This document discusses dislocations and strengthening mechanisms in metals. It begins by explaining how dislocations allow plastic deformation through slip and describes the slip systems in FCC and BCC crystals. It then discusses three main mechanisms for strengthening metals: reducing grain size, solid solution strengthening, and strain hardening. Reducing grain size increases the number of grain boundaries that impede dislocation motion. Solid solution strengthening involves alloying with impurity atoms that distort the lattice and impede dislocations. Strain hardening occurs through plastic deformation, which increases dislocation density and causes dislocations to impede each other. The document concludes by discussing recovery, recrystallization, and grain growth processes in metals after plastic deformation.

1. Dislocation and Strengthening
Mechanisms
Prepared by Hibistu Z.
Chapter Five
1

2. 2
Dislocations and Strengthening
What is happening during plastic deformation?
Chapter Outline
 Dislocations and Plastic Deformation
 Motion of dislocations in response to stress
 Slip Systems
 Plastic deformation in
 single crystals
 polycrystalline materials
 Strengthening mechanisms
 Grain Size Reduction
 Solid Solution Strengthening
 Strain Hardening
 Recovery, Recrystallization, and Grain Growth

3. 3
How do metals plastically deform?
Why does forging change properties?
Why deformation occurs at stresses smaller than those for
perfect crystals?
Introduction
Taylor, Orowan and Polyani 1934 :
Plastic deformation due to motion of large number
of dislocations.
Plastic deformation under shear stress

4. Why we study dislocations and strengthening
mechanisms?
With knowledge of
 the nature of dislocations and
 the role they play in the plastic deformation
process, we are able to understand the underlying
mechanisms of the techniques that are used to
strengthen and harden metals and their alloys.
Thus, it becomes possible to design and tailor
(Adjust to a specific need) the mechanical properties
of materials— for example, the strength or
toughness of a metal– matrix composite.
4

5. 5
Dislocation Motion
Dislocation motion & plastic deformation
 Metals - plastic deformation occurs by slip – an edge
dislocation (extra half-plane of atoms) slides over
adjacent plane half-planes of atoms.
• If dislocations can't move,
plastic deformation doesn't occur!
Adapted from Fig. 7.1,
Callister & Rethwisch 8e.

6. Dislocations allow deformation at much lower stress
than in a perfect crystal
Slip is The process by which plastic deformation is
produced by dislocation motion
The slip plane is the crystallographic plane of
dislocation motion in which the dislocation takes
place preferredly.
A dislocation moves along a slip plane in a slip
direction perpendicular to the dislocation line
6

7. 7
Direction of Dislocation Motion
Mixed dislocations: direction is in between parallel and
perpendicular to applied shear stress
Edge dislocation line moves parallel to applied stress
Screw dislocation line moves perpendicular to applied stress

8. Strain field around dislocations
 Atoms immediately above and adjacent to the dislocation line are
squeezed together and results in a compressive strain.
 Below the half-plane, the effect is just the opposite; lattice atoms
sustain an imposed tensile strain, These lattice distortions may be
considered to be strain fields that radiate from the dislocation line.
 Dislocations have strain fields arising from distortions at their
cores and the strain drops radially with distance from the
dislocation core
 Edge dislocations introduce compressive, tensile, and shear lattice
strains, screw dislocations introduce shear strain only.8

9. 9
Interactions between Dislocations
Strain fields around dislocations cause them to
exert force on each other.
Direction of Burgers vector  Sign
Same signs  Repel
Opposite signs  Attract (annihilate)

10. 12
Slip System
 Slip plane - Preferred planes for dislocation movement
Highest planar densities
 Slip directions Preferred crystallographic directions (slip
directions)
 Highest linear densities
Deformation Mechanisms
Adapted from Fig.
7.6, Callister &
Rethwisch 8e.
– FCC Slip occurs on {111} planes (close-packed) in <110>
directions (close-packed)
=> total of 12 slip systems in FCC
– For BCC & HCP there are other slip systems.

11.  BCC and FCC crystals have more slip systems as
compared to HCP, there are more ways for dislocation to
propagate ⇒FCC and BCC crystals are more ductile than
HCP crystals.
14

12. Slip Systems for Face-Centered Cubic, Body-Centered
Cubic, and Hexagonal Close-Packed Metals
15

13. 16
Figure
Geometric relationships between the tensile
axis, slip plane, and slip direction used in
calculating the resolved shear stress for a single
crystal.

