Topic7-Strengthening Mechanisms

7/30/2019 Topic7-Strengthening Mechanisms

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Dislocations and their dynamics

How are strength and dislocation motion related?

How do we increase strength?

How can heating change strength and other properties?

TOPIC 7:DISLOCATIONS AND

STRENGTHENING


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EDGE DISLOCATION

Extra half plane of atoms

Edge dislocation line: Directed into the page

Atoms above dislocation line are in compression, and

those below are in tension

Symbol


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SCREW DISLOCATION

Symbol

AB is screwdislocation line


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Incrementally breaking bonds

If dislocations don't move, deformation doesn't happen!

(But fracture will, like in a ceramic)

DISLOCATION MOTION


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Metals: Disl. motion easier.

-non-directional bonding

-close-packed directions

for slip. electron cloud ion cores

Covalent Ceramics(Si, diamond): Motion hard.

-directional (angular) bonding

Ionic Ceramics (NaCl):

Motion hard.-need to avoid ++ and --

neighbors.

DISLOCATIONS & MATERIALS

CLASSES


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DISLOCATION DENSITY

Dislocation density: total dislocation length per unitvolume of material

or, the number of dislocations that intersect a unitarea of a random section

The dislocation density typically determines thestrength of a material

Metals (carefully solidified): 103 mm-2

Metals (heavily deformed): 109-1010 mm-2

Metals (heat treated): 105-106 mm-2 Ceramics: 102-104 mm-2

Single crystal silicon for ICs: 0.1-1 mm-2


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LOCAL STRAIN FIELDS

Edge dislocation: compression (above dislocation

line) & tension (below dislocation line)

Screw dislocation: shear

Stress & strain fields decrease with radial

distance from dislocation line


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DISLOCATION INTERACTION

Strain field from one dislocation can affect aneighboring dislocation

Two like dislocations can repel each other

Unlike dislocations attract and annihilate each other


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SLIP SYSTEMS

Dislocations do not move with the same degree ofease on all crystallographic planes and directions

There are preferred planes (slip planes) and

preferred directions (slip directions)

Slip planes are planes with high planar density ofatoms, and slip directions are lines with high lineardensity

Slip system: the combination of slip plane and slipdirection


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SLIP SYSTEM: EXAMPLES

FCC (Al, Cu, Ni, Ag, Au) Close packed planes: {111}, e.g., ADF

Close packed directions: , e.g., AD, DF, AF

Slip system: {111} (12 independent slip systems)

BCC (Fe, W, Mo): {110} (12 independent slipsystems)

HCP (Zn, Cd, Mg, Ti, Be): 3 independent slip systems

FCC & BCC metals: ductile, HCP metals: brittle


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SLIP IN SINGLE CRYSTALS Single crystals easy to treat; can generalize to polycrystals later

Regardless of what type of external stress is applied to amaterial, plastic deformation or dislocation motion occurs due toa shear stress

Some component of the applied stress has to be a shear stresson a slip plane and along a slip direction

This component is called the resolved shear stress


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coscos

cos/

cos

A

F

R

ns

A

As

RESOLVED SHEAR STRESS

slip plane

normal, ns


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Condition for dislocation motion: R CRSS Crystal orientation can make it easy or hard to move disl.

R cos cos

CRITICAL RESOLVED SHEAR

STRESS (CRSS)

Maximum possible R = /2; thus y = 2CRSS


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BCC EXAMPLE

Slip system: {110}

= 45 degrees = tan-1(a2/a) = 54.7 degrees

From which or can be calculated if one ofthem is specified


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Slip planes & directions (, )

change from one crystal toanother.

Rwill vary from one crystal toanother.

The crystal with the largest Ryields first.

Other (less favorably

oriented) crystals yield later.

Polycrystalline materialsgenerally stronger than single

crystals, due to geometric

constraints & the requirement of

larger stresses for yielding

Adapted from Fig.

7.10, Callister 6e.

(Fig. 7.10 is

courtesy of C.

Brady, NationalBureau of

Standards [now the

National Institute of

Standards and

Technology,

Gaithersburg, MD].)

300 mm

DISL. MOTION IN POLYCRYSTALS


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STRENGTHENING MECHANISMS

Macroscopic plastic deformation corresponds to themotion of large numbers of dislocations The ability of a metal to plastically deform depends on the

ability of dislocations to move

Virtually all strengthening techniques rely onrestricting or hindering dislocation motion

We will look at 4 such mechanisms Reduce grain size

Solid-solution strengthening

Precipitation strengthening

Strain hardening (or cold working)


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Grain boundaries arebarriers to slip.

