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8/8/2019 Physical Metallurgy of Steel
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Steels
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Thispageintentionallyleftblank
Steels
MicrostructureandPro
perties
Thirdedition
H.K.D.H.Bhadeshia
ProfessorofPhysicalMetallu
rgy
UniversityofCambridge
and
A
djunctProfessorofComputationalMetallurgy
Gra
duatelnstituteofFerrousTechnolo
gy,POSTECH
and
SirRobertHoneycom
be
EmeritusGoldsmithsProfessorofMetallurgy
UniversityofCambridge
AMSTERDAMBOSTONHEIDELBERGLONDONNEWY
ORKOXFORD
PARISSANDIEGOSANFRANCISCOSINGAPORE
SYDNEYTOKYO
Butterworth-HeinemannisanimprintofElsevier
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vi
CONTENTS
4.3
Theeffectofalloyingelementsonthekineticsofthe
/transformation
77
4.4
Structuralchangesresultingfromalloyingadditions
84
4.5
Transformationdiagram
sforalloysteels
91
Furtherreading
92
5
Formationofmartensite
95
5.1
Introduction
95
5.2
Generalcharacteristics
95
5.3
Thecrystalstructureofmartensite
100
5.4
Thecrystallographyofm
artensitictransformations
103
5.5
Themorphologyofferrousmartensites
106
5.6
Kineticsoftransformationtomartensite
112
5.7
Thestrengthofmartensite
120
5.8
Shapememoryeffect
126
Furtherreading
127
6
Thebainitereaction
129
6.1
Introduction
129
6.2
Upperbainite(temperaturerange550400C)
129
6.3
Lowerbainite(temperaturerange400250C)
132
6.4
Theshapechange
135
6.5
Carboninbainite
135
6.6
Kinetics
139
6.7
Thetransitionfromuppertolowerbainite
143
6.8
Granularbainite
144
6.9
Temperingofbainite
145
6.10
Roleofalloyingelemen
ts
146
6.11
Useofbainiticsteels
147
6.12
Nanostructuredbainite
152
Furtherreading
154
7
Acicularferrite
155
7.1
Introduction
155
7.2
Microstructure
155
7.3
Mechanismoftransform
ation
157
7.4
Theinclusionsashetero
geneousnucleationsites
161
7.5
Nucleationofacicularferrite
162
7.6
Summary
164
Furtherreading
164
8
Theheattreatmentofsteels:h
ardenability
167
8.1
Introduction
167
8.2
UseofTTTandcontinu
ouscoolingdiagrams
168
CONTENTS
vii
8.3
H
ardenabilitytesting
170
8.4
E
ffectofgrainsizeandchemicalcomposition
onhardenability
176
8.5
H
ardenabilityandheattreatment
177
8.6
Q
uenchingstressesandquenchcracking
179
Further
reading
181
9
Thetemperingofmartensite
183
9.1
In
troduction
183
9.2
Temperingofplaincarbonsteels
184
9.3
M
echanicalpropertiesoftemperedplain
carbonsteels
190
9.4
Temperingofalloysteels
191
9.5
M
aragingsteels
207
Further
reading
207
10
Thermom
echanicaltreatmentofsteels
209
10.1
In
troduction
209
10.2
C
ontrolledrollingoflow-a
lloysteels
210
10.3
D
ual-p
hasesteels
220
10.4
TRIP-assistedsteels
223
10.5
TWIPsteels
229
10.6
In
dustrialsteelssubjectedtothermomechanicaltreatments
231
Furtherr
eading
233
11
Theembrittlementandfractureofsteels
235
11.1
In
troduction
235
11.2
C
leavagefractureinironandsteel
235
11.3
Factorsinfluencingtheonsetofcleavage
fracture
237
11.4
C
riterionfortheductile/brittletransition
240
11.5
Practicalaspectsofbrittlefracture
243
11.6
D
uctileorfibrousfracture
245
11.7
In
tergranularembrittlement
252
Furtherr
eading
258
12
Stainless
steel
259
12.1
In
troduction
259
12.2
Theironc
hromiumn
ickelsystem
259
12.3
C
hromiumcarbideinCrNiausteniticsteels
264
12.4
Precipitationofniobiumandtitaniumcarbides
267
12.5
N
itridesinausteniticsteels
270
12.6
In
termetallicprecipitationinaustenite
270
12.7
A
usteniticsteelsinpracticalapplications
273
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viii
CONTENTS
12.8
Duplexandferriticstainlesssteels
274
12.9
Mechanicallyalloyed
stainlesssteels
278
12.1
0
Thetransformationofmetastableaustenite
281
Furtherreading
286
13
Weldmicrostructures
287
13.1
Introduction
287
13.2
Thefusionzone
287
13.3
TheHAZ
298
Furtherreading
306
14
Modellingofmicrostructureandproperties
307
14.1
Introduction
307
14.2
Example1:alloydesign
high-s
trengthbainiticsteel
309
14.3
Example2:mechanicalpropertiesofmixedmicrostructures
315
14.4
Methods
321
14.5
Kinetics
326
14.6
Finiteelementmethod
329
14.7
Neuralnetworks
330
14.8
Definingcharacteristicsofmodels
333
Furtherreading
334
Index
335
PREFACETOTHEFIRST
EDITION
Inthisbook,
Ihaveattemptedtooutlinetheprincipleswhichdeterminethe
microstructuresofsteelsandthroughthesethemechanicalproperties.
Ata
timewhenourmetallographictechniquesarereachingalmosttoatomicresolu-
tion,i
tisessentialtoemphasizestructureonthefinestscale,especiallybecause
mechanicalpropertiesaresensitivetochangesatthislevel.Whilethisisnota
bookonthese
lectionofsteelsfordifferentuses,Ihave
triedtoincludesufficient
informationtodescribehowbroadcategoriesofstee
lsfulfilpracticalrequire-
ments
.However,themainthrustofthebookistoexamineanalyticallyhow
the
/phase
transformationisutilized
,andtoexplainthemanyeffectsthat
non-metallicandmetallicalloyingelementshave,bo
thonthistransformation
andonotherphenomena.
