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Lecture 09Lecture 09

Dislocations & Strengthening MechanismsDislocations & Strengthening Mechanisms

Chapter 7 - 1

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ISSUES TO ADDRESS...ISSUES TO ADDRESS... Why are dislocations observed primarily in metals Why are dislocations observed primarily in metals

and alloys?and alloys?

How are stren th and dislocation motion related? How are stren th and dislocation motion related?

How do we increase strength? How do we increase strength?

How can heating change strength and other properties? How can heating change strength and other properties?

Chapter 7 -

2

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Mechanical Behavior & StructureMechanical Behavior & Structure

Controlled by

Chemical bond

Controlled by Processing

via defects, crystal structure

Chapter 7 -

3

Chemistry an m crostr cture

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Dislocations & Materials ClassesDislocations & Materials Classes

Metals: Disl. motion easier.

-non-directional bonding ++++++++

-close-packed directionsfor slip. electron cloud ion cores++++++++

Covalent Ceramics

(Si, diamond): Motion hard.-

Ionic Ceramics (NaCl):

Motion hard.-need to avoid ++ and - -

nei hbors.

+++

+ + + +

- - -----

- - -

Chapter 7 - 4

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Dislocation MotionDislocation Motion

Dislocations & plastic deformation

Cubic & hexagonal metals - plastic deformation by

plastic shear or slip where one plane of atoms slides

over adjacent plane by defect motion (dislocations).

Chapter 7 - 5

If dislocations don't move, deformation doesn't occur!

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Dislocation Motion (Contd)Dislocation Motion (Contd)

Caterpillar

b

Chapter 7 - 6

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Dislocation MotionDislocation Motion

Dislocation moves along slip plane in slip direction

perpendicular to dislocation line

Slip direction same direction as Burgers vector

Edge dislocation

Screw dislocation

Chapter 7 - 7

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Comparison of Dislocation MotionComparison of Dislocation Motion

EdgeEdge vsvs Screw DislocationsScrew Dislocations

Chapter 7 - 8

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Deformation MechanismsDeformation Mechanisms

Slip System

Slip plane - plane allowing easiest slippage

Wide interplanar spacings - highest planar densities

Slip direction - direction of movement - Highest lineardensities

FCC Slip occurs on {111} planes (close-packed) in

directions (close-packed) => total of 12 slip systems in FCC

Chapter 7 - 9

in BCC & HCP other slip systems occur

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Deformation MechanismsDeformation Mechanisms

Common Slip SystemsCommon Slip Systems

Chapter 7 - 10

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Slip Systems in Common MetalsSlip Systems in Common Metals

After Dieter,

(1990)

Chapter 7 - 11

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Stress and Dislocation MotionStress and Dislocation Motion

Crystals slip due to a resolved shear stress, tR.

Applied tension can produce such a stress.

Resolved shear

stress: tR =Fs /As

Relation between

s and tR

Applied tensile

stress: = F/As

F

normal, ns

AS

tR R S S

Fcosl

A/cosf

A

tR

lFS

nS

AS

A

SchmidsSchmids LawLaw

Chapter 7 - 12

coscosR

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Critical Resolved Shear StressCritical Resolved Shear Stress

Condition for dislocation motion: CRSSR

it easy or hard to move dislocation 10-4 GPa to 10-2 GPa

typically

coscoss s s

tR = 0 tR = s /2 tR = 0

= =f=45 =

Chapter 7 - 13maximum at

=

= 45

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Single Crystal SlipSingle Crystal Slip

Single

crystal

w re

Chapter 7 - 14

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Ex: Deformation of single crystalEx: Deformation of single crystal

=60

a) Will the single crystal yield?

b) If not, what stress is needed?

cos cos=35

crss = ps

6500 psi

(6500 psi) (cos35)(cos60)

(6500 psi) (0.41)

2662 psi crss 3000 psi

= 6500 psi

Chapter 7 - 15

So the applied stress of 6500 psi will not cause the crystal

to yield.

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Ex 1:Ex 1: Deformation of single crystalDeformation of single crystal

What stress is necessary (i.e., what is the yield stress, y)?

)41.0(coscospsi3000crss yy

psi7325psi3000

crss

.

So for deformation to occur the applied stress must be

greater than or equal to the yield stress

Chapter 7 - 16

y

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Ex 2: Deformation of Single crystalEx 2: Deformation of Single crystal

Chapter 7 - 17After Dieter, Mechanical Metallurgy (1990)

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Slip Motion inSlip Motion in PolycrystalsPolycrystals

Stronger - grain boundaries

pin deformations

Slip planes & directionschange from one

crys a o ano er.

R will vary from one .

The crystal with the

.