- dislocation has to change

directions

- grain boundary regiondisordered, so discontinuity inslip planes

Barrier "strength

increases with

misorientation.

Smaller grain size: morebarriers to slip.

Hall-Petch Equation:

grain

bounda

ry

slip plane

grain AgrainB

yield o kyd1/ 2

Adapted from Fig. 7.12, Callister 6e.

(Fig. 7.12 is fromA Textbook of Materials

Technology, by Van Vlack, Pearson Education,

Inc., Upper Saddle River, NJ.)

STRENGTHENING STRATEGY 1:

REDUCE GRAIN SIZE


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70wt%Cu-30wt%Zn brass alloy

yield

o

kyd1/ 2

Adapted from Fig. 7.13,

Callister 6e.

(Fig. 7.13 is adapted from

H. Suzuki, "The Relation

Between the Structure

and Mechanical Properties

of Metals", Vol. II, National

Physical Laboratory

Symposium No. 15, 1963,

p. 524.)

GRAIN SIZE STRENGTHENING:

AN EXAMPLE

Grain size controlled by heat treatment (e.g., cooling rateduring solidification, annealing)


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Can be induced by rolling a polycrystalline metal

-before rolling -after rolling

235 mm

-isotropicsince grains areapprox. spherical

& randomly

oriented.

-anisotropicsince rolling affects grainorientation and shape.

rolling direction


Callister 6e. (Fig. 7.11 is 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.)

ANISOTROPY IN yield


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Impurity atoms distort the lattice & generate stress.

Stress can produce a barrier to dislocation motion.

Smaller substitutional

impurity

Larger substitutional

impurity

Impurity generates local shear atA

and B that opposes disl motion to the

right.

Impurity generates local shear at C

and D that opposes disl motion to the

right.

STRENGTHENING STRATEGY 2:SOLID SOLUTION STRENGTHENING


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SOLID SOLUTION STRENGTHENING

Impurity atoms attracted to dislocations so as to

reduce the overall strain energy, i.e., to partiallycancel the strain in the lattice surrounding thedislocation

If a dislocation wants to move, it has to tear itselffrom the impurity atoms which will cost energy

Smaller impurity atom

above dislocation line

Larger impurity atom

below dislocation line

EXAMPLE SOLID SOLUTION


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EXAMPLE: SOLID SOLUTION

STRENGTHENING IN COPPER


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Hard precipitates are difficult to shear.Ex: Ceramics in metals (SiC in Iron or Aluminum).

Result: y ~1

S

STRENGTHENING STRATEGY 3:PRECIPITATION STRENGTHENING

SIMULATION


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View onto slip plane of Nimonic PE16 Precipitate volume fraction: 10%

Simulation courtesy of Volker

Mohles, Institut fr Materialphysik

der Universitt, Mnster, Germany

(http://www.uni-munster.de/physik

/MP/mohles/). Used with

permission.

SIMULATION:

PRECIPITATION STRENGTHENING

APPLICATION


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Internal wing structure on Boeing 767

Aluminum is strengthened with precipitates formed

by alloying.

Adapted from Fig.

11.24, Callister 6e.

(Fig. 11.24 is courtesyof G.H. Narayanan

and A.G. Miller,

Boeing Commercial

Airplane Company.)

Adapted from Fig.

11.0, Callister 5e.

(Fig. 11.0 is courtesy

of G.H. Narayanan

and A.G. Miller,

Boeing Commercial

Airplane Company.)

1.5mm

APPLICATION:

PRECIPITATION STRENGTHENING

STRENGTHENING STRATEGY 4


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Room temperature deformation. Common forming operations change the cross sectional

area:

%CW Ao Ad

Ao

x100

Ao Ad

force

dieblank

force

-Forging -Rolling

-Extrusion-Drawing

Adapted from Fig.

11.7, Callister 6e.

tensile

forceAo

Addie

die

STRENGTHENING STRATEGY 4:

COLD WORK (%CW)


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Ti alloy after cold working:

Dislocations entangle

with one anotherduring cold work.

Dislocation motion

becomes more difficult.

Adapted from Fig.

4.6, Callister 6e.(Fig. 4.6 is courtesy

of M.R. Plichta,

Michigan

Technological

University.)

