1. ISSUES TO ADDRESS...
• Why are dislocations observed primarily in metals
and alloys?
• How are strength and dislocation motion related?
• How do we increase strength?
1
• How can heating change strength and other properties?
CHAPTER 8:
DEFORMATION AND STRENGTHENING
MECHANISMS
2. 3
• Produces plastic deformation,
• Depends on incrementally breaking
bonds.
Plastically
stretched
zinc
single
crystal.
• If dislocations don't move,
deformation doesn't happen!
DISLOCATION MOTION
3. 2
• Metals: Disl. motion easier.
-non-directional bonding
-close-packed directions
for slip. electron cloud ion cores
• Covalent Ceramics
(Si, diamond): Motion hard.
-directional (angular) bonding
• Ionic Ceramics (NaCl):
Motion hard.
-need to avoid ++ and --
neighbors.
DISLOCATIONS & MATERIALS
CLASSES
4. 6
• Structure: close-packed
planes & directions
are preferred.
• Comparison among crystal structures:
FCC: many close-packed planes/directions;
HCP: only one plane, 3 directions;
BCC: none
Mg (HCP)
Al (FCC)
tensile direction
• Results of tensile
testing.
view onto two
close-packed
planes.
DISLOCATIONS & CRYSTAL STRUCTURE
5. 7
• Crystals slip due to a resolved shear stress, tR.
• Applied tension can produce such a stress.
tR cos cos
ns
A
As
STRESS AND DISLOCATION MOTION
slip plane
normal, ns
6. 8
• Condition for dislocation motion: tR tCRSS
• Crystal orientation can make
it easy or hard to move disl.
10 -4G to 10 -2G
typically
tR cos cos
CRITICAL RESOLVED SHEAR STRESS
7. 9
• Slip planes & directions
(, ) change from one
crystal to another.
• tR will vary from one
crystal to another.
• The crystal with the
largest tR yields first.
• Other (less favorably
oriented) crystals
yield later.
300 mm
DISL. MOTION IN POLYCRYSTALS
8. 10
• Grain boundaries are
barriers to slip.
• Barrier "strength"
increases with
misorientation.
• Smaller grain size:
more barriers to slip.
• Hall-Petch Equation:
g
r
a
i
n
b
o
u
n
d
a
r
y
slip plane
grain A
grain
B
yield o kyd1/2
4 STRATEGIES FOR
STRENGTHENING: 1: REDUCE GRAIN
SIZE
9. 11
• 70wt%Cu-30wt%Zn brass alloy
yield o kyd1/2
• Data:
0.75mm
GRAIN SIZE STRENGTHENING:
AN EXAMPLE
10. • Can be induced by rolling a polycrystalline metal
12
-before rolling -after rolling
235 mm
-isotropic
since grains are
approx. spherical
& randomly
oriented.
-anisotropic
since rolling affects grain
orientation and shape.
rolling direction
ANISOTROPY IN yield
11. 14
• Impurity atoms distort the lattice & generate stress.
• Stress can produce a barrier to dislocation motion.
• Smaller substitutional
impurity
• Larger substitutional
impurity
Impurity generates local shear at A
and B that opposes disl motion to the
right.
Impurity generates local shear at C
and D that opposes disl motion to the
right.
STRENGTHENING STRATEGY 2: SOLID
SOLUTIONS
12. 15
• Tensile strength & yield strength increase w/wt% Ni.
• Empirical relation:
• Alloying increases y and TS.
y ~ C1/2
EX: SOLID SOLUTION
STRENGTHENING IN COPPER
13. 16
• Room temperature deformation.
• Common forming operations change the cross
sectional area:
%CW
Ao Ad
Ao
x100
Ao Ad
force
die
blank
force
-Forging -Rolling
-Extrusion
-Drawing
tensile
force
Ao
Ad
die
die
STRENGTHENING STRATEGY : COLD
WORK (%CW)
14. 17
• Ti alloy after cold working:
• Dislocations entangle
with one another
during cold work.
