Chapter 8 - 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 propertie Chapter 8: Deformation & Strengthening Mechanisms
Dec 16, 2015
Chapter 8 - 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: Deformation & Strengthening
Mechanisms
Chapter 8 - 2
Dislocations & Materials Classes
• Covalent Ceramics (Si, diamond): Motion difficult - directional (angular) bonding
• Ionic Ceramics (NaCl): Motion difficult - need to avoid nearest neighbors of like sign (- and +)
+ + + +
+++
+ + + +
- - -
----
- - -
• Metals (Cu, Al): Dislocation motion easiest - non-directional bonding - close-packed directions for slip
electron cloud ion cores
++
++
++++++++ + + + + +
+++++++
Chapter 8 - 3
Dislocation Motion
Dislocation 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.
• If dislocations can't move, plastic deformation doesn't occur!
Adapted from Fig. 8.1, Callister & Rethwisch 3e.
Chapter 8 - 4
Dislocation Motion
• A dislocation moves along a slip plane in a slip direction perpendicular to the dislocation line
• The slip direction is the same as the Burgers vector direction
Edge dislocation
Screw dislocation
Adapted from Fig. 8.2, Callister & Rethwisch 3e.
Chapter 8 - 5
Slip System– Slip plane - plane on which easiest slippage occurs
• Highest planar densities (and large interplanar spacings)
– Slip directions - directions of movement • Highest linear densities
Deformation Mechanisms
Adapted from Fig. 8.6, Callister & Rethwisch 3e.
– 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.
Chapter 8 - 6
Stress and Dislocation Motion• Resolved shear stress, R
– results from applied tensile stresses
slip plane
normal, ns
Resolved shear stress: R =Fs/As
slip
directi
on
AS
R
R
FS
slip
directi
on
Relation between and R
R =FS /AS
Fcos A/cos
F
FS
nS
AS
A
Applied tensile stress: = F/A
slip
directi
on
FA
F
coscosR
Chapter 8 - 7
• Condition for dislocation motion: CRSS R
• Ease of dislocation motion depends on crystallographic orientation
10-4 GPa to 10-2 GPa
typically
coscosR
Critical Resolved Shear Stress
maximum at = = 45º
R = 0
=90°
R = /2=45°=45°
R = 0
=90°
Chapter 8 - 8
Single Crystal Slip
Adapted from Fig. 8.8, Callister & Rethwisch 3e.
Adapted from Fig. 8.9, Callister & Rethwisch 3e.
Chapter 8 - 9
Ex: Deformation of single crystal
So the applied stress of 6500 psi will not cause the crystal to yield.
MPa 20.7
cos cos
= 35°
= 60°crss = 20.7 MPa
a) Will the single crystal yield? b) If not, what stress is needed?
= 6500 psi
Adapted from Fig. 8.7, Callister & Rethwisch 3e.
(45 MPa)
(45 MPa) (0.41)
18.5 MPa crss
(cos35)
(cos60)
20.7 MPa
Chapter 8 - 10
Ex: Deformation of single crystal
psi 732541.0
psi 3000
coscoscrss
y
What stress is necessary (i.e., what is the yield stress, y)?
)41.0(cos cos psi 3000crss yy
psi 7325 y
So for deformation to occur the applied stress must be greater than or equal to the yield stress
Chapter 8 - 11
• Stronger - grain boundaries pin deformations
• Slip planes & directions (, ) change from one crystal to another.
• R will vary from one crystal to another.
• The crystal with the largest R yields first.
• Other (less favorably oriented) crystals yield later.
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].)
Slip Motion in Polycrystals
300 m
Chapter 8 - 12
• Can be induced by rolling a polycrystalline metal
- before rolling
235 m
- isotropic since grains are approx. spherical & randomly oriented.
- after rolling
- anisotropic since rolling affects grain orientation and shape.
rolling direction
Adapted from Fig. 8.11, 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.)
