me 530-lecture #4,5-dislocations, schmid factor.pptx

1

Plas'cdeforma'onduetoslip

Slipduetoaperfect

disloca0on

Callister(2000)

slippedstateIntrinsicstackingfault

t2

t1 l

b1

b2

extendeddisloca0onAperfectdisloca0onmaysplitintopar0aldisloca0ons…

Leeetal.,ActaMater(2001)

Intrinsicstackingfault

ME530Lecture#4-H.Sehitoglu

2

Plas'cflowinfccmaterials:slipandcross-slip

Polycrystallinematerial

Singlecrystal/grain

twinning

sliplowSFEmetale.g.:pureAg

lowSFEalloyse.g.:nitrogensteels

strain

stress

StageI

StageI

twinningstarts

StageIII

medium/highSFEmetale.g.:pureAl

cross-slip

Fujietal.,Mater.Sci.Engg.A319(2001)415-461.Disloca0oncells

Karamanetal.,ActaMater(2001).disloca0onarrays

stackingfaultribbons

TEMimagefrom:Whelan,Hirsch,HorneandBollmann,Proc.Roy.Soc.London(1957).

4

Intrinsicstackingfault

( )111 plane ( )111 plane

1/ 2 110⎡ ⎤= ⎣ ⎦b

Plas'cdeforma'onduetocross-slip

IfSFEislow,cross-slipmaybedifficult–twinningcanoccur.

cross-slipduetoanextendeddisloca0on

W.Puschl,Prog.Mater.Sci.47(2002)415-461. Fujietal.,Mater.Sci.Engg.A319(2001)415-461.

PureAl 3003Al-alloy

5

Energylandscapeforastackingfault(g-surface)

xu1<110>2

zu1<112>6

isfγ

maxγ

S.Kibey,J.B.Liu,M.W.Cur0s,D.D.JohnsonandH.Sehitoglu,ActaMater.54(2006)2991-3001

usγunstablestackingfaultenergy(Rice,1992)

A

C

s

B <112> u

m

EnergyforSFforma0onduringpassageofaShockleypar0al=areaunderthissurface

Slip plane and Directions (Burger’s vectors)

• Eachcrystalstructure(e.g.,fcc,bcc,andhcp)hasdifferentallowedslipplanes,occurringatspecificanglestoappliedstress,anddifferentslipdirec/ons,occurringatotherangles.• Shearstress(notnormalstress)iswhatcausesplanarsliptooccur.• Ac3veslipplaneistypicallythemostCLOSE-PACKEDPlanes.• Ac3veslipdirec/onisthemostCLOSE-PACKEDDirec3ons.

b b

(111)planesinthedirec3onof Slipsystems:4x3=12

�

< 11 0 >

FCC Slip plane and Directions

BCC Slip Planes and Directions

{110}planesinthedirec3onof

Slipsystems:6x2=12

�

< 1 11>


Slipsystems:12x1=12

�

< 1 11>


Slipsystems:24x1=24

�

< 1 11>

Principalslipsystem,butotherclosed-packeddirec3ons

�Fe,K

�Fe,Mo,W,Na

�Fe,Mo,W,�brass

HCP Slip Planes and Directions


Slipsystems:1x3=3

�

< 112 0 >

planesinthedirec3onof

Slipsystems:3x1=3

Principalslipsystemcandependonc/aandrela/veorienta/onofloadtoslipplanes

�

{10 1 0}

�

< 112 0 >

planesinthedirec3onof

Slipsystems:6x1=6

�

{10 1 1}

�

< 112 0 >

c/a≥1.6333(ideal)

c/a≤1.6333(ideal)

hcp Zinc single crystal

Adapted from Fig. 7.9, Callister 6e.

Adapted from Fig. 7.8, Callister 6e.

Cd,Zn,Mg,Ti,Be…

Ti

Mg,Ti

(111)fccplane Par'alDisloca'onsb=b1+b2

�

a2

1 01[ ] = a6

2 11[ ] + a6

1 1 2[ ]

bb1y b2x

b1 b2b2y

b1x

b1yandb2yareaMrac3vescrewsegmentsb1xandb2xarerepulsiveedgesegments

Herepar'alsform,edgerepulsionwinsout,whichcreatesstackingfaultedregioninbetween.

FCC Partial Dislocations and Stacking Faults

EnergiesofFullandPar'alsare

�

E1 = Gb2 E1+2 = Gb12 + Gb2

2

�

E1+2 = 2Ga2

36(4 + 1+ 1) = Ga2

3

�

E = Gb2 = Gb •b = a2

4(1+ 0 + 1) = a2

2>

Favorableforpar'alstoform,i.e.disloca0ondisassociate.

Disloca'onsmaybesessileifnotonthecorrectslipplane.

Ifenergyisfavorable,Gb2>Gb12+Gb22,thenpar'aldisloca'onform.(Show:Ga2/2>Ga2/3)

b

dueto…ABC…stacking

Par3aldisloca3onsmoveapart.AstheymoveapartleavehcpSFribbon.ABC=3layersAB=2layersABCABCconvertstoABABAB

(111)fccplane Par'alDisloca'onsb=b1+b2

�

a2

1 01[ ] = a6

2 11[ ] + a6

1 1 2[ ]

b InFCC,dueto…ABC…stacking,ifpar'alsform,edgerepulsionwinsout,whichcreatesstackingfaultedregioninbetween.GreenPar/alsSeparate.

