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2012-04-29
1
Chapter 8: Deformation & Strengthening Mechanisms
School of Mechanical Engineering
Choi Hae Jin
Chapter 8 -
Choi, Hae-Jin
Materials Science - Prof. Choi, Hae-Jin 1
ISSUES TO ADDRESS…
• Why are the number of dislocations present greatest in metals ?
• How are strength and dislocation motion related?
• Why does heating alter strength and other properties?
Chapter 8 - 2
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Dislocations & Materials Classes
• Metals (Cu, Al): Dislocation motion easiest- non-directional bonding
+
+
+
+
+++++++
+ + + + + +
+++++++
• Covalent Ceramics(Si, diamond): Motion difficult- directional (angular) bonding
g- close-packed directions
for slipelectron cloud ion cores
++++++++
Chapter 8 - 3
• Ionic Ceramics (NaCl):Motion difficult- need to avoid nearest
neighbors of like sign (- and +)
+ + + +
+++
+ + + +
- - -
----
- - -
Dislocation MotionDislocation motion & plastic deformation
• Metals - plastic deformation occurs by slip – an edge dislocation (extra half-plane of atoms) slides over adjacent plane half-planes of atoms.
Chapter 8 - 4
• If dislocations can't move, plastic deformation doesn't occur!
Adapted from Fig. 8.1, Callister & Rethwisch 3e.
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Dislocation Motion
• A dislocation moves along a slip plane in a slip directionperpendicular to the dislocation line
• The slip direction is the same as the Burgers vector directionp g
Edge dislocation
Adapted from Fig. 8.2, Callister & Rethwisch 3e.
Chapter 8 - 5
Screw dislocation
Deformation MechanismsSlip System
– Slip plane - plane on which easiest slippage occurs• Highest planar densities (and large interplanar spacings)
Slip directions directions of movement– Slip directions - directions of movement • Highest linear densities
Adapted from Fig. 8.6, Callister & Rethwisch 3e.
Chapter 8 - 6
– FCC Slip occurs on {111} planes (close-packed) in <110> directions (close-packed)
=> total of 12 slip systems in FCC– For BCC & HCP there are other slip systems.
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Stress and Dislocation Motion• Resolved shear stress, R
– results from applied tensile stresses
Resolved shear t F /A
Relation between d
Applied tensile t F/A
slip plane
normal, ns
stress: R =Fs/As
AS
R
FS
and R
R=FS/AS
Fcos A/cos
F
F
nS
A
stress: = F/A
FA
Chapter 8 -
coscosR
7
RFS ASF
Critical Resolved Shear Stress
• Condition for dislocation motion: CRSS R
• Ease of dislocation motion depends on crystallographic orientation
typicallyon crystallographic orientation
10-4 GPa to 10-2 GPa coscosR
R = 0
= /2
R = 0
Chapter 8 - 8
maximum at = = 45º
R = 0
=90°
R = /2=45°=45°
R 0
=90°
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Single Crystal Slip
Adapted from Fig. 8 9 Callister &8.9, Callister & Rethwisch 3e.
Chapter 8 - 9
Adapted from Fig. 8.8, Callister & Rethwisch 3e.
Ex: Deformation of single crystal
= 35°
= 60°crss = 20.7 MPa
a) Will the single crystal yield? b) If not, what stress is needed?
MPa 20.7
cos cos
= 35
Adapted from Fig. 8.7, Callister &
(45 MPa)
(45 MP ) (0 41) (cos35) (cos60)
Chapter 8 -
So the applied stress of 6500 psi will not cause the crystal to yield.
10
= 6500 psi
Callister & Rethwisch 3e.