DISLOCATIONS DURING COLD WORK


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Dislocation density (rd) goes up:

Carefully prepared sample: rd ~ 103 mm/mm3Heavily deformed sample: rd ~ 1010 mm/mm3

Ways of measuring dislocation density:

OR

dN

A

Area , A

N dislocation

pits (revealed

by etching)

dislocation

pit

r

Yield stress increasesas rd increases:

Micrograph

adapted from Fig.

7.0, Callister 6e.

(Fig. 7.0 is

courtesy of W.G.

Johnson, General

Electric Co.)

40mm

RESULT OF COLD WORK

SIMULATION DISLOCATION


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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 disl. density.

SIMULATION: DISLOCATION

MOTION/GENERATION

Simulation courtesy

of Farid Abraham. Used withpermission from International

Business Machines Corporation.


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Dislocations generate stress.

This traps other dislocations.

DISLOCATION-DISLOCATION TRAPPING


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Yield strength increases.

Tensile strength (TS) increases. Ductility (%EL or %AR) decreases (dramatically).


Callister 6e. (Fig. 7.18 is

from Metals Handbook:

Properties and Selection:

Iron and Steels, Vol. 1, 9th

ed., B. Bardes (Ed.),

American Society for Metals,

1978, p. 221.)

IMPACT OF COLD WORK


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What is the tensile strength &

ductility after cold working?

Adapted from Fig. 7.17, Callister 6e. (Fig. 7.17 is adapted from Metals Handbook: Properties and Selection:

Iron and Steels, Vol. 1, 9th ed., B. Bardes (Ed.), American Society for Metals, 1978, p. 226; and Metals

Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker

(Managing Ed.), American Society for Metals, 1979, p. 276 and 327.)

%CW ro2 rd2

ro2x100 35.6%

COLD WORK ANALYSIS


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Results for

polycrystalline iron:

y and TS decrease with increasing test temperature. %EL increases with increasing test temperature.

Why?


Callister 6e.

-e BEHAVIOR VS TEMPERTURE

Vacancies helpdislocations past

obstacles.


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1 hour treatment at Tanneal...

decreases TS and increases %EL. Effects of cold work are reversed!

3 Annealingstages to

discuss...

Adapted from Fig. 7.20, Callister 6e. (Fig.

7.20 is adapted from G. Sachs and K.R. van

Horn, Practical Metallurgy, Applied Metallurgy,

and the Industrial Processing of Ferrous and

Nonferrous Metals and Alloys, American

Society for Metals, 1940, p. 139.)

EFFECT OF HEATING AFTER %CW


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Annihilation reduces dislocation density.

Scenario 1

Scenario 2

RECOVERY


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New crystals are formed that:

--have a small disl. density--are small

--consume cold-worked crystals.

33% cold

worked

brass

New crystals

nucleate after

3 sec. at 580C.

Adapted from

Fig. 7.19 (a),(b),

Callister 6e.

(Fig. 7.19 (a),(b)

are courtesy of

J.E. Burke,

General Electric

Company.)

0.6 mm 0.6 mm

RECRYSTALLIZATION


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All cold-worked crystals are consumed.

After 4

seconds

After 8

seconds

Adapted fromFig. 7.19 (c),(d),

Callister 6e.

(Fig. 7.19 (c),(d)

are courtesy of

J.E. Burke,

General Electric

Company.)

0.6 mm0.6 mm

FURTHER RECRYSTALLIZATION


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At longer times, larger grains consume smaller ones. Why? Grain boundary area (and therefore energy) is reduced.

Empirical Relation:

After 8 s,

580C

After 15 min,

580C

dn don

Ktelapsed time

coefficient dependent

on material and T.

grain diam.

at time t.

exponent typ. ~ 2

0.6 mm 0.6 mm

Adapted from

Fig. 7.19 (d),(e),

Callister 6e.

(Fig. 7.19 (d),(e)are courtesy of

J.E. Burke,

General Electric

Company.)

GRAIN GROWTH


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Dislocations motion correlates to plastic deformation.

Strength is increased by making dislocation motion difficult.

Particular ways to increase strength are to:--decrease grain size

--solid solution strengthening

--precipitate strengthening

--cold work

Heating (annealing) can reduce dislocation densityand increase grain size.

SUMMARY

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Topic7-Strengthening Mechanisms

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