The effect of grain volume distribution on the mechanical properties of high purity aluminum

179 Pages·1995·6.2 MB·English

by  Gokhale, Atul B., 1953-

THEEFFECTOFGRAINVOLUMEDISTRIBUTIONONTHE
MECHANICALPROPERTIESOFHIGHPURITYALUMINUM
By
ATULB.GOKHALE
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
1995
UNIVERSITYOFFLORIDALIBRARIES
Copyright1995
By
AtulB.Gokhale
Dedicatedtomywife,Jayoo
whosepatiencefinallyranout
and
Tomyparents,BalkrishnaandLeelaGokhale
ACKNOWLEDGEMENTS
IwouldfirstandforemostliketoexpressmydeepgratitudetolateProf.Frederick
N.Rhinesunderwhoseguidancethisworkwascompleted. Itwashishypothesiswhich
formedthebasisforthiswork,andhisgreatspirit,integrityandsupportwhichkeptme
going. Iwouldalsoliketoextendmysincerethankstomycommittee.Profs.RobertT.
DeHoff,RezaAbbaschian,RobertE.Reed-Hill,RichardG.Connell,Jr.andRobertL.
Scheaffer. Specialthanksarealsoduetomynumerouscolleagueswhogavemeconstant
supportandencouragementduringthecourseofthiswork.
1
TABLEOFCONTENTS
page
ACKNOWLEDGEMENTS
ABSTRACT
CHAPTERS
1. INTRODUCTION
2. THEGRAINSIZEDISTRIBUTION 4
2.3
2.1Introduction 4
2.2ExperimentalMethods 9
2.4
2.2.1Material 9
2.2.2ThermomechanicalTreatments 1
DeterminationoftheGrainVolumeDistribution 14
22..53.1EmbrittlementCharacteristics 14
2.3.2EmbrittlementandSeparationProcedure 16
2.3.3SeparationEfficiencyandMetalLoss 22
Results 25
2.4.1TestsofLognormality 31
2.4.2DataAnalysis 32
2.4.3EffectofStrainPriortoRecrystallization 34
2.4.4TransformationoftheVariable 41
GenesisoftheLognormalDistribution 42
2.5.1EvolutionDuringRecrystallization 43
2.5.2CellAreaCalculations 45
v
1
2.5.3
ConstancyoftheGrainVolumeDistributionWidth 46
3. MECHANICALBEHAVIOROFALUMINUMPOLYCRYSTALS 49
3.1Introduction 49
3.1.1AnalyticalApproach
3.1.2DislocationApproach 58
3.1.2. Dislocationpileupapproach 58
3.1.2.2Non-pileupapproach 63
3.1.3SizeDistributionApproach 67
3.1.4SummaryofAluminumTensileProperties 74
3.2ExperimentalProcedure 79
3.3ResultsandDiscussion 88
3.3.1Background 89
33..33..21.1Truestressandtruestrain 89
3.3.1.2Theyieldstrength 90
3.3.1.3Stressatuniformstrainlimit 91
3.3.1.4Truefracturestrain
Results 92
3.3.2.1Theyieldbehavior 92
3.3.2.2Postyieldflowbehavior 104
3.3.2.3Stressatinstability,maximumuniformstrain
andfracturestrain 131
4. DISCUSSION
4.1ProgressionofPlasticDeformationinPolycrystals 139
44..32.1Microyield
4.2.1ElasticIncompatibility 141
4.2.2OnsetofMicroyielding 142
4.3Macroyielding
ConnectiontotheGrainVolumeDistribution 147
4.4StrainHardening 153
4.5NeckFormation ; 156
vi
5. CONCLUSIONSANDFUTUREWORK 158
5.1Conclusions
5.2FutureWork 159
REFERENCES
161
BIOGRAPHICALSKETCH
,
vii
AbstractofDissertationPresentedtotheGraduateSchool
oftheUniversityofFloridainPartialFulfillmentofthe
RequirementsfortheDegreeofDoctorofPhilosophy
THEEFFECTOFGRAINVOLUMEDISTRIBUTIONONTHE
MECHANICALPROPERTIESOFHIGHPURITYALUMINUM
By
AtulB.Gokhale
December,1995
Chairman: R.T.DeHoff
MajorDepartment: MaterialsScienceandEngineering
Theplasticresponseofhighpurityaluminumpolycrystalswasfoundtodepend
stronglyonthedispersioningrainvolumes,quantifiedbydeterminingtheirdistribution
viaagrainseparationtechnique. Thedistributionssodeterminedwereconsistentlywell
approximated as lognormal, whose parameters could be systematically altered by
controllingthethermomechanicalhistoryofthesamples. Inparticular,theevolutionof
thewidthofthelognormaldistributionfunction,lnog,wasfoundtodependstronglyon
the absolute as well as the relative severities of deformation steps of the
deformation/recrystallization sequence. For all deformation histories, however, lnag
decreasedmonotonicallyin apowerlawmannerwithincreasing severity ofthe final
deformation step. In addition, it was found that the lnog attained in the final
recrystallizationstepremainedconstantduringsubsequentgraingrowth.
Usingastrategywhichcombinedthermomechanicaltreatments andisothermal
annealing,aseriesofsampleswereproducedwithdesiredlnoglevelsbutnominallythe
vm
sameaveragegrainboundaryareaperunitvolume(Sv). SampleswithtwolevelsofSv(8
and4.45mm2/mm3)andlncg’srangingfrom 1.01 to2.78wereused. Themechanical
behaviorofthesepolycrystals, tested at77 Kin uniaxialtension, indicated that lncg
exertedasignificantcontrolovertheplasticresponse. Inparticular,theyieldstrength,
workhardening rate anduniformelongationdecreasedmonotonically with increasing
lnog,theyieldstrengthandworkhardeningratebeingstronglylinearlydependenton
(lnag)'_2. Based on these observations, a view ofpolycrystalline deformation which
considersstraingradientsonthescaleofgrainsizeanddominationoftheplasticresponse
bythelargestgrainsinthemicrostructureispresented. Finally, microstructurebased
calculationsaredevelopedwhichshowthattheyieldstrengthcanbepredictedbyusinga
grainvolumedistributiondependentHall-Petchmechanism.
IX
CHAPTER
1
INTRODUCTION
Thisisafundamentalmetallurgicalinvestigationonthemechanicalbehaviorof
singlephasepolyciystals,basedonanhypothesisfirstputforthbyProf.F.N.Rhinesin
thelate1970’s. Hesuggestedthatthedispersionintheindividualgrainsizes(volumes)
inherenttoallpolycrystalsmayhaveaneffectontheirplasticresponse.
Ithaslongbeenrecognizedthatavariationingrainsizesisacommonfeatureof
all polycrystalline materials. However, the quantification of this property is not
straightforward. Onemay,forexample,readilyobserveavariationinthesizesofgrains
via classical metallographic techniques. This type of single microsection, two-
dimensional examination (which maybe assumedtooccurin more than 99% ofthe
cases) can not however be used to estimate the true grain size (and therefore the
dispersion in grain sizes) because: (1) a random section through an hypothetical
polycrystalcomprisedofgrainsofequalsizewouldneverthelessexhibitavariationinthe
grain areas, (2) on a random section through a real polycrystal, the probability of
sectioningagrainisgreater,thebiggeritis,leadingtoanoverestimationoflargergrains
and(3)thecurvatureofthegrainfaces.1
1Thesefactorsarediscussedingreaterdetailinsubsequentchapters.
1