(45 MPa) (0.41)
18.5 MPa crss 20.7 MPa
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Ex: Deformation of single crystal
What stress is necessary (i.e., what is the yield stress, y)?
psi 732541.0
psi 3000
coscoscrss
y
)41.0(cos cos psi 3000crss yy
S f d f ti t th li d t t
Chapter 8 - 11
psi 7325 y
So for deformation to occur the applied stress must be greater than or equal to the yield stress
Slip Motion in Polycrystals• Stronger - grain boundaries
pin deformations
• Slip planes & directions
• Slip planes & directions(, ) change from onecrystal to another.
• R will vary from onecrystal to another.
• The crystal with the
Adapted from Fig. 8.10, Callister & Rethwisch 3e.(Fig. 8.10 is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].)
Chapter 8 - 12
The crystal with thelargest R yields first.
• Other (less favorablyoriented) crystalsyield later.
g, ] )
300 m
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Anisotropy in y
• Can be induced by rolling a polycrystalline metal
- before rolling - after rollingAdapted from Fig. 8.11, Callister & Rethwisch 3e
235 m
rolling direction
Callister & Rethwisch 3e.(Fig. 8.11 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. I, Structure, p. 140, John Wiley and Sons, New York, 1964.)
Chapter 8 - 13
- isotropicsince grains areapprox. spherical& randomlyoriented.
- anisotropicsince rolling affects grainorientation and shape.
Strategies for Strengthening Metals
• Grain Size Reduction
• Solid SolutionsSolid Solutions
• Precipitation Strengthening
• Cold Work
Chapter 8 - 14
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4 Strategies for Strengthening Metals: 1: Reduce Grain Size
• Grain boundaries areb i t li
21 /yoyield dk
barriers to slip.• Barrier "strength"
increases withIncreasing angle of misorientation.
• Smaller grain size:more barriers to slip
Adapted from Fig. 8.14, Callister & Rethwisch 3e. (Fig. 8.14 is from A Textbook of Materials Technology, by Van Vlack, Pearson Education, Inc., Upper Saddle River, NJ.)
Chapter 8 - 15
more barriers to slip.
• Hall-Petch Equation:
4 Strategies for Strengthening Metals: 2: Solid Solutions
• Impurity atoms distort the lattice & generate stress.• Stress can produce a barrier to dislocation motion Stress can produce a barrier to dislocation motion.
• Smaller substitutionalimpurity
A
B
• Larger substitutionalimpurity
C
D
Chapter 8 - 16
Impurity generates local stress at Aand B that opposes dislocation motion to the right.
B
Impurity generates local stress at Cand D that opposes dislocation motion to the right.
D
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Stress Concentration at Dislocations
Chapter 8 - 17
Adapted from Fig. 8.4, Callister & Rethwisch 3e.
Strengthening by Alloying
• small impurities tend to concentrate at dislocations
• reduce mobility of dislocation increase strength
Chapter 8 - 18
Adapted from Fig. 8.17, Callister & Rethwisch 3e.
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Strengthening by Alloying
• large impurities concentrate at dislocations on low density side
Chapter 8 - 19
Adapted from Fig. 8.18, Callister & Rethwisch 3e.
Ex: Solid SolutionStrengthening in Copper
• Tensile strength & yield strength increase with wt% Ni.
Pa) a) 180
Adapted from Fig. 8.16 (a) and (b), Callister & Rethwisch 3e.
Tens
ile s
tren
gth
(MP
wt.% Ni, (Concentration C)
200
300
400
0 10 20 30 40 50 Yie
ld s
tren
gth
(MP
a
wt.%Ni, (Concentration C)
60
120
0 10 20 30 40 50
Chapter 8 - 20
• Empirical relation:
• Alloying increases y and TS.
21 /y C~
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4 Strategies for Strengthening Metals: 3: Precipitation Strengthening
• Hard precipitates are difficult to shear.Ex: Ceramics in metals (SiC in Iron or Aluminum).
Large shear stress needed to move dislocation toward precipitate and shear it.
