Engineering, 2013, 5, 870-876
Published Online November 2013 (http://www.scirp.org/journal/eng)
http://dx.doi.org/10.4236/eng.2013.511106
Open Access ENG
Optimization of the Annealing Parameters for Improved
Tensile Properties in Cold Draw n 0.12 wt% C Steel
Nurudeen A. Raji, Oluleke O. Oluwole
Mechanical Engineering Department, University of Ibadan, Ibadan, Nigeria
Email: kunle_raji@yahoo.com, lekeoluwole@gmail.com
Received July 29, 2013; revised August 29, 2013; accepted September 7, 2013
Copyright © 2013 Nurudeen A. Raji, Oluleke O. Oluwole. This is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
ABSTRACT
Drawn low carbon steel is characterized by brittle fracture. These defects are associated with the poor ductility and high
strain hardening due to the cold work. There is a need therefore to determine optimum heat treatment parameters that
could ensure improved toughness and ductility. Determining the optimum annealing parameters ensures valued recrys-
tallization and also minimizes grain growth that could be detrimental to the resulting product. 40% and 55% cold drawn
steels were annealed at temperatures 500˚C to 650˚C at intervals of 50˚C and soaked for 10 to 60 minutes at interval of
10 minutes to identify the temperature range and soaking time where optimum combination of properties could be ob-
tained. Tensile test and impact toughness experiments were done to determine the required properties of the steel. Po-
lynomial regression analysis was used to fit the properties relationship with soaking time and temperatures and the clas-
sical optimization technique was used to determine the minimum soaking time and temperature required for improved
properties of the steel. Annealing treatment at 588˚C for 11 minutes at grain size of 44.7 m can be considered to be the
optimum annealing treatment for the 40% cold drawn 0.12 wt% C steel and 539˚C for 17 minutes at grain size of 19.5
m for the 55% cold drawn 0.12 wt% C steel.
Keywords: Annealing; Steel; Cold Drawn; Soaking Time; Strength; Optimization
1. Introduction
Structural change occurs during cold drawn deformation
of metals in which the grains forming the basic matrix of
the metal are gradually stretched in the direction of the
principal deformation with directional arrangement of the
crystallographic lattice. The drawing process is consid-
ered to be one of the most effective and flexible methods
to improve surface finish, to obtain precise dimension
and to obtain the specified mechanical properties of a
product [1]. The individual grain of a polycrystalline
materials changes relative to the direction of applied
stress during the deformation which is distributed het-
erogeneously among the individual grains [2]. The ex-
tension of grains in the drawing direction also occurs
[3,4]. A typical feature of such deformed structure is
anisotropy of the metal mechanical properties [5]. An
initially isotropic material responds by developing ani-
sotropy when subjected to inelastic deformation. The
metal is strain hardened with the strength and hardness
increasing with increasing degree of the cold-work and
reducing ductility and impact value. Also unstable defect
structures are retained after the cold deformation includ-
ing accumulation of dislocation [6].
Effects of such cold work on the properties of poly-
crystalline structures have been studied extensively
[7-17]. It has been established that cold working and
subsequent aging enhances the hardness and tensile
strength (UTS) of the material but significantly deterio-
rate the ductility and impact energy [18]. The poor im-
pact property could be as a result of inhomogeneous de-
formation within some parts of the material and high
stress concentrations at points where the dislocations are
concentrated. Impact of cold deformation and annealing
on the mechanical properties of HSLA steel had been
studied [19]. Several studies follow to investigate the
effect of deformation and treatment on the properties of
materials. Finite element method was used [20] to deter-
mine the proportion of contribution of die radius, blank
holder force and friction coefficient in the deep-drawing
process. The study provided an insight into the deep
drawing of stainless steel blank sheet. The quality of the
N. A. RAJI, O. O. OLUWOLE 871
drawn part was found to depend on the forming condi-
tions, the optimal value of process parameters and their
favorable combination. Investigation on the mechanical
properties variation in drawn wires of high-alloy steel
and special alloys for optimum ranges of deformation has
been determined [21]. The non-uniformity of properties
on the cross-section of drawn wire was found to depend
individually on the grade of the drawn material.
Mechanical properties distributions on the cross sec-
tions of drawn products were investigated [22]. Specific
effective strain non-uniformities were found to influence
the distribution of mechanical properties in the final
product of the drawn bars. It was noticed that the non-
uniformity of mechanical properties in bars before de-
formation and different character of strain hardening of
the bars after deformation was contributing factor to the
influenced mechanical properties of the resulting product.
It is also evident that the rate of deformation as defined
by the die angle contributes to the state of the non-uni-
formity of the bar. Strain hardening is the work harden-
ing effect experienced by a metal which is deformed
plastically. It is a phenomenon whereby a ductile metal
becomes harder and stronger as it is plastically deformed
[23]. The strain hardening causes increase in the internal
stress of the material structure. The increase in the inter-
nal energy is associated with the increase in the disloca-
tion density of the metal structure due to the plastic de-
formation. Other defects such as vacancies and intersti-
tials could also generate due to the deformation [24,25].
Strengthening occurring at large strain plastic deforma-
tions has been discussed both experimentally [26] and
theoretically [27] in search of the relevant microscopic
strengthening processes. The strain hardening effect was
found to be due mainly to the movement of dislocation
within the metal crystal structure as deformation pro-
gresses.
It is possible to influence considerably a complex of
mechanical properties of particular steel by suitable
combination of size of previous cold deformation and
parameters of annealing properties. There is a need there-
fore to optimize so that the heat treatment process pa-
rameters can be defined to achieve best combination of
the metal properties [28,29]. Determining the optimum
annealing parameters can ensure valued recrystallization
and also minimize grain growth that could be detrimental
to the nails. The grain growth could be minimized by
doing the heat treatment at the lowest possible tempera-
ture and time. The optimum combination of the mini-
mum soaking time and temperature of annealing could
achieve recrystallized structures required for the im-
proved mechanical properties.
There have been several attempts to optimize heat
treatment parameters towards achieving improved prop-
erties of materials [30-37]. The several methods em-
ployed include the classical optimization technique to
quantify the mechanical property relationship with heat
treatment parameters [33,34]. The technique couples the
classical curve fitting with data obtained from experi-
ment to form regression equations after which optimiza-
tion of the low temperature impact properties was ob-
tained. In [31] evolutionary algorithm procedure was
attempted to optimize the heat treatment process for 7175
aluminum alloy. The procedure was compared with the
classical optimization technique with the classical me-
thod found to converge to local optimum solution as
against convergence of the evolutionary algorithm pro-
cedures to global optimal solution of heat treatment. Si-
milar attempt was done [32] using artificial neural net-
work combined with genetic algorithm to determine the
optimum heat treatment parameters for the 7175 alumi-
num alloy.
2. Methods
2.1. Experiments
The low carbon steel wire used for this study was ob-
tained from Nigeria Wire Industry Ltd, Ikeja, Nigeria.
The samples were cold drawn at 40% and 55% degree of
deformation and then annealed in a muffle furnace [38]
at temperature range of 500˚C - 650˚C at interval of 50˚C
for soaking time of 10 minutes, 20 minutes, 30 minutes,
40 minutes, 50 minutes and 60 minutes for each tem-
perature. The annealed samples were subjected to tensile
and impact toughness test [38]. The influence of the
soaking time and annealing temperature on these proper-
ties was optimized by formulating the dependency of the
properties on the phase field order parameter of the re-
crystallization kinetics for temperature range of 500˚C to
600˚C in order to avoid full recrystallization of all the
sample grains beyond this temperature range.
2.2. Regression Analysis
The recrystallization kinetics was obtained for the sam-
ples as presented in [39]. Sets of mathematical equations
are developed to represent the behavior of the yield
strength
Y
, tensile strength