Other (less favorably

Chapter 7 - 18

yield later.300 mm

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Anisotropy iny

Can be induced by rolling a polycrystalline metal

- before rollin - after rollin

235 mm

- isotropic - anisotropic

since grains areapprox. spherical

& randomly

since rolling affects grainorientation and shape.

Chapter 7 - 19

oriented.

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Anisotropy in DeformationAnisotropy in Deformation

1. Cylinder of

Tantalum

machined

2. Fire cylinder

at a target.

3. Deformed

cylinder

side view

from a

rolled plate:

ire

ction

rolling

The noncircular end view shows

endview

platethickness

direction

Chapter 7 - 20

anisotropic deformation of rolled material.

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Deformation byDeformation by MechlMechl TwinningTwinning

Twins also re-orient slip planes and contribute to dislocation slip indirectly

Twinning is an alternate (plastic)

deformation mechanism observed when the

strain rate is ver hi h or at low T dislocation sli is su ressed

Chapter 7 -

It is a strain-relief mechanism. Very common in BCC and HCP metals

when slip is restricted!

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MechlMechl Twinning vs.Twinning vs. Dislocation SlipDislocation Slip

Homogeneous

(Twin Band)

Chapter 7 -

After

Dieter.

Mechl Metallurgy

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Strategies for Strengthening:Strategies for Strengthening:

.. e uce ra n zee uce ra n ze

Grain boundaries arebarriers to slip.

" "

increases with

increasing angle ofm sor entat on.

Smaller grain size (d):

more barriers to slip.

21/

Chapter 7 -

yoy e

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. e uce ra n ze on. e uce ra n ze on

Very difficult

to synthesize polycrystalline

materials with d

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Primary mechanism

..

for strengthening by grain

boundaries

Chapter 7 - 25

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StrategiesStrategies for Strengthening:for Strengthening:

Im urit atoms distort the lattice & enerate stress.

. o. o o u onso u ons

Stress can produce a barrier to dislocation motion. Smaller substitutional impurity Larger substitutional impurity

A C

B D

Impurity generates local stress at A

and B that o oses dislocation motion

Impurity generates local stress at C

and D that o oses dislocation motion

Chapter 7 - 26

to the right. to the right.

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Stress Concentration atStress Concentration at DislocationsDislocationsWhat makes a dislocation move & interact?What makes a dislocation move & interact?

e stress e roun t e s ocat one stress e roun t e s ocat oninteracts with the applied stress (viainteracts with the applied stress (via RR))

and the Strain field of structuraland the Strain field of structural

im er ections such as rain boundariesim er ections such as rain boundaries

Chapter 7 -

and solute atomsand solute atoms

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Strengthening by AlloyingStrengthening by Alloying

Small impurities tend to concentrate at dislocations

Chapter 7 - 28

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Strengthening byStrengthening by alloying (Contd)alloying (Contd)

Large impurities concentrate at dislocations on low

density side

Chapter 7 -

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Ex: SolidEx: Solid Solution StrengtheningSolution Strengthening in Copperin Copper

Tensile strength & yield strength increase with wt% Ni.

Pa) 400

a)

180

rength(M

300

en

gth(M120

Tensiles

2000 10 20 30 40 50

Yieldstr

600 10 20 30 40 50

Empirical relation:21 /y C~

. , . ,

Chapter 7 -

Alloying increases sy and TS.

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DislocationDislocation Sources: FrankSources: Frank--Read SourcesRead Sources

Chapter 7 - 31

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Hard precipitates are difficult to shear.

. rec p a on. rec p a on reng en ngreng en ng

Ex: Ceramics in metals (SiC in Iron or Aluminum).

Large shear stress neededto move dislocation toward

precipitate

prec p a e an s ear .Side View

Unsli ed art of sli lane advances butprecipi tates act as pinning sites with

S.

op ew

Sspacing

Result: ~1

Slipped part of slip plane

The smaller the S, the larger the

dislocation line needs to bow out,

Chapter 7 -

the more surface energy needs to

be spend!

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ApplicationApplication:: Precipitation StrengtheningPrecipitation Strengthening

Internal wing structure on Boeing 767

Aluminum is strengthened with precipitates formedy a oy ng.

Black s ots

are the ppts.

Chapter 7 - 33

1.5mm

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. o. o oror

Room temperature deformation. Common forming operations change the cross sectional area:

-Forging force -Rolling

Ao Ad

die

blank

roll

Ao

Ad

force-Drawing

tensileAddie

-Extrusion

container die holder

Ao

forceo

dieram billet

container dieAdextrusion

Chapter 7 -

100x%

oA

CW

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Dislocations During Cold WorkDislocations During Cold Work

Ti alloy after cold working:

Dislocations entangle with oneanother during cold work.

