Engineering 45
Dislocations &
Strengthening (1)
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Learning Goals
 Understand Why DISLOCATIONS
are observed primarily in
METALS and ALLOYS
 Determine How Strength and
Dislocation-Motion are Related
 Techniques to Increase Strength
 Understand How HEATING
and/or Cooling can change
Strength and other Properties
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Theoretical Strength of Crystals
 The ideal or theoretical strength of a
“perfect” crystal is  E/10
• For Steel, E = 200 GPa
– Thus the theoretical strength 20 GPa
• 2,000 MPa is the practical limit for steel
and this is an ORDER of MAGNITUDE
Less than 20,000 MPa
• Most commercial steels have a strength 
500 MPa - Why is there such differences?
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Role of Crystal Imperfections
 Crystal imperfections explain why
metals are weak (relative to the
Theoretical) and why they are so ductile
• In most applications we need ductility as
well as strength - so there is a plus side to
the presence of imperfections
• The main task in deciding what
strengthening process to use in metal
alloys is to chose a method which
minimizes the loss of ductility
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Edge Dislocations
 Recall from Chp.4
The Crystal
Imperfection of an
Extra ½-Plane of
Atoms
Extra ½-Plane of Atoms
• Called an EDGE
DISLOCATION
 These imperfections
are the Source of
PLASTIC
Deformation in Xtals
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Dislocations vs. Metals
 Dislocation Motion is
RELATIVELY Easier
in Metals Due to
• NON-Directional
Atomic Bonding
• Close-Packed
Crystal Planes allow
“sliding” of the
Planes relative to
each other
Ion Cores
Electron Sea
Dislocations & Slip
(Deformation)
– Called SLIP
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Disloc vs. Covalent Ceramics
 For CoValent
Ceramics
Dislocation Motion is
RELATIVELY more
Difficult Due to
• Directional (angular)
and Powerful Atomic
Bonding
Strong, Directional
Bonds
Dislocations & Slip
(Deformation)
 Examples
• Diamond Carbon
• Silicon
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Disloc vs. Ionic Ceramics
 For Ionic Ceramics
Dislocation Motion is
RELATIVELY more
Difficult Due to
• Coulombic Attraction
and/or Repulsion
• Slip Will Encounter
++ & -- Charged
nearest neighbors
Engineering-45: Materials of Engineering
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+ Ion Cores
− Ion Cores
Dislocations & Slip
(Deformation)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Dislocations vs Matl Type
 Metals Allow Xtal Planes to Slip Relative
to Each other
• Relatively Low Onset of Plastic
Deformation (Yield Strength, σy)
• Relatively High Ductility: The amount of
Plastic deformation Prior to Breaking
 Ceramics Tend to Prevent Disloc. Slip
• Allow for little Plastic Deformation
• Failure by Brittle-Fracture (cracking)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Dislocation Motion
 Produces Plastic Deformation In Crystals
 Proceeds by Incremental, Step-by-Step
Breaking & Remaking of Xtal Bonds
 WithOut Dislocation motion Plastic (Ductile)
Deformation Does NOT Occur
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Screw Dislocations
 In the EDGE
configuration The
axis of  is Parallel
(||) to the Applied
Shear Stress
EDGE
Dislocation
SHEARING
Motion
 A SCREW
dislocation is
Perpendicular to the
Applied Force
SCREW
Dislocation
TEARING
Motion
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Role of Imperfections in
Plastic Deformation
No edge dislocation present Dislocation present (a)
Compression
stress field
Bond Broken
All bonds broken in the one plane
CRSS very high
Dislocation present (b)
Tension
stress field
Dislocation present (c)
Bond
reattached
Bond broken
Plastic Flow occurs by Dislocation Movement
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Dislocation Motion Analogies
 Caterpillar LoCoMotion
 Carpet-Layer
LoCoMotion
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Stress and Dislocation Motion
 Crystals slip due to a resolved shear stress, R
 Applied TENSION can Produce This -Stress
Resolved shear
stress: R =Fs /As
Applied tensile
stress: s = F/A
F
A
slip plane
R
normal, ns
As
Fs
F
R
Relation between
sand R
R =Fs /As
Fcos l
F
l
Fs
 R F Acos l cos   s cos l cos 
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
A/cos 
ns
A
As
Resolved Shear Stress, R (in detail)
 Consider a single
crystal of crosssectional area A
under compression
force F
•   angle between
the slip plane normal
and the compression
(or Tension) axis
• l  angle between
the slip direction and
the tensile axis.
