocal lattice strain. In Al-Mg alloys with a magnesiumconcentration above 2 wt pct, the operation of the SDcreep that shows no grain size dependence becomes acritical factor in extending the range of temperaturesand strain rates in places where commercial 5000 seriesalloys exhibit a superplastic response. In fact, recentstudies[26,27] have shown that temperatures of about723 K (450 �C) and fast rates (de/dt ‡ 10�3 s�1) duringblow forming often involve deformation by SD creep.Finite element analyses of blow forming (at 723 K(450 �C) and strain rates between 10�5 and 10�2 s�1)suggest that SD creep and GBS can occur simulta-neously.[28,29] Zener–Hollomon type analyses of exper-imental data gathered from coarse-grained Al-Mg alloysexhibiting SD creep have revealed that the stressexponent, n, has a value between 3 and 4.[25–27]

The commercial success of AA5083 is, thus, attributedto this alloy’s ability to exhibit multiple creep mecha-nisms under hot forming conditions. For the purpose ofunderstanding its tribological behavior, however, inves-tigations must still be made into the role that creepmechanisms play in developing the alloy surface mor-phology. Section I–B focuses on the oxide layers thatform on the alloy surface.

B. Microstructure of Oxide Layers Formed on AluminumAlloy Surfaces

The surface of aluminum alloy sheets subjected to hotrolling contains layers of oxides of nonuniform thick-ness that vary between 1.5 and 8.0 lm. These layers arecharacterized by rolled-in oxide patches and a distribu-tion of ultrafine aluminum grains mixed with thecomminuted fragments of fractured second-phase par-ticles.[30,31] Studies aimed at understanding the high-temperature oxidation behavior of Al-Mg alloysrevealed that these alloys tend to develop a thin,amorphous layer of Al2O3 during the early stages ofoxidation.[32] Once heated above 673 K (400 �C), theamorphous layer might transform into crystallinec-Al2O3, with the outward diffusion of magnesiumatoms into the surface promoting the formation ofMgAl2O4.

[33] These surface layers are generally observedto consist of a mixture of MgAl2O4, MgO, and Al2O3

(amorphous or crystalline), with the concentration ofMgO being the highest at the surface, and the size of theoxide particles in the subsurface layer ranging from 3.0to 30.0 nm.[33–35]

The oxide scales that form on metallic surfaces act ashard, protective layers that prove advantageous in somehigh-temperature applications. In many practical appli-cations, however, these oxides are stressed either by anexternally applied load, or by oxide growth stresses,which cause cracks to form that result in their failure.The thermal stresses induced by a mismatch of thermalexpansion coefficients of the oxide layer and substrate[36]

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 42A, AUGUST 2011—2385

are another cause of oxide failure. When the substrate issubjected to creep deformation, the surface oxide crackdensity initially increases with strain[37] and eventuallyreaches a saturation point. This behavior has beenillustrated in a model for viscous sliding of oxidesegments against a substrate subjected to creep.[37]

Evans[38] demonstrated that under tensile loading,sliding could occur at the oxide-metal interface, whichresults in oxide delamination and subsequent spallation.Le et al.[39] showed that the spacing between adjacentcracks increases with oxide film thickness during alumi-num rolling, exposing nascent aluminum. The reactionbetween the fresh metal surfaces and the atmosphereduring the subsequent hot deformation process dependson the thickness of the initial oxide layer. In addition,the fresh metal may be extruded to the surface throughthese cracks, because the bulk metal has a lower flowstress and a higher ductility than the oxide scale at hotworking temperatures.[39]

The formation of fibrous structures running in thetensile direction has been observed on the fracturesurfaces of Al-Mg alloys tested at temperatures between523 K and 823 K (250 �C and 550 �C).[40–43] Topo-graphic studies on Al-Cu-Mg alloys (AA2090)[40] indi-cated that bundles of fibers formed on oxidized surfacesand at grain boundaries that experienced sliding. Thefibers were 0.5 to 1.0 lm in diameter and extended up to15 lm. The appearance of these fibers suggests verylarge strains, e.g., superplasticity in the local regions.Zelin[40] and Chang et al.[44] reported that the formationof these fibers was associated with dynamic oxidegrowth that resulted from the interaction betweenfreshly exposed material and oxygen. Proposed mecha-nisms for fiber superplasticity include viscous flowinduced by the presence of liquid phase along the grainboundaries,[42,43,45] dislocation movement facilitated bythe oxygen atoms,[42,46] and submicron size of grainsthat promoted local superplastic deformation,[43,47]

prompting a phenomenon called ‘‘superplasticity inmicrovolume.’’ Although the mechanisms of their for-mation are still open to discussion, the high ductilityfibers that form on the surfaces of the AA5083 alloy areof particular interest in characterizing the tribologicalproperties of this alloy at elevated temperatures.

The preceding review of the literature highlights thecomplexities involved in understanding the high-tem-perature tribological behavior of superplastic Al-Mgalloys. The purpose of the current work is to evaluatethe tribological behavior of AA5083 under dynamicconditions generated by the simultaneous effects oftemperature and strain rate. In view of many factors

that must be considered in describing the high-temper-ature tribological behavior of Al-Mg alloys, thisresearch has taken a comprehensive experimentalapproach that consisted of designing and constructinga special high-temperature tribometer for the purpose ofmeasuring the COF of AA5083 alloy. The deformationmechanisms operating at different temperatures andstrain rates were determined. Friction maps that plottedCOF values over the ranges of dominant deformationmechanisms were constructed, establishing relationshipsbetween the tribological and mechanical properties. Inaddition, changes in surface topography and oxideproperties were determined.

