1. CRITICAL RESOLVED SHEAR STRESS
• Condition for dislocation motion:
• Crystal orientation can make
it easy or hard to move disl. 5

2. 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.
Adapted from Fig. 7.10, Callister 6e.
(Fig is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].)
300 mm 6

3. Strengthening Mechanisms
Are based on idea of restricting dislocation motion.
By reducing the mobility of dislocations, metals become harder and stronger but often less ductile.

4. Strengthening Methods
1. Reduce grain size
2. Add solute atoms (solid solution strengthening)
3. Increase dislocation density (called “strain hardening” or “cold working”)

5. Grain Size Reduction
There is a crystallographic orientation mismatch across grain boundaries - which also means slip system mismatch.
Grain boundaries thus act as barriers to dislocation motion and thus localizing the dislocations
Strength, toughness and ductility are often improved.

6. Grain Boundaries are Barriers to Slip.

7. Hall-Petch Equation
Relates grain size (diameter d) and yield strength (y)
o and ky are material constants

8. Solid Solution Strengthening
Pure metals are softer and weaker than impure metals.
Impurity atoms produce lattice strains which impede dislocation motion.
Dislocations (naturally occurring) attract solute atoms, and are then “pinned”
Strength increase is often accompanied by ductility decrease .

9. STRENGTHENING STRATEGY 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. 11

10. EX: SOLID SOLUTION STRENGTHENING IN COPPER
• Tensile strength & yield strength increase w/wt% Ni.
Adapted from Fig (a) and (b), Callister 6e.
• Empirical relation:
• Alloying increases sy and TS. 12

11. Strain Hardening
Plastic strain causes increase in dislocation density.
Higher dislocation density results in more disl.-disl. strain field interactions.
Dislocations intersections are an impediment to slip
Strength increase always accompanied by ductility decrease.
Effects eliminated by annealing.

12. STRENGTHENING STRATEGY 3: COLD WORK (%CW)
• Room temperature deformation.
• Common forming operations change the cross
sectional area:
-Forging
-Rolling
Adapted from Fig. 11.7, Callister 6e.
-Drawing
-Extrusion 16

13. DISLOCATIONS DURING COLD WORK
• Ti alloy after cold working:
• Dislocations entangle
with one another
during cold work.
• Dislocation motion
becomes more difficult.
Adapted from Fig. 4.6, Callister 6e.
(Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological University.) 17

14. RESULT OF COLD WORK • Dislocation density (rd) goes up:
Carefully prepared sample: rd ~ 103 mm/mm3
Heavily deformed sample: rd ~ 1010 mm/mm3
• Yield stress increases
as rd increases: 18

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

16. IMPACT OF COLD WORK • Yield strength (s ) increases.
• Tensile strength (TS) increases.
• Ductility (%EL or %AR) decreases. y
Adapted from Fig. 7.18, Callister 6e. (Fig is from Metals Handbook: Properties and Selection: Iron and Steels, Vol. 1, 9th ed., B. Bardes (Ed.), American Society for Metals, 1978, p. 221.) 21

17. Percent Cold Work
The degree of plastic deformation is often determined by percent cold work (% CW):
When Ao and Af are initial and final areas.

18. Strength vs Cold work

19. Ductility vs Cold Work

20. s-e BEHAVIOR VS TEMPERTURE
• Results for
polycrystalline iron:
Adapted from Fig. 6.14, Callister 6e.
• sy and TS decrease with increasing test temperature.
• %EL increases with increasing test temperature.
• Why? Vacancies
help dislocations
past obstacles. 23

21. ANNEALING HEAT TREATMENT
recovery
recrystallization
grain growth
internal strain energy
dislocation density
conductivity recovered
new strain-free grains
mech properties recovered
f (time, Temperature)
recrystallization temp
@ elevated temp
reduce interfacial energy

22. 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...
Adapted from Fig. 7.20, Callister 6e. (Fig.
7.20 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.) 24

23. RECOVERY Annihilation reduces dislocation density. • Scenario 125

24. RECRYSTALLIZATION • New crystals are formed that:
--have a small disl. density
--are small
--consume cold-worked crystals.
0.6 mm
0.6 mm
Adapted from Fig (a),(b), Callister 6e. (Fig (a),(b) are courtesy of J.E. Burke, General Electric Company.)
33% cold
worked
brass
New crystals
nucleate after
3 sec. at 580C. 26

25. FURTHER RECRYSTALLIZATION
• All cold-worked crystals are consumed.
0.6 mm
0.6 mm
Adapted from Fig (c),(d), Callister 6e. (Fig (c),(d) are courtesy of J.E. Burke, General Electric Company.)
After 4
seconds
After 8
seconds 27

26. 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
Adapted from Fig (d),(e), Callister 6e. (Fig (d),(e) are courtesy of J.E. Burke, General Electric Company.)
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. 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. 29