Chapter 10: Phase Transformations –
Considering Kinetic and Heat Treatment
ISSUES TO ADDRESS...
• Transforming one phase into another takes time.
Fe
g
(Austenite)
C
FCC
Fe C
3
Eutectoid
transformation (cementite)
+
a
(ferrite)
(BCC)
• How does the rate of transformation depend on
time and T?
• How can we slow down the transformation so that
we can engineer non-equilibrium structures?
• Are there other means to improve mechanical behavior?
Phase Transformations
Nucleation
– nuclei (like biological seeds) act as
template to grow crystals
– for nuclei to form, the rate of addition of
atoms to any nucleus must be faster than
rate of loss
– once nucleated, the “seed” must grow
until they reach the predicted equilibrium
Phase Transformations
Driving force to nucleate increases as we
increase T
– supercooling (eutectic, eutectoid)
– superheating (peritectic)
• With a Small amount of supercooling  few
nuclei - large crystals
• With a Large amount of supercooling 
rapid nucleation - many nuclei, small
crystals
Solidification: Nucleation Processes
• Homogeneous nucleation
– nuclei form in the bulk of liquid metal (as
“native chemistry”)
– requires sufficient supercooling (typically 80300°C max)
• Heterogeneous nucleation
– much easier since stable “nucleus” is already
present (they are non-native chemically)
• Could be wall of mold or impurities in the liquid
phase
– allows solidification with only minimal
supercooling (0.1-10ºC)
Homogeneous Nucleation & Energy Effects
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
GS  4r 2 g
g = surface tension
GT = Total Free Energy
= GS + GV
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
4
GV  r 3 G
3
volume free energy
unit volume
r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)
G 
Solidification
 2 gTm
r* 
H S T
r* = critical radius
g = surface free energy
Tm = melting temperature
HS = latent heat of solidification
T = Tm - T = supercooling
Note: HS is a strong function of T
g
is a weak function of T