II. EXPERIMENTAL WORK

A. Microstructure and Properties of the Alloy Tested

Strips 5.0-mm wide and 1.5-m long were sectionedfrom 1.2-mm-thick cold-rolled AA5083 alloy sheetobtained in the H18 condition (75 pct cold reductionof fully annealed starting material). The AA5083 alloycomposition is shown in Table I(a). The microstructureof the as-received alloy is shown in a scanning electronmicroscope (SEM) cross-sectional micrograph inFigure 1(a). The elongated grains of the alloy were1.3 ± 0.4 lm long in the rolling direction and0.3 ± 0.1 lm wide. The section of the strip shown inFigure 1(a) provides evidence of the presence of Al6Mnprecipitates.AA5083 strips were tested using a high-temperature

tribometer capable of applying tensile strains at knownstrain rates and temperatures (Section II–B). A typicalcross-sectional microstructure of the AA5083 strip thatwas tested at a temperature of 693 K (420 �C) and astrain rate of 4 9 10�2 s�1 using this tribometer (with-out placing the strip into sliding contact) is shown inFigure 1(b) and illustrates the equiaxed grain structureof the material at this temperature. The average grainsize in the near surface section was approximately3.6 ± 2.1 lm. Figure 1(c) shows the microstructure of astrip tested at 818 K (545 �C) and a strain rate of4 9 10�2 s�1, where equiaxed grains with a diameter of4.8 ± 2.5 lm near the free surface of the sheet can beseen. Once the equiaxed grain size was attained, thegrain morphology and size did not change significantlywith strain rate and temperature (Figures 1(b) and (c)).The volume fraction of Al6Mn particles remained thesame (1.6 to 2.0 pct) regardless of testing condition. TheAl6Mn particles, 0.35 ± 0.15 lm long and 0.13 ±0.03 lm wide, retained their shape and did not fracture

Table I. Composition of the Sliding Materials Used in the Experimental Work

(a) AA5083 alloyElements Mg Mn Si Fe Cr Cu AlWt pct 4.5 0.7 0.1 0.25 0.09 0.02 balance(b) P20 steel pinElements C Cr Mn Ni Si Mo S FeWt pct 0.35 1.90 0.83 0.40 0.70 0.49 £0.01 balance


during elevated temperature tests. Evidence of GBS thatproduced a step on the surface of the sample tested at818 K (545 �C) was also observed in Figure 1(c). Thedeformation mechanisms responsible for generatingthese microstructures are described in detail later inSection III–D.

The surface of the as-received alloy was covered withan oxide layer whose thickness varied between a fewhundred nanometers and 1 lm, as shown in Figure 2(a),which reveals that the surface oxide consisted ofnanocrystalline grains 10 to 100 nm in size. TEManalyses using a Gatan image filter (GIF) performedat equal depth intervals through the oxide layer wereused to obtain the elemental concentration distributionof the layer’s constituents. The magnesium profile inFigure 2(b) indicates that the magnesium concentrationnear the sheet surface was approximately 3 times highercompared with that of the bulk. According to theselected area diffraction patterns (SADPs) taken frommaterial adjacent to the surface MgAl2O4, MgO andAl2O3 were identified as the main constituents of the

oxide layers adjacent to the surfaces of the as-receivedsample (Figure 2(c)).One surface of the AA5083 strip (along the rolling

direction) was put in sliding contact with the cylindricalsurface of a 12-mm-diameter pin made of P20 tool steel(hardness of 302 BHN with composition given inTable I(b)). The pin contact configuration was selectedin such a way that a uniform line contact was main-tained while the strip was subjected to tensile deforma-tion. The width of the wear track created on the 5083strip surface varied between 60 and 100 lm dependingon the test temperature and strain rate used, providing asufficiently large area for the study of microstructuralfeatures that influenced the friction. The P20 steel pinsurface was polished with 3-lm diamond paste andcleaned ultrasonically in acetone. The strip was cleanedwith a clean fabric soaked in acetone prior to each test.No lubricant was used to ensure that a dry slidingcondition to measure the COF was maintained duringthe tests.

B. Description of the Hot Forming Simulator

There is no single, widely accepted experimentalprocedure to measure friction during conventional sheetmetal forming processes.[48–52] This is even more appar-ent in elevated temperature forming processes whereindustry experience is limited. Many of the existing testsdo not capture the deformation state, where the materialis stretched and subjected to sliding at the same time.Thus, a test that allows for the accurate measurement offriction during high-temperature plastic deformation isneeded.The critical capabilities of the equipment needed to

simulate forming processes such as QPF include theability to test at temperatures between 673 K and 773 K(400 �C and 500 �C) and strain rates between 10�3 and10�1 s�1. Equally important is the ability to continuallystretch the aluminum sheet while it is sliding against thedie surface—a state that produces a dynamic interface inwhich the surface morphology is constantly modified asa result of the operating plastic deformation mecha-nisms. In addition, as discussed previously, surfaceoxides are continually broken and reformed, or in caseswhere they remain ductile, they may show a largedeformation, or even superplasticity. All these complexbulk and surface events have an effect on the COF.To address these issues, a new high-temperature

tribometer with pin-on-strip configuration to simulatethe sliding contact during forming operations has beenbuilt (Figure 3(a)). This tribometer was used to measurethe COF during contact between the pin surfacerepresenting the tool material and a metallic stripstretching at different strain rates and temperatures.The tribometer consists of three main assembly parts(Figure 3(b)), which are described as follows.