Anisotropy in y
Chapter 8 - 13
side view
1. Cylinder of tantalum machined from a rolled plate:
rolli
ng d
irect
ion
2. Fire cylinder at a target.
• The noncircular end view shows anisotropic deformation of rolled material.
endview
3. Deformed cylinder
platethicknessdirection
Photos courtesyof G.T. Gray III,Los AlamosNational Labs. Used withpermission.
Anisotropy in Deformation
Chapter 8 - 14
4 Strategies for Strengthening Metals: 1: Reduce Grain Size
• Grain boundaries are barriers to slip.• Barrier "strength" increases with Increasing angle of misorientation.• Smaller grain size: more barriers to slip.
• Hall-Petch Equation: 21 /yoyield dk
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
• Impurity atoms distort the lattice & generate stress.• Stress can produce a barrier to dislocation motion.
4 Strategies for Strengthening Metals: 2: Solid Solutions
• Smaller substitutional impurity
Impurity generates local stress at A and B that opposes dislocation motion to the right.
A
B
• Larger substitutional impurity
Impurity generates local stress at C and D that opposes dislocation motion to the right.
C
D
Chapter 8 - 16
Stress Concentration at Dislocations
Adapted from Fig. 8.4, Callister & Rethwisch 3e.
Chapter 8 - 17
Strengthening by Alloying
• small impurities tend to concentrate at dislocations• reduce mobility of dislocation increase strength
Adapted from Fig. 8.17, Callister & Rethwisch 3e.
Chapter 8 - 18
Strengthening by Alloying
• large impurities concentrate at dislocations on low density side
Adapted from Fig. 8.18, Callister & Rethwisch 3e.
Chapter 8 - 19
Ex: Solid SolutionStrengthening in Copper
• Tensile strength & yield strength increase with wt% Ni.
• Empirical relation:
• Alloying increases y and TS.
21 /y C~
Adapted from Fig. 8.16 (a) and (b), Callister & Rethwisch 3e.
Ten
sile
str
engt
h (M
Pa)
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
180
0 10 20 30 40 50
Chapter 8 - 20
• Hard precipitates are difficult to shear. Ex: Ceramics in metals (SiC in Iron or Aluminum).
• Result:S
~y
1
4 Strategies for Strengthening Metals: 3: Precipitation Strengthening
Large shear stress needed to move dislocation toward precipitate and shear it.
Dislocation “advances” but precipitates act as “pinning” sites with
S.spacing
Side View
precipitate
Top View
Slipped part of slip plane
Unslipped part of slip plane
Sspacing
Chapter 8 - 21
• Internal wing structure on Boeing 767
• Aluminum is strengthened with precipitates formed by alloying.
Adapted from chapter-opening photograph, Chapter 11, Callister & Rethwisch 3e. (courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)
1.5m
Application: Precipitation Strengthening
Adapted from chapter-opening photograph, Chapter 11, Callister & Rethwisch 3e. (courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)
Chapter 8 - 22
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
tensile force
AoAddie
die
-Extrusion
ram billet
container
containerforce
die holder
die
Ao
Adextrusion
100 x %o
do
A
AACW
-Rolling
roll
AoAd
roll
Chapter 8 - 23
• Ti alloy after cold working:
• Dislocations entangle with one another during cold work.• Dislocation motion becomes more difficult.
Adapted from Fig. 5.11, Callister & Rethwisch 3e. (Fig. 5.11 is courtesy of M.R. Plichta, Michigan Technological University.)
Dislocations During Cold Work
0.9 m
Chapter 8 - 24
Result of Cold Work
Dislocation density =
– Carefully grown single crystal
ca. 103 mm-2
– Deforming sample increases density
109-1010 mm-2
– Heat treatment reduces density
105-106 mm-2
• Yield stress increases as d increases:
total dislocation lengthunit volume
large hardening
small hardening
y0 y1
Chapter 8 - 25
Effects of Stress at Dislocations
Adapted from Fig. 8.5, Callister & Rethwisch 3e.
