Phase transformation model for adjusting the cooling conditions in Stelmor process to obtain the targeted structure of thermomechanically rolled wire rod used for fastener production

. The paper demonstrates the capability of the developed phase transformation model to design the cooling conditions in the Stelmor process allowing for obtaining different types of microstructures in wire rod of 32CrB4steel.Themodelbasedonmodi ﬁ edJMAKequationwasdevelopedusingtheresultsofthetestsconductedin a DIL 805 A/D/T dilatometer. The model is composed of sub-models of ferritic, pearlitic, bainitic and martensitic transformations.Itspredictivecapabilitywascon ﬁ rmedinindustrialconditionsbyperformingtrialswithdifferent settings of fans involved in the cooling process on the Stelmor line of CMC Poland. Excellent performance of the modelwas achievedthroughthe modi ﬁ cationofcommonly usedequationswhichallows accuratepredictions ofthe phasetransformationsstartand ﬁ nishtemperatures,aswellasvolumefractionofmicrostructuralconstituents,ina wide range of cooling rates. It was demonstrated that the model can effectively be applied to design the cooling conditions in the Stelmor process, which will result in the required microstructural composition of the wire rod.


Introduction
In wire rod mills, billets are rolled to wire rods of different diameters with a wide spectrum of applications. Wire rods of various steel grades, usually containing alloying elements, are produced in these mills to fit the specialized applications. Required microstructure and mechanical properties are obtained by controlled cooling during rolling and Stelmor process. Cooling conditions in the Stelmor line applied for developing favourable microstructure of wire rod used for fasteners production are well known and widely used in industrial practice [1]. After the coil formation at the laying head, cooling is performed under covers to ensure low cooling rate throughout the phase transformations temperature range, leading to the formation of ferrite-pearlite microstructure in wire rod. New perspectives have been identified recently by developing in the wire rod different types of bainitic microstructures or a mixture of ferrite and bainite. To obtain these microstructures, perfect control of the cooling conditions must be applied including combination of fast and slow cooling stages. This can be achieved due to the wide flexibility of the Stelmor process, in which the wire rod can be forced cooled by sets of fans. Over the years, a trial-and-error method has been used at CMC Poland to determine cooling conditions in the Stelmor process to obtain the required volume fraction of microstructural constituents and thus the desired mechanical properties of the wire rod. However, this method is expensive and time consuming. Therefore, an alternative method is presented in this paper, which relies on applying the phase transformation model to identify the effect of Stelmor line cooling conditions on phase transformation occurring in the wire rod. This approach was used by many researchers and turned out to be very effective in the numerical modelling of pearlite transformation arising in the wire rod of eutectoid steels [2]. The examples of numerical simulations of cooling in the Stelmor line of the wire rod of ferrite-pearlite steels can also be found in the literature [3]. It is worth mentioning that recently, much emphasis concerning the Stelmor process numerical simulations has been focussed on the precise description of the boundary conditions.
In the process of phase transformations modelling in the Stelmor process, generally a simple form of the JMAK equation has been used [2,4]. Due to this, the accuracy of phase transformations predictions is limited and depends on the cooling rate. Therefore, one of the aims of the paper is to present the improved JMAK model's capability to predict phase transformations occurrence during the Stelmor process applied to the 32CrB4 steel. Also, an effective approach to the identification of the phase transformation model by using the results of dilatometric tests performed under continuous cooling conditions is presented.