(1) A loading system that consists of two linear actua-tors, each connected to one end of the strip to betested: The actuators are synchronized in such away that they apply tensile stress along the longitu-dinal axis of the strip at the required deformation

Fig. 1—Cross-sectional FIB/SEM micrographs of (a) elongated alu-minum grains in a cold-rolled AA5083 strip, (b) equiaxed grains inthe strips stretched at 693 K (420 �C) and 4 9 10�2 s�1, and (c) at818 K (545 �C) and 4 9 10�2 s�1.


(strain) rate, while the strip moves in a forwarddirection at a predetermined speed. This isachieved by the use of a synchronized slave actua-tor that can be assigned to pull the strip at a high-er speed than the master actuator. In this way,while the strip moves forward and each point onthe top surface of the strip comes in contact withthe pin, the material in contact is subjected to plas-tic deformation. Different constant strain rates canbe applied to the strip by adjusting the differencein linear velocities of the actuators. Tensile loadduring each experiment was measured using a1000 N maximum capacity load cell (OmegaLCMCD-100, purchased from Omega, Bergar

Laval, Quebec, Canada) with a sensitivity of±0.1 N attached between the strip holder and theactuator. Figure 3(a) shows the location of theload cell to measure the tensile load on the strip.

(2) A friction measurement assembly to measure theCOF of the strip being stretched against a loadedsteel pin in contact with the strip (Figure 3(c)): Animportant aspect of the friction measurement sys-tem is its ability to heat the strip in contact withthe pin to a constant temperature. The strip washeated while passing through a heated stainlesssteel roller using a 500 W cartridge heater insertedinside the roller. The hot roller, which had anouter diameter of 20 mm, was in contact with the

Fig. 2—(a) Cross-sectional TEM micrograph showing the oxide layer on the surface of a cold-rolled AA5083 strip; (b) GIF elemental map show-ing that the magnesium concentration near the surface was approximately 3 times higher than that in the bulk; and (c) SADP of the oxide layerthat identifies MgAl2O4, MgO, and Al2O3. The SADP was taken from an area of 250 nm in diameter.


Fig.3—

(a)Photographofthehigh-tem

perature

tribometer

designed

tosimulate

theslidingcontact

duringform

ingoperations.

(b)Isometricview

oftheexperim

entalsetup

thatshowstheAA5083stripunder

slidingcontact

against

theP20steelpin

beingstretched

bythelinearactuators.(c)Photographofthetribometer

andheaterassem

bly.

(d)AA5083stripinscribed

withgridsthatshowselongationalongthedirectionoftheapplied

strain

whilebeingpulled.(e)Majorandminorstrain

ofthestrip,measured

from

twoconsecutivegrids(shownin

plate

(d))

within

thehotzone.


bottom face of the strip in motion while the P20steel pin was in contact with the top surface. Threethermocouples were inserted in the holes circumfer-entially inside the roller 120 deg from each otherand situated 0.5 mm below the outer surface of thecylinder’s middle length to evenly control the tem-perature. The strip temperature during experimentswas determined from the average temperaturereading simultaneously obtained from these threethermocouples. The temperature of the upper sur-face of the strip was 3 K to 5 K (3 �C to 5 �C)lower than the average thermocouple reading. Theheating time of the AA5083 strip before reaching aconstant temperature and entering the hot zonewas approximately 15 seconds. Each section of thestrip remained in the hot zone at the set tempera-ture for 3 to 5 seconds. The COF between the P20steel pin in contact with the top face of the stripwas measured using the force measurement system,which consisted of a load cell with a sensitivity of±0.05 N. The hot roller was placed on a bearingsystem that allowed it to rotate freely, while a BNlubricant (purchased from VWR International AG,Dietikon, Switzerland) was applied to its surface tominimize friction. It was calculated that a constantstrain of 0.06 was applied to the strip surface dur-ing bending. No lubricant was used on the toppart of the strip so that a dry contact was main-tained between the P20 steel pin and the metallicstrip during the COF measurements. In this work,the COF between the stretching strip and the P20steel pin was measured at a normal load of 0.27 N.

(3) A camera system that records the in-situ deforma-tion of the grids inscribed on the sample surface:This was used to determine the strain withinthe hot zone and elsewhere. Details of strain mea-surements using the grid system are given inSection II–C.

C. Measurement of COF

As indicated in Section II–B, the two synchronizedactuators were programmed to pull the strip at aconstant differential speed of DV. The linear velocityof Actuator 1 was fixed at V = 1.0 mm/s in the currentexperiments. As the sample moved over the roller heatedto the test temperature, a constant temperature wasmaintained over a certain length, which was termed thehot zone (Figure 3(d)), where the COF and strain ratemeasurements were made. The temperature of the rest ofthe strip was lower than in the hot zone. No furtherdeformation occurred once the strip passed the hot zone.The average COF values were measured at a giventemperature and strain rate after 20 seconds from thestart of the experiments once a stable deformationcondition was reached.