Dislocation “advances” but precipitates act as “pinning” sites with
Side View
precipitate
Top ViewUnslipped part of slip plane
S
Chapter 8 - 21
• Result:S
~y
1
pinning sites with S.spacing
Slipped part of slip plane
Sspacing
Application:Precipitation Strengthening
• Internal wing structure on Boeing 767Adapted from chapter-opening photograph,
• Aluminum is strengthened with precipitates formedby alloying.
Adapted from chapter-
p g p g p ,Chapter 11, Callister & Rethwisch 3e. (courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)
Chapter 8 - 22
Adapted from chapteropening photograph, Chapter 11, Callister & Rethwisch 3e. (courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)
1.5m
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4 Strategies for Strengthening Metals: 4: Cold Work (%CW)
• Room temperature deformation.• Common forming operations change the cross
sectional area:
Adapted from Fig. 14.2, Callister & Rethwisch 3e.
-Forging
Ao Ad
force
dieblank
force-Drawing -ExtrusionA
-Rolling
roll
AoAd
roll
Chapter 8 - 23
tensile force
AoAddie
dieram billet
container
containerforce
die holder
die
Ao
Adextrusion
100 x %o
do
A
AACW
Dislocations During Cold Work• Ti alloy after cold working:
• Dislocations entanglewith one anotherwith one anotherduring cold work.
• Dislocation motionbecomes more difficult.
Chapter 8 - 24
Adapted from Fig. 5.11, Callister & Rethwisch 3e. (Fig. 5.11 is courtesy of M.R. Plichta, Michigan Technological University.)
0.9 m
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Result of Cold Work
Dislocation density =
– Carefully grown single crystal
total dislocation lengthunit volume
y g g y
ca. 103 mm-2
– Deforming sample increases density
109-1010 mm-2
– Heat treatment reduces density
105-106 mm-2
Chapter 8 - 25
• Yield stress increasesas d increases:
large hardening
small hardening
y0y1
Effects of Stress at Dislocations
Ad d f FiAdapted from Fig. 8.5, Callister & Rethwisch 3e.
Chapter 8 - 26
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Impact of Cold Work
As cold work is i d
Adapted from Fig. 8.20, Callister & Rethwisch 3e.
• Yield strength (y) increases.
• Tensile strength (TS) increases.
increased
Chapter 8 - 27
• Ductility (%EL or %AR) decreases.
Cold Work Analysis• What is the tensile strength &
ductility after cold working?
%6.35100x%2
22
do rr
CW
Cold Work
Copper
%6.35100 x %2 or
CW
300
500
700
Cu
yield strength (MPa)
300MPa
tensile strength (MPa)
400
600
800
ductility (%EL)
20
40
60
Cu
Do =15.2mm Dd =12.2mm
340MPa
Chapter 8 - 28
Adapted from Fig. 8.19, Callister & Rethwisch 3e. (Fig. 8.19 is adapted from Metals Handbook: Properties and Selection: Iron and Steels, Vol. 1, 9th ed., B. Bardes (Ed.), American Society for Metals, 1978, p. 226; and Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker (Managing Ed.),
% Cold Work
100
Cu
200 40 60
y = 300MPa% Cold Work
200Cu
0 20 40 60% Cold Work20 40 6000
340MPa
TS = 340MPa
7%
%EL = 7%
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Effect of Heating After %CW• 1 hour treatment at Tanneal...
decreases TS and increases %EL.• Effects of cold work are reversed!
• 3 Annealingstages todiscuss s
tren
gth
(MP
a)
uctil
ity (
%E
L)
tensile strength600
400
500
60
50
40
30
annealing temperature (ºC)200100 300 400 500 600 700
Chapter 8 - 29
discuss...Adapted from Fig. 8.22, Callister & Rethwisch 3e. (Fig. 8.22 is adapted from G. Sachs and K.R. van Horn, Practical Metallurgy, Applied Metallurgy, and the Industrial Processing of Ferrous and Nonferrous Metals and Alloys, American Society for Metals, 1940, p. 139.)
tens
ile duductility
300
400 30
20
Recrystallization• New grains are formed that:
-- have a small dislocation density-- are small
consume cold worked grains-- consume cold-worked grains.