Wire rod production process at CMC Poland
The wire rod production process at CMC Poland consists of two main technological stages. The first is the thermomechanical rolling of billets to the final shape, followed by the second stage of controlled cooling in the Stelmor line. Prior to rolling, the billets (160 mm Â 160 mm in cross section) are heated in a walking beam furnace to temperature in the range of 1080-1150°C and are held for 30-60 min. After rolling in the roughing group, accelerated cooling in three water boxes is performed, leading to a reduction of band temperature to 875 ± 20°C. This temperature is the temperature of entering the intermediate rolling mill stands when the final diameter of the wire rod is less than 14 mm. If the final wire rod diameter is greater than 14 mm, the intermediate rolling mill stand is not used. After the finishing mill (RSM), the band can be cooled in an accelerated manner using three water boxes. When the controlled cooling is used, the entry temperature on the laying head is held in the range of 875-750°C. After coils are formed at the laying head, the band is subjected to controlled cooling in the 120 m long Stelmor line. The wire rod cooling at the Stelmor conveyor is one of the most complex metallurgical processes [2,5]. The Stelmor line, which is the focus of this investigation, is composed of twelve consecutive cooling zones located along the conveyor, equipped with air blowing fans. Alternatively, retarded cooling can also be applied to the wire rod in the Stelmor line by using the covers over the Stelmor conveyer. Thus, the Stelmor process allows to control the cooling rate, and as a result, the phase transformations occurrence in the wire rod by adjusting the operational capacity of each fan and the distribution of air velocity within the coil. Accordingly, the well-designed Stelmor process tailors the microstructure and mechanical properties of the wire rod.
The capabilities of the Stelmor process were intensively investigated in the last decades of the 20th century, see for example [6][7][8]. Even though this air-cooling process looks simple, due to the complex geometrical structure of wire loops, the cooling rate is different in each region within the loop. Therefore, during the last four decades, there has been much research activity focused on the application of numerical modelling to support the design of the Stelmor cooling technology. The models are composed of the thermal and metallurgical. The former describes the changes of the temperature in the loops of wires. A comprehensive review of the thermal models of the Stelmor system can be found in [5]. The latter predict the kinetics of phase transformations during cooling and the mechanical properties of the final rods À and this part was the objective of this work.

Aim of the investigation
The investigation presented in this paper was a part of the research project "Execution of R&D works to create the innovative thermo-mechanical technology for rolling CHQ steels, necessary for development of innovative wire rod providing unique combination of technological, mechanical and structural parameters ensuring its highest susceptibility to cold heading processing" (Project No. POIR.01.02.00-00-0159). Generally, thermomechanical controlled rolling leads to the formation of nonrecrystallized austenite after the last deformation, which is a prerequisite for obtaining a fine ferrite-pearlite microstructure, characterised by a favourable combination of strength and ductility. This is caused by rolling in a finish mill below the so-called recrystallization stop temperature. The effective application of the thermomechanical rolling technology also requires the application of niobium microalloying, as Nb is the most effective element retarding static recrystallization [9]. It is worth mentioning that this type of rolling is associated with the accelerated-controlled cooling after rolling, which is another mechanism of microstructure refinement. The entire concept of thermomechanical rolling cannot be directly applied to the wire rod rolling process, since severe deformation, high strain rates and temperature increase due to the plastic working favours the occurrence of different types of recrystallization. Therefore, a new concept of thermomechanical processing, which is dynamic recrystallization-controlled rolling, was developed in the case of the wire rod rolling process [10]. In this concept, the rolling parameters are adjusted in such a way that during final passes, the growth of recrystallized grains is inhibited. As a result, a unique austenite microstructure is developed, composed of very fine austenite grains smaller than 20 mm. In the research project completed at CMC Poland, the retardation of austenite grain growth was achieved by reducing the ingot reheating temperature to 1080°C and by applying a low rolling rate in the roughing mill, combined with intense cooling in water boxes. As a result, the finish rolling temperature was lowered to 850-800°C. Another measure causing the retardation of austenite grain growth was the application of the titanium technology. Titanium in CHQ steels protects boron against the formation of boron nitride BN. However, a very fine distribution of TiN particles can substantially retard the kinetics of recrystallization and grain growth following the recrystallization [11]. Thus, a very fine distribution of austenite grains is obtained in the wire rod after rolling at CMC Poland, with size not exceeding 25 mm (Fig. 1).
The reduction of austenite grain size affects phase transformations and its positive influence is reflected in the wire rod's performance during drawing and cold forging operations, and the final microstructure and properties of fasteners.
Generally, lower austenite grain size speeds up the kinetics of phase transformation, which leads to an increase of the rate of phase transformations latent heat release. This necessitated the adjustment of the cooling conditions in the CMC Poland Stelmor line. This part of the investigation was performed by applying the numerical modelling of phase transformations.

