facansy
TRANSCRIPT
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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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Strategies for Strengthening:Strategies for Strengthening:
. e uce ra n ze on. e uce ra n ze on
Very difficult
to synthesize polycrystalline
materials with d
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Strategies for Strengthening:Strategies for Strengthening:
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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StrategiesStrategies for Strengthening:for Strengthening:
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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StrategiesStrategies for Strengthening:for Strengthening:
. 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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Stages ofStages of RecrystallizationRecrystallization
33% CW Brass 3 s 580 oC Initial Recryst.
Chapter 7 -
Stages ofStages of RecrystallizationRecrystallization
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Stages ofStages of RecrystallizationRecrystallization
4 s 580 oC Recryst. Contd 8 s 580 oC Recryst. Complete
Chapter 7 - 51
Stages ofStages of RecrystallizationRecrystallization
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Stages ofStages of RecrystallizationRecrystallization
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?
ColdworkColdwork Calc Solution: Cont.Calc Solution: Cont.
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ColdworkColdwork Calc Solution: Cont.Calc Solution: Cont.
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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Slip in a Perfect LatticeSlip in a Perfect Lattice
First hint as to why therehould be cr stalline de ects
involved!!!
Chapter 7 - 63
Slip in a Perfect LatticeSlip in a Perfect Lattice
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Slip in a Perfect LatticeSlip in a Perfect Lattice
Chapter 7 - 64
Slip in a Perfect LatticeSlip in a Perfect Lattice
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Slip in a Perfect LatticeSlip in a Perfect Lattice
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
Why ceramics do not exhibitWhy ceramics do not exhibit plastic deformationplastic deformation
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Chapter 7 - 68
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 - 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