Thisbookiswrittenwiththeneedsofmetallurgist
s,materialsscientistsand
engineersinm
ind
,andshouldbeusefulnotonlyinthelateryearsofthefirst
degreeanddiplomacoursesbutalsoinpostgraduatecourses.
Anelementary
knowledgeof
materialsscience,
metallography,crystallographyandphysicsis
assumed.
Iamindebtedtoseveralcolleaguesfortheirinteres
tinthisbook
,particularly
DrD
.V
.Edm
onds,whokindlyreadthemanuscript
,DrP.R
.Howell,DrB
.
MuddleandD
rH
.K.D.H.B
hadeshia
,whomadehelpfulcommentsonvarious
sections,andn
umerousothernumbersofmyresearch
groupwhohaveprovided
illustrations.I
wishalsotothankmycolleaguesindifferentcountriesfortheir
kindpermissi
ontousediagramsfromtheirwork.I
amalsoverygratefulto
MrS.D
.Charterforhiscarefulpreparationofthel
inediagrams.Finally
,my
warmestthan
ksgotoMrsDianaWalkerandMissR
osemaryLeachfortheir
carefulanddedicatedtypingofthemanuscript.
RWKH
Cambridge
1980
ix
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PREFACETOTHESECONDEDITION
Thisneweditionretainsthebasicframeworkoftheoriginalbook;howeve
r,the
opportunityhasbeentakentointro
duceseveraladditionalchaptersdealing
with
areaswhichhaveemergedorincr
easedinsignificancesincethebookwasfirst
publishedin1981
.Thereisnowaseparatechapteronacicularferritewhic
hhas
becomeadesirablestructureinsomesteels
.Thecontrolofmicrostructuresdur-
ingweldingisundoubtedlyacrucialtopicwhichnowrequiresachapter,while
themodellingofmicrostructurestoachieveoptimumpropertieshasemerged
asanimportantapproachjustifyin
gtheinclusionofafurthernewchapter
.The
opportunityhasalsobeentaken
toincludeacompletelyrevisedchapteron
bainitetransformations.
Theoverallaimofthebookremainstointroducestudentstotheprinciples
determiningthemicrostructuresofsteels
,andthroughthese,themecha
nical
propertiesandbehaviourinservice.Steelsremainthemostimportantg
roup
ofmetallicalloys,p
ossessingaverywiderangeofmicrostructuresandmechan-
icalproperties,
whichwillensure
theircontinuedextensiveusefarintothe
foreseeablefuture.
RW
KH
HKDHB
Camb
ridge
1995
x
PREFACETOTHETHIRD
EDITION
Steelhasthe
abilitytoadapttochangingrequireme
nts
.Thiscomesfromthe
myriadsofwaysinwhichitsstructurecanbeinfluencedbyprocessingand
alloying.This
iswhyitisthestandardagainstwhichemergingmaterialsare
compared.Ad
dedtothisisthecommercialsuccess,withoutputatrecordlevels
andaproductionefficiencywhichisuncanny.Itisple
asingtoseehow,a
llover
theworld
,iro
nanditsalloyscontributetoimprovingthequalityoflifeofso
manyhumanbeings.T
hetechnologyissogoodthatmostofthesepeoplerightly
takeitforgra
nted
.
Thisneweditioncapturesdevelopmentssince1995,e.g.,t
heextremelyfine-
grainedalloys
,steelswiththeabilitytoabnormallyelongateandtheproperties
ofminuteparticlesofiron.Q
uestionsareposedastothetheoreticallimittothe
finestcrystals
thatcanbemanufacturedonalargescale.Inaddition,t
hereare
majorrevisionsintheexplanationsofmicrostructur
e,strengthening,kinetics
andmodelling.
Theorigina
laimofthisbook
,tointroducestudentsandtechnologiststothe
principlesdeterminingthemicrostructureandpropertiesofironanditsalloys,
hasremained
theguidingprincipleinthenewedition
.
HKDHB
RWKH
Cambridge
2006
xi
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Supportingmaterialaccompanyingthisbook
Afullsetofaccompanyingexerc
isesandworkedsolutionsforthisbook
are
availableforteachingpurposes.
Pleasevisithttp://www.t
extbook
s.elsevier.c
omandfollowtheregistration
instructionstoaccessthismaterial,
whichisintendedforusebylecturers
andtutors.
Thecompilationofquestionshasbeendesignedtostimulatethestuden
tto
explorethesubjectwithintheco
ntextofthebook
.
Eachquestionisaccompaniedb
yacompleteanswer,w
iththeexceptionof
theproposedsetoftopicsforessays.Mostofthequestionsandanswersh
ave
beendevelopedasaconsequenc
eofmanyyearsofteachingandhaveb
een
testedonavarietyofundergraduates.
1
IRONANDITSINTERS
TITIAL
SOLIDSOLUTIONS
1.1INTROD
UCTION
Steelisfreque
ntlythegold-s
tandardagainstwhichemergingstructuralmater-
ialsarecompared.W
hatisoftennotrealizedisthatthisisamovingstandard
,
withnotoriou
slyregularandexcitingdiscoveriesbeingmadeinthecontextof
ironanditsalloys.T
hisiswhysteelremainsthemostsuccessfulandcost-e
ffective
ofallmateria
ls,
withmorethanabilliontonnesbeingconsumedannuallyin
improvingthe
qualityoflife
.Thisbookattemptstoex
plainwhysteelscontinue
totakethispr
e-eminentposition,a
ndexaminesindet
ailthephenomenawhose
exploitatione
nablesthedesiredpropertiestobeachieved
.
