Post on 26-Mar-2021
Chapter 7Dislocations & Strengthening Mechanisms
11/14/2015
11:31 AM
Mohammad Suliman Abuhaiba, Ph.D., PE1
HomeWork Assignment
7, 12, 17, 24, 29, 41, D7
Due Sunday 8/11/2015
4th Exam is on Tuesday 17/11/2015
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WHY STUDY Dislocations and Strengthening Mechanisms?
Understand techniques used to
strengthen & harden metals and
their alloys
Design & tailor mechanical
properties of materials
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WHY STUDY Dislocations and Strengthening Mechanisms?
Strengthening mechanisms will be
applied to the development of
mechanical properties for steel alloys
Why heat treating a deformed metal
alloy makes it softer & more ductile
and produces changes in its
microstructure
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1. Describe edge & screw dislocation motion
2. Describe how plastic deformation occurs by
motion of edge & screw dislocations in response
to applied shear stresses
3. Define slip system
4. Describe how grain structure of a polycrystalline
metal is altered when it is plastically deformed.
5. Explain how grain boundaries impede dislocation
motion & why a metal having small grains is
stronger than one having large grains.
Learning Objectives
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5. Describe & explain solid-solution strengthening
for substitutional impurity atoms in terms of lattice
strain interactions with dislocations
6. Describe & explain phenomenon of strain
hardening in terms of dislocations and strain field
interactions.
7. Describe recrystallization in terms of both
alteration of microstructure & mechanical
characteristics of the material
8. Describe phenomenon of grain growth from both
macroscopic and atomic perspectives.
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Learning Objectives
7.2 BASIC CONCEPTS
Dislocation MotionCubic & hexagonal metals - plastic deformation is
by plastic shear or slip where one plane of atoms
slides over adjacent plane by dislocations motion.
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7.3 Characteristics of Dislocations
When metals are plastically
deformed:
Around 5% of deformation energy is
retained internally
remainder is dissipated as heat
Major portion of stored energy is
strain energy associated with
dislocations
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7.3 Characteristics of Dislocations
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Figure 7.4: some atomic lattice distortion exists
around dislocation line because of presence of
extra half-plane of atoms.
7.3 Characteristics of Dislocations
Atoms immediately above and
adjacent to dislocation line are
squeezed together.
These atoms may be thought of as
experiencing a compressive strain relative
to atoms positioned in the perfect crystal
and far removed from the dislocation
Directly below half-plane, lattice
atoms sustain an imposed tensile strain
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7.3 Characteristics of Dislocations
Shear strains also exist in the vicinity of
edge dislocation
For a screw dislocation, lattice strains are
pure shear only
Consider lattice distortions as strain fields
that radiate from the dislocation line
Strains extend into the surrounding atoms,
and their magnitude decreases with radial
distance from the dislocation.
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7.3 Characteristics of DislocationsStrain fields surrounding
Figure 7.5 (a): Two edge dislocations of same sign
& lying on same slip plane exert a repulsive force
on each other
Compressive & tensile strain fields for both lie on
same side of the slip plane; there exists between
these two isolated dislocations a mutual repulsive
force that tends to move them apart
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Figure 7.5 (b) Edge dislocations of opposite
sign & lying on same slip plane exert an
attractive force on each other. Upon
meeting, they annihilate each other and
leave a region of perfect crystal
7.3 Characteristics of Dislocationsstrain fields surrounding
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7.4 Slip Systems Slip plane - plane allowing easiest slippage
Wide inter-planar spacing - highest planar densities
Slip direction - direction of movement - Highest
linear densities
FCC Slip occurs on {111} planes in <110> directions
=> total of 12 slip systems in FCC
in BCC & HCP other slip systems occur
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Table 7.1: Slip Systems for FCC,
BCC, and HCP Metals
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7.5 Slip in Single Crystals
coscosR
Crystals slip due to a
resolved shear stress, R.
Applied tension can
produce such a stress.