T
and impact tough-
ness
I
mT
to recrystallized fraction volume
obtained from the phase field model using the regression
analysis of the nth degree polynomial model which is
generally given as;
21
01 21
.
N
N
NN
f
xCCxCXCX CX
  (1)
N
C represents the polynomial coefficients.
The polynomial regression model is used to model
non-linear relationship between the independent variable
and the dependent variables

as
follows;
,,
YTImT
E

Open Access ENG
N. A. RAJI, O. O. OLUWOLE
872

,,
YTImT
ffE

F
 
 
(2)
where ,,
YTImT
E
are the yield strength, tensile strength
and impact toughness respectively and
represents the
fraction recrystallized grain evolution.
The polynomial regression method was also used to
develop the soaking time
s
t

relationship with the
phase field order parameter
as a function,
s
tf
.
These relations were used to optimize the annealing pa-
rameters required for improved desired properties of the
cold drawn 0.12 wt% C steel.
3. Results and Discussion
3.1. Mechanical Properties
Figures 1-12 show the properties dependence on the
soaking time of annealing of the cold drawn steel for the
20%, 25%, 40% and 55% degree of deformation an-
nealed at temperature within the range of 500˚C - 650˚C.
Annealing of cold drawn 0.12 wt% C steel influences
the strength and impact toughness of the steel considera-
bly. The yield strength of the annealed samples improved
when compared with the as-received control sample (CS)
of the steel for all the 40% and 55% degrees cold drawn
steel. The yield strength however decreases with in-
creasing annealing temperature as shown in Figure 1 and
7. A better improvement of the yield strength is observed
0
100
200
300
400
500
CS6001200 1800 2400 3000 3600
Yield strength, MPa
Soakin
g
time, sec.
500 deg.C
550 deg. C
600 deg.C
650 deg.C
Figure 1. Yield strength response of annealed 40% cold
drawn 0.12 wt% C annealed at temp. 500 deg. C to 650 deg.
C.
0
20
40
60
80
100
120
6001200 1800 2400 3000 3600
% Response of yield strength
Soaking time, sec.
500deg.C
550deg.C
600deg.C
650deg.C
Figure 2. % Response of yield strength of 40% cold drawn
0.12 wt% C steel annealed at temp. 500 deg. C to 650 deg.
C.
0
200
400
600
800
CS6001200 1800 2400 3000 3600
Tensile strength, MPa
Soaking time, sec.
500 deg.C
550 deg. C
600 deg.C
650 deg.C
Figure 3. Tensile strength response of annealed 40% cold
drawn 0.12wt% C annealed at temp. 500deg. C to 650 deg.
C.
-70
-60
-50
-40
-30
-20
-10
0
6001200 1800 2400 3000 3600
% Response of tensile strength
Soaking time, sec.
500deg.C
550deg.C
600deg.C
650deg.C
Figure 4. % Response of tensile strength of 40% cold drawn
0.12 wt% C steel annealed at temp. 500 deg. C to 650 deg.
C.
0
5
10
15
20
25
30
35
40
CS6001200 1800 2400 3000 3600
Impact toughness, J
Soaking time, sec.
500 deg.C
550 deg. C
600 deg.C
650 deg.C
Figure 5. Impact toughness response of annealed 40% cold
drawn 0.12 wt% C annealed at temp. 500 deg. C to 650 deg.
C.
0
50
100
150
200
250
300
350
400
6001200180024003000 3600
% response of impact
toughness
Soaking time, sec.
500deg.C
550deg.C
600deg.C
650deg.C
Figure 6. % Response of impact toughness of 40% cold
drawn 0.12 wt% C steel annealed at temp. 500 deg. C to 650
deg. C.
Open Access ENG
N. A. RAJI, O. O. OLUWOLE 873
0
100
200
300
400
500
600
CS6001200 1800 2400 3000 3600
Yield strength, MPa
soaking time, sec.
500 deg.C
550 deg. C
600 deg.C
650 deg.C
Figure 7. Yield strength response of annealed 55% cold
drawn 0.12 wt% C annealed at temp. 500 deg. C to 650 deg.
C.
0
50
100
150
200
250
6001200 1800 2400 3000 3600
% response of yield strength
Soaking time, sec.
500deg.C
550deg.C
600deg.C
650deg.C
Figure 8. % Response of yield strength of 55% cold drawn
0.12 wt% C steel annealed at temp. 500 deg. C to 650 deg.
C.
0
100
200
300
400
500
600
700
CS60012001800 2400 30003600
Tensile strength, MPa
Soaking time, sec.
500 deg.C
550 deg. C
600 deg.C
650 deg.C
Figure 9. Tensile strength response of annealed 55% cold