Onereaso
nfortheoverwhelmingdominanceofsteelsistheendlessvariety
ofmicrostruct
uresandpropertiesthatcanbegeneratedbysolid-s
tatetransform-
ationandpro
cessing.Therefore,
instudyingsteels,itisusefultoconsiderthe
behaviourofpureironfirst,thentheironcarbonalloys,
andfinallythemany
complexitiesthatarisewhenfurthersolutesareadded
.
Pureironisnotaneasymaterialtoproduce.I
thasneverthelessbeenmade
withatotalimpuritycontentlessthan60partsper
million(ppm),ofwhich
10ppmisacc
ountedforbynon-metallicimpurities
suchascarbon,
oxygen,
sulphurandp
hosphorus,withtheremainderreprese
ntingmetallicimpurities.
Ironofthispuritycanbeextremelyweakwhenreas
onablysizedsamplesare
tested:theresolvedshearstressofasinglecrystalatroomtemperaturecanbeas
lowas10MN
m
2,w
hiletheyieldstressofapolycrystallinesampleatthesame
temperaturec
anbewellbelow50MNm
2.H
owever,theshearstrengthofsmall
singlecrystals
hasbeenobservedtoexceed19
,000MN
m
2whenthesizeofthe
sampleisreducedtoabout2m.T
hisisbecausethe
chancesoffindingcrystal
defectssucha
sdislocationsbecomesmallasthesize
ofthecrystalisreduced
.
Thetheoreticalshearstrengthofaperfectcrystalofiro
nisestimatedtobeabout
21,0
00MNm
2,e
quivalenttoatensilestrengthofabout11
,000MNm
2.
1
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8
CHAPTER1
IRONAND
ITSINTERSTITIALSOLIDSOLUTIONS
Fig.1.5Schematicillustrationofthemechanismsoftransformation.Theparentcrystalcon-
tainstwokindsofatoms.Thefiguresontherightrepresentpartiallytransformedsample
swith
theparentandproductunitcellsoutline
dinbold.
shearcomponentsoftheshapedeformation,l
eavingonlytheeffectsofvo
lume
change.
Inalloys,
thediffusionprocessmayalsoleadtotheredistributionof
solutesbetweenthephasesinamannerconsistentwithareductionintheoverall
freeenergy.
Allthephasetransformationsinsteelscanbediscussedintheco
ntext
ofthesetwomechanisms(Fig
.1.6
).Thedetailsarepresentedinsubseq
uent
chapters.
1.4CARBONANDNITROGEN
INSOLUTIONIN-AND-IRON
1.4.1Solubilityofcarbonandnitrogenin-and-iron
Theadditionofcarbontoironis
sufficienttoformasteel.However,steelis
agenerictermwhichcoversaverylargerangeofcomplexcompositions
.The
1.4CARBONANDNITROGENINSOLUTIONIN
-AND-IRON
9
Fig.1.6Summaryofthevarietyofphasesgeneratedbythe
decompositionofaustenite.
Thetermparaequilibriumreferstothecasewherecarbonpa
rtitionsbutthesubstitutional
atomsdonotdiffuse.Thesubstitutionalsolutetoironatomratioisthereforeunchangedby
transformation.
presenceofevenasmallconcentrationofcarbon,e.
g.0.10.2weightpercent
(wt%);approximately0
.51.0
atomicpercent(at%),
hasagreatstrengthening
effectonferriticiron,
afactknowntosmithsover2500yearsagosinceiron
heatedinac
harcoalfirecanreadilyabsorbcarbon
bysolid-s
tatediffusion.
However,
the
detailedprocessesbywhichtheabsorptionofcarbonintoiron
convertsarelativelysoftmetalintoaverystrongan
doftentoughalloyhave
onlyrecentlybeenfullyexplored
.
Theatomicsizesofcarbonandnitrogen(Table1.2)aresufficientlysmall
relativetotha
tofirontoallowtheseelementstoenterthe-and-ironlattices
asinterstitialsoluteatoms.Incontrast,themetallicalloyingelementssuchas
manganese,n
ickelandchromiumhavemuchlarger
atoms,i.e.nearerinsize
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22
CHAPTER2THESTREN
GTHENINGOFIRONANDITSALLOYS
Fig.2.4(a)Schematicdiagramofyieldp
henomenaasshowninatensiletest,(b)Luders
bands
indeformedsteelspecimens(Hall,YieldPointPhenomenainMetalsandAlloys,Macmillan,London,
1970),(c)Ludersbandsinanotchedsteelspecimen.
2.3SOLIDSOLUTIONSTRENGTHENINGBYINTERSTITIALS
23
onreloadinganewyieldpointisobserved(D).Thisr
eturnoftheyieldpointis
referredtoas
strainageing.
2.3.2Theroleofinterstitialelementsinyieldphe
nomena
Thesharpupp
erandloweryieldpointinironiseliminatedbyannealinginwet
hydrogen,w
hichreducesthecarbonandnitrogentoverylowlevels
.However,
substantialstrainageingcanoccuratcarbonlevelsa
round0.002wt%
,andas
littleas0.001
0.002wt%Ncanresultinseverestrain
ageing.Nitrogenismore
effectiveinth
isrespectthancarbon,
becauseitsresidualsolubilitynearroom
temperaturei
ssubstantiallygreaterthanthatofcarbon(Table1.3)
.
CottrellandBilbyfirstshowedthatinterstitialatomssuchascarbonand
nitrogenwouldinteractstronglywiththestrainfields
ofdislocations.Theinter-
stitialatomsh
avestrainfieldsaroundthem,b
utwhen
suchatomsmovewithin
thedislocationstrainfields,thereshouldbeanover
allreductioninthetotal
strainenergy.Thisleadstotheformationofinterstitialconcentrationsoratmos-
pheresinthe
vicinityofdislocations,whichinanextremecasecanamountto
linesofinterstitialatomsalongthecoresofthedisloc
ations(condensedatmos-
pheres),e.g.inedgedislocationsattheregionofthestrainfieldwherethereis
maximumdilation(Figs2.5a
,b).Thebindingenergy
betweenadislocationin
ironandacarbonatomisabout0
.5eV.C
onsequentlydislocationscanbelocked
inpositionby
stringsofcarbonatomsalongthedislocations,thussubstantially
raisingthestresswhichwouldbenecessarytocaus
edislocationmovement.
