Strengthening mechanisms
Solid solution strengthening
Precipitation
hardening
http://www.tf.uni-kiel.de/matwis/amat/iss/index.html
Strain hardening
Grain size reduction
37
Strain Hardening
• Deformation at room temperature (for most metals).
• Common forming operations reduce the cross-sectional area
38
Flashback: Mechanical properties
F
Strength: maximum stress values
Engineering tensile stress
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True tensile stress
F
=
A0
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T
F
=
Ai
Ductility: plastic strain at fracture
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%EL =
lf
l0
l0
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⇤ 100%
%RA =
A0
Af
A0
⇤ 100%
39
Strain Hardening
• Deformation at room temperature (for most metals).
• Common forming operations reduce the cross-sectional area
Ao − Ad
%CW =
x 100
Ao
40
Grain Structure Before and After Heavy Deformation (Rolling)
before rolling
rolling direction
https://en.wikipedia.org/wiki/Rolling_(metalworking)
after rolling
adapted from Fig. 7.11 Callister Textbook
41
Strain hardening — dislocation interaction
•
Forming processes lead to introduction of more defects
undeformed:
dislocation density
= 103 cm-2
0%CW
25%CW
Dislocations entangle
with one another during
cold work.
Dislocation motion
becomes more
difficult.
deformed:
dislocation density
= 1010 cm-2
50%CW
from: Schaffer, J.P. et al: The Science and Design of Engineering Materials 2nd Ed., WCB/McGraw-Hill, 1999: ISBN: 0-256-24766-8
out of print
42
Strengthening Mechanisms and Annealing
An application calls for a brass rod of 7.5 mm diameter and the following mechanical properties:
minimum tensile strength = 380 MPa
minimum ductility = 15 %EL
The only brass material available has a diameter of 10 mm, a tensile strength of 310 MPa and a ductility
of 67 %EL.
How can we achieve the geometry and property requirements?
Impact of cold work
low carbon steel
As cold work is increased
•
•
•
Adapted from Fig. 7.20, Callister & Rethwisch 8e.
Yield strength (σy)
increases
Tensile strength (TS)
increases
Ductility (%EL or %RA)
decreases
43
Recovery, Recrystallization and Grain Growth
•
Is there a way to repair the worst defects without undoing the benefits of
cold work?
Annealing
0%CW
25%CW
heat treatment to reduce
the defect concentration
and regain some
ductility
f(T, t, %CW, material)
50%CW
from: Schaffer, J.P. et al: The Science and Design of Engineering Materials 2nd Ed., WCB/McGraw-Hill, 1999: ISBN: 0-256-24766-8
out of print
44
Annealing Treatment Brass Alloy
1 hour treatment
@ Tanneal
Recovery
Grain Growth
Stages of Annealing
Recrystallization
Recovery, Recrystallization
Adapted from Fig. 7.22, Callister & Rethwisch 8e. (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.)
45
Annealing: Recovery
heat treatment at low temperatures (or short times)
➜dislocations get
eliminated or rearranged
into arrays that
minimize energy
driving force: Strain
field energy around
dislocations
tilt boundary
46
Annealing: Recovery
even if half the
dislocations get
annihilated there
are still a lot left
47
Annealing: Recrystallization
New grains are formed that:
• have low dislocation densities ⬌ internal energy decrease
• are small in size
• consume and replace parent cold-worked grains.
0.6 mm
33% cold
worked
brass
0.6 mm
New crystals
nucleate after
3 sec. at 580°C.
Adapted from Fig. 7.21(a),(b), Callister & Rethwisch 8e. (Fig. 7.21(a),
(b) are courtesy of J.E. Burke, General Electric Company.)
0.6 mm
0.6 mm
After 4
seconds
After 8
seconds
48
Grain Growth
• At high temperatures (or longer times),
average grain size increases.
0.6 mm
0.6 mm
driving force: reduction
in grain boundary area
coefficient dependent
on material and T.
• Empirical Relation:
After 8 s,
580ºC
After 15 min,
580ºC
Adapted from Fig. 7.21(d),(e), Callister & Rethwisch 8e. (Fig. 7.21(d),
(e) are courtesy of J.E. Burke, General Electric Company.)
exponent typ. ~ 2
grain diam.
n
d
at time t.
n
o
− d = Kt
elapsed time
49
Summary: Recrystallization Temperature
º
TR = recrystallization temperature
0.4 - 0.7 Tmelt [K]
TR
Recrystallization Temperature
Temperature at which
recrystallization just reaches
completion in 1h
º
Adapted from Fig. 7.22, Callister & Rethwisch 8e.
50
Summary: Recrystallization Temperature
º
TR = recrystallization temperature
0.4 - 0.7 Tmelt [K]
TR
For a specific metal/alloy
TR depends on:
• %CW
• purity of the metal
º
Adapted from Fig. 7.22, Callister & Rethwisch 8e.
50
Coldworking and Annealing Summary
Cold working and annealing are utilized
•
to facilitate large amounts of deformation in forming
processes while retaining specific mechanical properties
e.g. production of thin sheets and wires
•
to achieve a specific microstructure
e.g. large grains exhibit better electrical or magnetic properties;
small grains have an increased strength
51
Deformation - microstructure relationship
deformation / %CW
An
nea
ling
Tem
per
Grain size
atu
re
Effect of prior deformation on annealing temperature
52
Deformation - microstructure relationship
An
deformation / %CW
nea
ling
Tem
per
Grain size
atu
re
Effect of prior deformation on grain size
53
Deformation - microstructure relationship
An
deformation / %CW
nea
ling
Tem
per
Grain size
atu
re
Effect of annealing temperature on grain size
54
Cold working vs. Hot working
• Hot working 
deformation above TR
Continuous recrystallization during the hot working process
large deformations possible
• Cold working 
deformation below TR
better control of final dimensions
55
Practice Problems Chapter 7
WileyPlus: Practice Deformation Strengthening
and Recrystallization
Callister 10th Edition
Chapter 7
7.01, 7.04, 7.11-7.13, 7.18, 7.29, 7.30
57