r*
decreases as T increases
For typical T
r* is around 100Å (10 nm)
Rate of Phase Transformations
Kinetics - measures approach to
equilibrium vs. time
• Hold temperature constant & measure conversion
vs. time
– How is the amount of conversion measured?
• X-ray diffraction – have to do many samples
• electrical conductivity – follows a single sample
• sound waves (insitu ultrasonic) – follows a single
sample
Thus, the rate of nucleation is a product of two
curves that represent two opposing factors
(instability and diffusivity).
Rate of Phase Transformation
All out of material – “done!”
Fixed Temp.
maximum rate reached – now amount
t0.5 unconverted decreases so rate slows
rate increases as surface area increases
& nuclei grow
Log Time
– Modeled by the Avrami Rate Equation:
y  1 e
 kt n
Avrami Equation
Avrami rate equation → y = 1- exp (-ktn)
k & n are fit for any specific sample
• By convention we define: r = 1 / t0.5 as “the rate of transformation”
– it is simply the inverse of the time to complete half of the
transformation
• The initial slow rate can be attributed to the time required for a
significant number of nuclei of the new phase to form and begin
growing.
• During the intermediate period the transformation is rapid as the
nuclei grow into particles and consume the old phase while nuclei
continue to form in the remaining parent phase.
• Once the transformation begins to near completion there is little
untransformed material for nuclei to form in and the production of
new particles begins to slow. Further, the particles already existing
begin to touch one another, forming a boundary where growth stops.
Rate of Phase Transformations
135C 119C
1
10
113C 102C
88C
102
43C
104
• In general, rate increases as T 
adapted from B.F. Decker and
D. Harker, "Recrystallization in
Rolled Copper", Trans AIME,
188, 1950, p. 888.
r = 1/t0.5 = A e -Q/RT
–
–
–
–
Arrhenius expression
R = gas constant
T = temperature (K) (higher causes higher rate too)
A = ‘preexponential’ rate factor
Q = activation energy
• r is often small so equilibrium is not possible!
Transformations & Undercooling
g  a + Fe3C
• Eutectoid transf. (Fe-C System):
0.76 wt% C
6.7 wt% C
0.022 wt% C
• M. Eng. Can make it occur at:
...727ºC (cool it slowly)
...below 727ºC (“supercool” or “Undercool” it!)
T(°C)
1600
d
1200
1148°C
1000
L+Fe3C
g +Fe3C
Eutectoid:
Equil. Cooling: Ttransf. = 727ºC
800
727°C
400
0
(Fe)
T
a +Fe3C
Undercooling by Ttransf. < 727C
0.76
600
0.022
a
ferrite
g +L
g
(austenite)
1
2
3
4
5
6
Fe3C (cementite)
L
1400
6.7
Co , wt%C
adapted from Binary Alloy Phase
Diagrams, 2nd ed., Vol. 1, T.B.
Massalski (Ed.-in-Chief), ASM
International, Materials Park, OH,
1990
Eutectoid Transformation Rate
• Growth of pearlite from austenite:
Adapted from
Fig. 9.15,
Callister 7e.
a
a
g a
a
a
a
• Recrystallization
rate increases
with T.
g
cementite (Fe3C)
Ferrite (a)
a
g
a
pearlite
growth
direction
a
100
y (% pearlite)
Austenite (g)
grain
boundary
Diffusive flow
of C needed
127°C
(600 ˚C)
50
77°C
52°C
(675˚C)
0
Coarse pearlite  formed at higher T - softer
Fine pearlite
 formed at low T - harder
g
Nucleation and Growth
• Reaction rate is a result of nucleation and growth
of crystals.
• Examples from previous slide:
g
pearlite
colony
T: just below TE
Nucleation rate low
Growth rate high
g
T: moderately belowTE
Nucleation rate med
Growth rate med.
g
T: way below TE
Nucleation rate high
Growth rate low
The ideas of “reality” and the “ideal” meet in
the Material Engineering’s Transformation
Curves
Isothermal Transformation (TTT) Diagrams
y,
% transformed
• Fe-C system, Co = 0.76 wt% C
• Transformation at T = 675°C.
100
T = 675°C
50
0
10 2
1
T(°C)
Austenite (stable)
10 4
time (s)
TE (727C)
700
Austenite
(unstable)
600
Pearlite
isothermal transformation at 675°C
500
400
1
10
10 2 10 3 10 4 10 5
time (s)
adapted from H. Boyer (Ed.) Atlas of Isothermal
Transformation and Cooling Transformation Diagrams,
American Society for Metals, 1977, p. 369.
Effect of Cooling History in Fe-C System
• Eutectoid composition, Co = 0.76 wt% C
• Begin at T > 727°C
• Rapidly cool to 625°C and hold isothermally.
T(°C)
Austenite (stable)
700
Austenite
(unstable)
600
g
g
500
TE (727C)
Pearlite
g
g
g
g
400
1
10
10 2
10 3
time (s)
10 4
10 5
adapted from H. Boyer (Ed.) Atlas
of Isothermal Transformation and
Cooling Transformation Diagrams,
American Society for Metals, 1997,
p. 28.
Transformations with Proeutectoid Materials
CO = 1.13 wt% C
T(°C)
T(°C)
900
d
A
800
+
C
A
+
P
g +L
g
L+Fe3C
(austenite)
1000
a
P
g +Fe3C
800
600
1
10
102
103
time (s)
Adapted from Fig. 10.16,
Callister 7e.
104 400
0
(Fe)
0.76
500
T
1.13
600
A
1200
0.022
700
TE (727°C)
A
L
1400
1
727°C
a +Fe3C
2
3
4
Adapted from Fig. 9.24,
Callister 7e.
5
6
Fe3C (cementite)
1600
6.7
Co , wt%C
Hypereutectoid composition – proeutectoid cementite
Non-Equilibrium Transformation Products in Fe-C
• Bainite:
--a lathes (strips) with long
rods of Fe3C
--diffusion controlled.
• Isothermal Transf. Diagram
800
Austenite (stable)
T(°C)
A
