Modeling Dynamic Recrystallization Kinetics in BS 080M46 Medium Carbon Steel: Experimental Verification and Finite Element Simulation

Utilized the experimental data to construct models that describe DRX kinetics and the evolution of grain size, employing the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation, this study investigates the dynamic recrystallization (DRX) characteristics and the microstructure evolution within BS 080M46 medium carbon steel under high-temperature conditions. Several trials were carried out to analyze hot compression, covering a temperature range of 900°C to 1200°C and utilizing varying strain rates of 0.1, 1, and 10 s-1. The incorporation of these models into QForm V10.2.1 facilitated finite element modeling (FEM) simulation, enabling the evaluation of DRX behavior. A comparative analysis was carried out to confirm the efficacy of the developed models, aligning the simulation results with the data obtained through metallographic observations. The high level of agreement between the simulation and experimental findings related to the DRX grain size was quantified by a correlation coefficient (R) of 0.991, along with an average absolute relative error (AARE) of 7.412%. These results confirm the capability of the developed DRX kinetics and grain size evolution models in accurately predicting the grain size of BS 080M46 medium carbon steel.  In addition, the study suggests that higher temperatures or lower strain rates can result in an increased volume fraction of dynamic recrystallization (DRX) and grain size. This highlights the importance of Finite Element Method (FEM) as a crucial tool for comprehending the evolution of microstructure during hot working processes.

BS 080M46 medium carbon steel; DRX behavior; Finite element modeling; Grain size; Hot compression test

BS 080M46 is a versatile medium carbon steel known for its excellent mechanical properties and ease of processing, making it ideal for high-stress applications requiring wear resistance. Its strength, toughness, and wear resistance have led to its widespread use in various machinery parts such as gears, axles, crankshafts, and connecting rods, as well as in shafts, bolts, studs, and hydraulic cylinders (Mizuguchi et al., 2009). Typically, during the hot working process of BS 080M46 medium carbon steel, the material is heated to a temperature exceeding the recrystallization temperature range. This allows for the material to be plastically shaped and formed easily using various hot working processes, including hot forging, hot rolling, and hot extrusion (Altan, 2005). Lv et al. (2018) emphasized that thermo-mechanical processing, utilized in the production of large structural components, tailors the microstructure for desired mechanical properties, necessitating predictive models due to the sensitivity of the microstructure to processing conditions, and the intricate relationship between processing parameters, material deformation behavior, and resulting microstructures.

In the realm of metallurgy, three significant phenomena – work hardening (WH), dynamic recovery (DRV), and dynamic recrystallization (DRX) – significantly shape the flow behavior, microstructure, and energy required during the hot working process, occurring concurrently during material deformation and controlling flow stress under varying conditions (Derazkola et al., 2022; Kooiker, Perdahcioglu, and Boogaard, 2018). These phenomena ultimately impact material properties and behavior, playing a critical role in determining the quality of the final product (Chen et al., 2021b). Through these occurrences, the microstructure evolution of metals is notably influenced by DRX. The existing coarse grains undergo notable deformation and eventually transform into smaller, equiaxed grains, contributing to both grain refinement and homogenization (Bharath et al., 2021; Zheng et al., 2018; Quan, 2013). Consequently, this process leads to enhanced mechanical properties, particularly in terms of increased strength, ductility, and toughness (Tukiat et al., 2024; Zou et al., 2022; Anwar et al., 2021; Kurnia and Sofyan, 2017; Kozmel et al., 2014). The effects of DRX on metals depend on several factors, including the composition of the metal, the deformation temperature, the strain rate, and the processing history (Alaneme and Okotete, 2019). In addition, the occurrence of DRX and the resulting microstructure can also be affected by prior cold work, which may require higher processing temperatures or longer processing times to achieve DRX (Stefani et al., 2016; Sanrutsadakorn, Uthaisangsuk, and Suranuntchai, 2014).