Aparticulara
ttractionofthistheoryisthatonlyave
rysmallconcentrationof
interstitialato
msisneededtoproducelockingalongthewholelengthofall
dislocationlin
esinannealediron.
Foratypicaldislocationdensityof10
8lines
cm
2inannealediron,a
carbonconcentrationof10
6wt%wouldbesufficient
toprovideoneinterstitialcarbonatomperatomicplanealongallthedisloca-
tionlinespres
ent,i.e.tosaturatethedislocations.Con
sequently,thistheorycan
explaintheobservationofyieldphenomenaatvery
lowcarbonandnitrogen
concentration
s.
Theforma
tionofinterstitialatmospheresatdislocationsrequiresdiffusion
ofthesolute.A
sbothcarbonandnitrogendiffuseverymuchmorerapidlyiniron
Fig.2.5Interstitialatomsinthevicinityofanedgedisloca
tion(a)randomatmosphere
(b)condensed.
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28
CHAPTER2THESTREN
GTHENINGOFIRONANDITSALLOYS
Fig.2.7Solidsolutionstrengtheningof
-ironcrystalsbysubstitutionalsolutes.Ratio
ofthe
criticalresolvedshearstress0toshea
rmodulus
asafunctionofatomicconcent
ration
(Takeuchi,JournalofthePhysicalSocietyof
Japan27,929,1969).
ironbyHallandPetch,
ledtotheHallPetchrelationshipbetweenthe
yield
stressy
andthegraindiameterd,
y=0+kyd
,
(2.9
)
where0andk
yareconstants
.Thistypeofrelationshipholdsforawideva
riety
ofironsandsteelsaswellasform
anynon-ferrousmetalsandalloys.A
ty
pical
setofresultsformildsteelisgiveninFig
.2.7,wherethelinearrelationship
betweeny
andd
isclearlyshownforthethreetesttemperatures.
2.5GRAINSIZE
29
Fig.2.8Depen
denceoftheloweryieldstressofmildsteelo
ngrainsize(Petch,inFracture
(edsAverbachetal.),JohnWiley,USA,1959).
Theconsta
nt
0iscalledthefrictionstress
.Itistheinterceptonthestressaxis
,
representingthestressrequiredtomovefreedislocationsalongtheslipplanes
inthebcccry
stals,andcanberegardedastheyield
stressofasinglecrystal
(d
=
0).Th
isstressisparticularlysensitivetotempe
rature(Fig
.2.7
)andcom-
position.T
hekytermrepresentstheslopeofthey
d
plotwhichhasbeen
foundnottob
esensitivetotemperature(Fig
.2.8
),compositionandstrainrate
.
InlinewiththeCottrellB
ilbytheoryoftheyield
pointinvolvingthebreak
awayofdisloc
ationsfrominterstitialcarbonatmospheres,ky
hasbeenreferred
toastheunpinningparameter.H
owever,t
heinsensitivityofk
ytotemperature
suggeststhatunpinningrarelyoccurs,a
ndemphasizesthetheorythatnewdis-
locationsare
generatedattheyieldpoint.Thisisconsistentwiththetheories
explainingtheyieldpointintermsofthemovementofnewdislocations,the
velocitiesofw
hicharestressdependent(Section2.3.2)
.
Thegrainsizeeffectontheyieldstresscanthereforebeexplainedbyassum-
ingthatadislocationsourceoperateswithinacrystalcausingdislocationsto
moveandeventuallytopile-upatthegrainboundary.Thepile-upcausesa
stresstobegeneratedintheadjacentgrain,
which,whenitreachesacritical
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48
CHAPTER3
IRONCARBON
EQUILIBRIUMANDPLAINCARBONSTEE
LS
(a)
(b)
Fig.3.6Phasediagramanditsrelationsh
iptotheconcentrationprofileattheferrite/austenite
interfaceduringdiffusion-controlledgrowth.
Oncombiningtheseexpressionstoeliminatezweget:
z t=
D C(cc)2
2z(c
c)(c
c).
Itfollowsthat:
z=
(cc)
[2(c
c)(c
c)]1 2
D
Ct.
(3.2
)
Considernowaternarysteel,sayF
eMnC.I
twouldbenecessarytosatisfytwo
equationsoftheformofEquation
(3.1
),simultaneously,foreachofthesolutes:
(c
C
cC)v=D CcC
(c
Mnc
M
n)v=D M
ncM
n
.
(3.3
)
BecauseD CD M
n,t
heseequatio
nscannotingeneralbesimultaneously
satis-
fiedforthetie-linepassingthrough
thealloycompositioncC
,cMn.I
tis
,how
ever,
possibletochooseothertielineswhichsatisfyequation(3
.3).Ifthetie-lineis
suchthatcC
=cC(e
.g.
linecdfor
alloyAofFig
.3.7a),thencCwillbecome
verysmall,thedrivingforceforcarbondiffusionineffectbeingreduced,so
that
thefluxofcarbonatomsisforcedtoslowdowntoarateconsistentwiththe
diffusionofmanganese.Ferritefo
rmingbythismechanismissaidtogro
wby
aPartitioning,LocalEquilibrium
(orPLE)mechanism,i
nrecognitiono
fthe
factthatc
Mn
candiffersignificantlyfromcM
n,g
ivingconsiderablepartitioning
andlong-rangediffusionofmanganeseintotheaustenite.
