Optimization of the Annealing Parameters for Improved Tensile Properties in Cold Drawn 0 . 12 wt % C Steel

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 recrystallization 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 obtained. Tensile test and impact toughness experiments were done to determine the required properties of the steel. Polynomial regression analysis was used to fit the properties relationship with soaking time and temperatures and the classical 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.


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 considered 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 heterogeneously among the individual grains [2].The extension 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 anisotropy 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 including accumulation of dislocation [6].
Effects of such cold work on the properties of polycrystalline structures have been studied extensively [7][8][9][10][11][12][13][14][15][16][17].It has been established that cold working and subsequent aging enhances the hardness and tensile strength (UTS) of the material but significantly deteriorate the ductility and impact energy [18].The poor impact property could be as a result of inhomogeneous deformation 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 determine 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 drawn part was found to depend on the forming conditions, 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 sections 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 nonuniformity of mechanical properties in bars before deformation 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-uniformity of the bar.Strain hardening is the work hardening 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 internal energy is associated with the increase in the dislocation density of the metal structure due to the plastic deformation.Other defects such as vacancies and interstitials could also generate due to the deformation [24,25].Strengthening occurring at large strain plastic deformations 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 progresses.
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 therefore to optimize so that the heat treatment process parameters 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 temperature and time.The optimum combination of the minimum soaking time and temperature of annealing could achieve recrystallized structures required for the improved mechanical properties.
There have been several attempts to optimize heat treatment parameters towards achieving improved properties of materials [30][31][32][33][34][35][36][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 experiment to form regression equations after which optimization of the low temperature impact properties was obtained.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 method found to converge to local optimum solution as against convergence of the evolutionary algorithm procedures to global optimal solution of heat treatment.Similar attempt was done [32] using artificial neural network combined with genetic algorithm to determine the optimum heat treatment parameters for the 7175 aluminum alloy.

Experiments
The low carbon steel wire used for this study was obtained 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 temperature.The annealed samples were subjected to tensile and impact toughness test [38].The influence of the soaking time and annealing temperature on these properties was optimized by formulating the dependency of the properties on the phase field order parameter of the recrystallization 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.

Regression Analysis
The recrystallization kinetics was obtained for the samples as presented in [39] .
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; , , .These relations were used to optimize the annealing parameters required for improved desired properties of the cold drawn 0.12 wt% C steel.

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 annealed 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 considerably.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 increasing annealing temperature as shown in Figure 1    for the annealing temperature of 500˚C and 550˚C between 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 temperature of annealing for both degrees of cold drawn deformation 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 minutes.
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 below the impact toughness of the control sample but with improved yield strength.The 40% cold drawn steel annealed 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 annealed between 500˚C and 650˚C.The tensile strength of the annealed cold drawn 0.12 wt% C steels drops considerably with increasing soaking time for both 40% and 55% cold drawn steel as shown in Figures 3 and 9.

Optimization
It has evidently been shown as discussed above that the heat treatment of cold drawn 0.12 wt% C steel considerable influences the mechanical properties of the steel such as its yield strength, tensile strength and impact toughness.Optimum annealing parameters could be obtained for improved properties of the steel.The mathematical 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 estimated from the first derivatives of the property equations and used to determine the required time for the 500˚C, 550˚C and 600˚C.An objective function is formulated from the values of the fraction recrystallized with the corresponding temperature value.The classical technique is used to optimize the objective function ensuring that the necessary and sufficient conditions are satisfied.Table 3 shows the optimized results for the different degree of cold drawn deformation.

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.The heat treatment influences the strength and impact toughness of both cold drawn steels samples considerably.The yield strength and impact toughness of the samples for both degrees of cold drawn deformed steels increases with increasing soaking time at the annealing temperature range of 500˚C to 650˚C.The rate of increasing yield strength and impact toughness however reduces with increasing soaking time.A better improvement 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 reduction of the tensile strength increases at soaking time between 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.
. Sets of mathematical equations are developed to represent the behavior of the yield strength   Y  , tensile strength   T  and impact toughness   ImT  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; 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   phase field order parameter  as a function,

and 7 .Figure 1 .
Figures 1-12show the properties dependence on the soaking time of annealing of the cold drawn steel for the 20%, 25%, 40% and 55% degree of deformation annealed 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 considerably.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 increasing annealing temperature as shown in Figure1 and 7. A better improvement of the yield strength is observed