Adapted from Fig. 8.21 (a),(b), Callister & Rethwisch 3e. (Fig. 8.21 (a),(b) are courtesy of J E B k
0.6 mm 0.6 mm
Chapter 8 - 30
J.E. Burke, General Electric Company.)
33% coldworkedbrass
New crystalsnucleate after3 sec. at 580C.
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Further Recrystallization• All cold-worked grains are consumed.
0.6 mm0.6 mm
Adapted from Fig. 8.21 (c),(d), Callister & Rethwisch 3e. (Fig. 8.21 (c),(d) are courtesy of J.E. Burke, General Electric
Chapter 8 - 31
General Electric Company.)
After 4seconds
After 8seconds
Grain Growth• At longer times, larger grains consume smaller ones. • Why? Grain boundary area (and therefore energy)
is reduced.0 6 0 6
After 8 s,580ºC
After 15 min,580ºC
0.6 mm 0.6 mm
Adapted from Fig. 8.21 (d),(e), Callister & Rethwisch 3e. (Fig. 8.21 (d),(e) are courtesy of J.E. Burke, General Electric Company.)
Chapter 8 - 32
580ºC 580ºC
• Empirical Relation:
Ktdd no
n elapsed time
coefficient dependenton material and T.
grain diam.at time t.
exponent typ. ~ 2
Ostwald Ripening
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º
TR = recrystallization temperature
TR
Adapted from Fig. 8.22, Callister & Rethwisch 3e
Chapter 8 - 33
Callister & Rethwisch 3e.
º
Recrystallization Temperature, TR
TR = recrystallization temperature = point of highest rate of property changeg p p y g1. Tm => TR 0.3-0.6 Tm (K)
2. Due to diffusion annealing time TR = f(time) shorter annealing time => higher TR
3. Higher %CW => lower TR – strain hardening
4. Pure metals lower TR due to dislocation movements
Chapter 8 -
• Easier to move in pure metals => lower TR
34
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Coldwork Calculations
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 Across section will be maintained during deformation. A cold-worked tensile strength in excess of 55,000 psi (380 MPa) and a ductility of at least 15 %EL are desired. Further more, the final diameter must be 0.30 in (7.6 mm). Explain how this may be accomplished.
Chapter 8 - 35
Coldwork Calculations Solution
If we directly draw to the final diameter what happens?
%CWAo Af
x 100 1
Af
x 100
Do = 0.40 in
BrassCold Work
Df = 0.30 in
Chapter 8 - 36
%CW o f
Ao
x 100 1 f
Ao
x 100
1 Df2 4
Do2 4
x 100 1 0.30
0.40
2
x 100 43.8%
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Coldwork Calc Solution: Cont.
F %CW 43 8%
540420
6
Adapted from Fig 8 19
Chapter 8 -
• For %CW = 43.8%
37
– y = 420 MPa– TS = 540 MPa > 380 MPa– %EL = 6 < 15
• This doesn’t satisfy criteria…… what can we do?
Adapted from Fig. 8.19, Callister & Rethwisch 3e.
Coldwork Calc Solution: Cont.
380
12
15
27
Chapter 8 - 38
For %EL > 15
For TS > 380 MPa > 12 %CW
< 27 %CW
our working range is limited to %CW = 12-27
Adapted from Fig. 8.19, Callister & Rethwisch 3e.
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Coldwork Calc Soln: RecrystallizationCold draw-anneal-cold draw again
• For objective we need a cold work of %CW 12-27
– We’ll use %CW = 20
• Diameter after first cold draw (before 2nd cold draw)?