Dislocation motion becomes

more difficult.

Strain hardening due to

-

interactions

cutting through a forest ofcutting through a forest of

Chapter 7 -

s ocat onss ocat ons. mm

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Dislocations During Cold WorkDislocations During Cold Work

Edge and screw

dislocation interaction

leads to strain hardening

After

Dieter.

Mechl Metallur

Chapter 7 - 36

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Result of Cold WorkResult of Cold Work

Dislocation density =total dislocation length

unit volume

Carefully grown single crystal ca. 103 mm-2

Deforming sample increases density 109-1010 mm-2

eat treatment re uces ens ty - mm-

Yield stress increases as rdincreases:

large hardening

y1

small hardeningy0

Chapter 7 -

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Effects of Stress at DislocationsEffects of Stress at Dislocations

Chapter 7 -

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Cold Work AnalysisCold Work Analysis What is the tensile strength &

ductility after cold working?22

Cold

Work

Copper

%6.35100x%2

o

do

rCW

Do =15.2mm Dd=12.2mm

700

yield strength

(MPa)

tensile strength

(MPa)800

ductility

(%EL)60

300

500

Cu300MPa

400

600

20

40

Cu340MPa

% Cold Work

100200 40 60

% Cold Work

200Cu

0 20 40 60% Cold Work20 40 600

07%

Chapter 7 -

y = a = a %EL= 7%

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-- Behavior vs. TemperatureBehavior vs. Temperature

Results for

polycrystalline iron:-200C

800

600

MPa)

-

25C

400

200Stres

s(

and TS decrease with increasing test temperature.

0

Strain0 0.1 0.2 0.3 0.4 0.5

%ELincreases with increasing test temperature.

Why? Vacancies

hel dislocations 2. vacancies

3 . disl. glides past obstacle

move past obstacles. replaceatoms on thedisl. half

plane 1. disl. trapped

obstacle

Chapter 7 -

y o s ac e

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Effect of Heating After %Effect of Heating After %CWCW

1 hour treatment at Tannealdecreases TS& increases %EL.

Annealing temperature (C)200100 300 400 500 600 700

th(MPa

(%

EL)tensile strength

500

50

stagesstages to discussto discuss......

ilestren

ductility

400

40

30

te

n ductility

30020

Chapter 7 -

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RecoveryRecovery

Annihilation reduces dislocation density.

Scenario 1 extra half-plane

Results from

diffusion

annihilate

and form

a perfect

atomsdiffuse

atomic

plane.extra half-plane

of atoms

of tension

cenar o

tR3. Climbed disl. can nowmove on new slip plane

4. opposite dislocationsmeet and annihilate

.

vacancy diffusionallowing disl. to climb1. dislocation blocked; Obstacle dislocation

Chapter 7 -

cant move to the right

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RecrystallizationRecrystallization

New grains are formed that:

- Have a small dislocation density

- re sma

- Consume cold-worked grains.

. .

33% cold New crystals

Chapter 7 -

worked

brass

nucleate after

3 sec. at 580C.

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FurtherFurther RecrystallizationRecrystallization

AllAll coldcold--worked grains are consumed.worked grains are consumed.

0.6 mm0.6 mm

After 4 After 8

Chapter 7 -

secon s secon s

G i G hG i G h

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Grain GrowthGrain Growth

At longer times, larger grains consume smaller ones. Why? Grain boundary area (and therefore energy) is reduced.

0.6 mm 0.6 mm

After 8 s,

580C

After 15 min,

580C

Empirical Relation:

Elapsed time

Coefficient dependent

on material and T.

Grain diam.

Eexponent typ. ~ 2

Chapter 7 -

o at time t.Ostwald Ripening

G i G thG i G th

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Grain GrowthGrain Growth

TR = Recrystallization

TR

Cold work state, is

A metastable state.

The ener stored Due to cold work

is the driving for

Recrystallized

grain are strain

Chapter 7 -

free.

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RecrystallizationRecrystallization Temperature,Temperature, TTRR

TR = recrystallization temperature = point of

. m R . - . m

2. Due to diffusion annealing time TR = f(t)

shorter annealing time => higher T3. Higher %CW=> lower TR strain hardening

4. Pure metals lower TR due to dislocation movements

Easier to move in pure metals => lower TR

Chapter 7 -

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Recrystallization Temperature,Recrystallization Temperature, TTRR

Chapter 7 - 49

Stages ofStages of RecrystallizationRecrystallization

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33% CW Brass 3 s 580 oC Initial Recryst.