pearlite/bainite boundary
100% bainite
400
B
A
200
10-1
10
103
a (ferrite)
TE
P pearlite
100%
600
Fe3C
(cementite)
105
time (s)
adapted from H. Boyer (Ed.) Atlas of Isothermal
Transformation and Cooling Transformation Diagrams,
American Society for Metals, 1997, p. 28.
5 mm
from Metals Handbook, 8th ed., Vol. 8, Metallography,
Structures, and Phase Diagrams, American Society for
Metals, Materials Park, OH, 1973.)
TTT Curves showing the Bainite Transformation
(a) Plain Carbon Steels; (b) Alloy Steel w/ distinct
Bainite “Nose”
From: George Krauss, Steels: Processing, Structure,
and Performance, ASM International, 2006.
Martensite: Fe-C System
• Martensite:
--g(FCC) to Martensite (BCT)
Fe atom
sites
60 mm
(involves single atom jumps)
x
x
x
x
x
xpotential
C atom sites
• Isothermal Transf. Diagram
800
Austenite (stable)
T(°C)
A
10-1
courtesy United States
Steel Corporation.
• g to M transformation..
B
A
200
TE
P
600
400
Martensite needles
Austenite
0%
50%
90%
M+A
M+A
M+A
10
103
105
-- is rapid!
-- % transf. depends on T only.
time (s)
Transformation to Martensite
Martensite formation
requires that the steel
be subject to a minimum
– Critical – Cooling Rate
(this value is ‘TTT’ or
‘CCT’ chart dependent
for alloy of interest)
For most alloys it
indicates a quench into
a RT oil or water bath
Martensite Formation
g (FCC)
slow cooling
a (BCC) + Fe3C
quench
M (BCT)
tempering
M = martensite is body centered tetragonal (BCT)
Diffusionless transformation
BCT  few slip planes
BCT if C > 0.15 wt%
 hard, brittle
Martensite Transformation Crystallography:
FCC Austenite to BCT Martensite
From: George Krauss, Steels: Processing, Structure,
and Performance, ASM International, 2006.
Austenite to Martensite: Size Issues and
Material Response
From: George Krauss, Steels: Processing, Structure,
and Performance, ASM International, 2006.
Spheroidite: Fe-C System
a
(ferrite)
(Fig. 10.19 copyright United States
Steel Corporation, 1971.)
Fe3C
(cementite)
60 mm
• Spheroidite:
--a grains with spherical Fe3C
--diffusion dependent.
--heat bainite or pearlite for long times (below the AC1
critical temperature)
--driven by a reduction in interfacial area of Carbide
Phase Transformations of Alloys
Effect of adding other
elements
Change transition temp.
Cr, Ni, Mo, Si, Mn
retard g  a + Fe3C
transformation delaying
the time to entering the
diffusion controlled
transformation reactions
– thus promoting
“Hardenability’ or
Martensite development
Continuous Cooling Transformations
(CCT)
• Isothermal Transformations are “Costly”
requiring careful “gymnastics” with heated
(and cooling) products
• CC Transformations change the observed
behavior concerning transformation
– With Plain Carbon Steels when cooled
“continuously” we find that the Bainite
Transformation is suppress(see Figure 10.26)
Cooling Curve
Plot:
temp vs. time
CCT for Eutectoid Steel
Figure: 10-26
CCT for Eutectoid Steel
Alloy Steel CCT Curve – again note distinct
Bainite Nose
Adapted from Fig. 10.23, Callister 7e.
Dynamic Phase Transformations
On the isothermal transformation
diagram for 0.45 wt% C Fe-C alloy,
sketch and label the time-temperature
paths to produce the following
microstructures:
a) 42% proeutectoid ferrite and 58% coarse
pearlite
b) 50% fine pearlite and 50% bainite
c) 100% martensite
d) 50% martensite and 50% austenite
Example Problem for Co = 0.45 wt%
a) 42% proeutectoid ferrite and 58% coarse
pearlite
800
A
T (°C)
first make ferrite
600
then pearlite
A+a
P
B
A+P
A+B
A
400
coarse pearlite
 higher T
Adapted from
Fig. 10.29,
Callister 5e.
50%
M (start)
M (50%)
M (90%)
200
0
0.1
10
103
time (s)
105
Example Problem for Co = 0.45 wt%
b) 50% fine pearlite and 50% bainite
800
A+a
A
first make pearlite T (°C)
then bainite
P
B
600
fine pearlite
A+B
 lower T
A
400
NOTE: This “2nd step” is
sometimes referred to as
an “Austempering” step,
quenching into a heated
salt bath held at the
temperature of need
A+P
50%
M (start)
M (50%)
M (90%)
200
0
0.1
10
103
time (s)
Adapted from Fig. 10.29, Callister 5e.
105
Example Problem for Co = 0.45 wt%
c) 100 % martensite: quench @ 380C/s {(850-600)/.7s}
800
A+a
A
T
(°C)
P
B
600
A+P
d) 50%martensite/50%(retained)
austenite
A+B
A
400
50%
M (start)
M (50%)
M (90%)
d)
200
c)
0
0.1
10
103
time (s)
Adapted from Fig. 10.29, Callister 5e.
105
CT for CrMo Med-carbon steel
Hardness of cooled samples at various cooling rates in bubbles -- Dashed lines
are IT solid lines are CT regions
Tempering Martensite
• reduces brittleness of martensite,
• reduces internal stress caused by quenching.
TS(MPa)
YS(MPa)
1800
from Fig.
furnished
courtesy of
Republic Steel
Corporation.)
1400
TS
YS
1200
1000
60
50
%RA
40
30
%RA
800
200
400
9 mm
1600
copyright by
United States
Steel Corporation,
1971.
600
Tempering T (°C)
• produces extremely small Fe3C particles surrounded by a.
• decreases TS, YS but increases %RA
The microstructure of tempered martensite, although an equilibrium
mixture of α-Fe and Fe3C, differs from those for pearlite and bainite.
This micrograph produced in a scanning electron microscope (SEM)