– must be calculated as follows:
100
%1 100 1% 2
02
22
202
22 CW
D
Dx
D
DCW ff
50%
.CWD 2fD
D
Chapter 8 - 39
02
2
100
%1f CW
D
D
50
202
100%
1.
f
CWD
m 335010020
130050
021 ..DD.
f
Intermediate diameter =
Coldwork Calculations Solution
Summary:
1. Cold work D01= 0.40 in Df1 = 0.335 m
2. Anneal above D02 = Df1
3. Cold work D02= 0.335 in Df2 =0.30 m
302
MPa 340y
%CW1 10.335
0.4
2
x 100 30
Fig 7.19
Chapter 8 -
Therefore, meets all requirements
40
20100 3350
301% 2
x
.
.CW
24%
MPa 400
EL
TSy
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Mechanical Properties of Polymers –Stress-Strain Behaviorbrittle polymer
plasticelastomer
elastic moduli – less than for metals Adapted from Fig. 7.22,
Callister & Rethwisch 3e.
Chapter 8 - 4141
• Fracture strengths of polymers ~ 10% of those for metals
• Deformation strains for polymers > 1000%
– for most metals, deformation strains < 10%
Mechanisms of Deformation—Brittle Crosslinked and Network Polymers
(MPa)Near Nearbrittle failure
plastic failure
( )
x
xInitial Failure Initial Failure
Chapter 8 - 4242
aligned, crosslinkedpolymer Stress-strain curves adapted from Fig. 7.22,
Callister & Rethwisch 3e.
network polymer
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Mechanisms of Deformation —Semicrystalline (Plastic) Polymers
brittle failure(MPa)
x
fibrillar structure
nearStress-strain curves adapted from Fig 7 22 Callister &
plastic failure
x
near failureonset of
necking
unload/reload
from Fig. 7.22, Callister & Rethwisch 3e. Inset figures along plastic response curve adapted from Figs. 8.27 & 8.28, Callister & Rethwisch 3e. (Figs. 8.27 & 8.28 are from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp. 500-501.)
Chapter 8 - 4343
crystallineblock segments
separate
crystallineregions align
undeformedstructure amorphous
regionselongate
Predeformation by Drawing• Drawing…(ex: monofilament fishline)
-- stretches the polymer prior to use-- aligns chains in the stretching direction
• Results of drawing:-- increases the elastic modulus (E) in the
stretching direction-- increases the tensile strength (TS) in the
stretching direction-- decreases ductility (%EL)
• Annealing after drawing...
Adapted from Fig. 8.28, Callister & Rethwisch 3e. (Fig. 8.28 is from J.M. Schultz, Polymer Materials Science, Prentice-Hall,
Chapter 8 - 44
g g-- decreases chain alignment-- reverses effects of drawing (reduces E and
TS, enhances %EL)• Contrast to effects of cold working in metals!
Inc., 1974, pp. 500-501.)
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Mechanisms of Deformation—Elastomers
Stress-strain curves adapted from Fig. 7.22, Callister & Rethwisch 3e.Inset figures along
(MPa)brittle failurex
elastomer curve (green) adapted from Fig. 8.30, Callister & Rethwisch 3e. (Fig. 8.30 is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.)
x
final: chainsare straighter,
stillcross-linked
elastomer
plastic failurex
Chapter 8 - 45
• Compare elastic behavior of elastomers with the:-- brittle behavior (of aligned, crosslinked & network polymers), and-- plastic behavior (of semicrystalline polymers)
(as shown on previous slides)
initial: amorphous chains are kinked, cross-linked.
deformation is reversible (elastic)!
Summary
• Dislocations are observed primarily in metalsand alloys.
St th i i d b ki di l ti• Strength is increased by making dislocationmotion difficult.
• Particular ways to increase strength are to:-- decrease grain size-- solid solution strengthening-- precipitate strengthening-- cold work
Chapter 8 - 46
cold work
• Heating (annealing) can reduce dislocation densityand increase grain size. This decreases the strength.
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