•

Why are dislocations observed primarily in metalsand alloys?

•

How are strength and dislocation motion related?

•

How do we manipulate properties?

StrengtheningHeat treating

1

CHAPTER 8: DEFORMATION AND STRENGTHENING MECHANISMS

Slip on close packed planes

•

In a given crystal, slip is easiest –

on the most densely packed plane

–

in the most densely packed direction

Single crystal Zn (hcp)

3

DISLOCATIONS

Edge

Screw

•

Produce plastic deformation,•

Incrementally breaking/reforming bonds.

Stress at dislocation

From: Van Vlack, 1985

Highest stress with no impurity at core

Under shear, atoms in the highly strained area will shift more easily

5

•

Dislocation motion requires the successive bumpingof a half plane of atoms (from left to right here).

•

Bonds across the slipping planes are broken andremade in succession.

Atomic view of edgedislocation motion fromleft to right as a crystalis sheared.

(Courtesy P.M. Anderson)

BOND BREAKING AND REMAKING

+ +

+

+ + + + + + + +

+ + + + + +

+ + + + + + +

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

+ + + +

+ + +

+ + + +

- - -

- - - -

- - -

3

•

Strain field around dislocation core•

Interaction between strain fields can effect motion

DISLOCATION MOTION -

SLIP

Edge

Dislocations allow slip at lower shear stress, but when they become entangled the metal is stronger.

6

•

close-packed

planes &

directions are preferred.

DISLOCATIONS & CRYSTAL STRUCTURE

WHY? – more nearest neighbors, easier to transfer bond from one atom to next

FCC slip directions

• How many slip directions? (100)<011>

Ex.: In (111) planeAlong [10-1] direction

(110)<-110>FCC

Slip plane/directions

NO CLOSE-PACKED PLANES, but still has preferred slip directions and planes

•

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

3

Shear stress

shear and normal stress on plane

Applied tensile stress produces shear on internal planes

Resolved components of pure shear and pure tension for the plane of interest

θσσ 2cos=′

θθστ cossin=′

Max shear stress at this angle (45)

7

•

Crystals slip due to a resolved shear stress, τR.

on favorably oriented plane/direction

τR= σcos λcos φ

STRESS AND DISLOCATION MOTION

Plasticallystretchedzincsinglecrystal.

Adapted from Fig. 7.9, Callister 6e. (Fig. 7.9 is from C.F. Elam, The Distortion of Metal Crystals, Oxford University Press, London, 1935.)

for shear stress on particular plane and direction

8

•

Condition for dislocation motion τR > τCRSS•

Orientation of slip system (crystal orientation) can make it easy or hard to move dislocation on that system

10-4G to 10-2G

typically

τR= σcos λcos φ

CRITICAL RESOLVED SHEAR STRESS (CRSS)

τR = 0

φ=90°

σ

τR = σ/2λ=45°φ=45°

σ

τR = 0

λ=90°

σ

Material property

9

•

Slip planes & directions(λ, φ) change from onecrystal to another.

•

τR

for most favorabledirection

will vary from one crystal to another.

•

The crystal with thelargest τR

yields first.

•

Other (less favorablyoriented) crystalsyield later.

σ

Adapted from Fig. 7.10, Callister 6e.(Fig. 7.10 is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].)300 μm

DISL. MOTION IN POLYCRYSTALS

•

Unfavorably oriented grains inhibit deformation of favorably oriented grains

Manipulation of properties

1. Strengthening

2. Heat treating

10

•

Grain boundaries arebarriers to slip.

•

Barrier "strength"

increases withmisorientation.

•

Smaller grain size:

more barriers to slip.

•

Hall-Petch Equation:

grain boundary

slip plane

grain Agra

in B

σyield = σo + kyd−1/2

Adapted from Fig. 7.12, Callister 6e.(Fig. 7.12 is from A Textbook of Materials Technology, by Van Vlack, Pearson Education, Inc., Upper Saddle River, NJ.)

3 STRATEGIES FOR STRENGTHENING: 1: REDUCE GRAIN SIZE

Example: Solidification conditions can change grain size

•

Can be induced by rolling a polycrystalline metal

12

-before rolling -after rolling

235 μm

-isotropicsince grains areapprox. spherical& randomlyoriented.

-anisotropicsince rolling affects grainorientation and shape.

rolling direction

Adapted from Fig. 7.11, 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 σyield

14

•

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

14

•

Impurity atoms distort the lattice & generate stress.•

Stress can produce a barrier to dislocation motion.