The camera system installed over the top face of thestrip was used to measure in-situ major and minorstrains in the hot zone by measuring changes in theinitial diameter (2.5 mm) of circular grids inscribed onthe strip’s surface (Figure 3(d)). The calculated major

and minor strains from two consecutive grids at thelocation of the strip’s hot deformation zone are shownin Figure 3(e). The instantaneous (true) strain rate forthe strip shown in Figure 3(d) tested at 818 K (545 �C)was de/dt = (e1 – e2)/Dt = 4 9 10�2 s�1 (where Dt =2.5 s).AA5083 strips were placed in dry contact with the P20

steel pin and tested under constant strain rates appliedin the range of 5 9 10�3 s�1 and 4 9 10�2 s�1 atdifferent temperatures ranging from 693 K to 818 K(420 �C to 545 �C). Typical COF vs sliding time plotswere obtained at two different strain rates of 1 9 10�2

and 4 9 10�2 s�1 at 818 K (545 �C) and are shown inFigure 4. The COF measured at a strain rate of1 9 10�2 s�1 (at a constant strain of 0.4) resulted inan average value of 1.0 ± 0.21. At the same tempera-ture, the AA50803 strip subjected to the same totalstrain but deformed at a higher rate of 4 9 10�2 s�1

revealed a higher COF of 2.09 ± 0.34. A comparisonbetween the COF curves subjected to strains of 0.1and 0.4, but at the same strain rate of 4 9 10�2 s�1

(Figure 4), indicates that there is negligible effect on theCOF due to the amount of strain applied to the strip at afixed strain rate. The role of the applied strain rate onthe bulk and surface deformation and damage isdescribed later.

D. Measurement of Mechanical Properties

Not all experiments were performed while the P20steel pin was in contact with the strip. A series of‘‘noncontact’’ tests were conducted using the same high-temperature tribometer to measure the flow stress of thestrip at each temperature at the strain rates used in theCOF tests. This information, together with the mea-sured strain rates, was used to determine the creep ratesand the stress exponents. The deformation mechanismsoperating in the AA5083 alloy at different temperaturesand strain rates were determined with electron micro-scopy and by analyzing the experimental creep data.

Fig. 4—COF vs sliding time plot at 818 K (545 �C) that shows themeasured COF during experiments at two different strains and strainrates.


Similarly, damage mechanisms on the surfaces undernoncontact conditions and imposed strain rates andtemperatures were observed using analytical micro-scopy. Strip surfaces subjected to deformation at differ-ent temperatures and strain rates were observed using aWYKO NT 1100 optical surface profilometer (pur-chased from Bruker AXS, Tucson, AZ) for morpholog-ical analyses.

E. Surface and Subsurface Characterization

A JEOL* 840 SEM and a ZEISS NVision 40

CrossBeam workstation (focused ion beam (FIB), pur-chased from Carl Zeiss NTS, LLC, Peabody, MA) wereused for microstructural studies of the surfaces andcross-sectional layers. Cross-sectional trenches were ionmilled on the deformed surface using the CrossBeamworkstation to investigate deformation-induced damagein the vicinity of the surface. Care was taken to avoidion-beam damage to the surface by depositing a layer ofcarbon. A trench was milled, using a Ga ion beam at anaccelerating voltage of 30 kV with beam currentsranging from 13 nA to 700 pA. Final polishing wasdone at a low ion-beam current of 80 pA to reduce anydamage to the microstructure due to the high energybeam. Details of the FIB milling processes used onaluminum alloys can be found in elsewhere.[53]

TEM cross-sectional microstructures were preparedusing a FIB lift-out method and the microstructureswere observed by a JEOL JEM-2100F field emissionelectron microscope operating at 200 kV. SADPs werealso taken to identify oxide structures. A GIF was usedto perform the elemental mapping of the oxides.Additionally, electron probe microanalysis (EPMA)was also used to obtain elemental composition anddistribution mapping of the surface. EPMA measure-ments were made using a Camica model SX-100 electronprobe (purchased from CAMECA Instruments, Inc.,Madison, WI). X-ray images and quantitative analyseswere done at 15 kV and 20 nA beam conditions.

III. EXPERIMENTAL RESULTS

A. Variation of COF with Temperature and AppliedStrain Rate

The COF of the AA5083 alloy measured at roomtemperature against the P20 steel pin with no appliedtensile strain was 0.29 ± 0.11. Figure 5(a) shows COFvariations at two temperatures characteristic of the hotforming process (693 K and 818 K (420 �C and545 �C)). The average COF values are plotted againstthe instantaneous strain rate in the strip inside the hotzone. The reported values are averages of two tests ateach temperature and strain rate. Error bars indicate the

Fig. 5—(a) Average COF vs strain rate plot. (b) Average COF vstemperature plot. (c) Average COF values plotted on temperature vsstrain rate axes. Error bars indicate the range of fluctuations inmean COF values measured over 100 s time test period on each strip(following the initial 20 s heating period).

*JEOL is a trademark of Japan Electron Optics Ltd., Tokyo.


range of fluctuation in mean COF values measuredover the 100-second time period (following the initial20-second heating period). The COF value increasedwith strain rate at each of the two temperatures and wasmore prominent at 818 K (545 �C). The mean COFvalues were dramatically higher than the value at roomtemperature, the lowest being 0.95 at T = 693 K(420 �C) and de/dt = 5 9 10�3 s�1. The COF increasedto 1.16 at a higher strain rate of 4 9 10�2 s�1. Temper-ature had a significant effect on COF; it increased to avalue of 2.09 at a higher temperature of 818 K (545 �C)at a strain rate of 4 9 10�2 s�1, which was 80 pct higherthan that at 693 K (420 �C).

The friction data can also be represented by plottingthe average COF values as a function of the testtemperature, but at constant strain rates (Figure 5(b)).The average COF values plotted at two differentconstant strain rates of 5 9 10�3 and 4 9 10�2 s�1 inFigure 5(b) for each test temperature indicate that theCOF values were higher when the strips were subjectedto higher strain rates.