A AB BC

FCC

HCP

C

par'al

FCC Partial Dislocations and Stacking Faults

StackingFaultsaredefectsthatcostenergyEnergybalancebetweensepara3ngpar3alstolowerelas3cenergyandcrea3onofmoreSF.

Mo'onofpar'als

Separa'onofpar'als

16

Deforma'ontwinning

Deforma0ontwininFe-Mn-Csteel[001]orienta0on3%strain

TEMimagefrom:I.Karaman,H.Sehitoglu,K.Gall,Y.I.ChumlyakovandH.J.Maier,ActaMater.(2000).

fcc

fcc

twin

B

C

C

A

B

A

C

<112>

<111>

fcc

fcc

twin

Mirrorsymmetryisseenacrossthetwinboundary.

Twinboundary

Twinning:mechanismofplas0cdeforma0onatcrystallevel.

twinboundary

twinningshear

a a

17fcc

uz fcc0.5

usγu

unstable

1.0 1.5 2.0 2.5 3.0

[ ]111

112⎡ ⎤⎣ ⎦

A

A

BC

BC

A

fcc

primi0vecell

pq

rs

(111)

Energypathwayforastackingfault

hcp

isfγs

isf

ABC

AC

A

intrinsicstackingfault(isf)

B

Generalizedstackingfaultenergy(GSFE)

(Vitek,1968)

12bp bp

maximum

maxγ

m

AB

AA

C

BC

12bp

Specimensurfaceafertest

Specimensurfaceafertest

(112)[111]

__

Mode Plane Angle[°]

Schmidtfactor

Twin (-1-12)[111] -75.7 0.49

Twin (1-12)[-111] -59.5 0.43

Twin (112)[-1-11] 74.4 0.41

Twin (-112)[1-11] 53.3 0.49

(112)[111]

__

Ex-situDIC(10x)–SEMresults

[001]tension,εmean=0.32%

εxx[%]

Ex-situDIC(10x)–SEMresults

[001]tension,εmean=0.32%

18

εxx[%]

Deforma'onleadstoPlas'cSlip

•  Defini'onofslip–theslidingofplanesofatomsoveroneanother

•  Slipmo'onisaccomplishedbythemo'onofdisloca'ons

•  Sliptypicallyoccursalongthecrystal’sslipdirec'onontheslipplane

•  Asanexample,wewillexamineaFCCcrystalstructure(Cu,Al,Ni,etc.)–  12totalslipsystems–  4dis'nctslipplanes:{111}

•  Largestdistancebetweenplanes–  3dis'nctslipdirec'onperplane:<110>

•  Smallestdistancebetweenatoms

SchmidFactor

•  Thestressrequiredtoinduceslipinacrystallaqcecanbecalculatedasafunc'onofit’sorienta'on

•  SchmidFactor,m:Thera'oofmaximumshearstressonaslipsystemtotheuniaxialstressapplied

PicturefromSim,2008

3-CFPSPECIMENFE47.8–CRPOLY-CRYSTAL

COMPRESSIONTEST

WaelAbuzaid,LucaPatriarca

Prepara'onofthespecimen

• MaterialFe–47.8Cr,poly-crystal• HeatTreatment900°Cfor1hr,quenchedinwater(January252011)

• Polishing(March182011)• EBSD(March182011)• Spekle(March192011)

• Compressiontest(March202011)• Geometryinforma'onsw=3.93mm,t=3.89mm,Lo=9.99mm

EBSDresults

EBSDresults–Eulerangles⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

5.283.351.56

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

2.55.434.85

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

1.812.239.200

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

4.313.195.343⎥

⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

0.261.199.344

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

6.771.171.298⎥

⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

0.436.486.338

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

5.48.231.278

1

2

3

4

56

7

8

EBSDresults–Eulerangles

1

2

3

4567

8

EBSDresults–Eulerangles

1

2

3

4567

8

[111]

[133]

[011]

Singlecrystal

StressHistoryVsGripdisplacement

Ex-situanalyses5x

0.1 2.4

εresidual=0.48%

5x

Ex-situanalyses5x

0.1 2.4

εresidual=0.48%

5x

25x

SchmidtFactor0.33

Ex-situanalyses5x

0.1 2.4

εresidual=0.48%

5x25x

Twin(121)[111]_

Slip(321)[111]_

Twin(121)[111]_

Slip(321)[111]_

SchmidtFactor0.44

SchmidtFactor0.2

Ex-situanalyses5x

0.1 2.4

εresidual=0.48%

5x

25x

SF0.46

SF0.5

SF0.35

Ex-situanalyses5x

0.1 2.4

εresidual=0.48%

5x

25x

SF0.46 SF0.39

SF0.37

Ex-situanalyses5x

0.1 2.4

εresidual=0.48%

5x

25x

me 530-lecture #4,5-dislocations, schmid factor.pptx

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