shows carbide clusters in relief above an etched ferrite. (From ASM
Handbook, Vol. 9: Metallography and Microstructures, ASM
International, Materials Park, OH, 2004.)
Temper Martensite Embrittlement – an issue
in Certain Steels
From: George Krauss, Steels: Processing, Structure,
and Performance, ASM International, 2006.
Suspected to be due to the deposition of very fine
carbides during 2nd and 3rd phase tempering along
original austenite G. B. from the transformation of
retained austenite,
Increasing Strength and Hardness of Alloy
involves some Heat Treatment
• The effect of quenching in steels is determined
by the Jominey End Quench Test
• Precipitation Hardness is a method used for may
alloy systems (mostly Non-Ferrous ones)
• Grain Size control is also an important
consideration – which can be controlled by
annealing processes
• Recovery after cold work (cold work can also increase
strength of alloys)
• Recrystalization
• Grain Growth
Schematic illustration of the Jominy end-quench test for hardenability.
(After W. T. Lankford et al., Eds., The Making, Shaping, and Treating of
Steel, 10th ed., United States Steel, Pittsburgh, PA, 1985. Copyright
1985 by United States Steel Corporation.)
Hardenability--Steels
• Ability to form martensite
• Jominy end quench test to measure hardenability.
flat ground
specimen
(heated to g
phase field)
24°C water
(adapted from A.G. Guy,
Essentials of Materials
Science, McGraw-Hill Book
Company, New York,
1978.)
Rockwell C
hardness tests
Hardness, HRC
• Hardness versus distance from the quenched end.
Distance from quenched end
Figure 10.22 The cooling rate for the Jominy bar (see Figure 10.21)
varies along its length. This curve applies to virtually all carbon and
low-alloy steels. (After L. H. Van Vlack, Elements of Materials Science
and Engineering, 4th ed., Addison-Wesley Publishing Co., Inc.,
Reading, MA, 1980.)
Figure 10.23 Variation in hardness along a typical Jominy
bar.
(From W. T. Lankford et al., Eds., The Making, Shaping, and Treating of Steel, 10th ed., United States Steel, Pittsburgh, PA, 1985. Copyright 1985 by United
States Steel Corporation.)
Why Hardness Changes W/Position
Hardness, HRC
• The cooling rate varies with position.
60
40
20
0
1
2
3
distance from quenched end (in)
T(°C)
0%
100%
600
(adapted from H. Boyer (Ed.) Atlas of
Isothermal Transformation and Cooling
Transformation Diagrams, American
Society for Metals, 1977, p. 376.)
400
200
M(start)
AM
0 M(finish)
0.1
1
10
100
1000
Time (s)
Hardenability vs Alloy Composition
(adapted from figure furnished courtesy
Republic Steel Corporation.)
100
Hardness, HRC
• Jominy end quench
results, C = 0.4 wt% C
(4140, 4340, 5140, 8640)
--contain Ni, Cr, Mo
(0.2 to 2wt%)
--these elements shift
the "nose".
--martensite is easier
to form.
3
2 Cooling rate (°C/s)
60
100
80 %M
4340
50
40
4140
8640
20
• "Alloy Steels"
10
5140
0 10 20 30 40 50
Distance from quenched end (mm)
800
T(°C)
600
A
TE
shift from
A to B due
to alloying
B
400
M(start)
M(90%)
200
0 -1
10
10
10
3
5
10 Time (s)
Figure 10.24 Hardenability curves for various steels with the same carbon
content (0.40 wt %) and various alloy contents. The codes designating the
alloy compositions are defined in Table 11.1.
(From W. T. Lankford et al., Eds., The Making, Shaping, and Treating of Steel, 10th ed., United States Steel, Pittsburgh, PA, 1985. Copyright 1985 by United
States Steel Corporation.)
Quenching Medium & Geometry
• Effect of quenching medium:
Medium
air
oil
water
Severity of Quench
low
moderate
high
Hardness
low
moderate
high
• Effect of geometry:
When surface-to-volume ratio increases:
--cooling rate increases
--hardness increases
Position
center
surface
Cooling rate
low
high
Hardness
low
high
Precipitation Hardening
• Particles impede dislocations.
700
• Ex: Al-Cu system
T(°C)
• Procedure:
600
--Pt A: solution heat treat
(get a solid solution)
--Pt B: quench to room temp.
--Pt C: reheat to nucleate
small q crystals within
a crystals.
400
a+L
q+L
A
a+q
C
300
(Al) 0 B 10
20
30
40
q
50
wt% Cu
composition range
needed for precipitation hardening
• Other precipitation
systems:
• Cu-Be
• Cu-Sn
• Mg-Al
500
a
CuAl2
L
Adapted from Fig. 11.24, Callister 7e. (Fig. 11.24 adapted from J.L.
Murray, International Metals Review 30, p.5, 1985.)
Temp.
Pt A (sol’n heat treat)
Pt C (precipitate q)
Pt B
Time
Consider: 17-4
PH St. Steel and
Ni-Superalloys
too!
Figure 10.25 Coarse precipitates form at grain boundaries in an Al–
Cu (4.5 wt %) alloy when slowly cooled from the single-phase (κ) region
of the phase diagram to the two-phase (θ + κ) region. These isolated
precipitates do little to affect alloy hardness.
Figure 10.26 By quenching and then reheating an Al–Cu (4.5 wt %) alloy, a
fine dispersion of precipitates forms within the κ grains. These precipitates are
effective in hindering dislocation motion and, consequently, increasing alloy
hardness (and strength). This process is known as precipitation hardening, or
age hardening.