Analternativechoiceoftie-linecouldallowc
Mn
cMn
(e.g.
linecdfor
alloyBofFig
.3.7b),sothatcM
n
isdrasticallyincreasedsinceonlyverysmall
amountsofMnarepartitionedintotheaustenite.Thefluxofmanganesea
toms
attheinterfacecorrespondinglyincreasesandmanganesediffusioncan
then
keeppacewiththatofcarbon,sa
tisfyingthemassconservationconditio
nsof
Equation(3
.3).Thegrowthofferr
iteinthismannerissaidtooccurbyaN
egli-
giblePartitioning,LocalEquilibrium(orNPLE)mechanism,i
nrecognitionof
3.4THEKINETICSOFTHE
TRANSFO
RMATION
49
(a) (b)
Fig.3.7Schem
aticisothermalsectionsoftheFeMnCsystem,illustratingferritegrowth
occurringwithlocalequilibriumatthe/
interface.(a)Growthatlowsupersaturations
(PLE)withbulkredistributionofmanganese,(b)growthathigh
supersaturations(NPLE)with
negligiblepartitioningofmanganeseduringtransformation.Th
ebulkalloycompositionsare
designatedbyth
esymbolineachcase.
thefactthatthemanganesecontentoftheferriteapp
roximatelyequalscM
n,s
o
thatlittleifan
ymanganesepartitionsintoaustenite.
WhatcircumstancesdeterminewhethergrowthfollowsthePLEorNPLE
mode?Figure3.8showstheFeMnCphasedia
gram,
nowdividedinto
domainswhereeitherPLEorNPLEispossiblebu
tnotboth
.Thedomains
areobtained
bydrawingright-handedtrianglesoneachtie-lineinthe+
phasefieldan
djoiningupallthevertices.
Forexample
,ifanattemptismade
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50
CHAPTER3
IRONCARBON
EQUILIBRIUMANDPLAINCARBONSTEE
LS
Fig.3.8Regionsofthetwo-phasefield
whereeitherPLEorNPLEmodesoftransform
ation
arepossible.
Fig.3.9Apara-equilibriumphasediagram.
todefineNPLEconditionsinthe
PLEdomain,
thenthetie-linedeterm
ining
interfacecompositionswillincor
rectlyshowthatbothausteniteandferrite
containlesscarbonthancC
,acircumstancewhichisphysicallyimpossible
.
Para-equilibriumisaconstrainedequilibrium.
Itoccursattempera
tures
wherethediffusionofsubstitution
alsolutesisnotpossiblewithinthetime
scale
oftheexperiment.Nevertheless,interstitialsmayremainhighlymobile.Thus,
inasteel,manganesedoesnotpartitionbetweentheferriteandaustenite,but
subjecttothatconstraint,thecarbonredistributesuntilithasthesamechemical
potentialinbothphases.
Therefore,t
hetielinesintheph
asediagram(Fig
.3.9
)areallvirtuallyparallel
tothecarbonaxis
,sinceMndoesnotpartitionbetweenferriteandausten
ite.
Inanisothermalsectionofthe
ternaryphasediagram,t
hepara-equilib
rium
phaseboundariesmustliewithinth
eequilibriumphaseboundariesasillustrated
inFig
.3.1
0.
3.4THEKINETICSOFTHE
TRANSFO
RMATION
51
(a)
(b)
Fig.3.10Thepara-equilibriumphasefieldlieswithintheequilibriumfield.Thetielines
illustratedarefo
requilibrium.
Fig.3.11(a)Plo
toftheparabolicthickeningprocessdescribedbyEquation(3.1).(b)Interfacial
energiesattheadvancingedgeofaferriteallotriomorph(afterHillert,JernkontoretsAnnaler
141,757,1957).
Sincethe
thicknessofanallotriomorphincrease
sparabolicallywithtime
(Fig
.3.11a),t
hegrowthratedecreasesastheferrite
thickens.Thisisbecause
increasingquantitiesofcarbonarerejectedintotheausteniteastheferrite
thickens,mak
ingthediffusionofcarbonawayfrom
thetransformationfront
moredifficult.
Zener,and
laterHillert,i
nvestigatedtheoreticallytheedgewisegrowthofan
allotriomorph
withcurvedends(Fig
.3.1
1b)assuming
thattherateiscontrolled
bythediffusionofcarbonintheaustenite.Theplateshapeensuresthatthe
carbonrejectedbythegrowingferriteisdistributed
tothesidesoftheplates.
Thecarbonco
ncentrationprofileaheadoftheplatetipthereforeremainscon-
stantasthep
latelengthens.Consequently,unliketh
ethickeningprocess,
the
allotriomorph
icferritelengthensataconstantrateG
L:
GL=D C
(c
c)
4r(cc)sin
,
(3.4
)
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CHAPTER3
IRONCARBON
EQUILIBRIUMANDPLAINCARBONSTEE
LS
Fig.3.16Fe13Mn0.8Cpartlytransfo
rmedat600C.Austeniteisretainedinconjunction
withferriteandcementite:(a)nucleatio
nofapearlitenoduleongrainboundarycementite,
(b)interfaceofnodulewithaustenite.Th
in-foilelectronmicrographs(courtesyofDippe
naar).
Hillertandco-workerswereabletoshowbysuitableheattreatments
that
pearlitedidnucleateinthisway,whileonthelow-energyinterfaces
Wid-
manstttengrowthofferrite(or
cementite)wasusuallyobserved.
Electron
microscopyobservationshaveconfirmedthatthepearliteinterfacewithau
sten-
iteisanincoherentone.Figure3.1
6bshowsatypicalinterfaceona13Mn0.8
C
wt%
steel,wheretheuntransformedaustenitehasbeenretainedatroom
temperature.
Thespacingofthelamellaein
pearliteisasensitiveparameterwhich
,ina
particularsteel,islargerthehigher
thetransformationtemperature.T
hespacing
wasfirstmeasuredsystematicallyforanumberofsteelsbyMehlandco-workers,
whodemonstratedthatthespacing
decreasedasthedegreeofundercooling
,T
,
belowtheeutectoidtemperatureincreased
.Zenerprovidedthefirsttheoretical
analysisoftheseobservationsbyc
onsideringavolumeofpearlite(Fig
.3.1
7)of
depthandinterlamellarspacingS
0growingunidirectionallyinthex-direction.
