ISSUES TO ADDRESS...• Why are dislocations observed primarily in metals and alloys?

• How are strength and dislocation motion related?

• How do we increase strength?

1

• How can heating change strength and other properties?

CHAPTER 8: DEFORMATION AND

STRENGTHENING MECHANISMS

3

• Produces plastic deformation,• Depends on incrementally breaking bonds.

Plasticallystretchedzincsinglecrystal.

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

DISLOCATION MOTION

+ +

+ +

+ + + + + + + + + + + + +

+ + + + + + +

2

• 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

+ + + +

+ + +

+ + + +

- - -

- - - -

- - -

6

• Structure: close-packed planes & directions are preferred.

• Comparison among crystal structures: FCC: many close-packed planes/directions; HCP: only one plane, 3 directions; BCC: none

close-packed plane (bottom)close-packed plane (top)

close-packed directions

Mg (HCP)

Al (FCC)tensile direction

• Results of tensile testing.

view onto twoclose-packedplanes.

DISLOCATIONS & CRYSTAL STRUCTURE

7

• Crystals slip due to a resolved shear stress, R. • Applied tension can produce such a stress.

Rcoscos

Relation between and R

R=Fs/As

Fcos A/cosns

AAs

STRESS AND DISLOCATION MOTION

Applied tensile stress: = F/A

FA

Fsli

p

direct

ion

Resolved shear stress: R=Fs/As

As

R

R

Fs

slip

direct

ion

slip plane

normal, ns

F

Fssli

p

direct

ion

8

• Condition for dislocation motion: R CRSS

• Crystal orientation can make it easy or hard to move disl.

10-4G to 10-2G

typically

Rcoscos

CRITICAL RESOLVED SHEAR STRESS

R = 0

=90°

R = /2=45°=45°

R = 0

=90°

9

• Slip planes & directions (, ) change from one crystal to another.

• R will vary from one crystal to another.

• The crystal with the largest R yields first.

• Other (less favorably oriented) crystals yield later.

300 m

DISL. MOTION IN POLYCRYSTALS

10

• Grain boundaries are barriers to slip.• Barrier "strength" increases with misorientation.• Smaller grain size: more barriers to slip.

• Hall-Petch Equation:

grain boundary

slip plane

grain Agr

ain

B

yield o kyd 1/2

4 STRATEGIES FOR STRENGTHENING: 1: REDUCE

GRAIN SIZE

11

• 70wt%Cu-30wt%Zn brass alloy

yield o kyd 1/2

• Data:

[grain size (mm)]-0.5

yie

ld(M

Pa)

50

100

150

200

04 8 12 16

10-1 10-2 5x10-3grain size, d (mm)

1

ky

0

0.75mm

GRAIN SIZE STRENGTHENING: AN EXAMPLE

• Can be induced by rolling a polycrystalline metal

12

-before rolling -after rolling

235 m

-isotropic since grains are approx. spherical & randomly oriented.

-anisotropic since rolling affects grain orientation and shape.

rolling direction

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 at A 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 SOLUTIONS

C

D

A

B

15

• Tensile strength & yield strength increase w/wt% Ni.

• Empirical relation:

• Alloying increases y and TS. y ~C1/2

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

EX: SOLID SOLUTIONSTRENGTHENING IN COPPER

16

• Room temperature deformation.• Common forming operations change the cross sectional area:

%CW

Ao AdAo

x100

Ao Ad

force

dieblank

force

-Forging -Rolling

-Extrusion-Drawing

tensile force

AoAddie

dieram billet

container

containerforce

die holder

die

Ao

Adextrusion

roll

AoAd

roll

STRENGTHENING STRATEGY : COLD WORK (%CW)

17

• Ti alloy after cold working:

• Dislocations entangle with one another during cold work.• Dislocation motion becomes more difficult.

0.9 m

DISLOCATIONS DURING COLD WORK

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• Dislocation density (d) goes up: Carefully prepared sample: d ~ 103

mm/mm3

Heavily deformed sample: d ~ 1010

mm/mm3

• Ways of measuring dislocation density:

ORlength, l1

length, l2length, l3

Volume, V

l1 l2 l3V

dd

NA

Area, A

N dislocation pits (revealed by etching)

dislocation pit

• Yield stress increases as d increases:

large hardeningsmall hardening

y0 y1

40m

RESULT OF COLD WORK

• Dislocation generate stress.• This traps other dislocations.

20

DISLOCATION-DISLOCATION TRAPPING

Red dislocation generates shear at pts A and B that opposes motion of green disl. from left to right.

A

B

Str

ess

% cold work Strain

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

21

y

IMPACT OF COLD WORK

• What is the tensile strength & ductility after cold working?