Experimental methodology
The chemical composition of the investigated 32CrB4 steel is presented in Table 1. The data for the model identification were generated during dilatometric investigations performed using the DIL 805 A/D/T deformation dilatometer. This method relies on the measurement of the sample's dilations caused by the occurrence of phase transformations [12]. The tests were performed with Ø5 mm Â 10 mm samples. The temperature changes during the tests were monitored by means of a thermocouple spot welded to the samples' surface at half-height. S-type (PtRh10-Pt) thermocouples with a 0.1 mm diameter were used for this purpose. Prior to the cooling stage, the samples were subjected to a deformation sequence reproducing the deformation conditions of the rolling process.
Dilatometric constant cooling rate tests were performed to supply data for the identification of the phase transformation model. TTT diagrams are used by some researchers [13,21]. The reasons that CCT diagrams were applied are twofold. The first is connected with the fact that massive samples were used and they were deformed before the cooling process. For these samples, it would be difficult to achieve high cooling rates to reach isothermal temperature, which are necessary to perform TTT tests. In consequence, the ferritic transformation can begin before reaching isothermal temperature, what can cause errors in experimental data. Ferritic transformation may be launched directly after the end of deformation. The second reason for using CCT diagrams is connected with the fact that an algorithm which allows the identification of the phase transformation model on the basis of constant cooling rate experiments, could be used. This algorithm is described in [14,15] and an example of its practical application can be found in [16].
Metallographic samples were prepared after each test by grinding and polishing with diamond paste. The investigation was carried out at a distance of approximately 0.2 mm from the spotted thermocouple. Microstructure observations were carried out with an optical and digital Olympus DSX500i microscope and with highresolution scanning electron microscope (SEM) À JSM-7200F produced by Jeol. The samples were etched with 3% nital. The quantitative measurement of the surface fraction of the samples' microstructural constituents was performed with the Metilo program [17].

Phase transformation model description
The characterisation of phase transformations occurring in steels is most frequently performed using the dilatometric method. However, obtained results of dilatometric investigations cannot directly be transferred into the conditions of the Stelmor line. In dilatometric tests, a constant cooling rate is maintained which, in general, is against the physics of the cooling process. Moreover, to maintain the constant cooling rate, the dilatometer control system attenuates the heat generated due to the occurrence of the phase transformations (latent heat of transformations). Therefore, the correct application of the dilatometric investigation results into the Stelmor process requires the development of the phase transformations model which can be applied to different and varying cooling conditions.
The model is based on the classical JMAK equation: where X À volume fraction of a new phase, t À time, k, n À coefficients.
The development and identification of the phase transformation model for the 32CrB4 steel and the application of this model to simulations of the cooling of rods in the Stelmor system was the objective of the work. The model should allow for a precise prediction of the cooling parameters, which provide the targeted microstructure of the wire rods after cooling. Therefore, an upgrade of the JMAK model described in [18] was applied. Phase transformations modelling is based on the equilibrium diagram, and the model describes the kinetics of the transient state between two states of the equilibrium [19]. The modification of the JMAK model, which noticeably improved the accuracy and reliability of the predictions, included the modification of equations describing the incubation time and coefficient (k) in equation (1). The incubation time was not introduced in the case of the ferritic transformation, and it was assumed that this transformation begins when 5% of ferrite is obtained. The Avrami coefficient for ferrite (k f ) is calculated as [20]: where D g À austenite grain size, T À temperature in°C, and The modification of equations describing incubation time (t p ) and Avrami coefficient (k p ) for pearlitic transformation, as well as incubation time (t b ) and Avrami coefficient (k b ) for bainitic transformation are calculated as follows: The introduction of the modified Gauss function in the k(T) relation was the main modification. This function allowed reproducing the C-shape of the isothermal transformation curve. The exponential functions, which were originally used in [19], provided a continuous increase of the rate of transformation with decreasing temperature, which is not physical. The remaining equations in the model include: Martensite start temperature: Martensite volume fraction [21]: where F f , F p , F b , F m , À volume fractions of ferrite, pearlite, bainite and martensite. Coefficient a 20 in equation (6) represents the bainite start temperature. During the simulation of the ferritic transformation, the carbon concentration in the austenite is calculated as: where c 0 -carbon content in steel. The numerical predictions of phase transformations using the equations above require the knowledge of the equilibrium phase boundary's location. A part of the phase equilibrium diagram, which was calculated using the ThermoCalc software [22], is presented in Figure 2. The equilibrium carbon concentrations were approximated using the following equations: where c ga À carbon concentration in austenite at the g-a interface, c gb À carbon concentration in austenite at the g-cementite interface, c ga0 , c ga1 , c gb0 , c gb1 -coefficients which were determined on the basis of the ThermoCalc results. These coefficients are given in Table 2.
6 Results of the investigation 6