14. 17
Stress and Dislocation Motion
• Resolved shear stress, tR
– results from applied tensile stresses
slip plane
normal, ns
Resolved shear
stress: tR =Fs/As
AS
tR
tR
FS
Relation between
s and tR
tR
= FS /AS
Fcos l A/cos f
l
F
FS
fnS
AS
A
Applied tensile
stress: = F/As
F
A
F
flst coscosR
Critical resolved shear stress is the minimum resolved
shear stress required to initiate dislocation motion
The quantity CosφCosλ is known as the SchmidFactor (M)

15. 18
• Condition for dislocation motion: CRSSttR
• Ease of dislocation motion depends on crystallographic
orientation
flst coscosR
Critical Resolved Shear Stress
t maximum at l = f = 45º
tR = 0
l = 90°
s
tR = s/2
l = 45°
f = 45°
s
tR = 0
f = 90°
s
Yield strength is the stress at which plastic deformation begins.

16. 19
Ex: Deformation of single crystal
So the applied stress of 45 MPa will not cause the
crystal to yield.

t  s cosl cosf
s  45 MPa
l = 35°
f = 60°
tcrss = 20.7 MPa
a) Will the single crystal yield?
b) If not, what stress is needed?
s = 45 MPa
Adapted from
Fig. 7.7,
Callister &
Rethwisch 8e.
MPa7.20MPa4.18
)41.0(MPa)45(
)60)(cos35cos(MPa)45(
crss tt

t 

17. 20
Ex: Deformation of single crystal
What stress is necessary (i.e., what is the
yield stress, sy)?
)41.0(coscos7.20crss yyMPa sflst 
MPa0.55
41.0
MPa0.72
coscos
crss
y 
fl
t
s
MPa5.50y ss
So for deformation to occur the applied stress must
be greater than or equal to the yield stress

18. Generally:
Resolved t (shear stress) is
maximum at l = f = 45º
And
tCRSS = sy/2 for dislocations to
move (in single crystals)

19. Determining f and l angles for Slip in Crystals
f and l angles are respectively angle between tensile
direction and Normal to Slip plane and angle between
tensile direction and slip direction (these slip directions
are material dependent)
In General for cubic xtals, angles between directions
are given by:
Thus for metals we compare Slip System (normal to
slip plane is a direction with exact indices as plane) to
applied tensile direction using this equation to determine
the values of f and l to plug into the tR equation to
determine if slip is expected
   
1 1 2 1 2 1 2
2 2 2 2 2 2
1 1 1 2 2 2
u u v v w w
Cos
u v w u v w
 
 
  
       

20. 23

21. 24

22. 25

23. Slip in a single crystal
28

24. Plastic Deformation of polycrystalline materials
 Grain orientations with respect to applied stress are
random. The dislocation motion occurs along the slip systems
with favorable orientation (i.e. that with highest resolved shear
stress).
29

25. Plastic Deformation of polycrystalline materials
 Larger plastic deformation corresponds to elongation of
grains along direction of applied stress.
30

26. Plastic deformation of polycrystalline materials
 Slip directions vary from crystal to crystal ⇒Some grains are
unfavorably oriented with respect to the applied stress (i.e. cos φ
cos λ low).
 Even those grains for which cosφ cosλ is high may be limited in
deformation by adjacent grains which cannot deform so easily
 Dislocations cannot easily cross grain boundaries because of
changes in direction of slip plane and atomic disorder at grain
boundaries
 As a result, polycrystalline metals are stronger than single crystals
31

27. Strengthening
 the ability of a metal to deform plastically depends on the
ability of dislocations to move.
 Restricting or hindering dislocation motion renders
(causes to become) a material harder and stronger
Mechanisms of strengthening in single-phase metals:
grain-size reduction
solid-solution alloying
strain hardening
Ordinarily, strengthening reduces ductility
32

28. 34
3 Strategies for Strengthening:
1: Reduce Grain Size
Grain boundaries are
barriers to slip.
 Barrier "strength"
increases with
Increasing angle of
mis orientation.
 Smaller grain size:
more barriers to slip.

29. Strengthening by grain-size reduction (II)
 The finer the grains, the larger the area of grain
boundaries that impedes (Be a hindrance or obstacle to )
dislocation motion. Grain-size reduction usually improves
toughness as well. Usually, the yield strength varies with
grain size d according to Hall-Petch equation:
 where σo and ky are constants for a particular material, d is
the average grain diameter.
35

30.  Grain size d can be controlled by the rate of solidification, by
plastic deformation and by appropriate heat treatment. 36

31. 39
3 Strategies for Strengthening:
2: Form Solid Solutions
 Impurity atoms distort the lattice & generate lattice strains.
 These strains can act as barriers to dislocation motion.

32. 40
Lattice Strains Around Dislocations
Adapted from Fig. 7.4,
Callister & Rethwisch 8e.