= angle between
stress direction & Slip
direction
= angle between
stress direction &
normal to slip plane
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Condition for dislocation motion: CRSS R
Crystal orientation can make it
easy or hard to move dislocation
10-4 GPa to 10-2 GPa
typically
coscosR
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Critical Resolved Shear Stress
R = 0
=90°
R = /2=45°=45°
R = 0
=90°
7.5 Slip in Single Crystals
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Resolved (shear stress) ismaximum at = = 45º
And
CRSS = y/2 for dislocations tomove (in single crystals)
Determining & angles for Slip in
Crystals
For cubic crytals, angles betweendirections are given by:
1 1 2 1 2 1 2
2 2 2 2 2 2
1 1 1 2 2 2
u u v v w wCos
u v w u v w
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EXAMPLE PROBLEM 7.1Consider a single crystal of BCC iron oriented
such that a tensile stress is applied along a
[010] direction.
a. Compute the resolved shear stress along a
(110) plane and in a direction when a
tensile stress of 52 MPa is applied.
b. If slip occurs on a (110) plane and in a [-
111] direction, and the critical resolved
shear stress is 30MPa, calculate magnitude
of the applied tensile stress necessary to
initiate yielding.
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Stronger since grain boundaries
pin deformations
Slip planes & directions (, )
change from one crystal to
another
R will vary from one crystal to
another.
Crystal with largest R yields first
Other (less favorably oriented)
crystals yield (slip) later.
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7.6 Plastic Deformation ofPolycrystalline Materials
300 mm
7.6 Plastic Deformation of Polycrystalline Materials
Ordinarily ductility is sacrificed when analloy is strengthened.
The ability of a metal to plasticallydeform depends on the ability ofdislocations to move.
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7.6 Plastic Deformation of Polycrystalline Materials
Strengthening principle: Restricting orHindering dislocation motion renders amaterial harder & stronger
We will consider strengthening singlephase metals by:
1. Grain size reduction
2. Solid-solution alloying
3. Strain hardening
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7.8 Strengthening by Grain Size Reduction
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Grain boundaries are barriers to slip
Barrier "strength" increases with Increasing
angle of mis-orientation.
Smaller grain size: more barriers to slip
Hall-Petch equation:
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21 /
yoyield dk
7.8 Strengthening by Grain
Size Reduction
Figure 7.15: Influence
of grain size on yield
strength of a 70 Cu–
30 Zn brass alloy
D-1/2, (mm-1/2)
Yie
ld S
tren
gth
(M
Pa
)
Yie
ld S
trength
(K
si)
Increase Rate of solidification from liquid phase
Perform Plastic deformation followed by an
appropriate heat treatment
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7.8 Strengthening by Grain Size
ReductionGrain Size Reduction Techniques:
Grain size reduction improves toughness of many
alloys.
Small-angle grain boundaries are not effective in
interfering with the slip process because of small
crystallographic misalignment across the boundary.
Boundaries between two different phases are also
impediments to movements of dislocations.
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7.8 Strengthening by Grain Size Reduction
Impurity atoms distort the lattice & generate stress.
Stress can produce a barrier to dislocation motion.
7.9 Solid-solution Strengthening
• 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
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7.9 Solid-solution Strengthening
small impurities tend to concentrate at
dislocations on the “Compressive stress side”
reduce mobility of dislocation increase
strength
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Large impurities concentrate at dislocations on
“Tensile Stress” side – pinning dislocation
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7.9 Solid-solution Strengthening
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• Tensile strength & yield strength increase with wt% Ni.
• Empirical relation:
• Alloying increases y and TS
21 /
y C~
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7.9 Solid-solution Strengthening
-Forging
Ao Ad
force
die
blank
force
7.10 Strain Hardening Low temperature (varies with material) deformation
Common forming operations change cross
sectional area:
-Drawing
tensile force
Ao
Addie
die
-Extrusion
ram billet
container
container
forcedie holder
die
Ao
Adextrusion
100 x %o
do
A
AACW
-Rolling
roll
Ao
Adroll
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Ti alloy after cold working:
Dislocations entangle &
multiply
Thus, Dislocation motion
becomes more difficult
0.9 mm
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7.10 Strain Hardening
Dislocation density =
Carefully grown single crystal
up to 103 mm / mm3
Deforming sample increases density
109-1010 mm / mm3
Heat treatment reduces density
105-106 mm / mm3
Yield stress increases as rd increases
total dislocation length
unit volume
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7.10 Strain Hardening
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7.10 Strain Hardening
Figure 7.20:
influence of cold
work on stress
strain behavior of a
low-carbon steel
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7.10 Strain Hardening
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7.10 Strain Hardening
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7.10 Strain Hardening
What is the tensile strength & ductility after cold
working?