.1 Dilatometry
The input parameters for the identification of the phase transformation model coefficient include the phase transformation start and finish temperatures, as well as fractions of microstructural constituents as function of cooling rate. These parameters were measured in the experiments conducted using the DIL 805 dilatometer. The experiments were composed of three stages: heating to 1080°C and holding, cooling combined with two deformations, and cooling at a constant cooling rate to ambient temperature (Fig. 3). The maximum heating temperature corresponds to the applied soaking temperature of ingots in the heating furnace during wire rod rolling at the CMC Poland rolling mill. The deformation parameters were adjusted to obtain the austenite grain size after the last deformation in the range of 15-20 mm. This corresponds to the austenite grain size obtained during industrial thermomechanical rolling in the industrial process. Prior to the experiments described in Figure 3, the critical temperatures for the 32CrB4 steel were determined by heating the sample to 1000°C at a rate of 2.5°C/s. The determined temperatures were: A c1 = 734°C, A c3 = 795°C.
The obtained phase start and finish temperatures for the applied cooling rates obtained in the dilatometric experiments are given in Table 3, and the results of the fraction of microstructural constituent measurements are given in Table 4.
The measured fractions of microstructural constituents are presented in Figure 4 and the examples of the microstructures obtained in the dilatometric samples are presented in Figures 5-8. In these figures, the same description of microstructural constituents was applied as in Tables 2 and 3. The results of the measurements show that up to a cooling rate of around 0.5°C/s the microstructure is composed of ferrite and pearlite. Moreover, an increase in the cooling rate causes a slight increase of the pearlite volume fraction. This means that the so-called diluted pearlite forms at higher cooling rates. From the practical point of view, the most important feature of the developed model is its capability to accurately predict the threshold cooling rates for obtaining the desired microstructure in 32CrB4 wire rods. Figure 4 shows that the maximum volume fraction of bainite occurs in the microstructure of the wire rod after cooling at a rate of around 2°C/s.

Phase transformations model identification and validation
The model contains several coefficients, which were grouped in vector a. An inverse algorithm developed by the Authors of [14] was applied in the identification procedure. The adaptation of this algorithm to the dilatometric tests is described in [15]. The results of the CCT tests were used in the objective function: where w T , w F À weighting factors, T m , T c À measured and calculated start and end temperatures of phase transformations in the CCT tests, F m , F c À measured and calculated volume fractions of phases, k, l À number of temperatures and volume fractions, respectively.
Weighting factor w T = 0.9 was used for the temperatures and w F = 0.1 for volume fractions. The coefficients in all models were determined by searching for the minimum of the objective function (12) with respect to confidents a. These optimal coefficients are given in Table 5.
The model was verified by the comparison of measured and calculated start and end temperatures for the phase  transformations in the CCT tests. The results of this comparison are shown in Figure 9a. In all figures in this report F stands for ferrite, P for pearlite, B for bainite and M for martensite. Beyond pearlitic transformation, a very good agreement between the measurements and the calculations was obtained. Since the goal was to manufacture wire rods with ferritic-bainitic microstructure, less attention was paid to pearlite. Due to the problems with reproducing the start and end transformation temperatures for pearlite, the weighting factors were decreased for this transformation. The measured and calculated volume fractions of phases were compared as well, and the results are shown in Figure 9b.