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Resolved Shear Stress, R cont.1
 F projected on Slip
Direction:
Fs  F cos l
As
Fcosλ
 The Slip Direction
Slant Area, As,
Relative to the
Compression Area, A
A = Ascos
Engineering-45: Materials of Engineering
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A  As cos 
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Resolved Shear Stress, R cont.2
 Thus the Resolved
Shear Stress
F cos l
 R  Fs As 
A cos 
As
F
  cos l cos  
A
 But F/A = σ; the
Compression
(or
Fcosλ
Tension) Stress - So
A = Ascos
Engineering-45: Materials of Engineering
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 R  s cos l cos  
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Critical Resolved Shear Stress
 Condition for Dislocation Motion: R>CRSS
• CRSS  CRITICAL Resolved Shear Stress
 Xtal Orientation Can Facilitate Dicloc. Motion
R  s cos l cos 
s
s
R = 0
l = 90°
HARD
to
Slip
Engineering-45: Materials of Engineering
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R = s/2
l = 45°
 = 45°
EASY
to
Slip
s
R = 0
 = 90°
HARD
to
Slip
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Yield Stress, sy
 An Xtal Plastically
Deforms When
 R ,max   CRSS and
 R ,max  s cos  cos l
 To Get Yield
Strength, Need
sminimum →
(cos cosl)max
cos  cos l max
 Thus
sy = 2CRSS
Plastically
stretched
zinc
single
crystal.

cos 45  cos 45  1 2
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
PolyXtal Disloc Motion
 Slip planes & directions (l, )
change from one crystal to
another
 R varies from one crystal,
or Grain, to another
300 mm
Engineering-45: Materials of Engineering
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 The Xtal/Grain with the
LARGEST R Yields FIRST
 Other (less favorably oriented)
crystals Yield LATER
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Summary  Edge Dislocations
 Plastic flow can occur in a crystal by the
breaking and reattachment of atomic
bonds one at a time
• This dramatically reduces the required
shear stress
– Consider how a caterpillar gets from A to B
 A similar mechanism applies to screw
dislocations
 Screw & Edge dislocations often occur
together
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
1-Phase Metal Strengthening
 Basic Concept
Plastic Deformation in Metals is CAUSED
by DISLOCATION MOVEMENT
 Strengthening Strategy
RESTRICT or HINDER Dislocation
Movement
 Strengthening Tactics
1. Grain Size Reduction
2. Solid Solution Alloying
Engineering-45: Materials of Engineering
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3. Strain Hardening
4. Precipitation (2nd-ph)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Strengthen-1  G.S. Reduction
 Grain boundaries are
barriers to slip due to
Discontinuity of the
Slip Plane
 Barrier "Strength“
Increases with Grain
MisOrientation
 Smaller grain size →
more Barriers to slip
 Hall-Petch Reln →
Engineering-45: Materials of Engineering
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slip plane
grain A
s y s 0  k y
d
• Where
– s0  “BaseLine” Yield
Strength (MPa)
– ky  Matl Dependent
Const (MPa•m)
– d  Grain Size (m)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Example  GS Reduction
 Calc The Hall-Petch
Slope, ky, for
70Cu-30Zn (C2600,
or Cartridge) Brass
k y  s y d
s y
1 2
 Find the ’s
d 1 2
d 1 2  12  4  8 mm1 2
s y  180  70  110 MPa
 Then the Slope
Engineering-45: Materials of Engineering
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k y  110MPa 8mm
1 2
 k y  435 kPa  m
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Strengthen-2  Solid Solution
 Impurity Atoms distort the Lattice & Generate Stress
 Stress Can produce a Barrier to Dislocation Motion
• Smaller substitutional
impurity
• Larger substitutional
impurity
A
C
B
• Impurity generates local
shear at A and B that
opposes dislocation
motion to the right.