• Dislocation motion
becomes more difficult.
DISLOCATIONS DURING COLD WORK
15. 18
• Dislocation density (rd) goes up:
Carefully prepared sample: rd ~ 103 mm/mm3
Heavily deformed sample: rd ~ 1010 mm/mm3
• Ways of measuring dislocation density:
OR
d
N
A
Area , A
N dislocation
pits (revealed
by etching)
dislocation
pit
r
• Yield stress increases
as rd increases:
40mm
RESULT OF COLD WORK
16. • Dislocation generate stress.
• This traps other dislocations.
20
DISLOCATION-DISLOCATION TRAPPING
17. • Yield strength ( ) increases.
• Tensile strength (TS) increases.
• Ductility (%EL or %AR) decreases.
21
y
IMPACT OF COLD WORK
18. • What is the tensile strength &
ductility after cold working?
22
%CW
ro
2 rd
2
ro
2
x100 35.6%
COLD WORK ANALYSIS
19. • Results for
polycrystalline iron:
23
• y and TS decrease with increasing test temperature.
• %EL increases with increasing test temperature.
• Why? Vacancies
help dislocations
past obstacles.
-e BEHAVIOR VS TEMPERTURE
20. • 1 hour treatment at Tanneal...
decreases TS and increases %EL.
• Effects of cold work are reversed!
24
• 3 Annealing
stages to
discuss...
EFFECT OF HEATING AFTER %CW
22. • New crystals are formed that:
--have a small disl. density
--are small
--consume cold-worked crystals.
26
33% cold
worked
brass
New crystals
nucleate after
3 sec. at 580C.
0.6 mm 0.6 mm
RECRYSTALLIZATION
23. • All cold-worked crystals are consumed.
27
After 4
seconds
After 8
seconds
0.6 mm
0.6 mm
FURTHER RECRYSTALLIZATION
24. • At longer times, larger grains consume smaller ones.
• Why? Grain boundary area (and therefore energy)
is reduced.
28
• Empirical Relation:
After 8 s,
580C
After 15 min,
580C
dn
do
n
Kt
elapsed time
coefficient dependent
on material and T.
grain diam.
at time t.
exponent typ. ~ 2
0.6 mm 0.6 mm
GRAIN GROWTH
29. 30
• Drawing...
--stretches the polymer prior to use
--aligns chains to the stretching direction
• Results of drawing:
--increases the elastic modulus (E) in the
stretching dir.
--increases the tensile strength (TS) in the
stretching dir.
--decreases ductility (%EL)
• Annealing after drawing...
--decreases alignment
--reverses effects of drawing.
• Compare to cold working in metals!
Adapted from Fig. 15.12, Callister
6e. (Fig. 15.12 is from J.M.
Schultz, Polymer Materials
Science, Prentice-Hall, Inc.,
1974, pp. 500-501.)
PREDEFORMATION BY DRAWING
30. 31
• Thermoplastics:
--little cross linking
--ductile
--soften w/heating
--polyethylene (#2)
polypropylene (#5)
polycarbonate
polystyrene (#6)
• Thermosets:
--large cross linking
(10 to 50% of mers)
--hard and brittle
--do NOT soften w/heating
--vulcanized rubber, epoxies,
polyester resin, phenolic resin
Callister,
Fig. 16.9
T
Molecular weight
Tg
Tm
mobile
liquid
viscous
liquid
rubber
tough
plastic
partially
crystalline
solid
crystalline
solid
THERMOPLASTICS VS THERMOSETS
31. 32
• Compare to responses of other polymers:
--brittle response (aligned, cross linked & networked case)
--plastic response (semi-crystalline case)
TENSILE RESPONSE: ELASTOMER
CASE
32. 33
• Dislocations are observed primarily in metals
and alloys.
• Here, 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.
SUMMARY
