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Transcript of [email protected] ENGR-45_Lec-17_DisLoc_Strength-1.ppt 1 Bruce Mayer, PE Engineering-45:...
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt1
Bruce Mayer, PE Engineering-45: Materials of Engineering
Bruce Mayer, PELicensed Electrical & Mechanical Engineer
Engineering 45
Dislocations &Dislocations &Strengthening Strengthening
(1)(1)
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt2
Bruce Mayer, PE Engineering-45: Materials of Engineering
Learning GoalsLearning 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
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt3
Bruce Mayer, PE Engineering-45: Materials of Engineering
Theoretical Strength of CrystalsTheoretical 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?
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt4
Bruce Mayer, PE Engineering-45: Materials of Engineering
Role of Crystal ImperfectionsRole 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
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt5
Bruce Mayer, PE Engineering-45: Materials of Engineering
Edge DislocationsEdge Dislocations Recall from Chp.4
The Crystal Imperfection of an Extra ½-Plane of Atoms• Called an EDGE
DISLOCATION
These imperfections are the Source of PLASTIC Deformation in Xtals
Extra ½-Plane of Atoms
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt6
Bruce Mayer, PE Engineering-45: Materials of Engineering
Dislocations vs. MetalsDislocations 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– Called SLIP
+ +
+ +
+ + + + + + + + + + + + +
+ + + + + + +
Ion Cores
Electron Sea
Dislocations & Slip (Deformation)
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt7
Bruce Mayer, PE Engineering-45: Materials of Engineering
Disloc vs. Covalent CeramicsDisloc vs. Covalent Ceramics For CoValent
Ceramics Dislocation Motion is RELATIVELY more Difficult Due to• Directional (angular)
and Powerful Atomic Bonding
Examples• Diamond Carbon
• Silicon
Strong, Directional Bonds
Dislocations & Slip (Deformation)
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt8
Bruce Mayer, PE Engineering-45: Materials of Engineering
Disloc vs. Ionic CeramicsDisloc 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
+ Ion Cores
− Ion Cores
Dislocations & Slip (Deformation)
+ + + +
+ + +
+ + + +
- - -
- - - -
- - -
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt9
Bruce Mayer, PE Engineering-45: Materials of Engineering
Dislocations vs Matl TypeDislocations 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)
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt10
Bruce Mayer, PE Engineering-45: Materials of Engineering
Dislocation Motion 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
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt11
Bruce Mayer, PE Engineering-45: Materials of Engineering
Screw DislocationsScrew Dislocations In the EDGE
configuration The axis of is Parallel (||) to the Applied Shear Stress
EDGEDislocation
A SCREW dislocation is Perpendicular to the Applied Force SCREW
Dislocation
SHEARING Motion
TEARING Motion
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt12
Bruce Mayer, PE Engineering-45: Materials of Engineering
Role of Imperfections in Role of Imperfections in Plastic DeformationPlastic Deformation
Bond Broken
Bond broken
All bonds broken in the one planeCRSS very high
No edge dislocation present Dislocation present (a)
Bondreattached
Plastic Flow occurs by Dislocation Movem ent
Dislocation present (b) Dislocation present (c)
Compressionstress field
Tensionstress field
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt13
Bruce Mayer, PE Engineering-45: Materials of Engineering
Dislocation Motion AnalogiesDislocation Motion Analogies Caterpillar LoCoMotion
Carpet-Layer LoCoMotion
Disloc
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt14
Bruce Mayer, PE Engineering-45: Materials of Engineering
Stress and Dislocation Motion Stress and Dislocation Motion
Crystals slip due to a resolved shear stress, R
Applied TENSION can Produce This -Stress
slip
direct
ion
slip plane
normal, ns
Resolved shear stress: R =Fs/As
As
R
R
Fs ns
AAs
slip
direct
ion
F
Fs
Relation between and R
R=Fs/As
Fcos A/cos
slip
direct
ion
Applied tensile stress: = F/A
FA
F
coscoscoscos AFR
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt15
Bruce Mayer, PE Engineering-45: Materials of Engineering
Resolved Shear Stress, Resolved Shear Stress, RR (in detail) (in detail)
Consider a single crystal of cross-sectional area A under compression force F angle between
the slip plane normal and the compression (or Tension) axis
angle between the slip direction and the tensile axis.
