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8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Lecture 12. Dislocations andStrengthening Mechanisms (2)Learning Objectives
After this lecture, you should be able to do the following:
1. Explain how grain boundaries impede dislocation motion and why a
metal having small grains is stronger (grain size reduction).
2. Describe solid-solution strengthening for substitutional impurity atoms
(solid-solution alloying).
3. Explain the phenomenon of strain hardening (or cold working) in terms
of dislocations and strain field interactions.
Reading
• Chapter 7: Dislocations and Strengthening Mechanisms (7.8–7.13)
Multimedia
• Virtual Materials Science & Engineering (VMSE):
http://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/
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8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Mechanisms of Strengthening in
Metals
2
• Early materials studies: the theoretical strengths of perfect crystals are many
times greater than those actually measured.
• The discrepancy could be explained by a type of linear crystalline defect:
dislocation (1930s).
• Design materials to have high strength yet some ductility and toughness
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
1. Elastic Deformation• Elastic deformation is nonpermanent: when the applied load is released, the
piece returns to its original shape (not breaking atomic bonds).
• Hooke’s Law
E [Pa]: Modulus of elasticity, or Young’s modulus
3
Linear elastic deformation Nonlinear elastic deformation
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Yield Strength,σ
y
4
• Yield strength: The stress level at which plastic deformation begins, or
yielding occurs.
P: Proportional limit
(onset of plastic
deformation at the
microscopic level
Strain offset of 0.002
Yield Strength, σ y
Yield point phenomenon
* Yield stress for nonlinear elastic deformation
(Figurer 6.6): stress required to produce some
amount of strain (e.g., =0.005)
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 5
Tensile Strength, TS
• Metals: occurs when noticeable necking starts.
• Polymers: occurs when polymer backbone chains are aligned and about to break.
• Tensile strength: Maximum
stress on engineering
stress-strain curve;
maximum stress that can besustained by the structure in
tension
• If this stress is applied,
fracture will result.Necking
TS
F = Fracture or ul timate
strength
Neck acts as stress
concentrator; fracture
occurs at the neck.
M = Tensile strength (TS)
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Ductility
6
S t r e s s
Strain
• Ductility: Measure of the degree
of plastic deformation that has
been sustained at fracture
• Brittle: little or not plastic
deformation (approximately, afracture strain < 5%)
• Ductility usually increases with
temperature.
• Percent elongation
• Percent reduction in area
1. It indicates the degree to which a structure will deform plastically before fracture
2. It specifies the degree of allowable deformation during fabrication operations
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 7
• Tensile toughness: Measure of the ability of the material to absorb energy
without fracture
• The area under the entire stress-strain curve up to fracture (Unit: J/m3)
• Fracture toughness: Material’s resistance to fracture when a crack (or otherdefect) is present
Measures of Energy Capacity 2:
Toughness
Brittle fracture: elastic energy
Ductile fracture: elastic + plastic energy
very small toughness(unreinforced polymers)
Engineering tensile strain, e
Engineering
tensile
stress, σ
small toughness (ceramics)
large toughness (metals):strength + ductili ty
f
d U f
0
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Measures of Energy Capacity 1:
Resilience
8
S t r e
s s
Strain
• Resilience: Capacity of a material to absorb
energy when it is deformed elastically and
then, upon, unloading, to have the energy
recovered.
• Modulus of resilience [J/m3] Measure of
the ability of material to store elastic energy;
Strain energy per unit volume required to
stress a material from an unloaded state upto the point of yielding
y
d U r
0
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Mechanisms of Strengthening in
Metals
9
• Early materials studies: the theoretical strengths of perfect crystals are many
times greater than those actually measured.
• The discrepancy could be explained by a type of linear crystalline defect:
dislocation (1930s).
• Design materials to have high strength yet some ductility and toughness
• Strengthening mechanisms: Relation between dislocation motion and
mechanical behavior of metals
• Macroscopic plastic deformation: motion of large numbers of dislocations; theability of a metal to deform plastically depends on the ability of dislocations to
move.
- Reduce the mobility of dislocations enhance mechanical strength
• Principles: Restricting or hindering dislocation motion renders a material
harder and stronger (1) Grain size reduction
(2) Solid-solution alloying
(3) Strain hardening
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
1. Mechanism of Strengthening:
Grain Size Reduction
10
• The size of the grains, or average grain diameter, in a polycrystalline metal
influence the mechanical properties. Why?
• Grain boundary: Barrier to dislocation motion(1) When crossing a grain boundary, a dislocation’s direction of motion must change.
(2) There is a discontinuity of slip planes within the vicinity of a grain boundary.
Slip planes are discontinuous andchange directions across the
boundary
For high angle grain boundaries,
dislocations tend to “pile up” at
the boundaries, which introduce
stress concentration and
generate new dislocations in
adjacent grains.
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Hall-Petch equation
The yield strength varies withgrain size:
where d is the average grain
diameter.
* A metal that has small grains is
stronger than one with largegrains because the former has
more grain boundary area (more
barriers to dislocation motion).
Mechanism of Strengthening:
Grain Size Reduction
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8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 12
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:
Fig. 7.14, Callister & Rethwisch 9e.(From L. H. Van Vlack, A Textbook of Materials
Technology , Addison-Wesley Publishing Co., 1973.
Reproduced with the permission of the Estate of
Lawrence H. Van Vlack.)
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Grain Size Influences Properties
• Metals having small grains – relatively strong
and tough at low temperatures
• Metals having large grains – good creep
resistance at relatively high temperatures
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8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
2. Mechanism of Strengthening:
Solid-Solution Strengthening
14
• Solid-solution strengthening: Alloying with impurity atoms that go into either
substitutional or interstitial solid solution.