Chapter 8 - 26
Impact of Cold Work
Adapted from Fig. 8.20, Callister & Rethwisch 3e.
• Yield strength (y) increases.• Tensile strength (TS) increases.• Ductility (%EL or %AR) decreases.
As cold work is increased
Chapter 8 - 27
• What is the tensile strength & ductility after cold working?
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.), American Society for Metals, 1979, p. 276 and 327.)
%6.35100 x %2
22
o
do
r
rrCW
Cold Work Analysis
% Cold Work
100
300
500
700
Cu
200 40 60
yield strength (MPa)
y = 300MPa
300MPa
% Cold Work
tensile strength (MPa)
200Cu
0
400
600
800
20 40 60
ductility (%EL)
% Cold Work
20
40
60
20 40 6000
Cu
Do =15.2mm
Cold Work
Dd =12.2mm
Copper
340MPa
TS = 340MPa
7%
%EL = 7%
Chapter 8 - 28
• Results for polycrystalline iron:
• y and TS decrease with increasing test temperature.• %EL increases with increasing test temperature.• Why? Vacancies help dislocations move past obstacles.
Adapted from Fig. 7.14, Callister & Rethwisch 3e.
- Behavior vs. Temperature
2. vacancies replace atoms on the disl. half plane
3. disl. glides past obstacle
-200C
-100C
25C
800
600
400
200
0
Strain
Str
ess
(M
Pa)
0 0.1 0.2 0.3 0.4 0.5
1. disl. trapped by obstacle
obstacle
Chapter 8 - 29
• 1 hour treatment at Tanneal... decreases TS and increases %EL.• Effects of cold work are reversed!
• 3 Annealing stages to 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.)
Effect of Heating After %CW te
nsi
le s
tre
ngth
(M
Pa)
duc
tility
(%
EL
)tensile strength
ductility
Recovery
Recrystallization
Grain Growth
600
300
400
500
60
50
40
30
20
annealing temperature (ºC)200100 300 400 500 600 700
Chapter 8 - 30
Annihilation reduces dislocation density.
Recovery
• Scenario 1Results from diffusion
• Scenario 2
4. opposite dislocations
meet and annihilate
Dislocations annihilate and form a perfect atomic plane.
extra half-plane of atoms
extra half-plane of atoms
atoms diffuse to regions of tension
2. grey atoms leave by vacancy diffusion allowing disl. to “climb”
R
1. dislocation blocked; can’t move to the right
Obstacle dislocation
3. “Climbed” disl. can now move on new slip plane
Chapter 8 - 31
• New grains are formed that: -- have a small dislocation density -- are small -- consume cold-worked grains.
Adapted from Fig. 8.21 (a),(b), Callister & Rethwisch 3e. (Fig. 8.21 (a),(b) are courtesy of J.E. Burke, General Electric Company.)
33% coldworkedbrass
New crystalsnucleate after3 sec. at 580C.
0.6 mm 0.6 mm
Recrystallization
Chapter 8 - 32
• All cold-worked grains are consumed.
Adapted from Fig. 8.21 (c),(d), Callister & Rethwisch 3e. (Fig. 8.21 (c),(d) are courtesy of J.E. Burke, General Electric Company.)
After 4seconds
After 8seconds
0.6 mm0.6 mm
Further Recrystallization
Chapter 8 - 33
• At longer times, larger grains consume smaller ones. • Why? Grain boundary area (and therefore energy) is reduced.
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.)
Grain Growth
• Empirical Relation:
Ktdd no
n elapsed time
coefficient dependenton material and T.
grain diam.at time t.
exponent typ. ~ 2
Ostwald Ripening
Chapter 8 - 34
TR
Adapted from Fig. 8.22, Callister & Rethwisch 3e.