STRENGTHENING STRATEGY 2: SOLID SOLUTIONS

Solid Solution: Stress at dislocation

From: Van Vlack, 1985

Highest stress with no impurity at core

Under shear, atoms in the highly strained area will shift more easily

Effect of adding impurity at core of dislocation – added stress needed to move dislocation past the impurity

15

•

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

•

Empirical relation:

•

Alloying increases σy

and TS.

2/1

~ impurityy Cσ

Adapted from Fig. 7.14 (a) and (b), Callister 6e.

Yie

ld s

tre

ng

th (

MP

a)

wt. %Ni, (Concentration C)

60

120

180

0 10 20 30 40 50

Te

nsi

le s

tre

ng

th (

MP

a)

wt. %Ni, (Concentration C)

200

300

400

0 10 20 30 40 50

EX: SOLID SOLUTION

STRENGTHENING IN COPPER

16

•

Room temperature deformation. –

increase # of dislocations•

Common forming operations change the cross sectional area:

%CW =

Ao −AdAo

x100

Ao Ad

force

dieblank

force

-Forging -Rolling

-Extrusion-Drawing

Adapted from Fig. 11.7, Callister 6e.

tensile force

AoAddie

die

ram billet

container

containerforce

die holder

die

Ao

Adextrusion

roll

AoAd

roll

STRENGTHENING STRATEGY 3: COLD WORK (%CW)

17

•

Ti alloy after cold working:

•

Dislocations entanglewith one anotherduring cold work.

•

Dislocation motionbecomes more difficult.

0.9 μm

Adapted from Fig. 4.6, Callister 6e.(Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological University.)

DISLOCATIONS DURING COLD WORK

18

•

Dislocation density (ρd) goes up:Carefully prepared sample: ρd

~ 103

mm/mm3

Heavily deformed sample: ρd

~ 1010

mm/mm3

•

Measuring dislocation density:

d= N

A

Area, A

N dislocation pits (revealed by etching)

dislocation pit

ρ

•

Yield stress increasesas ρd

increases:large hardening

small hardening

σ

ε

σy0 σy1

40μm

RESULT OF COLD WORK

Str

ess

% cold work Strain

•

Yield strength (σ

) increases.

•

Tensile strength (TS) increases.

•

Ductility (%EL

or %AR) decreases.

21

y

Adapted from Fig. 7.18, 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

22

Cold work ----->

Do=15.2mm Dd=12.2mm

Copper

%CW =

πro2 − πrd

2

πro2

x100 = 35.6%

COLD WORK ANALYSIS

Ductility decreased,Tensile strength increased

•

What is the tensile strength &ductility after cold working?

Effect of Temperature on Strength

•

Results forpolycrystalline iron:

23

•

σy

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

Why? Vacancieshelp dislocationspast obstacles.

1. disl. trapped by obstacle

2. vacancies replace atoms on the disl. half plane

3. disl. glides past obstacle

obstacle

σ-ε

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 Annealingstages todiscuss...

RecoveryRecrystallizationGrain growth

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.)

Heat treatment: EFFECT OF HEATING AFTER %CWte

nsi

le s

tre

ng

th (

MP

a)

du

cti

lity

(%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.

25

• diffusion

atoms diffuse to regions of tension

extra half-plane of atoms

extra half-plane of atoms

Disl. annhilate and form a perfect atomic plane.

RECOVERY

Dislocation motion without externally applied stress

Reduction of dislocation density reduces strength

•

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.

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

The higher the internal strain, the faster recrystallization will occur

•

All cold-worked crystals are consumed.

27

After 4seconds

After 8seconds

Adapted from Fig. 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

•

At longer times, larger grains consume smaller ones. • Why?

28

After 8 s,580C

After 15 min,580C

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

Grain boundary area (and therefore internal energy)is reduced.

28

Heat Treatment of cold worked metal

One hour of baking at each temperature

Grain growth and recovery have a moderate effect on properties compared to recrystallization where disclocation density is more severely affected

Deformation and strengthening of polymers

29

0

unload/reload

0

brittle failure

plastic failure

20

40

60

2 4 6

σ(MPa)

ε

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

Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along plastic response curve (purple) 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.)

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

32

•

Compare to responses of other polymers:--brittle response

(aligned, cross linked & networked case)

--plastic response

(semi-crystalline case)

Stress-strain curves adapted from Fig. 15.1, Callister 6e.

Inset figures along elastomer curve (green) adapted from Fig. 15.14, Callister 6e. (Fig. 15.14 is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.)

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

σ(MPa)

ε 8

x

x

x

elastomer

plastic failure

brittle failure

Deformation is reversible!