Figure 10.27 (a) By extending the reheat step, precipitates coalesce and
become less effective in hardening the alloy. The result is referred to as
overaging. (b) The variation in hardness with the length of the reheat step
(aging time).
Figure 10.28 (a) Schematic illustration of the crystalline geometry of a Guinier–Preston
(G.P.) zone. This structure is most effective for precipitation hardening and is the
structure developed at the hardness maximum shown in Figure 10.27b. Note the
coherent interfaces lengthwise along the precipitate. The precipitate is approximately 15
nm × 150 nm.
(From H. W. Hayden, W. G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. 3: Mechanical Behavior, John Wiley & Sons, Inc., NY, 1965.)
(b) Transmission electron micrograph of G.P. zones at 720,000×. (From ASM Handbook, Vol. 9: Metallography and Microstructures, ASM International,
Materials Park, OH, 2004.)
Figure 10.30 Annealing can involve the complete recrystallization and
subsequent grain growth of a cold-worked microstructure. (a) A cold-worked brass
(deformed through rollers such that the cross-sectional area of the part was
reduced by one-third). (b) After 3 s at 580°C, new grains appear. (c) After 4 s at
580°C, many more new grains are present.
All micrographs have a magnification of
75×. (Courtesy of J. E. Burke, General
Electric Company, Schenectady, NY.)
(d) After 8 s at 580°C, complete recrystallization has occurred. (e) After 1 h at
580°C, substantial grain growth has occurred. The driving force for this growth
is the reduction of high-energy grain boundaries. The predominant reduction in
hardness for this overall process had occurred by step (d)
Figure 10.31 The sharp drop in hardness identifies the recrystallization
temperature as ~290°C for the alloy C26000, “cartridge brass.”
(From Metals Handbook, 9th ed., Vol. 4, American Society for Metals, Metals Park, OH, 1981.)
Recrystallization Temperature, TR
TR = recrystallization temperature = point
of highest rate of property change
1. TR  0.3-0.6 Tm (K)
2. Due to diffusion  annealing time TR = f(t)
shorter annealing time => higher TR
3. Higher %CW => lower TR – strain hardening
4. Pure metals lower TR due to easier dislocation
movements
Figure 10.32 Recrystallization temperature versus melting points for
various metals. This plot is a graphic demonstration of the rule of thumb
that atomic mobility is sufficient to affect mechanical properties above
approximately 1/3 to 1/2 Tm on an absolute temperature scale.
(From L. H. Van
Vlack, Elements of
Materials Science
and Engineering, 3rd
ed., Addison-Wesley
Publishing Co., Inc.,
Reading, MA, 1975.)
Figure 10.33 For this cold-worked brass alloy, the recrystallization
temperature drops slightly with increasing degrees of cold work.
(From L. H. Van Vlack, Elements of Materials
Science and Engineering, 4th ed., AddisonWesley Publishing Co., Inc., Reading, MA, 1980.)
Grain Growth
• At longer times, larger grains consume smaller ones.
• Why? Grain boundary area (and therefore energy)
is reduced.
0.6 mm
0.6 mm
Adapted from
Fig. 7.21 (d),(e),
Callister 7e.
(Fig. 7.21 (d),(e)
are courtesy of
J.E. Burke,
General Electric
Company.)
After 8 s,
580ºC
After 15 min,
580ºC
coefficient dependent on
material & Temp.
• Empirical Relation:
Exponent is typ.  2
d  d  Kt
n
grain dia. At time t.
n
o
elapsed time
This is: Ostwald Ripening
Figure 10.34 Schematic
illustration of the effect of
annealing temperature on the
strength and ductility of a brass
alloy shows that most of the
softening of the alloy occurs
during the recrystallization
stage.
(After G. Sachs and K. R. Van Horn, Practical Metallurgy: Applied
Physical Metallurgy and the Industrial Processing of Ferrous and
Nonferrous Metals and Alloys, American Society for Metals,
Cleveland, OH, 1940.)
Figure 10.29 Examples of cold-working operations: (a) cold-rolling a
bar or sheet and (b) cold-drawing a wire. Note in these schematic
illustrations that the reduction in area caused by the cold-working
operation is associated with a preferred orientation of the grain
structure.
We can then find that the “cold working of an
alloy” is an effect tool for improving
performance –
• if done properly!
– so as not to cause the material to exceed its
% EL which was a fracture deformation limit
as we saw earlier
– If we impose appropriate intermediate
recrystalization (and maybe even grain growth
steps)
– Finish with a cold working step to achieve the
desired hardness and finished size
Coldwork Hardening Example
A cylindrical rod of brass originally 0.40 in (10.2
mm) in diameter is to be cold worked by
drawing. The circular cross section will be
maintained during deformation. A cold-worked
tensile strength in excess of 55,000 psi (380
MPa) and a ductility of at least 15 %EL are
desired. Further more, the final diameter must
be 0.30 in (7.6 mm). Explain how this may be
accomplished.
Coldwork Calculations Solution
If we directly draw to the final diameter what
happens?
Brass
Cold
Work
Do = 0.40 in
 Ao  Af
%CW  
 Ao
Df = 0.30 in