The combined effects of strain rate and temperatureon COF are plotted on temperature–strain rate axes inFigure 5(c). This map enables easier visualization of theeffect of hot deformation conditions on the COF.

B. Observation of Surface Morphologies DevelopedDuring High-Temperature Deformation

The characteristics of the surface morphologies pro-duced as a result of high-temperature deformation wereexamined. Typical secondary electron images of thesurfaces of as-received AA5083 strips, and those thatformed at various temperatures and strain rates, arepresented in Figures 6(a) through (c). Distinctly differ-ent surface morphologies were observed when compar-ing the surfaces of the as-received condition (298 K(25 �C) with no strain applied) with those at 693 K and818 K (420 �C and 545 �C) (both subjected to the samestrain rate of 4 9 10�2 s�1). The as-received surface wascovered with a compacted oxide layer (Figure 6(a)),whose morphology is typical of rolled aluminum sur-faces.[39] The damage due to rolling manifested itself ascontinuous lines extending parallel to the rolling direc-tion and the formation of surface cracks normal to therolling direction. These cracks were almost equallyspaced and usually 20- to 100-lm long and 1- to 5-lmwide. Bands of such oxide cracks formed in someportions of the strip, whereas other portions were free ofcracks altogether.

During the COF measurements, the P20 pin comes incontact with a surface that has undergone tensiledeformation. Two examples of surfaces from deformedstrips that have not yet contacted the P20 pin areshown in Figures 6(b) and (c). The surface morphologyof samples deformed at T = 693 K (420 �C) and atde/dt = 4 9 10�2 s�1 exhibited substantially more dam-age (Figure 6(b)) and roughening compared to theas-received samples. The oxide layer showed moreextensive cracking, resulting in increases in both crackwidth and crack density. The surface grains weresubjected to an out-of-plane sliding of 0.9 lm in average

height as a result of plastic deformation. (Statisticalanalysis was done to determine the surface step heightsformed as a result of out-of-plane sliding, as described inSection IV–A.) The extent of out-of-plane sliding is farmore evident on the surface of the strip deformed at

Fig. 6—Surface morphology of the strip in the (a) initial cold-rolledcondition, (b) deformed at T = 693 K (420 �C) and de/dt =4 9 10�2 s�1, and (c) deformed at T = 818 K (545 �C) and de/dt = 4 9 10�2 s�1. (The surfaces in (b) and (c) were formed duringdeformation without contact against the P20 steel pin.).


T = 818 K (545 �C), where the elevated and sunken-ingrains are clearly visible below the oxide layer (Fig-ure 6(c)). Another characteristic of surface damage atthis temperature is the absence of surface oxide cracks,indicating the ductile nature of the oxide. The oxidelayers that were stretched along the GB steps, in turn,formed fibrous structures marked as oxide ligaments inFigure 6(c). This appearance is akin to microfibers thatwere observed on the fracture surfaces of alumi-num,[42,43] suggesting local superplasticity.

The wear track on the AA5083 surface after slidingagainst the P20 steel counterface at high temperaturesand strain rate showed the formation of debris withcylindrical (roll) morphology. An example of this debrisformed at T = 773 K (500 �C) and de/dt = 4910�2 s�1 is shown in Figure 7(a). Elemental electronmicroprobe maps taken from the worn surface(Figures 7(b) through (e)) showed that the roll-shapedwear debris consisted of magnesium and oxygen but notaluminum, implying that the roll-shaped wear debriswere formed as a result of detachment of the oxide layer.The roll-shaped debris may have formed by folding ofthe detached oxide layer during sliding, and the abilityof the oxide debris to roll over itself suggests that theoxide layers were ductile while in contact with the P20steel pin.

C. Quantification of Surface Roughness

The surface morphology of the as-received samplesand those tested at high temperatures were studied witha digital optical interferometer. The distribution of thesurface heights and the frequency of surface heightdistributions were plotted in the form of histograms(Figures 8(a) through (d)). Measurements were madeon areas of 120 lm 9 90 lm, which were sufficientlylarge to contain typical surface features on about 70 to100 grains depending on the testing condition. Thehistograms show the relative frequency of the heightdistribution, which obey the Gaussian probability dis-tribution. Figure 8(a) shows the surface height distribu-tion obtained from the surface subjected to T = 693 K(420 �C) at four strain rates of 5 9 10�3 s�1,1 9 10�2 s�1, 2 9 10�2 s�1, and 4 9 10�2 s�1. Thearithmetic mean deviation of the surface height, Ra

(average roughness), is seen to increase with strain rate,as does the standard deviation of the height distribution.At higher temperatures (Figures 8(b) through (d)), theGaussian behavior is preserved, but the distributionpeaks become wider with increasing temperature. TheRa values also increased with temperature.

Five different locations on two sets of samples wereconsidered for measuring Ra, and the values are given inTable III. The lowest Ra of 0.29 lm was found fordeformation at 693 K (420 �C) at a strain rate of5 9 10�3 s�1. The Ra increased to 0.52 lm at a highertemperature and strain rate of 818 K (545 �C) and4 9 10�2 s�1, respectively. Thus, the temperature andstrain rate conditions resulting in high Ra values alsocorresponded to high COF values. The surface rough-ness, in turn, depended on the mechanisms of oxide

damage (Figures 6(b) and (c)) and plastic deformationfor the AA5083 alloy.

