CHAPTER 8: and alloys? DEFORMATION AND STRENGTHENING MECHANISMS - - PowerPoint PPT Presentation

• Why are dislocations observed primarily in metals

and alloys?

• How are strength and dislocation motion related?
• How do we manipulate properties?

Strengthening Heat treating

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CHAPTER 8:

DEFORMATION AND STRENGTHENING MECHANISMS

Slip on close packed planes

• In a given crystal, slip is easiest

–

• n 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 bumping
• f a half plane of atoms (from left to right here).
• Bonds across the slipping planes are broken and

remade in succession.

Atomic view of edge dislocation motion from left to right as a crystal is 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.

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• 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) plane Along [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

• n internal planes

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

θ σ σ

2

cos = ′ θ θ σ τ cos sin = ′

Max shear stress at this angle (45)

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• Crystals slip due to a resolved shear stress, τR.
• n favorably oriented plane/direction

τR= σcos λcos φ STRESS AND DISLOCATION MOTION

Plastically stretched zinc single crystal.

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

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• 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/2 λ=45° φ=45°

σ

τR = 0 λ=90°

σ

Material property

9

• Slip planes & directions

(λ, φ) change from one crystal to another.

• τR

for most favorable direction will vary from

• ne crystal to another.
• The crystal with the

largest τR yields first.

• Other (less favorably
• riented) crystals

yield 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

• riented grains

Manipulation of properties

• 1. Strengthening
• 2. Heat treating

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• 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 A g r a i n B

σyield = σo + k yd−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

• isotropic

since grains are

• approx. spherical

& randomly

• riented.
• anisotropic

since rolling affects grain

• rientation 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

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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

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• 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

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• Tensile strength & yield strength increase w/wt% Ni.
• Empirical relation:
• Alloying increases σy

and TS.

2 / 1

~

impurity y C

σ

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

Yield strength (MPa)

• wt. %Ni, (Concentration C)

60 120 180 0 10 20 30 40 50

Tensile strength (MPa)

• wt. %Ni, (Concentration C)

200 300 400 0 10 20 30 40 50 EX: SOLID SOLUTION STRENGTHENING IN COPPER

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• Room temperature deformation. –

increase # of dislocations

• Common forming operations change the cross sectional area:

%CW = Ao − Ad Ao x100

Ao Ad force die blank force

• Forging
• Rolling
• Extrusion
• Drawing

Adapted from Fig. 11.7, Callister 6e.

tensile force Ao Ad die die ram

billet container container

force die holder die Ao Ad

extrusion

roll Ao Ad roll

STRENGTHENING STRATEGY 3: COLD WORK (%CW)

17

• Ti alloy after cold working:
• Dislocations entangle

with one another during cold work.

• Dislocation motion

becomes more difficult.

0.9 μm

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

• f M.R. Plichta,

Michigan Technological University.)

DISLOCATIONS DURING COLD WORK

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• 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 increases

as ρd increases:

large hardening small hardening σ ε σy0 σy1

40μm

RESULT OF COLD WORK

Stress % cold work Strain

• Yield strength (σ

) increases.

• Tensile strength (TS) increases.
• Ductility (%EL
• r %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

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Cold work

• ---->

Do=15.2mm Dd=12.2mm Copper

%CW = πro

2 − πrd 2

πro

2

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 for

polycrystalline iron:

23

• σy

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
• bstacle

σ-ε BEHAVIOR VS TEMPERTURE

00 0.1 0.2 0.3 0.4 0.5 200 400 600 800

Stress (MPa) Strain

• 200°C
• 100°C

25°C

• 1 hour treatment at Tanneal...

decreases TS and increases %EL.

• Effects of cold work are reversed!

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• 3 Annealing

stages to discuss... Recovery Recrystallization Grain 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 %CW tensile strength (MPa) ductility (%EL) Annealing Temperature (°C) 300 400 500 600 60 50 40 30 20 Recovery Recrystallization Grain Growth

ductility tensile strength

300 700 500 100

Annihilation reduces dislocation density.

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• diffusion

atoms diffuse to regions

• f tension

extra half-plane

• f atoms

extra half-plane

• f 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.

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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

The higher the internal strain, the faster recrystallization will occur

• All cold-worked crystals are consumed.

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After 4 seconds After 8 seconds

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 mm 0.6 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.

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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

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unload/reload

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

• nset 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

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• 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

• f 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

20 40 60 2 4 6

σ(MPa)

ε

8 x x x

elastomer plastic failure brittle failure

Deformation is reversible!