Stored Energy of Cold Work

103 Pages·2015·4.94 MB·English

Chapter 8
物理冶金 魏茂國
Annealing
 Stored energy of cold work
 The relationship of free energy to strain energy
 The release of stored energy
 Recovery
 Recovery in single crystals
 Polygonization
 Dislocation movements in polygonization
 Recovery process at high and low temperatures
 Recrystallization
 The effect of time and temperature on recrystallization
 Rerystallization temperature
 The effect of strain on recrystallization
 The rate of nucleation and the rate of nucleus growth
 Formation of nuclei
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 Driving force for recrystallization
Chapter 8
物理冶金 魏茂國
Annealing
 The recrystallized grain size
 Other variables in recrystallization
 Purity of the metal
 Initial grain size
 Grain growth
 Geometrical coalescence
 Three-dimensional changes in grain geometry
 The grain growth rate
 Impurity atoms in solid solution
 Impurities in the form of inclusions
 The free-surface effects
 The limiting grain size
 Preferred orientation
 Secondary recrystallization
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 Strain-induced boundary migration
Stored Energy of Cold Work
物理冶金 魏茂國
 Stored energy of cold work
- When a metal is plastically deformed at temperatures that are low relative to its
melting point, it is said to be cold worked. A rough rule-of-thumb is to assume that
plastic deformation corresponds to cold working if it is carried out at temperatures
lower than one-half of the melting point measured on an absolute scale.
- Most of the energy expended in cold work appears in the form of heat, but a finite
fraction is stored in the metal as strain energy associated with various lattice defects
created by the deformation. Fig. 8.1 shows the relationship between the stored
energy and the amount of deformation in a specific metal (polycrystalline 99.999%
pure copper) for a specific type of deformation
(tensile strain). The stored energy increases with
increasing deformation, but at a decreasing rate,
so that the fraction of the total energy stored
decreases with increasing deformation.
Fig. 8.1 Stored energy of cold work and fraction of the total work
of deformation remaining as stored energy for high purity copper 3
plotted as functions of tensile elongation.
Stored Energy of Cold Work
物理冶金 魏茂國
- The amount of stored energy can be greatly increased by increasing the severity of the
deformation, lowering the deformation temperature, and by changing the pure metal
to an alloy.
- Cold working is known to increase greatly the number of dislocations in a metal. A
soft annealed metal can have dislocation densities of the order of 1010 to 1012 m-2, and
heavily cold-worked metals can have approximately 1016. Accordingly, cold working
is able to increase the number of dislocations in a metal by a factor as large as 104 to
106. Since each dislocation represents a crystal defect with an associated lattice strain,
increasing the dislocation density increases the strain energy of the metal.
- A screw dislocation that cuts another screw dislocation may be capable of generating
a close-packed row of either vacancies or interstitials as it glides.
- Since the strain energy associated with a vacancy is much smaller than that associated
with an interstitial atom, it can be assumed that vacancies will be formed in greater
numbers than interstitial atoms during plastic deformation.
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Relationship of Free Energy to Strain Energy
物理冶金 魏茂國
 Relationship of free energy to strain energy
- While plastic deformation certainly increases the entropy of a metal, the effect is
small compared to the increase in internal energy (the retained strain energy). The
term -T∆S in the free energy equation may be neglected and the free-energy
increase equated directly to the stored energy.
G  H TS
TS  H  G  H (8.1)

where ∆G is the free energy associated with the cold work, ∆H is the enthalpy, or
stored strain energy, S is the entropy increase due to the cold work, and T is the
absolute temperature.
- Since the free energy of cold-worked metals is greater than that of annealed metals,
they may soften spontaneously. Heating a deformed metal greatly speeds up its
return to the softened state.
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Release of Stored Energy
物理冶金 魏茂國
 Release of stored energy
- Two of the more important studies of the release of the stored energy will be briefly
indicated. In the first , the anisothermal anneal (非等溫退火) method, the cold-
worked metal is heated continuously from a lower to a higher temperature and the
energy release is determined as a function of temperature. One form of the
anisothermal anneal measures the difference in the power required to heat 2 similar
specimens at the same rate. One specimen of the 2 is cold worked before the heating
cycle, while the other serves as a standard and is not deformed. During the heating
cycle, the cold-worked specimen undergoes reactions that release heat and lower the
power required to heat it in comparison
with that required to heat the standard
specimen. Measurements of the difference
in power give direct evidence of the rate at
which heat is released in the cold-worked
specimen (Fig. 8.2).
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Fig. 8.2 Anisothermal anneal curve. Electrolytic copper.
Release of Stored Energy
物理冶金 魏茂國
It is noteworthy that some heat is released at temperatures only slightly above room
temperature (Fig. 8.2).
- The other method of studying energy release involves isothermal annealing (恆溫退
火). Here the energy is measured while the specimen is maintained at a constant
temperature. In Fig. 8.3, the data for this particular curve were obtained with the aid
of a microcalorimeter with a sensitivity capable of measuring a heat flow as low as 13
mJ/hr.
- Both the anisothermal anneal and the isothermal anneal curves of Figs. 8.2 and 8.3
shown maxima corresponding to large energy releases. These large energy releases
appear simultaneously with the growth
of an entirely new set of essentially
strain-free grains, which grow at the
expense of the original badly deformed
grains.
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Fig. 8.3 Isothermal anneal curve. High purity copper.
Release of Stored Energy
物理冶金 魏茂國
The process by which this occurs is called recrystallization and may be understood as
a realignment of the atoms into crystals with a lower free energy.
- In Figs. 8.2 and 8.3, the area under each solid curve that lies to the left and above the
dashed lines represents an energy release not associated with recrystllization. The part
of the annealing cycle that occurs before recrystallization is called recovery.
- It is necessary to define the third stage of annealing-grain growth. In grain growth,
certain of the recrystallized grains continue to grow in size, but only at the expense of
other crystals which must disappear.
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Release of Stored Energy
物理冶金 魏茂國
- The release of stored energy in cold-rolled high-purity iron using a differential
scanning calorimeter (DSC) is shown in Fig. 8.4. In this figure, where the heat
generation by the metal shows as a negative deviation in the heat flow curve, after the
initial transient peak below 100C, a broad exothermic peak extending from ~100 to
280C can be seen. This broad exothermic peak is followed by a larger one extending
from ~300 to 480C. The energy release in these 2 peaks has been calculated by the
authors as 3.9 and 15.1 J/mol, corresponding to 19 J/mol for the total stored energy.
- The changes in the microstructure of the
cold-rolled iron during heating, revealed
by interrupted quenching, are shown in
Figs. 8.5A-F.
- The deformed structure is retained up to
300C, but new grains form as the metal is
heated further.
Fig. 8.4 Heat flow versus temperature for 80% cold-rolled
ultra-high-purity iron. 9
Release of Stored Energy
物理冶金 魏茂國
- The new-formed grains can be clearly seen as isolated spots in Fig. 5C, while other
regions still show the deformed microstructure. At 460C (Fig. 8.5E), most of the
deformed regions have been replaced by new grains which grow considerably larger
at the higher temperature
(Fig. 8.5F).
- The 3 stages of annealing
are recovery,
recrystallization, and grain
growth.
Fig. 8.5 Optical view of microstructure
of deformed iron at different annealing
temperatures; (a) as cold rolled, (B)
annealed at 300C, (C) annealed at
370C, (D) annealed at 410C, (E)
annealed at 460C, and (F) annealed 10
at 650C.