22

Cold work ----->

Do=15.2mm Dd=12.2mm

Copper

%CW ro

2 rd2

ro2

x10035.6%

COLD WORK ANALYSIS

ductility (%EL)

7%

%EL=7%% Cold Work

20

40

60

20 40 6000

Cu

% Cold Worky=300MPa

100

300

500

700

Cu

200 40 60

yield strength (MPa)

300MPa

% Cold Work

tensile strength (MPa)

340MPa

TS=340MPa

200Cu

0

400

600

800

20 40 60

• Results for polycrystalline iron:

23

• y and TS decrease with increasing test temperature.• %EL increases with increasing test temperature.• Why? Vacancies help dislocations past obstacles.

1. disl. trapped by obstacle

2. vacancies replace atoms on the disl. half plane

3. disl. glides past obstacle

obstacle

- BEHAVIOR VS TEMPERTURE

00 0.1 0.2 0.3 0.4 0.5

200

400

600

800

Str

ess

(M

Pa)

Strain

-200°C

-100°C

25°C

• 1 hour treatment at Tanneal... decreases TS and increases %EL.• Effects of cold work are reversed!

24

• 3 Annealing stages to discuss...

EFFECT OF HEATING AFTER %CW

ten

sile

str

en

gth

(M

Pa)

du

ctilit

y (

%E

L)

Annealing Temperature (°C)

300

400

500

600 60

50

40

30

20Recovery

Recrystallization

Grain Growth

ductility

tensile strength300 700500100

Annihilation reduces dislocation density.

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• Scenario 1

• Scenario 2

atoms diffuse to regions of tension

extra half-plane of atoms

extra half-plane of atoms

Disl. annhilate and form a perfect atomic plane.

1. dislocation blocked; can’t move to the right

obstacle dislocation

2. grey atoms leave by vacancy diffusion allowing disl. to “climb”

4. opposite dislocations meet and annihilate

3. “Climbed” disl. can now move on new slip plane

R

RECOVERY

• New crystals are formed that: --have a small disl. density --are small --consume cold-worked crystals.

26

33% coldworkedbrass

New crystalsnucleate after3 sec. at 580C.

0.6 mm 0.6 mm

RECRYSTALLIZATION

• All cold-worked crystals are consumed.

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After 4seconds

After 8seconds

0.6 mm0.6 mm

FURTHER RECRYSTALLIZATION

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

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• Empirical Relation:

After 8 s,580C

After 15 min,580C

dn do

n Ktelapsed time

coefficient dependenton material and T.

grain diam.at time t.

exponent typ. ~ 2

0.6 mm 0.6 mm

GRAIN GROWTH

Example

Using the diagram, compute the time for the average grain size to increase form 0.01-mm to 0.1-mm at (a) 500 oC and (b) 600 oC

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0

unload/reload

0

brittle failure

plastic failure

20

40

60

2 4 6

(MPa)

x

x

semi- crystalline

case

amorphous regions elongate

crystalline regions align

crystalline regions

slide

8

onset of necking

aligned, cross- linked case

networked case

Initial

Near Failure

near failure

TENSILE RESPONSE: BRITTLE & PLASTIC

30

• Drawing... --stretches the polymer prior to use --aligns chains to the stretching direction• Results of drawing: --increases the elastic modulus (E) in the stretching dir. --increases the tensile strength (TS) in the stretching dir. --decreases ductility (%EL)• Annealing after drawing... --decreases alignment --reverses effects of drawing.• Compare to cold working in metals!

Adapted from Fig. 15.12, Callister 6e. (Fig. 15.12 is from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp. 500-501.)

PREDEFORMATION BY DRAWING

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• Thermoplastics: --little cross linking --ductile --soften w/heating --polyethylene (#2) polypropylene (#5) polycarbonate polystyrene (#6)

• Thermosets: --large cross linking (10 to 50% of mers) --hard and brittle --do NOT soften w/heating --vulcanized rubber, epoxies, polyester resin, phenolic resin

Callister, Fig. 16.9

T

Molecular weight

Tg

Tmmobile liquid

viscous liquid

rubber

tough plastic

partially crystalline solid

crystalline solid

THERMOPLASTICS VS THERMOSETS

32

• Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (semi-crystalline case)

TENSILE RESPONSE: ELASTOMER CASE

initial: amorphous chains are kinked, heavily cross-linked.

final: chains are straight,

still cross-linked

0

20

40

60

0 2 4 6

(MPa)

8

x

x

x

elastomer

plastic failure

brittle failure

Deformation is reversible!

33

• Dislocations are observed primarily in metals and alloys.• Here, 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 density and increase grain size.

SUMMARY