• Solid-solution strengthening results from lattice strain interactions between
impurity atoms and dislocations; these interactions decrease dislocationmobility.
(a) Tensile lattice strains imposed on
host atoms. (b) Partial cancellation of
impurity-dislocation lattice strains.
(a) Compressive strains imposed on
host atoms. (b) Partial cancellation of
impurity-dislocation lattice strains.
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 15
Dislocation Motion: Edge Dislocation
Dislocation motion and 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!
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Mechanism of Strengthening:
Solid-Solution Strengthening
16
• Solid-solution strengthening: Alloying with impurity atoms that go into either
substitutional or interstitial solid solution
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 17
Lattice Strains Around Dislocations
Fig. 7.4, Callister & Rethwisch 9e.(Adapted 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.)
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 18
Strengthening by Solid
Solution Alloying• Small impurities tend to concentrate at dislocations
(regions of compressive strains) - partial cancellation ofdislocation compressive strains and impurity atom tensile strains
• Reduce mobility of dislocations and increase strength
Fig. 7.17, Callister &
Rethwisch 9e.
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 19
Strengthening by Solid
Solution Alloying• Large impurities tend to concentrate at
dislocations (regions of tensile strains)
Fig. 7.18, Callister &
Rethwisch 9e.
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
VMSE Solid-Solution Strengthening Tutorial
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8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 21
Ex: Solid Solution
Strengthening in Copper • Tensile strength & yield strength increase with wt% Ni.
• Empirical relation:
• Alloying increases σ y and TS.
Adapted from Fig.
7.16 (a) and (b),
Callister &
Rethwisch 9e.
T e n s i l e
s t r e n g t h ( M P
a )
wt.% Ni, (Concentration C )
200
300
400
0 10 20 30 40 50 Y i e l d
s t r e n g t h ( M P a
)
wt.%Ni, (Concentration C )
60
120
180
0 10 20 30 40 50
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
3. Mechanism of Strengthening:
Strain Hardening
22
• Strain hardening: The enhancement of strength (and decrease of ductility) of
a metal as it is deformed plastically deformed (cold working or work
hardening)
>
• Percent cold work (%CW):
Degree of plastic deformation
Fig. 6.17, Callister &
Rethwisch 9e.
S t r e s
s
Strain
3. Reapplyload
2. Unload
D
Elastic strain
recovery
1. Load
σ y o
σ y i
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Mechanism of Strengthening:
Strain Hardening
23
• Strain hardening: A ductile metal becomes harder and stronger as it is
plastically deformed (cold working or work hardening)
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 24
Strategies for Strengthening:
Cold Work (Strain Hardening)
• Deformation at room temperature (for most metals).
• Common forming operations reduce the cross-sectional
area:
Adapted from Fig.11.9, Callister &
Rethwisch 9e.
-Forging
Ao Ad
force
die
blank
force-Drawing
tensileforce Ao
Ad die
die
-Extrusion
ram billet
container
container
force
die holder
die
Ao
Ad extrusion
-Rolling
roll
Ao
Ad roll
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 25
• Dislocation structure in Ti after cold working.
• Dislocations entangle with one another
during cold work.
• Dislocation motion becomes more
difficult.
• During plastic deformation, dislocation
density increases, the average
distance between dislocationsdecreases, and, because dislocation-
dislocation strain field interactions are
on average repulsive, dislocation
mobility becomes more restricted; thus
the metal becomes harder andstronger.
Dislocation Structures Change
During Cold Working
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 26
Dislocation Density Increases
During Cold Working
Dislocation density =
– Carefully grown single crystals
ca. 103 mm-2
– Deforming sample increases density 109-1010 mm-2
– Heat treatment reduces density
105
-106
mm-2
• Yield stress increases as ρd increases:
total dislocation length
unit volume
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 27
Impact of Cold Work
Adapted from Fig. 7.20,
Callister & Rethwisch 9e.
• Yield strength (σ y) increases.
• Tensile strength (TS) increases.
• Ductility (%EL or % AR ) decreases.
As cold work is increased
low carbon steel
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
• What are the values of yield strength, tensile strength &
ductility after cold working Cu?
Mechanical Property Alterations
Due to Cold Working
Do = 15.2 mm
Cold
Work
Dd = 12.2 mm
Copper
28
8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Mechanical Property Alterations
Due to Cold Working
% Cold Work
100
300
500
700
Cu
200 40 60
σ y = 300 MPa
300 MPa
% Cold Work
200
Cu
0
400
600
800
20 40 60
% Cold Work
20
40
60
20 40 6000
Cu340 MPa
TS = 340 MPa
7%
%EL = 7%
• What are the values of yield strength, tensile strength &
ductility for Cu for %CW = 35.6%?
y i e l d s t r e
n g t h ( M P a )
t e n s i l e s t r e
n g t h ( M P a )
d u c t i l i t
y ( % E L )
Fig. 7.19, Callister & Rethwisch 9e. [Adapted from Metals Handbook: Properties and Selection: Ironsand Steels, Vol. 1, 9th edition, B. Bardes (Editor), 1978; and Metals Handbook: Properties and Selection: Nonferrous
Alloys and Pure Metals, Vol. 2, 9th edition, H. Baker (Managing Editor), 1979. Reproduced by permission of ASM
International, Materials Park, OH.]29
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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -
Summary
1. Plastic deformation and dislocation mobility:
Restricting dislocation motion leads to increased
hardness and strength
2. Mechanisms of Strengthening in Metals:
(1) Grain size reduction
(2) Solid-solution alloying
(3) Strain hardening
30