%6.35100 x %2
22
o
do
r
rrCW
Cold Work Analysis
Do =15.2mm Dd =12.2mm
Copper Cold Work
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Results for polycrystalline iron:
y & TS decrease with increasing temperature
%EL increases with increasing temperature
- e Behavior vs. Temperature
-200C
-100C
25C
800
600
400
200
0
Strain
Str
ess (
MP
a)
0 0.1 0.2 0.3 0.4 0.5
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Recovery, Recrystallization,
and Grain Growth
Properties & structures may revert back to
the precold-worked states by appropriate
heat treatment (annealing treatment).
Restoration results from different processes
that occur at elevated temperatures:
1. Recovery
2. Recrystallization
3. Grain growth
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1 hour treatment at
Tanneal... decreases TS and
increases %EL.
Effects of cold work
are reversed!
3 Annealing stages
to discuss...
Recovery, Recrystallization, & Grain
Growth
ten
sile
str
en
gth
(M
Pa
)
du
ctilit
y (
%E
L)tensile strength
ductility
600
300
400
500
60
50
40
30
20
Annealing Temperature (ºC)200100 300 400 500 600 700
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7.11 RECOVERYDuring recovery, some of the stored internal strain
energy is relieved by virtue of dislocation motion,
due to enhanced atomic diffusion at elevated
temperature.
There is some reduction in number of dislocations,
and dislocation configurations are produced
having low strain energies.
Physical properties such as electrical and thermal
conductivities are recovered to their precold-
worked states.
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Even after recovery is complete, grains are still
in a relatively high strain energy state.
Recrystallization = formation of a new set of
strain-free and equiaxed grains that have
low dislocation densities and are
characteristic of the pre-cold-worked condition.
7.12 Recrystallization
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The driving force to produce this new grain
structure is the difference in internal energy
between the strained and unstrained
material.
The new grains form as very small nuclei and
grow until they completely consume the
parent material, processes that involve short-
range diffusion.
7.12 Recrystallization
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33% cold
worked
brass
New crystals
nucleate after
3 sec. at 580C.
0.6 mm 0.6 mm
7.12 Recrystallization
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Figure 7.21
All cold-worked grains are consumed.
After 4
seconds
After 8
seconds
0.6 mm0.6 mm
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7.12 Recrystallization
7.12 Recrystallization
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7.12 Recrystallization
Recrystallization temperature =
temperature at which recrystallization just
reaches completion in 1 h.
Recrystallization temperature for brassalloy of Figure 7.22 is about 450°C.
Typically, TR = 1/ 3 to 1 / 2 Tm
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TR
º
º
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Figure 7.22: Annealing
temperature influence
(for an annealing time
of 1 h) on tensile
strength & ductility of a
brass alloy.
7.12 Recrystallization
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Figure 7.23
Critical degree
of CW below
which
recrystallization
cannot be
made to occur
(between 2%
and 20% CW)
Recrystallization proceeds more
rapidly in pure metals than in
alloys.
During recrystallization, grain
boundary motion occurs as the
new grain nuclei form and then
grow.
For pure metals, TRC = 0.4Tm
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7.12 Recrystallization
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7.12 Recrystallization
At longer times, larger
grains consume
smaller ones.
Grain boundary area
(and therefore energy)
is reduced.
Empirical Relation:
After 8 s,
580ºC
After 15 min,
580ºC
0.6 mm 0.6 mm
7.13 Grain Growth
Ktdd n
o
n
coefficient dependent on
material & Temp.
grain dia. At time t.
elapsed timeexponent typ. ~ 2
This is: Ostwald Ripening
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Design Example 7.1
A cylindrical rod of non-cold-worked brass
having an initial diameter of 6.4 mm is to be
cold worked by drawing such that the cross-
sectional area is reduced. It is required to
have a cold-worked yield strength of at least
345 MPa and a ductility in excess of 20 %EL; in
addition, a final diameter of 5.1 mm is
necessary. Describe the manner in which this
procedure may be carried out.
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