D. Deformation Mechanisms at Elevated Temperature

The change in tensile load with time applied to theAA5083 strip at a given temperature was determined fordifferent constant strain rates. Typical data are given inFigures 9(a) and (b) for tests conducted at 723 K and818 K (450 �C and 545 �C), respectively. The flow stressof the AA5083 was calculated using the cross-sectionalarea of the sample when it passed through the hot zone(Figure 3(d)) within a time interval, dt, shown in thesefigures and given in Table II. The flow stress values areplotted in temperature and strain rate space inFigure 9(c). The relationship between the imposed strainrate and temperature-compensated flow stress of thestrip was determined using the general phenomenolog-ical creep equation (Eq. [A1] in the Appendix) from thedata plotted in Figure 10. The slope of the data shownin Figure 10 is equal to the stress exponent, n. A value ofn of approximately 2 was calculated for a temperaturerange of 693 K to 818 K (420 �C to 545 �C) and strainrate range of 2 9 10�2 s�1 to 4 9 10�2 s�1. Asdescribed earlier, a stress exponent of n = 2 is indicativeof creep by GBS, which is a well-characterized creepmechanism operating in AA5083 with a small grainsize.[1–4,20–22,26,27] This was, thus, the operative mecha-nism in this case.Microscopic evidence for GBS is given in Fig-

ures 11(a) and (b), which shows an FIB cross sectiontaken from an AA5083 strip tested at 818 K (545 �C).The sliding displacement that took place between grain1 and grain 2, as marked in Figure 11(a), resulted in theformation of the surface offset. A high-magnificationmicrograph of the same set of grains, in Figure 11(b),shows the formation of a step on the oxide layer as aresult of sliding of the surface grains relative to eachother. The grain interiors appear to have a lowdislocation density, and the grains retained their originalshape during GBS, consistent with the observation ofequiaxed grains after creep deformation.At low temperatures and high strain rates, the

stress exponent gradually increased to higher values(Figure 10). The n value observed at temperaturesbetween 693 K and 723 K (420 �C and 450 �C) and atstrain rates greater than 3 9 10�2 s�1 was approxi-mately 3.5, suggesting that the mechanism of SD creepoccurs under these conditions.[26,27] SD creep is associ-ated not only with higher n values (between 3 and 4)compared with GBS, but also with inverse creeptransients,[26] specifically an abrupt drop in flow stressfollowing a sudden strain rate change, which could beattributed to dislocations detaching from obstacles onslip planes. In general terms, any dislocation glideobstructed by precipitates and Mg atoms in AA5083during creep (at relatively low temperatures and highstrain rates) promotes climb into the subgrain bound-aries that are formed within the grains, which, in turn,accommodate the imposed strain. Figure 11(c) showsthe surface grains on a AA5083 strip tested at 693 K(420 �C) and 4 9 10�2 s�1. The formation of a sub-


structure (cells of 200 nm in diameter) can be observedin the high-magnification micrograph shown inFigure 11(d). While this alone is not proof of SD creep,this, together with the measured stress exponent of 3 andhigher flow stress values of 56 to 69 MPa compared with25 to 43 MPa for GBS, as shown in Figure 9, is evidenceof SD creep operating under these conditions. Subgrains

were not formed during GBS, and grain interiors werevirtually free of dislocations (Figure 11(a)).An effective way of summarizing the observed creep

mechanisms for AA5083 is best achieved by construct-ing a stress exponent map in temperature and strain ratespace to delineate the operating plastic deformationmechanisms during SD and GBS (Figure 12). At low

Fig. 7—(a) Secondary electron SEM image of the wear track at T = 773 K (500 �C) that shows the roll-shaped debris. Electron microprobemaps showing the elemental composition of the roll-shaped debris taken from the (b) backscattered SEM image, (c) aluminum map, (d) magne-sium map, and (e) oxygen map. Color denotes relative concentration: white ” highest, red ” high, blue ” low, and black< detection limit.


strain rates, 1.5 9 10�2 s�1, diffusional flow (viscouscreep) with a stress exponent of n = 1 becomes dom-inant.

IV. DISCUSSION

A. Relationships Between COF and DeformationMechanisms

The delineation of deformation mechanisms thatoperate at elevated temperatures and their effect onsurface conditions constitute an important step towardrationalizing the friction behavior of AA5083. Byanalyzing the COF values simultaneously with theprincipal deformation mechanisms, a COF–deformationmechanism map was developed, as shown in Figure 13.This map incorporates iso-COF contours plottedtogether with the dominant deformation mechanismregimes. The map facilitates visualizing the effects ofdifferent mechanisms of deformation on the COFvalues. Accordingly, within a narrow temperature andstrain rate region, where plastic deformation occurs bySD creep, COF is comparatively low, i.e., varies between1.2 and 1.4. Deformation by SD does not induce theroughening of the strip surface (Figures 11(c) and (d)) atthe same extent as the GBS, which is evident from the

comparison of Ra values (Table III). Furthermore, theflow stress (hardness) of the alloy is the highest in theSD-controlled region (Figure 9(c)). Thus, the relativelylow COF can be attributed to two factors: high hardnessand low average roughness of the strip. At low strainrates, where diffusional flow occurs, the COF increasesfrom 1.0 (693 K (420 �C)) to 1.6 (818 K (545 �C)),which corresponds to a 60 pct increase in COF at atemperature of 120 K (120 �C). Diffusional flow is notexpected to induce surface roughening, and the Ra