33. 41
Strengthening by Solid
Solution Alloying
Small impurities tend to concentrate at dislocations
(regions of compressive strains) - partial cancellation
of dislocation compressive strains and impurity atom
tensile strains
Reduce mobility of dislocations and increase
strength

34. 42
Strengthening by Solid
Solution Alloying
 Large impurities tend to concentrate at
dislocations (regions of tensile strains)

35. 43

36. 3. Strengthening by increase of dislocation density (Strain
Hardening = Work Hardening = Cold Working
44
 Ductile metals become stronger when they are deformed
plastically at temperatures well below the melting point.
 The reason for strain hardening is the increase of
dislocation density with plastic deformation.
 The average distance between dislocations decreases and
dislocations start blocking the motion of each other.
cold working: is the strengthening of a metal by plastic deformation.

37. 45
3: Cold Work (Strain Hardening)
• Deformation at room temperature (for most metals).
• Common forming operations reduce the cross-sectional area:
Adapted from Fig.
11.8, Callister &
Rethwisch 8e.
-Forging
Ao Ad
force
die
blank
force-Drawing
tensile
force
Ao
Addie
die
-Extrusion
ram billet
container
container
force
die holder
die
Ao
Adextrusion
-Rolling
roll
Ao
Ad
roll

38. 46
 The percent cold work (%CW) is often used to express the
degree of plastic deformation:
where A0 is the original cross-section area,
Ad is the area after deformation.
 %CW is just another measure of the degree of plastic
deformation, in addition to strain.

39. 47
 New yield strength σyi is higher than the initial yield
strength, σyo. The reason for this effect - strain
hardening.

40. Yield strength and hardness are increasing as a result of
strain hardening but ductility is decreasing (material
becomes more brittle).
48

41. 49

42. • What are the values of yield strength, tensile strength & ductility after
cold working Cu?
100x
4
44%CW
2
22
o
do
D
DD





Mechanical Property Alterations
Due to Cold Working
Do = 15.2 mm
Cold
Work
Dd = 12.2 mm
Copper
%6.35100x
mm)2.15(
mm)2.12(mm)2.15(
CW%
2
22



100x
2
22
o
do
D
DD 

50

43. Mechanical Property Alterations
Due to Cold Working
% Cold Work
100
300
500
700
Cu
200 40 60
sy = 300 MPa
300 MPa
% Cold Work
200
Cu
0
400
600
800
20 40 60
% Cold Work
20
40
60
20 40 6000
Cu
340 MPa
TS = 340 MPa
7%
%EL = 7%
• What are the values of yield strength, tensile strength & ductility for Cu for
%CW = 35.6%?
yieldstrength(MPa)
tensilestrength(MPa)
ductility(%EL)
51

44. Recovery, recrystallization, and grain growth
52
 Plastic deformation increases dislocation density (single and
polycrystalline materials) and changes grain size distributions
(polycrystalline materials).
 This corresponds to stored strain energy in the system
(dislocation strain fields and grain distortions).
 When applied external stress is removed - most of the
dislocations, grain distortions and associated strain energy are
retained.
Restoration to the state before cold-work can be done by heat-
treatment and involves two processes: recovery and
recrystallization. These may be followed by grain growth.

45. Recovery
53
 Heating →increased diffusion →enhanced dislocation motion
→ decrease in dislocation density by annihilation, formation
of low-energy dislocation configurations →relieve of the
internal strain energy.
Recovery is a process
by which deformed
grains can reduce their
stored energy by the
removal or
rearrangement of
defects in their crystal
structure.

46. Recrystallization
54
 Even after recovery the grains can be strained. These strained grains
of cold-worked metal can be replaced, upon heating, by strain-free
grains with low density of dislocations.
 This occurs through recrystallization – nucleation and growth of
new grains.
 The driving force for recrystallization is the difference in internal
energy between strained and unstrained material.
 Grain growth involves short-range diffusion →the extend of
recrystallization depends on both temperature and time.
 Recristallization is slower in alloys as compared to pure metals.
Crystallization = Crystal growth
Recrystallization = Seed crystal

47. 55
 Recrystallization temperature: The temperature at which the process
is complete in one hour. It is typically 1/3 to 1/2 of the melting
temperature (can be as high as 0.7 Tm in some alloys).
 Recrystallization temperature increases as the %CW is decreased.
Below a "critical deformation", recrystallization does not occur.
where Tm is the absolute melting
temperature

48. 56

49. Grain growth
57
 If deformed polycrystalline material is maintained at annealing
temperature following complete recrystallization, then further
grain growth occurs.
 Driving force is reduction of the total grain boundary area and,
hence, the energy of the system. Big grains grow at the
expense of the small ones.
 Grain growth during annealing occurs in all polycrystalline
materials (i.e. they do not have to be deformed or undergo
recrystallization first).

50. 58
 Boundary motion occurs by short range diffusion of atoms across
the grain boundary →strong temperature dependence of the grain
growth.

51. 59

52. 60
Quiz Section B @ 04/04/2010 E .C
1) Determine the tensile stress that
is applied along the axis of a
silver crystal to cause slip on the
slip system The critical
resolved shear stress is 6MPa
]011[
1]1)[011(1

53. 61
Thank you so much