Cold Working is Actually Strain Hardening

Basic equation relating flow stress (strain hardening) to structure is:

o = i +Gb1/2

• Yield stress increases as increases:

large hardening

small hardening

y0 y1

o is the yield stress i is the “friction stress” – overall resistance of lattice to dislocation motion is numerical constant 0.3 – 0.6 G shear modulus b is the burger’s vector is the dislocation density

21 /yoyield dk

Effects of Cold Work

• Yield strength (y) increases

• Tensile strength (TS) increases

• Ductility (%EL or %AR) decreases

As cold work is increased

Other Cold Work Effects

• Usually a small decrease in density (few 10ths of a percent)

• An appreciable decrease in electrical conductivity (increased number of scattering centers)

• Small increase in the thermal coefficient of expansion

• Because of increased internal energy – chemical reactivity is increased (decreased resistance to corrosion)

• Results for polycrystalline iron:

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

Climb ofEdge DislocationsNever Screw

- Behavior vs. Temperature-200C

-100C

25C

800

600

400

200

0

Strain

Str

ess

(M

Pa)

0 0.1 0.2 0.3 0.4 0.5

2. vacancies replace atoms on the disl. half plane

3. disl. glides past obstacle

1. disl. trapped by obstacle

obstacle

Positive Climb

Strain Energy Related to Cold Work• Mentioned that ~10% of the

energy imparted during cold working is stored as strain energy

• Amount of strain energy is increased by increasing the severity of deformation, lowering the deformation temperature, and by impurity additions

• The strain energy increase is stored in the highly deformed microstructure – dislocation tangles

• Metastable microstructure!Figure: Stored energy of cold work and fraction of the total work of deformation remaining as stored energy for high purity copper

Source: Reed-Hill & Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.

Annealing

• Can we release the stored strain energy? YES!

• The material is in an unstable state – but there is an activation energy barrier to releasing that energy

• By heating the material and adding energy to the system we can increase the probability of moving past the activation barrier

• Heat treating cold worked material is called Annealing

Release of Stored Energy

• What happens as we heat up cold worked material?

• Curve to the left is an anisothermal anneal curve

• Two samples – one cold worked and the other not

• Samples are heated continuously from low temperature to a higher temperature

• Energy release is determined as a function of temperature

• Difference in power to heat the specimens at same rate

Figure: Anisothermal anneal curve for electrolytic copper

Source: Reed-Hill & Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.

Annealing Stages

1. Recovery

2. Recrystallization

3. Grain Growth

• The cold worked state is thermodynamically unstable.

• With increasing temperature it becomes more and more unstable

• Eventually the metal softens and returns to a strain-free condition

• Complete process is known as Annealing

• Annealing is easily divided into 3 distinct processes:

ten

sile

str

eng

th (

MP

a)

duc

tility

(%

EL

)

tensile strength

ductility

Recovery

Recrystallization

Grain Growth

600

300

400

500

60

50

40

30

20

Annealing Temperature (ºC)200

100 300 400 500 600 700

Recovery• Defined as: Restoration of physical properties of a cold

worked metal without any observable change in microstructure– Electrical conductivity increases and lattice strain is reduced

– Strength properties are not affected

• Involves:– Dislocation Annihilation

– Polygonization:

• Removal of grain curvature created during deformation

• Regrouping of edge dislocations into low angle boundaries within grains

• Reduces the energy of system by creating reduced energy subgrains

Source 2: Reed-Hill & Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.

Source 1: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

Recrystallization

Recrystallization is:

• The replacement of the cold worked structure by the nucleation and growth of a new set of strain free grains– Density of dislocations is reduced

– Strain hardening is eliminated

– The hardness and strength is reduced and the ductility is increased

– Driving force for recrystallization is the release of stored strain energy

Note this is also the driving force for recovery and therefore they are sometimes competing processes

Source 1: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

How does it work?

• Nucleation of strain free grains occurs at points of high lattice curvature– Slip line intersections

– Deformation twin intersections

– Areas close to grain boundaries

• Several models (unproven) that propose mechanisms for nucleation:– Grain boundary bulging due to a local variance in strain energy

– Sub-boundary rotation and coalescence

Source 2: Reed-Hill & Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.

• New grains are formed that: -- have a small dislocation density -- are small -- consume cold-worked grains.

33% coldworkedbrass

New crystalsnucleate after3 sec. at 580C.

0.6 mm 0.6 mm

Recrystallization

• All cold-worked grains are consumed.

After 4seconds

After 8seconds

0.6 mm0.6 mm

Further Recrystallization

TR

º

º

TR = recrystallization temperature

Variables for RecrystallizationSix main variables influence recrystallization behavior:

1. The amount of prior deformation2. Temperature3. Time4. Initial grain size5. Composition6. Amount of recovery or polygonization prior to the start of

recrystallization

Because the temperature at which recrystallization occurs depends Recrystallization temperature is not a fixed temperature like melting point

The practical definition for recrystallization temperature is:The temperature at which a given alloy in a highly cold worked state completelyrecrystallizes in 1 hour.

Source: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

Affect of Variables on Recrystallization

1. Minimum amount of deformation is required

2. The smaller the deformation, the higher the temperature required for recrystallization

3. Increasing annealing time decreases required recrystallization temperature. Temperature is more important than time. Doubling annealing time is approximately equivalent to increasing annealing temperature 10oC

4. Final grain size depends most on the degree of deformation and to lesser extent on the annealing temperature. The greater the deformation & the lower the annealing temp., the smaller the recrystallized grain size.

5. The larger the original grain size, the greater the amount of cold work required to produce same recrystallization temp.

Source: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

Affect of Variables on Recrystallization

6. The recrystallization temperature decreases with increasing purity of the metal. Solid solution alloying additions ALWAYS raise the recrystallization temperature.

7. The amount of deformation required to produce equivalent recrystallization behavior increases with increased working temperature

8. For a given reduction in cross-section – different metal working processes produce different effective deformations. Therefore, identical recrystallization behavior may not be obtained.

Source: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.