Model validation in industrial conditions
Simulations of the cooling of a 32CrB4 steel wire rod with a diameter of Ø12.5 mm in the industrial Stelmor process were performed to assess the sensitivity of the developed model to varying cooling conditions. Three cases were considered: -Standard cooling under covers with a rate of around 0.5°C/s; -Transient cooling at a rate of 0.8°C/s leading to the formation of small amounts of bainite; -Fast cooling at rates intended to maximise the fraction of bainite in the wire rod's microstructure.     The second variant is aimed at verifying the developed model's capability to identify the critical cooling rate at which bainite occurs in the wire rod's microstructure. From industrial practice, it is known that due to the variation of the 32CrB4 steel composition, the critical cooling rate for bainite formation is about 0.55°C/s, which is well seen in Figure 10, where a zoom for a small range of cooling rates is presented.
During the industrial experiments, the temperature of the wire rod was monitored using an infrared camera and for reference the set of pyrometers located along the Stelmor conveyor. The temperature profiles at the loop centre were used for the phase transformation numerical simulations. The results for the standard cooling of the wire rod under cover at the rate of 0.5°C/s, and for comparison with a rate of 0.8°C/s, as well as accelerated cooling intended to develop predominantly bainitic microstructure in the wire rod were considered for model validation. Figure 11 shows a comparison of the kinetics of phase transformations and Figure 12 shows fractions of microstructural constituents for the three investigated cases.
During industrial trials, a cooling rate of around 0.5°C/s was achieved by using covers over the Stelmor conveyor and adjusting the conveyor's speed. An increase in the cooling rate to around 0.8°C/s was achieved by increasing the conveyor's speed. The accelerated controlled cooling conditions were achieved by adjusting the cooling rates by the proper calculated setting capacity of the fans to limit the ferrite and martensite formation, and the fans were stopped when the coil reached a temperature of around 400°C to limit the ferrite and martensite formation, and at the same time to obtain th maximum fraction of bainite.
The obtained microstructures of the wire rod after applying both cooling variants are shown in Figures 13À15.
The measured and calculated fractions of microstructural constituents are given in Table 6. The presented results demonstrate a very good capability of the developed phase transformation model to quantitatively predict the effect of cooling conditions on the phase transformation kinetics in the wire rod cooled in the Stelmor process.      The Stelmor system used in CMC Poland allows precise control of the temperature during cooling of wire rods. This feature will further be used to develop the technology of wire rod production characterized by complex phase structures, with prospective application to the production of fasteners without applying additional heat treatment operations. The main feature of these structures is that they do not contain pearlite, and bainite is the leading constituent. To develop cooling strategies aimed at obtaining the complex phase structures in the wire rod, a more robust approach is required than an intuitive analysis of the CCT diagram. Therefore, an accurate and reliable model of phase transformations was developed to translate the time-temperature profiles into the resulting microstructural compositions of the products. The modified JMAK model was applied in the present work. The modification comprised the introduction of coefficient k in the JMAK equation as a function of temperature. A modified Gauss function was used for all diffusive transformations, which allowed to reproduce a typical Cshape of the isothermal transformations' curves. The application of the inverse solution for the results of the dilatometric tests allowed to obtain a very good accuracy of the model. The developed model is capable of predicting the required cooling conditions to develop different types of microstructural constituents. This is seen in Figures 9 and  12. The dependence of bainite volume fraction on the cooling rate is of special interest. Figure 9 shows that bainitic transformation in the 32CrB4 steel starts at a cooling rate slightly higher than 0.5°C/s, and the volume fraction of bainite increases as the cooling rate increases till approximately 2.7°C/s. Further increase of the cooling rate leads to a fast decrease of bainite volume fraction in the microstructure, however, this constituent is present in the microstructure even if high cooling rates are applied. It is noteworthy that this scenario is valid for austenite having a mean grain size of 25 mm. Since the developed model accounts for austenite grain size, the effect of grain size on phase transformation kinetics and the resulting structure can also be accounted for. The experimental part of the research using dilatometry was performed by applying constant cooling rate conditions. However, the development of a complex phase microstructure in the wire rod will require varying cooling conditions in the Stelmor process. The capability of predicting the kinetics of phase transformations under varying cooling conditions was achieved by applying the additivity rule.

Conclusions
-The modified JMAK model was successfully applied to numerically calculate the effect of cooling conditions in the CMC Poland Stelmor process to obtain the targeted microstructure of the 32CrB4 steel wire rod. -To improve the accuracy of currently applied models, a modified Gauss function was used for all diffusive transformations, what allowed to reproduce a typical C-shape of the isothermal transformations' curves. -The developed model allows a transfer of dilatometric tests' results into industrial conditions. The direct application for this purpose of commonly used CCT or DCCT diagrams is not justified, since constant cooling rates are applied for the development of these diagrams. -By using the phase transformation model, an inverse algorithm was developed, capable of adjusting the cooling conditions in the CMC Poland Stelmor line to obtain the targeted microstructure of the wire rod. This algorithm will be used for further development of the wire rod characterised by DP or TRIP assisted microstructure.