Ifgrowthisallowedtooccurbydxthenthevolumeofaustenitetransforme
dper
lamellarspacingisS0dx
,where
isthedensity
.ThefreeenergyG
,available
toformthisvolumeofpearliteis:
G=H
T
eTT
e
S
0dx
,
(3.6
)
where
Te=eutectoidtemperature
T=
transformationtemperature
H=
latent
heatoftransformation.
3.5THEAUSTENITEPEARLITEREACT
ION
57
Fig.3.17Apea
rlitegrowthmodel.
Theforma
tionofthisnewvolumeofpearlitecause
sanincreaseininterfacial
energybyvirt
ueofthenewferriteandcementiteinte
rfacesformed.T
herefore:
increaseininterfacialarea=
2
dx,
and
increaseininterfaceenergy=
2dx,
(3.7
)
where
isinterfacialenergyperunitarea.
Growthofthelamellaecanonlyoccuriftheincreasesinsurfaceenergyis
lessthanthedecreaseinenergyresultingfromthetransformation.
Therefore,
thecondition
forgrowthcanbefoundfromEquation
s(3
.4)and(3
.5):
H
T
eTT
e
S0=
2.
(3.8
)
Thisisaverysimpletreatmentwhichneglectsanystrainenergyterm.A
lsothe
freeenergychangeisfoundfromtheenthalpychangeperunitmass,andit
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64
CHAPTER3
IRONCARBON
EQUILIBRIUMANDPLAINCARBONSTEE
LS
Fig.3.21HultgrenextrapolationofphaseboundariesinFeCdiagram(Mehland
Hagel,
ProgressinMetalPhysics6,74,1956).
However,t
heseearlytheories
havenowbeensupplantedbyothersdueto
Hillert,C
ahnandHagel,K
irkaldy
andLundquistwhichhavebeendeveloped
toastagewherethesimpleironcarbidesystemhasbeentreatedinaso
phis-
ticatedway,
andtheroleofalloyingelementsalsoexplained.
Whilediffusion
ofcarboninaustenitehasagainb
eenassumedtobetherate-controlling
pro-
cess,s
ometreatmentshaveassumedthatboundarydiffusionisratecontro
lling.
Hillertusingthislatterapproach,
andassumingthattheaustenitehasper
iodic
compositionaldifferencesalongtheinterface,
dependingonwhetheraferrite
orcarbidelamellaisinthevicinity,arrivedatthefollowingrelationship:
G=
12AD
bS
2 0
(c2c1)
SS(cc)
1 S2 0
1
ScS0
,
(
3.15)
where
Db=
interphaseboundarydiffusioncoefficient
=
thicknessofinterphaseboundary
A=constant
c1andc2=concentrationspreviouslyreferredto
,fromtheHultgren
extrapolation
c=concentrationofcar
bonincementite
c=concentrationofcar
boninferrite
3.5THEAUSTENITEPEARLITEREACT
ION
65
S0=
interlamellarspacingofthepearlite
Sc=
spacingatzerogrowthrateand
SandS=
widthsoftheferriteandcementitelam
ellae.
Theequat
ionissimilarinformtoequationsinv
olvingvolumediffusion,
exceptthatit
involvesanS2 0termratherthanS0
.Alsothepresentmodelmust
involvesome
volumediffusionintheausteniteahead
oftheinterfacetoallow
thedifference
sinaustenitecompositionattheinterfa
cetodevelop.
3.5.5Thestrengthofpearlite
Thestrength
ofpearlitewouldbeexpectedtoincreaseastheinterlamellar
spacingisdecreased.E
arlyworkbyGensamerandcolleaguesshowedthatthe
yieldstressof
aeutectoidplaincarbonsteel,i.e.fully
pearlitic
,variedinversely
asthelogarit
hmofthemeanfreeferritepathinthepearlite.Later,Hugo
andWoodhea
dused3wt%nickelsteelstoobtainau
niformpearliticstructure
throughoutth
etestpieces.Theyconfirmedthattheinterlamellarspacingwas
inverselyproportionaltothedegreeofundercooling
.Itwasshownthatboth
theyieldstren
gthandtheultimatetensilestress(UTS)couldbelinearlyrelated
tothereciprocalofthesquarerootoftheinterlamella
rspacingorofthedegree
ofundercooling.Figure3.22givesresultsfora3Ni0
.67Cwt%
eutectoidsteel
wherethislin
earrelationshipisillustrated
.Steelso
flowercarboncontents
,
Fig.3.22Effectofdegreeofundercoolingonthestrengthofapearliticnickelsteel0.67C,
0.49Mn,2.92Niw
t%(HugoandWoodhead,JournaloftheIronandSteelInstitute186,174,1957).
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74
CHAPTER4
EFFECTSOF
ALLOYINGELEMENTSONFECALLOYS
Fig.4.2Twobasicphasediagrams:(a)
Hnegative,H>
H,favoured;(b)Hpo
sitive,
H
1200C
Fine-grainedaustenite
1200C>T
P>
Ac3
Partiallyaustenitizedzone
Ac3>
TP>
Ac1
Temperedregions
Ac1>
TP
Fig.13.14AcomparisonoftheTTTcur
vesforthe
transformation,andforthereverse
transformation.GrepresentsthedrivingforcefortransformationandDisthediffusion
coefficient.
austenitegrainscoarsenrapidlyasTP
isapproached.I
nsteelswhicharemic
roal-
loyed
,itmaynecessaryforthegrainboundarypinningparticles(e
.g.
niobium
carbonitrides)todissolvebeforesu
bstantialgraincoarseningoccurs.I
nany
case,
oncethecoarseningbegins,itproceedsveryrapidlybecausetheeffectof
tem-
peratureincreasesexponentiallyd
uringheating.Theaustenitegraingrowthcan
beexpressedconvenientlyinthe
formofgraingrowthdiagrams(Fig
.13
.15b)
whichcontaincontoursofequalgr
ainsizeasafunctionofthepeaktemperature
andt8
5.
