1. Chapter 7: Dislocations & 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?

2. Dislocations & Materials Classes
• Metals: Disl. mvt easier.
-non-directional bonding
-close-packed directions
for slip.
electron cloud
ion cores +
• Covalent Ceramics
(Si, diamond): Movement difficult.
-directional (angular) bonding
• Ionic Ceramics (NaCl):
Movement difficult.
-need to avoid ++ and - -
neighbors. + -

3. Dislocation Motion Dislocations & plastic deformation
Cubic & hexagonal metals - plastic deformation by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations).
So we saw that above the yield stress plastic deformation occurs. But how? In a perfect single crystal for this to occur every bond connecting tow planes would have to break at once! Large energy requirement
Now rather than entire plane of bonds needing to be broken at once, only the bonds along dislocation line are broken at once.
If dislocations don't move, deformation doesn't occur!
Adapted from Fig. 7.1, Callister 7e.

4. Dislocation Motion
Dislocation moves along slip plane in slip direction perpendicular to dislocation line
Slip direction same direction as Burgers vector
Edge dislocation
Adapted from Fig. 7.2, Callister 7e.
Screw dislocation

5. photomicrograph of a lithium fluoride (LiF) single crystal, the small pyramidal pits represent
those positions at which dislocations intersect the surface. The surface was polished and then
chemically treated; these “etch pits” result from localized chemical attack around the dislocations
and indicate the distribution of the dislocations. 750X

6. f03_07_pg177
Dislocation Motion
f03_07_pg177.jpg

7. Deformation Mechanisms
Slip System
Slip plane - plane allowing easiest slippage
Wide interplanar spacings - highest planar densities
Slip direction - direction of movement - Highest linear densities
FCC Slip occurs on {111} planes (close-packed) in <110> directions (close-packed)
=> total of 12 slip systems in FCC
in BCC & HCP other slip systems occur
Adapted from Fig. 7.6, Callister 7e.

8. Resolved Shear Stress
Resolved shear stress is the shear component of an applied tensile (or compressive) stress resolved along a slip plane that is other than perpendicular or parallel to the stress axis. The critical resolved shear stress is the value of resolved shear stress at which yielding begins; it is a property of the material.

9. Critical Resolved Shear Stress
• Condition for dislocation motion:
10-4 GPa to 10-2 GPa
typically
• Crystal orientation can make
it easy or hard to move dislocation
 = 60°
 = 35°

10. Single Crystal Slip Adapted from Fig. 7.9, Callister 7e.

11. Slip Motion in Polycrystals
300 mm
• Stronger - grain boundaries pin deformations
• 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 7e.
(Fig is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].)

12. Anisotropy in sy • Can be induced by rolling a polycrystalline metal
- before rolling
- after rolling
- anisotropic
since rolling affects grain
orientation and shape.
rolling direction
Adapted from Fig. 7.11, Callister 7e. (Fig 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.)
235 mm
- isotropic
since grains are
approx. spherical
& randomly
oriented.

13. f12_07_pg187 Deformation by Twinning HRTEM Image of Si
f12_07_pg187.jpg
HRTEM Image of Si

14. Difference between Slip and Twinning

15. Difference Between Slip and Twinning
Slip occurs in distinct atomic spacing multiples, whereas the atomic displacement for twinning is less than the inter-atomic separation, usually proportional to their distances from the twin plane.
for slip, the crystallographic orientation above and below the slip plane is the same both before and after the deformation; for twinning, there will be a reorientation across the twin plane.
The amount of bulk plastic deformation from twinning is normally small relative to that resulting from slip; twinning may however place new slip systems in orientations that are favorable relative to the stress axis such that the slip process can now take place.

16. 4 Strategies for Strengthening: 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:
Adapted from Fig. 7.14, Callister 7e.
(Fig is from A Textbook of Materials Technology, by Van Vlack, Pearson Education, Inc., Upper Saddle River, NJ.)

17. 4 Strategies for Strengthening: 2: Solid Solutions
• Impurity atoms distort the lattice & generate stress.
• Stress can produce a barrier to dislocation motion.
• 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

18. Stress Concentration at Dislocations
Don’t move past one another – hardens material
Adapted from Fig. 7.4, Callister 7e.

19. Strengthening by Alloying
small impurities tend to concentrate at dislocations
reduce mobility of dislocation  increase strength
Adapted from Fig. 7.17, Callister 7e.

20. Strengthening by alloying
large impurities concentrate at dislocations on low density side
Adapted from Fig. 7.18, Callister 7e.

21. Ex: Solid Solution Strengthening in Copper
• Tensile strength & yield strength increase with wt% Ni.
Tensile strength (MPa)
wt.% Ni, (Concentration C)
200
300
400 10 20 30 40 50
Yield strength (MPa)
wt.%Ni, (Concentration C) 60
120
180 10 20 30 40 50
Adapted from Fig (a) and (b), Callister 7e.
• Empirical relation:
• Alloying increases sy and TS.

22. 4 Strategies for Strengthening: 3: Precipitation Strengthening
• Hard precipitates are difficult to shear.
Ex: Ceramics in metals (SiC in Iron or Aluminum).
Side View
precipitate
Top View
Slipped part of slip plane
Unslipped part of slip plane S
spacing
Large shear stress needed
to move dislocation toward
precipitate and shear it.
Dislocation
“advances” but
precipitates act as
“pinning” sites with
spacing S .
• Result:

23. Application: Precipitation Strengthening
• Internal wing structure on Boeing 767
Adapted from chapter-opening photograph, Chapter 11, Callister 5e. (courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)
• Aluminum is strengthened with precipitates formed
by alloying.
1.5mm
Adapted from Fig , Callister 7e.
(Fig is courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.)

