[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

[email protected]

Engineering 45

Dislocations &Dislocations &Strengthening Strengthening

(1)(1)



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



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?



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



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



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)



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




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 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)



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



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



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



Dislocation Motion AnalogiesDislocation Motion Analogies Caterpillar LoCoMotion

Carpet-Layer LoCoMotion

Disloc



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



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.



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



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



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



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.



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



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



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)



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



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



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



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



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



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



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



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



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



-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



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



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?



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Documents

pe engineering

deformation slide

metals dislocation motion

loss of ductility slide

directional bonds dislocations

perfect crystal

presence of imperfections

source of plastic deformation