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt16
Bruce Mayer, PE Engineering-45: Materials of Engineering
Resolved Shear Stress, Resolved Shear Stress, RR cont.1 cont.1
F projected on Slip Direction:
Fcosλ
As
A = Ascos
cosFFs The Slip Direction
Slant Area, As, Relative to the Compression Area, A
cossAA
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt17
Bruce Mayer, PE Engineering-45: Materials of Engineering
Resolved Shear Stress, Resolved Shear Stress, RR cont.2 cont.2
Thus the Resolved Shear Stress
Fcosλ
As
A = Ascos
coscos
cos
cos
A
F
A
FAF ssR
But F/A = σ; the Compression (or Tension) Stress - So
coscosR
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt18
Bruce Mayer, PE Engineering-45: Materials of Engineering
Critical Resolved Shear Stress Critical Resolved Shear Stress Condition for Dislocation Motion: R>CRSS
CRSS CRITICAL Resolved Shear Stress
Xtal Orientation Can Facilitate Dicloc. Motion Rcoscos
R = 0
= 90°
R = /2
= 45° = 45°
HARDto
Slip
R = 0
= 90°
HARDto
Slip
EASYto
Slip
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt19
Bruce Mayer, PE Engineering-45: Materials of Engineering
Yield Stress, Yield Stress, y
An Xtal Plastically Deforms When
To Get Yield Strength, Need minimum → (cos cos)max
coscos
and
max,
max,
R
CRSSR
Thus y = 2CRSS
2145cos45cos
coscos max
Plasticallystretchedzincsinglecrystal.
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt20
Bruce Mayer, PE Engineering-45: Materials of Engineering
PolyXtal Disloc MotionPolyXtal Disloc Motion
Slip planes & directions (, ) change from one crystal to another
R varies from one crystal, or Grain, to another
The Xtal/Grain with the LARGEST R Yields FIRST
Other (less favorably oriented) crystals Yield LATER
300 m
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt21
Bruce Mayer, PE Engineering-45: Materials of Engineering
Summary Summary Edge Dislocations 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
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt22
Bruce Mayer, PE Engineering-45: Materials of Engineering
1-Phase Metal Strengthening1-Phase Metal Strengthening
Basic ConceptPlastic Deformation in Metals is CAUSED
by DISLOCATION MOVEMENT
Strengthening StrategyRESTRICT or HINDER Dislocation
Movement
Strengthening Tactics1. Grain Size Reduction
2. Solid Solution Alloying
3. Strain Hardening
4. Precipitation (2nd-ph)
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt23
Bruce Mayer, PE Engineering-45: Materials of Engineering
Strengthen-1 Strengthen-1 G.S. Reduction 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 →
• Where 0 “BaseLine” Yield
Strength (MPa)
– ky Matl Dependent Const (MPa•m)
– d Grain Size (m)
grain boundary
slip plane
grain Agra
in B
dk yy 0
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt24
Bruce Mayer, PE Engineering-45: Materials of Engineering
Example Example GS Reduction GS Reduction Calc The Hall-Petch
Slope, ky, for 70Cu-30Zn (C2600, or Cartridge) Brass
Find the ’s
21 dk yy 21d
y
2121 8412 mmd
MPay 11070180 Then the Slope
mkPak
mmMPak
y
y
435
8110 21
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt25
Bruce Mayer, PE Engineering-45: Materials of Engineering
Strengthen-2 Strengthen-2 Solid Solution Solid Solution Impurity Atoms distort the Lattice & Generate Stress Stress Can produce a Barrier to Dislocation Motion
• Smaller substitutional impurity
A
B
• Impurity generates local shear at A and B that opposes dislocation motion to the right.