values vary only between 0.29 and 0.35 lm (Table III).The increase in COF that occurs with temperature couldbe attributed to the softening of the alloy as its flowstress decreases from 16.9 at 693 K (420 �C) to 5.5 MPaat 818 K (545 �C) (Figure 9(c)).The GBS deformation operates in a wide temperature

and strain rate region in Figure 13 and embraces COFvalues that are as low as 1.2 (713 K [440 �C], and2.0 9 10�2 to 2.5 9 10�3 s�1) to over 2.0 (818 K[545 �C] and 4.0 9 10�2 s�1). GBS has proven respon-sible for the high surface roughness values due to theformation of GB offsets on the surfaces. The exposedsurfaces were covered with an oxide layer of nonuniformthickness. In order to determine GBS’s contribution tothe formation of surface offsets, these oxide layers onthe surfaces of AA5083 strips were removed by mechan-ically polishing the surfaces to an initial roughness of

Fig. 8—Surface height distribution profiles for surfaces deformed at four temperatures: (a) T = 693 K (420 �C), (b) T = 723 K (450 �C), (c)T = 773 K (500 �C), and (d) T = 818 K (545 �C). Measurements at each surface were taken from areas of 120 lm 9 90 lm, which were suffi-ciently large to contain typical surface features, and encompassed 70 to 100 grains.


Ra = 0.04 lm, and the polished strips were subjected tothe plastic deformation under temperatures and strainrates of interest. Although a (thinner) oxide layer againformed on the surfaces, the surface grain topographycould be distinctly observed using optical interfer-ometery (Figures 14(a) through (c)). As shown inFigure 14(d), an increase in the strain rate increasedthe average GB step height on the free surface.A thorough quantification of the GB step height is

provided by conducting a statistical analysis comprisedof 100 to 150 grains at each temperature and strain rate.As shown in the histograms in Figures 15(a) and (b),GBS-induced plastic flow at T = 693 K (420 �C) andde/dt = 4 9 10�2 s�1 (Figure 15(a)) resulted in a meanGB step height of 0.90 lm on the surface, whereas atT = 818 K (545 �C) and de/dt = 4 9 10�2 s�1, theaverage step height increased to 1.45 lm (Figure 15(b)).

B. Role of Surface Damage Mechanisms on COF

In the Section IV–A, the temperature and strain ratedependence of COF were discussed in terms of thegoverning mechanisms of deformation and their role in

Table II. Flow Stress at 723 K (450 �C) and at 818 K

(545 �C)

Strain Rate, s�1

Flow Stress, MPa

723 K (450 �C) 818 K (545 �C)

4 9 10�2 55.6 26.33 9 10�2 — 24.72 9 10�2 42.8 16.51.5 9 10�2 35.7 —1 9 10�2 — 10.75 9 10�3 13.3 5.8

Fig. 9—Tensile loads applied to AA5083 strips at different strainrates at (a) 723 K (450 �C) and (b) 818 K (545 �C). (The time axisindicates the duration of the test, during which a different section ofthe forward moving strip—170 mm in length—passes through thehot zone, as shown in Fig. 3(d). The flow stress of the strip wasmeasured at the section that enters the hot zone at t = 140 s. Truestrain rate was determined from the strain differences within a timeinterval of dt.) (c) Flow stress calculated from experimental data in(a) and (b) and plotted on temperature vs strain rate axes.

Fig. 10—Strain rate vs modulus-compensated flow stress plots fol-lowing the general creep equation where n is the stress exponent.


modifying the surface roughness of the alloy. Thissection discusses the role of the surface oxide layers onCOF. The elemental composition of the near surfacematerial and the oxide layer changed with temperature.As stated in Section I–B, oxides formed on Al-Mgsurfaces at temperatures above 673 K (400 �C) normallyconsisted of a mixture of MgAl2O4, MgO, and Al2O3,with the concentration of MgO being the highest at thetop surface.[33,34] It was shown that an increase in theMgO concentration and the thickness of the MgO-richlayers decreased the COF.[54] The oxide layers on thesurface had a thickness of less than 1 lm and consisted

of nanocrystalline grains that were 10 to 100 nm in size.Topographic studies by SEM have indicated the devel-opment of oxide fiber structures or ligaments, whichformed as a result of the stretching of the oxide layerslying above grain boundaries that experienced signifi-cant sliding (Figure 6(c)). Individual ligaments had adiameter of approximately 200 nm, and they extendedalong the grain boundaries as far as 2 lm at 818 K(545 �C) and 4 9 10�2 s�1. Under these conditions,

Fig. 12—Deformation mechanism map for AA5083 plotted on tem-perature vs strain rate axes, where the regions of dominance for eachmechanism are identified based on the stress exponent value n. Thecontours are for constant stress exponent values.

Fig. 13—COF-deformation mechanism map plotted on temperaturevs strain rate axes, where the COF values from Fig. 5(c) are super-imposed on the deformation mechanism map from Fig. 12. The con-tours represent iso-COF values.

Fig. 11—(a) Cross-sectional TEM micrographs showing the subsur-face microstructure of AA5083 alloys deformed at 818 K (545 �C) at4 9 10�2 s�1. (b) High-magnification image taken from plate (a)showing that grain 1 is at a higher elevation than grain 2, whichindicates the occurrence of relative sliding between them. (c) Cross-sectional TEM micrographs showing the subsurface microstructureof AA5083 alloys deformed at 693 K (420 �C) and 4 9 10�2 s�1. (d)High-magnification image taken from plate (c) that shows the for-mation of a substructure.


almost 40 pct of the deformed surface was covered byoxide ligament bundles. Ligaments formed in this waydid not show evidence of rupture; hence, the very largeelongations were indicative of the oxide’s local super-plastic behavior.