Engineering-45: Materials of Engineering
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D
• Impurity generates local
shear at C & D that
opposes dislocation
motion to the right.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Example  Ni-Cu Solid-Soln
 Tensile (Ultimate) Strength, σu, and & Yield
Strength, σy, increase with wt% Ni in Cu
 Empirical Relation: σy ~ C½
 Basic Result: Alloying increases σy & σu
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Strengthen-3  Strain Harden
 COLD WORK  Room Temp Deformation
 Common forming operations Change The
Cross-Sectional Area:
-Forging
force
die
Ao blank
-Drawing
die
Ao
die
Ad
force
Ad
-Extrusion
tensile
force
Ao  Ad
%CW 
x100
Ao
Engineering-45: Materials of Engineering
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-Rolling
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Dislocations During Cold Work
 ColdWorked Ti Alloy
• Dislocations entangle
with one another during
COLD WORK
• Dislocation motion
becomes more difficult
0.9 mm
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
ColdWorking Consequences
 Dislocation linear density, ρd, increases:
• Carefully prepared sample: ρd ~ 103 mm/mm3
• Heavily deformed sample: ρd ~ 1010 mm/mm3
 Measuring Dislocation Density
40mm
Volume, V
length, l 1
length, l 2
length, l 3
 
r  l1 l2 l3
d
V
 σy Increases
as ρd increases:
Engineering-45: Materials of Engineering
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Area , A dislocation
pit
OR
r N
d
A
N dislocation
pits (revealed
by etching)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Typical Dislocation
Densities
(Total Length of Dislocation
Line/unit Volume)
0 - 103
Very Pure Crystals
(whiskers)
Annealed Single Crystals
105 - 106
Annealed Polycrystals
107 - 108
Highly Cold Worked Metals
Engineering-45: Materials of Engineering
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mm/mm3
1011 - 1012
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
CW Strengthening Mechanism
 Strain Hardening Explained by
Dislocation-Dislocation InterAction
 Cold Work INCREASES ρd
• Thus the Average - Separation-Distance
DECREASES with Cold Work
 Recall - interactions are, in general,
REPULSIVE
 Thus Increased ρd IMPEDES -Motion
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Simulation – DisLo Generator
 Tensile loading
(horizontal dir.) of a
FCC metal with
notches in the top
and bottom surface
 Over 1 billion atoms
modeled in 3D block.
 Note the large
increase in
Dislocation Density
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
-Motion Impedance
 Dislocations Generate Stress
• This Generates -Traps
Reddislocation
generates shear at
pts Aand Bthat
opposes motion of
green disl. from
left to right.
Engineering-45: Materials of Engineering
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A
B
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
ColdWork Results-Trends
 As Cold Work
Increases
• Yield Strength, sy,
INcreases
• Ultimate Strength,
su, INcreases
• Ductility (%EL or
%RA) DEcreases
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
Cold Work Example
 What is the Tensile Strength &
Ductility After Cold Working?
%CW 
ro2  rd2
ro2
x100  35.6%
yield strength (MPa)
700
500
300
300MPa
100
0
20
Cu
40
% Cold Work
sy=300MPa
60
Engineering-45: Materials of Engineering
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Post-Work
Ductility is
HAMMERED
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt
WhiteBoard Work
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-17_DisLoc_Strength-1.ppt