Effects of Cold Work - Materials Science - Lecture Slides, Slides of Materials science

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Effects of Cold Work

Stress-strain curvesfor a material withprogressively increasingcold work What happens to theenergy to failure (toughness)with increasing cold work?

• Results for

polycrystalline iron:

σ

y

and TS

decrease with increasing test temperature.

• %EL

increases with increasing test temperature.

• Why? Vacancies

help dislocationspast obstacles.

1. disl. trapped

by obstacle

2. vacanciesreplaceatoms on thedisl. halfplane
3. disl. glides past obstacle

obstacle

σ Adapted from Fig. 6.14,Callister 6e.

Behavior vs Temperature

0

0

800600400200 Stress (MPa)

Strain

-200°C

-100°C

25°C

Annihilation reduces dislocation density.

• Scenario 1 • Scenario 2

atomsdiffuseto regionsof tension

extra half-plane

of atoms

extra half-plane

of atoms

Disl.annhilateand forma perfectatomicplane.

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

obstacle dislocation

2. grey atoms leave byvacancy diffusionallowing disl. to “climb”
   4. opposite dislocations

meet and annihilate

3. “Climbed” disl. can nowmove on new slip plane

R

Recovery

• New crystals are formed that:

--have a small disl. density--are small--consume cold-worked crystals. 33% coldworkedbrass

New crystalsnucleate after3 sec. at 580C.

Adapted fromFig. 7.19 (a),(b),Callister 6e.(Fig. 7.19 (a),(b)are courtesy ofJ.E. Burke,GeneralElectricCompany.)

0.6 mm

0.6 mm

Recrystallization

Recrystallization Temperature

Larger deformation

→

Higher stored elastic energy

Larger deformation

→

Higher dislocation density

Larger deformation

→

Lower recrystallization temperature

• 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

d

n

d

n o

Kt

coefficient dependenton material and T.elapsed time

grain diam.at time t.

exponent typ. ~ 2

0.6 mm

0.6 mm

Adapted fromFig. 7.19 (d),(e),Callister 6e.(Fig. 7.19 (d),(e)are courtesy ofJ.E. Burke,GeneralElectricCompany.)

Grain Growth

Atomic Scale Processes in Grain Growth

Grain Growth Local processes involveshort range atomic migrationacross the boundaryLarge grains consumesmall grains Driving force for grain growth Reduction in grain boundary area

Summary of Annealing of Metals

ISSUES TO ADDRESS...

• How does diffusion occur?• Why is it an important part of processing?• How can the rate of diffusion be predicted for

some simple cases?

• How does diffusion depend on structure

and temperature?

Chapter 5:

Diffusion in Solids

• Glass tube filled with water.• At time t = 0, add some drops of ink to one end

of the tube.

• Measure the diffusion distance, x, over some time.• Compare the results with theory. t

o t

1 t

2 t

3

x

o

x

1

x

2

x

3

time (s)

x (mm)

Diffusion Demo

• Self-diffusion:

In an elemental solid, atoms

also migrate.Label some atoms

After some time

C A B

D

A

B

C

D

Diffusion: The Phenomena (2)

Diffusion Mechanisms

Vacancy-Assisted DiffusionMotion of host or substitutionalImpurity into a vacant siteEnergetics:Two factors

Energy to form vacancyEnergy to move vacancy

Host atom motion:

Self-diffusion

Impurity atom motion:

Impurity diffusion

Interstitial DiffusionMotion of interstitial atom fromIntersticial site to interstial siteEnergetics:Main factors

Energy to move atom# of interstitial atoms

(self-diffusion)

• Doping Silicon with P for n-type semiconductors:• Process:
  1. Deposit P rich

layers on surface.

2. Heat it.3. Result: Doped

semiconductorregions.

silicon

silicon

magnified image of a computer chip

0.5mm

light regions: Si atomslight regions: Al atoms

Fig. 18.0,Callister 6e.

Processing Using Diffusion (2)

• Flux (#/area/time):

J

1 A

dMdt

kg m

2

s

or

atoms

m

2

s

• Directional Quantity• Flux can be measured for:

--vacancies and interstitials--host (A) atoms--impurity (B) atoms

Jx

Jy Jz

x

y

z

x-direction

Unit area Athroughwhichatomsmove.

Modeling Diffusion: Flux