Transcript Cold Working is Actually Strain Hardening s a r

Cold Working is Actually Strain Hardening
Basic equation relating flow stress (strain hardening) to structure is:
so = si +aGbr1/2
 so is the yield stress
 si is the “friction stress” – overall resistance of lattice to dislocation motion
 a is numerical constant 0.3 – 0.6
 G shear modulus
 b is the burger’s vector
syield  so  k y d 1/ 2
 r is the dislocation density
s
• Yield stress increases
s
as r increases:
s y1
y0
large hardening
small hardening
e
Effects of Cold Work
As cold work is increased
• Yield strength (sy) increases
• Tensile strength (TS) increases
• Ductility (%EL or %AR) decreases
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)
s-e Behavior vs. Temperature
• Results for
polycrystalline iron:
Stress (MPa)
800
-200C
600
-100C
400
25C
200
0
0
0.1
0.2
0.3
0.4
Strain
• sy and TS decrease with increasing test temperature.
• %EL increases with increasing test temperature.
• Why? Vacancies
3. disl. glides past obstacle
help dislocations
2. vacancies
move past obstacles. replace
Climb of
Edge Dislocations
Never Screw
atoms on the
disl. half
plane
Positive Climb
obstacle
1. disl. trapped
by obstacle
0.5
Strain Energy Related to Cold Work
Figure: Stored energy of cold work and
fraction of the total work of deformation
remaining as stored energy for high purity
copper
• 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!
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
Figure: Anisothermal anneal curve
for electrolytic copper
• 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
Source: Reed-Hill & Abbaschian, Physical Metallurgy Principles, 3rd
Edition, PWS Publishing Company, 1994.
• The cold worked state is
thermodynamically unstable.
Annealing Temperature (ºC)
100 20
600
0
300 400 500 600 700
60
tensile strength
50
500
40
400
30
ductility
300
20
ductility (%EL)
tensile strength (MPa)
Annealing Stages
• 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:
1. Recovery
2. Recrystallization
3. Grain Growth
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 1: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.
Source 2: Reed-Hill & Abbaschian, Physical Metallurgy Principles, 3rd Edition,
PWS Publishing Company, 1994.
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.
Recrystallization
• New grains are formed that:
-- have a small dislocation density
-- are small
-- consume cold-worked grains.
0.6 mm
33% cold
worked
brass
0.6 mm
New crystals
nucleate after
3 sec. at 580C.
Further Recrystallization
• All cold-worked grains are consumed.
0.6 mm
After 4
seconds
0.6 mm
After 8
seconds
º
TR = recrystallization
temperature
TR
º
Variables for Recrystallization
Six main variables influence recrystallization behavior:
1.
2.
3.
4.
5.
6.
The amount of prior deformation
Temperature
Time
Initial grain size
Composition
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 completely
recrystallizes 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.
7.
8.
The recrystallization temperature decreases with increasing
purity of the metal. Solid solution alloying additions
ALWAYS raise the recrystallization temperature.
The amount of deformation required to produce equivalent
recrystallization behavior increases with increased working
temperature
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.