The ligament formation was intimately linked to theextent of GBS, suggesting that as the test temperatureand the strain rate imposed on the strip decreased, thesurface covered by ligament bundles decreased too. Atlow temperature and strain rate, the applied strain wasaccommodated by cracks formed in the surface oxide,rather than the local superplasticity of the oxide layers.The two types of oxide damage mechanisms are sche-matically illustrated in Figures 16(a) and (b).

An interpretation of COF data at elevated tempera-tures requires additional quantitative characterization ofthe material transferred to the P20 steel pin counterface.Further investigations of the aluminum-steel interface

are expected to shed light on the adhesion mechanisms,at which point questions of whether the superplasticligaments would transfer to the counterface contributingto adhesion and the role of exposed portions of AA5083grains under fractured oxide layers on adhesion could beanswered. This approach will help to establish relation-ships between the adhesion and friction mechanisms.

V. CONCLUSIONS

1. Friction experiments conducted on the AA5083strips showed that the COF increased from 0.95 at693 K (420 �C) and 5 9 10�3 s�1, to 2.09 at 818 K(545 �C) and 4 9 10�2 s�1.

2. The measured COF values were plotted on temper-ature and strain rate axes to create diagrams thatrepresent the dynamic nature of friction. Three

Table III. Surface Roughness at Different Temperatures and Strain Rates

Strain Rate, s�1

Roughness, lm

693 K (420 �C) 723 K (450 �C) 773 K (500 �C) 818 K (545 �C)

5 9 10�3 0.29 0.28 0.24 0.351 9 10�2 0.39 0.35 0.27 0.372 9 10�2 0.37 0.43 0.40 0.494 9 10�2 0.37 0.44 0.49 0.52

Fig. 14—3-D optical surface interferometry profiles of the polished surfaces of strips deformed at 818 K (545 �C) and (a) 5 9 10�3 s�1, (b)2 9 10�2 s�1, and (c) 4 9 10�2 s�1. (d) 2-D profiles that show GB step heights on the strip surface.


types of operating bulk deformation mechanisms(diffusional flow, GBS, and SD creep) were identi-fied within the temperature and strain rate rangesstudied. The COF maps described the correlationsbetween the dominant creep mechanisms and theCOF values.

3. The largest variation in COF occurred in the regionwhere GBS was the dominant bulk deformationmechanism. GBS increased with increasing tempera-ture and strain rate and led to a higher surfaceroughness, and thus higher COF, due to steps thatformed at the grain boundaries on the surface.

4. Diffusional flow did not induce surface roughening,and the Ra values varied within a small range. Theincrease in COF that occurred with temperature in thisregime was attributed to the softening of the alloy.

5. Low average roughness and retention of strength(hardness) during deformation led to low COF val-ues in the SD regime.

6. The surface oxide damage mechanisms were sensi-tive to the operating bulk deformation mechanisms.

The creation of GBS-induced steps led to the for-mation of microsuperplastic fibrous structures (liga-ments) at high temperatures. At low temperatures,the surface oxide layer damage involved oxidecracks that formed along the grain boundaries nor-mal to the tensile direction.

ACKNOWLEDGMENTS

The authors acknowledge Messrs. M.P. Balogh’s(GM) and R.A. Waldo’s (GM) assistance with thecharacterization work and Mr. A. Jenner’s (Universityof Windsor) contributions to the construction of thehigh-temperature tribometer. This work is supportedby General Motors of Canada and the Natural Sci-

Fig. 15—Histograms showing the distribution of GB step height onthe surface of samples deformed at (a) 693 K (420 �C) and4 9 10�2 s�1 and (b) 818 K (545 �C) and 4 9 10�2 s�1.

Fig. 16—Schematic representation of two types of surface damagefeatures at two temperatures: (a) cracks appeared on the oxide layerat 693 K (420 �C) and (b) superplastic oxide ligaments, triggered bysurface offset due to GBS, observed at 818 K (545 �C).


ences and Engineering Council of Canada through anIndustrial Research Chair Grant (ATA).

APPENDIX

General creep equation:

_e ¼ ArE

� �nexp � Q

RT

� �½A1�

where A is the material constant, r is the flow stress, n isthe stress exponent, E is the temperature-compensatedYoung’s modulus, Q is the activation energy fordeformation, and R is the universal gas constant.

Diffusional flow creep:

_e ¼ k1DL

d2

� �Eb3

kT

� �rE

� �lattice diffusionð Þ ½A2�

_e ¼ k2Dgb

d2

� �Eb3

kT

� �rE

� �grain boundary diffusionð Þ

½A3�

SD creep:

_e ¼ k3Ds

b2

� �rE

� �3½A4�

GBS:

_e ¼ k4DL

d2

� �rE

� �2lattice diffusion controlledð Þ ½A5�

_e ¼ k5Dgbb

d3

� �rE

� �2boundary diffusion controlledð Þ

½A6�

For Eqs. [A2] through [A6], DL is the lattice diffusioncoefficient, Dgb is the GB diffusion coefficient and Ds isthe solute atom diffusion coefficient, b is the Burgersvector, d is the grain size, E is the temperaturecompensated Young’s modulus, k is the Boltzmann’sconstant, and k1 through k5 are material constants.

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