24. 4 Strategies for Strengthening: 4: Cold Work (%CW)
• Room temperature deformation.
• Common forming operations change the cross
sectional area:
Adapted from Fig. 11.8, Callister 7e.
-Forging A o d
force
die
blank
-Rolling
roll A o d
-Drawing
tensile
force A o d
die
-Extrusion
ram
billet
container
force
die holder
die A o d
extrusion

25. Dislocations During Cold Work
• Ti alloy after cold working:
0.9 mm
• Dislocations entangle
with one another
during cold work.
• Dislocation motion
becomes more difficult.
Adapted from Fig. 4.6, Callister 7e.
(Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological University.)

26. Result of Cold Work total dislocation length Dislocation density =
unit volume
Dislocation density =
Carefully grown single crystal
 ca. 103 mm-2
Deforming sample increases density
 mm-2
Heat treatment reduces density
 mm-2
Again it propagates through til reaches the edge
large hardening
small hardening s e y0 y1
• Yield stress increases
as rd increases:

27. Impact of Cold Work As cold work is increased
• Yield strength (sy) increases.
• Tensile strength (TS) increases.
• Ductility (%EL or %AR) decreases.
Adapted from Fig. 7.20, Callister 7e.

28. Cold Work Analysis Cu Cu Cu • What is the tensile strength &
=12.2mm
Copper
• What is the tensile strength &
ductility after cold working? D o
=15.2mm
% Cold Work
100
300
500
700 Cu 20 40 60
yield strength (MPa)
% Cold Work
tensile strength (MPa)
200 Cu
400
600
800 20 40 60
ductility (%EL)
% Cold Work 20 40 60 Cu s y
= 300MPa
300MPa
340MPa
TS = 340MPa 7%
%EL
= 7%
Adapted from Fig. 7.19, Callister 7e. (Fig 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.)

29. s- e Behavior vs. Temperature
• Results for
polycrystalline iron:
-200C
-100C
25C
800
600
400
200
Strain
Stress (MPa)
0.1
0.2
0.3
0.4
0.5
Adapted from Fig. 6.14, Callister 7e.
• sy and TS decrease with increasing test temperature.
• %EL increases with increasing test temperature.
• Why? Vacancies
help dislocations
move past obstacles. 3
. disl. glides past obstacle
2. vacancies
replace
atoms on the
disl. half
plane
1. disl. trapped
by obstacle
obstacle

30. Effect of Heating After %CW
• 1 hour treatment at Tanneal...
decreases TS and increases %EL.
• Effects of cold work are reversed!
tensile strength (MPa)
ductility (%EL)
tensile strength
ductility
Recovery
Recrystallization
Grain Growth
600
300
400
500 60 50 40 30 20
annealing temperature (ºC)
200
100
700
• 3 Annealing
stages to
discuss...
Adapted from Fig. 7.22, Callister 7e. (Fig.
7.22 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.)

31. Recovery & Dislocation Movement
Adapted from Fig. 7.5, Callister 7e.

32. Recovery tR Annihilation reduces dislocation density. • Scenario 1
Results from diffusion
extra half-plane
of atoms
Dislocations
annihilate
and form
a perfect
atomic
plane.
atoms
diffuse
to regions
of tension
• Scenario 2 tR
1. dislocation blocked;
can’t move to the right
Obstacle dislocation 3
. “Climbed” disl. can now
move on new slip plane 2
. grey atoms leave by
vacancy diffusion
allowing disl. to “climb”
4. opposite dislocations
meet and annihilate

33. f08_04_pg94
f08_04_pg94.jpg

34. Recrystallization • New grains are formed that:
-- have a small dislocation density
-- are small
-- consume cold-worked grains.
33% cold
worked
brass
0.6 mm
Adapted from Fig (a),(b), Callister 7e. (Fig (a),(b) are courtesy of J.E. Burke, General Electric Company.)
New crystals
nucleate after
3 sec. at 580C.
0.6 mm

35. Further Recrystallization
• All cold-worked grains are consumed.
After 4
seconds
After 8
0.6 mm
Adapted from Fig (c),(d), Callister 7e. (Fig (c),(d) are courtesy of J.E. Burke, General Electric Company.)

36. Grain Growth • At longer times, larger grains consume smaller ones.
• Why? Grain boundary area (and therefore energy)
is reduced.
After 8 s,
580ºC
After 15 min,
0.6 mm
Adapted from Fig (d),(e), Callister 7e. (Fig (d),(e) are courtesy of J.E. Burke, General Electric Company.)
• Empirical Relation:
elapsed time
coefficient dependent
on material and T.
grain diam.
at time t.
exponent typ. ~ 2
Ostwald Ripening

37. Grain Growth Occurs by grain boundary migration.
Large grains grow at the expense of smaller grains.
Grain Boundary movement occurs by short range diffusion of atoms from one side of the boundary to the other.

38. Grain Growth
Atoms and Grain Boundaries move in opposite directions!!!

39. TR = recrystallization temperatureTR
TR = recrystallization temperature
Adapted from Fig. 7.22, Callister 7e.

40. Recrystallization Temperature, TR
TR = Recrystallization temperature = point of highest rate of property change
Tm => TR  Tm (K)
Due to diffusion  annealing time TR = f(t) shorter annealing time => higher TR
Pure metals lower TR due to dislocation movements easier to move in pure metals => lower TR
Cold work  below TR
Hot work  above TR

41. Recrystallization Temperature for Metals

42. Summary • Dislocations are observed primarily in metals and alloys.
• Strength is increased by making dislocation
movement difficult.
• Particular ways to increase strength are to:
--decrease grain size
--solid solution strengthening
--precipitation strengthening
--cold work
• Heating (annealing) can reduce dislocation density
and increase grain size. This decreases the strength.