Chapter 7 -


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4 s 580 oC Recryst. Contd 8 s 580 oC Recryst. Complete

Chapter 7 - 51


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15 min 580 oC Grain Growth 10 min 700 oC Grain Growth

Chapter 7 - 52

C ld W kC ld W k C l l tiC l l ti

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Cold WorkCold Work CalculationsCalculations

A cylindrical rod of brass originally 0.40 in (10.2 mm)

in diameter is to be cold worked by drawing. The

circular cross section will be maintained during

deformation. A cold-worked tensile strength in excess

,

%EL are desired. Further more, the final diameter

mus e . n . mm . xp a n ow s may e

accomplished.

Chapter 7 -

C ld W kC ld W k C l l ti S l tiC l l ti S l ti

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Cold WorkCold Work Calculations SolutionCalculations Solution

If we directly draw to the final diameterIf we directly draw to the final diameter

Brass

Cold

Do = 0.40 in

Work

D = 0.30 in

1001100x% xAAA

CW ffo

%843100x300

1100x4

1

2

2

2

..Df

oo

Chapter 7 -

.o

ColdworkColdwork Calc Solution: ContCalc Solution: Cont

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ColdworkColdwork Calc Solution: Cont.Calc Solution: Cont.

540420

6

For %CW= 43.8%

y = 420 MPa TS = 540 MPa > 380 MPa

Chapter 7 -

This doesnt satisfy criteria what can we do?


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380 15

12 27

ForFor %%ELEL < 15< 15

oror aa

< 27 %< 27 %CWCW

Chapter 7 - 56

OurOur working range is limited to %working range is limited to %CWCW= 12= 12--2727

ColdworkColdwork CalcCalc SolnSoln:: RecrystallizationRecrystallization

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ColdworkColdwork CalcCalc SolnSoln:: RecrystallizationRecrystallization

Cold draw-anneal-cold draw again

For objective we need a cold work of %CW 12-27

Well use %CW= 20

Diameter after first cold draw (before 2nd cold draw)?

mus e ca cu a e as o ows:

%11001%

2

2

2

2

2

2 CWDxD

CW ff

0202

50

2 %1

.

f CWD

50

202 .

fDD

02

1001

2050.

Chapter 7 - 57

100021 ..f

n erme a e ame er =

Cold Work Calculations:Cold Work Calculations: SolutionSolution

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Cold Work Calculations:Cold Work Calculations: SolutionSolution

Summary:

= =

%CW1 1 0.3350.4

2

x100 30

2. Anneal above D02 =Df1

=

=

. . .

2010030

1%

2

2

x.

CWMPa340y

Therefore, meets all requirements

.

24% EL

Chapter 7 -

Rate ofRate of RecrystallizationRecrystallization

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Rate ofRate of RecrystallizationRecrystallization

kT

ERtR logloglog 0 start

50%

T

BCtlog RT1 finish

t/R 1:note

Hot work above TR

Cold work below TR

log t

ma er gra ns

stronger at low temperature

Chapter 7 - 59

SummarySummary

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SummarySummary

Dislocations are observed primarily in metals

an a oys.

Strength is increased by making dislocationmotion difficult.

Particular ways to increase strength are to:

--decrease grain size

-- --precipitate strengthening

--cold work

eat ng annea ng can re uce s ocat on ens ty

and increase grain size. This decreases the strength.

Chapter 7 - 60

HomeworkHomework

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HomeworkHomework

Problems: 7.9, 7.12, 7.13, 7.15, 7.17, 7.19

7.27, 7.29, 7.31, 7.32, 7.36, 7.41,

7.D3, 7.D4.

Due date:

.

Chapter 7 - 61

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Advanced Topics in DislocationAdvanced Topics in Dislocation

PhenomenaPhenomena

Chapter 7 - 62

Slip in a Perfect LatticeSlip in a Perfect Lattice

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First hint as to why therehould be cr stalline de ects

involved!!!

Chapter 7 - 63


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Chapter 7 - 64


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Chapter 7 - 65

Atomic movements near dislocation inAtomic movements near dislocation in

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slip (plastic deformation)slip (plastic deformation)

Chapter 7 - 66

Why ceramics do not exhibitWhy ceramics do not exhibit plastic deformationplastic deformation

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yy pp

at ambient Temperatures?at ambient Temperatures?

Chapter 7 - 67


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Chapter 7 - 68


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yy pp

at ambient Temperatures?at ambient Temperatures?

Chapter 7 - 69

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Chapter 7 - 70

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Stages of DislocationStages of Dislocation slip in FCC Metalsslip in FCC Metals

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Chapter 7 - 72

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Chapter 7 - 73

the slide

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Forces on DislocationsForces on Dislocations

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Chapter 7 - 75

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DislocationDislocation SourcesSources

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Chapter 7 -77

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