Theimportanceofthecoarse-grainedaustenitezoneisinthemecha
nical
propertieswhichdevelopastheau
stenitetransformsduringthecoolingpartof
thethermalcycle.Thecoarsegrain
structureleadstoanincreaseinharden
abil-
ity,becauseitbecomeseasiertoav
oidintermediatetransformationproducts,so
thatuntemperedmartensiteorotherhardphasescanformduringcooling
.The
weldingprocessintroducesatomichydrogenintotheweldmetal,w
hichisable
todiffuserapidlyintotheHAZ
.H
ardmicrostructuresareparticularlysuscepti-
bletoembrittlementbyhydrogen,t
hefractureoccurringshortlyafterthe
weld
13.3THEHAZ
305
Fig.13.15(a)
TheTTTandCHTdiagramsforthebeginningofaustenitegrowthina
Fe0.15C0.5Si
1.5Mnwt%alloy(courtesyofSuzuki).(b)Schematicaustenitegraingrowth
diagramforamicroalloyedsteelweldedusingapreheatof200C(afterAshbyandEasterling,
1982).
hascooledto
roomtemperature.T
hishydrogen-inducedphenomenoniscalled
cold-cracking
.ThisiswhytheCEofthesteelhast
obekeptlowenoughto
preventthehardnessinthecoarse-grainedregionfrombecomingunacceptably
large.
13.3.4Fine-g
rainedaustenitezone
Thisregionistypifiedbyaustenitegrainssome204
0
minsize.T
hegrainstruc-
tureandhard
enabilityare,therefore,
notverydifferentfromthoseassociated
withcontrol-rollingoperationsduringthemanufactureofthesteel.Thefine
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CHAPTER14
MODELLING
OFMICROSTRUCTUREANDPROPERTIES
Fig.14.5(a)Experimentallydeterminedimpacttransitioncurvesshowinghowthetoughness
improvesastheamountofblockyausteniteisreduced.(b)CalculatedT 0curvesforthe
FeC,
FeMnSiCandFeNiSiCsteels.
Manganeseisseentohavealarge
effectindepressingtheT 0temperature.An
examinationofTable14
.2showsth
atonepossibilityistoreplaceallofthe
man-
ganesewithnickel.T
hus,foraFe4Ni2Si0.4Cwt%(3
.69Ni,3.85Siat%)
alloy,
asimilarcalculationshowsthat
T072sothat:
T 0(K)
970
80xc
72.
(
14.9
)
Theremarkableimprovementin
toughnessachievedbydoingthis
,without
anysacrificeofstrength
,isillustratedinFig
.14
.5,
alongwiththeT 0curves
ascalculatedabove.
14.3EXAMPL
E2:MECHANICALPROPERTIESOFMIXED
MICROSTRUCTURES315
Table14.2ValuesofTMandTNMforavarietyofsubstitutional
solutes(Aaronsonetal.,T
ransitionsoftheMetallurgicalSocietyofAIME
236,753780,1966)
Allo
yingelement
TM
/Kperat%
TNM
/Kperat%
Si
3
0
Mn
37
.5
39
.5
Ni
6
18
Mo
26
17
Cr
19
18
V
44
32
Co
19.5
16
Al
8
15
Cu
4.5
11
.5
14.2.3Theprecisionofthemodel
Themodeldis
cussedabovehashelpedinachievingthe
desiredgoalofimproved
toughness,eventhoughthemethodusedisinfactcru
de.TheT 0curvesarenot
reallylinearfu
nctionsofcarbon,a
ndtheinteractionso
fcarbonwiththesubstitu-
tionalsolutes
arenotaccountedfor.Rigorousmethodsareavailableandcould
beusedwhenconsideringahigherdegreeofoptimizationofsteelchemistry.The
modelalsodo
esnotincorporatekinetics.Thiscould
beamajordisadvantage
becauseinco
mmercialpractice,microstructuresare
usuallygeneratedusing
complexnon-
isothermalheattreatments
.
Referring
toFig
.14
.1,
itisobviousthattheexplo
itationoftheseconcepts
wouldrequire
severaliterationstoimproveprecision
,andtoadaptthemodel
forcomplexi
ndustrialprocessing.Theseexamplesillustratetheessentialsof
themodelling
technique.Modelscanbeconstructed
instages,w
ithsignificant
advancesbein
gmadeateachstage,eventhoughtheu
ltimateproblemmaynot
besolvedcom
pletely
.Thesesuccessesateachstageof
themodelcanbeusedto
justifyfurther
developmentuntilapointofdiminishingreturnsisreached.
14.3EXAMP
LE2:MECHANICALPROPERTIESOFMIXED
MICRO
STRUCTURES
Apeculiarfea
tureofmixedmicrostructuresofbainite
andtemperedmartensite
,
isthatthestr
engthisfoundtogothroughapeaka
sthevolumefractionof
martensitede
creases(Fig
.14
.6).Thisisagainstintuitioninthatmartensiteis
usuallyconsid
eredtobethestrongestmicrostructureinsteels
,inwhichcasethe
strengthshoulddecreasecontinuouslyasthefraction
ofmartensiteisreduced
.
However,q
ua
ntitativemodelling,byhelpingtoreveal
themechanismsinvolved,
canexplainth
isanomalousbehaviour.