Af 
 x 100  1 
 x 100

 Ao 
  0.30  2 
 Df2 4 
 x 100  43.8%
 x 100  1  
 1 

2
  0.40  
 Do 4 


Coldwork Calc Solution: Cont.
420
540
6
• For %CW = 43.8%
– y = 420 MPa
– TS = 540 MPa > 380 MPa
– %EL = 6
< 15
• This doesn’t satisfy criteria…… what can we do?
Coldwork Calc Solution: Cont.
15
380
27
12
For TS > 380 MPa
> 12 %CW
For %EL > 15
< 27 %CW
Adapted from Fig.
7.19, Callister 7e.
 our working range is limited to %CW = 12 – 27%
This process Needs an Intermediate
Recrystallization
i.e.: Cold draw-anneal-cold draw again
• For objective we need a cold work of %CW  12-27
– We’ll use %CW = 20
• Diameter after first cold draw (before 2nd cold draw)
– must be calculated as follows:
 D f 22 
%CW  1 
x 100
2 


Ds 2 

 %CW 
 1 

Ds 2 
100 
Df 2
Intermediate diameter =
0.5
 1
D f 22
Ds 2 2
 Ds 2  
%CW

100
Df 2
%CW 
1



100 

20 

D f 1  Ds 2  0.30 1 

100


0.5
0.5
 0.335 in

Coldwork Calculations Solution
Summary:
1. Initial Cold work
D01= 0.40 in  Df1 = 0.335 in
2.
Anneal above TR
Ds2 = Df1
1.
Secondary Cold work
Ds2= 0.335 in  Df 2 =0.30 in

2


0.335 
%CW1  1 
x 100  30
  0.4  


  0.3 
%CW2  1  
  0.335 

2

 x 100  20


Therefore, we have met all requirements
 y  340 MPa

TS  400 MPa
%EL  24