1. CHAPTER 8: DEFORMATION AND STRENGTHENING MECHANISMS
ISSUES TO ADDRESS...
• Why are dislocations observed primarily in metals
and alloys?
• How are strength and dislocation motion related?
• How do we increase strength?
• How can heating change strength and other properties? 1

2. DISLOCATION MOTION • Produces plastic deformation,
Plastically
stretched
zinc
single
crystal.
• Produces plastic deformation,
• Depends on incrementally breaking
bonds.
• If dislocations don't move,
deformation doesn't happen! 3

3. DISLOCATIONS & MATERIALS CLASSES
• 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. 2

4. DISLOCATIONS & CRYSTAL STRUCTURE
• Structure: close-packed
planes & directions
are preferred.
view onto two
close-packed
planes.
• Comparison among crystal structures:
FCC: many close-packed planes/directions;
HCP: only one plane, 3 directions;
BCC: none
• Results of tensile
testing.
Mg (HCP)
tensile direction
Al (FCC) 6

5. STRESS AND DISLOCATION MOTION
• Crystals slip due to a resolved shear stress, tR.
• Applied tension can produce such a stress.
slip plane
normal, ns
direction
slip
direction
slip
direction
slip 7

6. CRITICAL RESOLVED SHEAR STRESS
• Condition for dislocation motion:
• Crystal orientation can make
it easy or hard to move disl. 8

7. DISL. MOTION IN POLYCRYSTALS
• Slip planes & directions
(l, f) change from one
crystal to another.
• tR will vary from one
• The crystal with the
largest tR yields first.
• Other (less favorably
oriented) crystals
yield later.
300 mm 9

8. 4 STRATEGIES FOR STRENGTHENING: 1: REDUCE GRAIN SIZE
• Grain boundaries are
barriers to slip.
• Barrier "strength"
increases with
misorientation.
• Smaller grain size:
more barriers to slip.
• Hall-Petch Equation: 10

9. GRAIN SIZE STRENGTHENING: AN EXAMPLE
• 70wt%Cu-30wt%Zn brass alloy
• Data:
0.75mm 11

10. • Can be induced by rolling a polycrystalline metal
ANISOTROPY IN syield
• Can be induced by rolling a polycrystalline metal
-before rolling
-after rolling
rolling direction
235 mm
-isotropic
since grains are
approx. spherical
& randomly
oriented.
-anisotropic
since rolling affects grain
orientation and shape. 12

11. STRENGTHENING STRATEGY 2: SOLID SOLUTIONS
• 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. 14

12. EX: SOLID SOLUTION STRENGTHENING IN COPPER
• Tensile strength & yield strength increase w/wt% Ni.
• Empirical relation:
• Alloying increases sy and TS. 15

13. STRENGTHENING STRATEGY : COLD WORK (%CW)
• Room temperature deformation.
• Common forming operations change the cross
sectional area:
-Forging
-Rolling
-Drawing
-Extrusion 16

14. DISLOCATIONS DURING COLD WORK
• Ti alloy after cold working:
• Dislocations entangle
with one another
during cold work.
• Dislocation motion
becomes more difficult. 17

15. RESULT OF COLD WORK • Dislocation density (rd) goes up:
Carefully prepared sample: rd ~ 103 mm/mm3
Heavily deformed sample: rd ~ 1010 mm/mm3
• Ways of measuring dislocation density:
40mm OR
• Yield stress increases
as rd increases: 18

16. DISLOCATION-DISLOCATION TRAPPING
• Dislocation generate stress.
• This traps other dislocations. 20

17. IMPACT OF COLD WORK • Yield strength (s ) increases.
• Tensile strength (TS) increases.
• Ductility (%EL or %AR) decreases. y 21

18. COLD WORK ANALYSIS • What is the tensile strength &
ductility after cold working? 22

19. s-e BEHAVIOR VS TEMPERTURE
• Results for
polycrystalline iron:
• sy and TS decrease with increasing test temperature.
• %EL increases with increasing test temperature.
• Why? Vacancies
help dislocations
past obstacles. 23

20. EFFECT OF HEATING AFTER %CW
• 1 hour treatment at Tanneal...
decreases TS and increases %EL.
• Effects of cold work are reversed!
• 3 Annealing
stages to
discuss... 24

21. RECOVERY Annihilation reduces dislocation density. • Scenario 125

22. RECRYSTALLIZATION • New crystals are formed that:
--have a small disl. density
--are small
--consume cold-worked crystals.
0.6 mm
0.6 mm
33% cold
worked
brass
New crystals
nucleate after
3 sec. at 580C. 26

23. FURTHER RECRYSTALLIZATION
• All cold-worked crystals are consumed.
0.6 mm
0.6 mm
After 4
seconds
After 8
seconds 27

24. GRAIN 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
coefficient dependent
on material and T.
• Empirical Relation:
exponent typ. ~ 2
elapsed time
grain diam.
at time t. 28

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. TENSILE RESPONSE: BRITTLE & PLASTIC29

29. PREDEFORMATION BY 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
--decreases ductility (%EL)
• Annealing after drawing...
--decreases alignment
--reverses effects of drawing.
• Compare to cold working in metals!
Adapted from Fig , Callister 6e. (Fig is from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp ) 30

30. THERMOPLASTICS VS THERMOSETS
--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 31

31. TENSILE RESPONSE: ELASTOMER CASE
• Compare to responses of other polymers:
--brittle response (aligned, cross linked & networked case)
--plastic response (semi-crystalline case) 32

32. SUMMARY • 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. 33