drawn 0.12 wt% C annealed at temp. 500 deg. C to 650 deg.
C.
-60
-50
-40
-30
-20
-10
0
10
6001200 1800 2400 3000 3600
% Response of tensile strength
Soaking time, sec
500deg.C
550deg.C
600deg.C
650deg.C
Figure 10. % Response of tensile strength of 55% cold
drawn 0.12 wt% C steel annealed at temp. 500 deg. C to 650
deg. C.
0
5
10
15
20
CS6001200 1800 2400 3000 3600
Impact toughness, J
Soaking time, sec.
500 deg.C
550 deg. C
600 deg.C
650 deg.C
Figure 11. Impact toughness response of annealed 55% cold
drawn 0.12 wt% C annealed at temp. 500 deg. C to 650 deg.
C.
-50
0
50
100
150
200
250
300
350
400
450
6001200 1800 2400 3000 3600
% Response of Impact
toughness
Soaking time, sec.
500deg.C
550deg.C
600deg.C
650deg.C
Figure 12. % Response of impact toughness of 55% cold
drawn 0.12 wt% C steel annealed at temp. 500 deg. C to 650
deg. C.
for the annealing temperature of 500˚C and 550˚C be-
tween the soaking time of 10 minutes and 30 minutes
after which the rate at which the yield strength increases
for the treated samples reduces with increasing tempera-
ture of annealing for both degrees of cold drawn defor-
mation as shown in Figures 2 and 8. The yield strength
of the 40% cold drawn steel is higher at 650˚C compared
to when annealed at 500˚C at soaking time above 30 mi-
nutes.
The impact toughness was also observed to improve
considerably for the 40% degrees of cold drawn steels
when annealed at temperature between 500˚C and 650˚C
as shown in Figure 5. However the impact toughness of
the 55% cold drawn steel annealed at 650˚C reduces be-
low the impact toughness of the control sample but with
improved yield strength. The 40% cold drawn steel an-
nealed at 500˚C exhibits increasing rate of reduction in
impact toughness at soaking time between 10 minutes
and 30 minutes after which it slows down between 40
minutes and 60 minutes.
The tensile strength of the annealed samples reduces
considerable for all the degrees of cold drawn steel an-
nealed between 500˚C and 650˚C. The tensile strength of
the annealed cold drawn 0.12 wt% C steels drops con-
siderably with increasing soaking time for both 40% and
55% cold drawn steel as shown in Figures 3 and 9.
Open Access ENG
N. A. RAJI, O. O. OLUWOLE
874
3.2. Optimization
It has evidently been shown as discussed above that the
heat treatment of cold drawn 0.12 wt% C steel consider-
able influences the mechanical properties of the steel
such as its yield strength, tensile strength and impact
toughness. Optimum annealing parameters could be ob-
tained for improved properties of the steel. The mathe-
matical functions of the soaking time determined from
recrystallization kinetics and the properties relation with
the fraction recrystallized are obtained from the hardness
test for each of the degree of cold drawn deformation and
annealing temperature using the polynomial regression
methods. The values of the coefficients are obtained as
given in Tables 1 and 2.
The optimal values of the fraction recrystallized is es-
timated from the first derivatives of the property equa-
tions and used to determine the required time for the
500˚C, 550˚C and 600˚C. An objective function is for-
mulated from the values of the fraction recrystallized
with the corresponding temperature value. The classical
technique is used to optimize the objective function en-
suring that the necessary and sufficient conditions are
satisfied. Table 3 shows the optimized results for the
different degree of cold drawn deformation.
4. Conclusion
Heat treatment of 40% and 55% cold drawn 0.12 wt% C
steel was investigated. The cold drawn steel samples
were annealed at temperature range of 500˚C to 650˚C
for soaking time between 10 minutes and 60 minutes.
Table 1. Coefficients of property relation with recrystallized
fraction for annealed 40% cold drawn 0.12 wt% c steel.
40% cold drawn steel annealed at various temperature
Property Temp. Co C
1 C
2 C
3