º
º
TR = recrystallization temperature
Chapter 8 - 35
Recrystallization Temperature, TR
TR = recrystallization temperature = point of highest rate of property change1. 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
• Easier to move in pure metals => lower TR
Chapter 8 - 36
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. 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 - 37
Coldwork Calculations Solution
If we directly draw to the final diameter what happens?
%CW Ao Af
Ao
x 100 1 Af
Ao
x 100
1 Df2 4
Do2 4
x 100 1 0.30
0.40
2
x 100 43.8%
Do = 0.40 in
BrassCold Work
Df = 0.30 in
Chapter 8 - 38
Coldwork Calc Solution: Cont.
• For %CW = 43.8%
540420
y = 420 MPa– TS = 540 MPa > 380 MPa
6
– %EL = 6 < 15• This doesn’t satisfy criteria…… what can we do?
Adapted from Fig. 8.19, Callister & Rethwisch 3e.
Chapter 8 - 39
Coldwork Calc Solution: Cont.
380
12
15
27
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.
Chapter 8 - 40
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
02
2
100
%1
.
f CW
D
D
50
202
100%
1.
f
CW
DD
m 335010020
130050
021 ..DD.
f
Intermediate diameter =
Chapter 8 - 41
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 Df 2 =0.30 m
Therefore, meets all requirements
20100 3350
301%
2
2
x
.
.CW
24%
MPa 400
MPa 340
EL
TSy
%CW1 10.335
0.4
2
x 100 30
Fig 7.19
Chapter 8 - 42
Rate of Recrystallization
• Hot work above TR
• Cold work below TR
• Smaller grains – stronger at low temperature– weaker at high temperature
t/RT
BCt
kT
ERtR
1:note
log
logloglog 0
RT1
log t
start
finish
50%
Chapter 8 - 4343
Mechanical Properties of Polymers – Stress-Strain Behavior
• Fracture strengths of polymers ~ 10% of those for metals
• Deformation strains for polymers > 1000%
– for most metals, deformation strains < 10%
brittle polymer
plasticelastomer
elastic moduli – less than for metals Adapted from Fig. 7.22,
Callister & Rethwisch 3e.
Chapter 8 - 4444
Mechanisms of Deformation—Brittle Crosslinked and Network Polymers
brittle failure
plastic failure
(MPa)
x
x
aligned, crosslinkedpolymer Stress-strain curves adapted from Fig. 7.22,
Callister & Rethwisch 3e.
InitialNear
Failure Initial
network polymer
NearFailure
Chapter 8 - 4545
Mechanisms of Deformation — Semicrystalline (Plastic) Polymers
brittle failure
plastic failure
(MPa)
x
x
crystallineblock segments
separate
fibrillar structure
near failure
crystalline regions align
onset of necking
undeformedstructure amorphous
regionselongate
unload/reload
Stress-strain curves adapted 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 - 4646
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... -- decreases chain alignment -- reverses effects of drawing (reduces E and TS, enhances %EL)• Contrast to effects of cold working in metals!
Adapted from Fig. 8.28, Callister & Rethwisch 3e. (Fig. 8.28 is from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp. 500-501.)
Chapter 8 - 4747
• 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)
Stress-strain curves adapted from Fig. 7.22, Callister & Rethwisch 3e. Inset figures along 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.)
Mechanisms of Deformation—Elastomers
(MPa)
initial: amorphous chains are kinked, cross-linked.
x
final: chainsare straighter,
stillcross-linked
elastomer
deformation is reversible (elastic)!
brittle failure
plastic failurex
x
Chapter 8 - 48
• Dislocations are observed primarily in metals and alloys.• Strength is increased by making dislocation motion difficult.
• Particular ways to increase strength are to: -- decrease grain size -- solid solution strengthening -- precipitate strengthening -- cold work
• Heating (annealing) can reduce dislocation density and increase grain size. This decreases the strength.
Summary