• Impurity generates local shear at C & D that opposes dislocation motion to the right.
C
D
• Larger substitutional impurity
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt26
Bruce Mayer, PE Engineering-45: Materials of Engineering
Example Example Ni-Cu Solid-Soln 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
Yield
str
ength
(M
Pa)
wt. %Ni, (Concentration C)
60
120
180
0 10 20 30 40 50
Tensi
le s
trength
(M
Pa)
wt. %Ni, (Concentration C)
200
300
400
0 10 20 30 40 50
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt27
Bruce Mayer, PE Engineering-45: Materials of Engineering
Strengthen-3 Strengthen-3 Strain Harden Strain Harden COLD WORK Room Temp Deformation Common forming operations Change The
Cross-Sectional Area:
Ao Ad
force
dieblank
force
-Forging
-Drawing
tensile force
AoAddie
die
-Rolling
-Extrusion
ram billet
container
containerforce
die holder
die
Ao
Adextrusion
roll
AoAd
roll
100% xA
AACW
o
do
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt28
Bruce Mayer, PE Engineering-45: Materials of Engineering
Dislocations During Cold Work Dislocations During Cold Work
• Dislocations entangle with one another during COLD WORK
• Dislocation motion becomes more difficult
ColdWorked Ti Alloy
0.9 m
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt29
Bruce Mayer, PE Engineering-45: Materials of Engineering
ColdWorking ConsequencesColdWorking Consequences Dislocation linear density, ρd, increases:
• Carefully prepared sample: ρd ~ 103 mm/mm3
• Heavily deformed sample: ρd ~ 1010 mm/mm3
Measuring Dislocation Density
OR
length, l1length, l2length, l3Volume, Vl1l2l3Vd
40m
dN
A
Area , A
N dislocation pits (revealed by etching)
dislocation pit
σy Increases
as ρd increases:
large hardeningsmall hardening
y0 y1
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt30
Bruce Mayer, PE Engineering-45: Materials of Engineering
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt31
Bruce Mayer, PE Engineering-45: Materials of Engineering
CW Strengthening MechanismCW 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
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt32
Bruce Mayer, PE Engineering-45: Materials of Engineering
Simulation – DisLo Generator 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
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt33
Bruce Mayer, PE Engineering-45: Materials of Engineering
-Motion Impedance-Motion Impedance Dislocations Generate Stress
• This Generates -Traps
Red dislocation generates shear at
pts A and B that opposes motion of
green disl. from left to right.
A
B
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt34
Bruce Mayer, PE Engineering-45: Materials of Engineering
ColdWork Results-Trends ColdWork Results-Trends
As Cold Work Increases• Yield Strength, y,
INcreases
• Ultimate Strength, u, INcreases
• Ductility (%EL or %RA) DEcreases
Str
ess
% cold work Strain
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt35
Bruce Mayer, PE Engineering-45: Materials of Engineering
Cold Work ExampleCold Work ExampleCold work ----->
Do=15.2mm Dd=12.2mm
Copper
%CW ro
2 rd2
ro2
x10035.6%
ductility (%EL)
7%
%EL=7%% Cold Work
20
40
60
20 40 6000
Cu
% Cold Work
tensile strength (MPa)
340MPa
TS=340MPa
200Cu
0
400
600
800
20 40 60
Post-Work Ductility is
HAMMERED
y=300MPa% Cold Work
100
300
500
700
Cu
200 40 60
yield strength (MPa)
300MPa
What is the Tensile Strength & Ductility After Cold Working?
[email protected] • ENGR-45_Lec-17_DisLoc_Strength-1.ppt36
Bruce Mayer, PE Engineering-45: Materials of Engineering
WhiteBoard WorkWhiteBoard Work