Dislocations are observed primarily in metals and alloys because the metallic and ionic bonding allows for easier dislocation motion compared to covalent and directional bonding in ceramics. Strength is related to dislocation motion, with higher strength occurring when dislocation motion is impeded. Key ways to increase strength discussed are decreasing grain size, solid solution strengthening, precipitate strengthening, and cold working, all of which make dislocation motion more difficult. Heating can reduce strength by allowing recovery processes like dislocation annihilation and recrystallization, which reduce dislocation density and increase grain size.

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 kyd1/2
4 STRATEGIES FOR
STRENGTHENING: 1: REDUCE GRAIN
SIZE

9. 11
• 70wt%Cu-30wt%Zn brass alloy
yield  o kyd1/2
• 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

21. Annihilation reduces dislocation density.
25
• Scenario 1
• Scenario 2
RECOVERY

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

27. Example
Using the diagram,
compute the time
for the average
grain size to
increase form 0.01-
mm to 0.1-mm at
(a) 500 oC and (b)
600 oC

28. 29
TENSILE RESPONSE: BRITTLE & PLASTIC

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