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CHAPTER14
MODELLING
OFMICROSTRUCTUREANDPROPERTIES
Therearemanythermodynamicmethodswhichexpressthechemicalpoten-
tialasafunctionofthemixingofsolutesinaphase.Mostofthesemethod
sare
eithertoosimpleorsocomplexthattheycannoteasilybegeneralized.T
here-
fore,
inthecomputercalculations,thedeviationofthefreeenergyofm
ixing
fromthatofanidealsolution,1
i.e.t
heexcessGibbsfreeenergy,i
swritten
asan
empiricalpolynomialequation:
eGAB=xAxB
iLAB
,i(xAxB)i
,
whereLiaremeasuredinteraction
coefficients
,inthiscaseforabinarysolu
tion.
Foraternarysolution:
eGABC=xAx
B iLAB
,i(xAxB)i
,
+x
BxC
iLBC
,i(xBxC)i
,
+x
CxA
iLCA
,i(xCxA)i.
Theadvantageofthiskindofap
olynomialbecomesclear,
sincetherel
ation
reducestothebinaryproblemwhe
noneofthecomponentsissettobeidentical
toanother,e.g.BC
.Themethod
canbeextendedtodealwithanynumb
erof
components
,withthegreatadvantagethatfewcoefficientshavetobecha
nged
whenthedataduetoonecompon
entareimproved
.Itisthereforeadopt
edin
manyofthephasediagramcalculationprogramsavailablecommercially.
Althoughthermodynamicsisusuallyassociatedwiththestateofequilib-
rium,t
hecalculationmethodcanalsobeusedtoestimateconstrainedequilibria,
e.g.para-equilibrium(Chapter3)anddiffusionlesstransformation(Chapter5)
.
Figure14
.12illustratescalculatedisothermalFeCrCphasediagramsfor
both
theequilibriumandpara-equilibriumstatesnoticethedramaticchangewhen
substitutionalsolutesarenotallow
edtopartitionbetweenthephases.
Thereisanothersubtleapplicationofthermodynamicsinthedesignofs
teels,
dealingwithsteady-stateprocessesinwhichthesystemisnotatequilib
rium
butanappropriateobservermaynotperceivechange.A
nexampleisdiffusion
acrossaconstantgradient;neitherthefluxnortheconcentrationatanypoint
changeswithtime,andyetthefr
eeenergyofthesystemisdecreasing
since
diffusionoccurstominimizefreeenergy.T
herateatwhichenergyisdissipated
istheproductofthetemperatureandtherateofentropyproduction(i.e.
T
):
T=JX
,
1Anidealsolutionisoneinwhichtheatomsmixatrandomatalltemperatures.
Fig.14.12IsothermalsectionoftheFeCrCsystem.Thebody-centredcubicphaseisferrite
andMstandsfor
amixtureofironandchromiumatomsinavarietyofcarbidephases(courtesy
ofJ.Robson).
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328
CHAPTER14
MODELLING
OFMICROSTRUCTUREANDPROPERTIES
Thefreeenergyperatomisthenwrittenforthewholeofthe(heterogeneous)
phasefieldasasinglefunctionala
ndtheevolutionofmicrostructurewith
time
isassumedtobeproportionaltothevariationofthisfunctionalwithrespectto
theorderparameter.
Themethodhasbeenextremelysuccessfulindealingwithspinodalreac
tions
andinthemodellingofsolidification,
butitsutilitywithrespecttosolid-s
tate
reactionsofthekindimportant
insteelshasyettobedemonstrated
.The
definitionofthewidthoftheinte
rfaceandassociatedcoefficients
,andh
and-
lingnucleationaretwodifficultieswhichrequirefittingtoexperimental
data.
Ontheotherhand
,effectssuchastheoverlapofdiffusionfieldsarena
tural
outcomes.
14.5.1Finitedifferencemethod
Thefinitedifferenceisadiscret
eanalogueofaderivative.
Consider
one-
dimensionaldiffusioninaconcentrationgradientalongacoordinatez
(Fig
.14.14).Theconcentrationprofileisdividedintoslices,e
achofthicknessh.
Thematterenteringaunitareaofthefaceatainatimeincrement
isgiven
approximatelybyJa=D
(C1
C0
)/h.ThatleavingthefaceatbisJb=D
(C2C
1)/h
.IfC 1isthenewconcentrationinslice1,thenthenetgaininsolute
is(C 1C
1)hsothat:
C 1C
1=
Dh2
(C0
2C
1+C
2).
(
14.2
)
Thisallowstheconcentrationata
pointtobecalculatedasafunctionofthatat
thetwoneighbouringpoints
.Bysu
ccessivelyapplyingthisrelationateach
slice,
andadvancingthetime,t
heentireconcentrationprofilecanbeestimatedas
afunctionoftime.
Fig.14.14Finitedifferencerepresentationofdiffusion.
14.6FINITEELEMENTMETHOD
329
Theappro
ximationisthattheconcentrationgrad
ientwithineachslicehas
beenassumed
tobeconstant.Thisapproximationwillbebetterforsmallerval-
uesofh
,butattheexpenseofcomputationtime.Theaccuracycanbeassessedby
changinghandseeingwhetheritmakesasignificantdifferencetothecalculated
profile
.
14.6FINITE
ELEMENTMETHOD
Inthis
,contin
uousfunctionsarereplacedbypiecew
iseapproximations.The
consequenceofapplyingforcetoabodyrepresented
asasetofspringsisillus-
tratedhere,a
ssumingthattheforceFineachspringvarieslinearlywiththe
displacement
,w
iththeconstantofproportionalityla
belledthestiffnessk
.The
bodyisatrestatequilibrium,s
oforthecaseillustrate
dinFig
.14
.15a
,F1=F
2
sothat:
F
1F
2
=kk
k
k12,
TheforcesatthenodesofthespringsillustratedinFi
g.14
.15baretherefore
F
1F
20
=
k
1k
1
0
k
1
k1
0
0
0
0 123
0 F
2F
3
= 0
0
0
0
k2
k2
0
k
2
k2 123
, (
a)
(b)
Fig.14.15Forcesonsprings.
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