Physical Metallurgy of Steel

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


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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56

CHAPTER3

IRONCARBON


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


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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314

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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324

CHAPTER14

MODELLING


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


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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Physical Metallurgy of Steel

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