y
148.67 982.7 965.53 -
t
406.97 200.12 196.66 -

Imp
E
13.492 10.632 10.416 -
s
t
500˚C
13,688 73,198 121,842 68,001

y
2730.6 7310.7 4308.3 -
t
1602.8 4762.3 2806.5 -

Imp
E
45.046 138.41 81.481 -
s
t
550˚C
3673.7 1E + 06 2E + 06 634,921

y
27,249 8109 30,600 -
t
16,425 35,400 18,608 -

Imp
E
363.96 791.5 416.67 -
s
t
600˚C
675,839 1E + 06 762,431 -
Table 2. Coefficients of property relation with recrystallized
fraction for annealed 55% cold drawn 0.12 wt% c steel.
55% cold drawn steel annealed at various temperature
PropertyTemp. Co C
1 C
2 C
3
y
148.67982.7 965.53-
t
406.97200.12 196.66-
Imp
E
13.49210.632 10.416-
s
t
500˚C
13,68873,198 121,842 68,001
y
2730.67310.7 4308.3-
t
1602.84762.3 2806.5-
Imp
E
45.046138.41 81.481-
s
t
550˚C
3673.71E + 06 2E + 06634,921
y
27,2498109 30,600-
t
16,42535,400 18,608-
Imp
E
363.96791.5 416.67-
s
t
600˚C
675,839 1E + 06 762,431-
Table 3. Optimized results for heat treat cold drawn 0.12
wt% C steel.
Optimized results of annealing for cold drawn 0.12 wt% C steel
% degree of deformation 40 55
Annealing temperature (deg. C) 588 539
Soaking time (minutes) 11 17
The heat treatment influences the strength and impact
toughness of both cold drawn steels samples considera-
bly. The yield strength and impact toughness of the sam-
ples for both degrees of cold drawn deformed steels in-
creases with increasing soaking time at the annealing
temperature range of 500˚C to 650˚C. The rate of in-
creasing yield strength and impact toughness however
reduces with increasing soaking time. A better improve-
ment of these properties is observed at soaking time
range of 10 minutes to 30 minutes for both degrees of
cold drawn steel samples. The tensile strength however
reduces with increasing soaking time of annealing at
temperature range of 500˚C to 650˚C. The rate of reduc-
tion of the tensile strength increases at soaking time be-
tween 40 minutes and 60 minutes. The optimal heat
treatment parameters are obtained for the annealed 40%
cold drawn steel samples at 588˚C soaked for 11 minutes
and for the 55% cold drawn steel samples at 539˚C
soaked for 17 minutes.
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