Precisely characterizing the DRX behaviors and the mechanisms of grain evolution is of utmost importance for achieving the desired microstructure and mechanical properties. The construction of DRX kinetic models has involved several attempts to represent material behavior and the evolution of grain size effectively. Studies by Hu and Wang (2020) and Yang et al. (2018) have shown that flow curves can represent the hot working behaviors of BT25y titanium alloy and 5CrNiMoV steel, respectively, due to their close correlation with microstructural changes. Therefore, stress-strain data derived from isothermal compressions can be employed to formulate DRX kinetics, with the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation widely utilized to depict the correlation between the volume fraction of deformation-induced DRX, deformation temperature, and strain rate (Irani et al., 2019). For instance, Wang et al. (2016), through their research, established an Arrhenius-type constitutive equation incorporating a Zener-Hollomon parameter, along with DRX volume fraction and grain size models, all based on the JMAK equation. This comprehensive approach accurately describes the deformation behavior observed during the hot-working processes of the carburizing steel alloy 20Cr2Ni4A. Similarly, models for the DRX volume fraction and grain size, applicable to 33Cr23Ni8Mn3N heat-resistant steel, were developed by Ji et al. (2020) and integrated these models into the DEFORM-3D software. The finding stemming from microstructural observations obtained through LOM and SEM, along with finite element simulations, exhibited highly consistent, thereby validating the precision of the established DRX model. Quan et al. (2019) investigated the DRX behavior of AlCu4SiMg alloys using the JMAK equation and verified its feasibility through both FE simulations and experiments. Additionally, studies on various alloys such as Ti-5Al-5Mo-5V-3Cr-1Zr near b Titanium alloy (Lv et al., 2018), medium Mn steel (Sun et al., 2020), solution-treated Ni-based superalloy (Chen et al., 2016), Cr8 alloy (Chen et al., 2022), and TB8 Titanium alloys (Zhang et al., 2020) used FEM simulations of DRX behavior. The concordance between simulation results and microstructural observations underscores the potential of finite element simulations as valuable tools for predicting the DRX behavior across various alloys, which can be helpful in designing and optimizing manufacturing processes for these materials.

        Despite extensive research into understanding dynamic recrystallization (DRX) phenomena in various alloys, the specific behavior of DRX in BS 080M46 medium carbon steel remains relatively unexplored. This knowledge gap presents significant challenges in optimizing the hot working processes of this material to achieve the desired microstructural characteristics and mechanical properties. Furthermore, the lack of accurate predictive models tailored to BS 080M46 medium carbon steel further hinders process optimization efforts. Therefore, the present work aims to address these challenges by studying the DRX behavior and microstructure evolution of BS 080M46 medium carbon steel through hot compression testing. Experimental data were collected to establish both a DRX kinetics model and a grain size model based on the JMAK equation. These models were subsequently incorporated into QForm V10.2.1 software to simulate microstructure evolution, with a specific emphasis on grain size under different deformation conditions. By comparing these finite element simulation results with microstructure observations, the accuracy and reliability of the models are verified. Providing insights into DRX behavior specific to BS 080M46 medium carbon steel and developing accurate predictive models, this study aims to contribute to the advancement of metallurgical science and materials engineering, facilitating enhanced process optimization and product development in engineering applications.

        The material being studied is BS 080M46 medium carbon steel, which was supplied by S.B.-CERA Co., Ltd. The weight percentage (wt%) of the steel's chemical composition was analyzed using an Emission Spectrometer (OES) and is detailed in Table 1. Figure 1(a) illustrates the conceptual methodology diagram used in this study. The flow curves under high temperatures required for input into the finite element model were obtained by a hot compression test using a Baehr DIL-805 deformation dilatometer. Samples were prepared in a cylindrical shape, 5 mm in diameter and 10 mm in height, with a thermocouple attached to the surface for direct temperature detection during deformation. The hot compression test covered four temperatures: 900°C, 1000°C, 1100°C, and 1200°C, along with three strain rates: 0.1, 1, and 10 s^-1, to characterize deformation conditions. Samples were placed in a vacuum chamber filled with inert Argon gas and heated by an induction coil to reach the deformation temperatures. The heating rate of 1.625°C/s was maintained for 1 minute to ensure uniform temperature distribution. Samples were then compressed using an Alumina punch to achieve a 60% reduction in height, followed by immediate quenching in Argon gas with a cooling rate of 40°C/s until reaching room temperature. Figure 1(b) depicts the temperature–time path during the hot compression test. Metallographic preparation involved cutting samples along the cylindrical axis, mounting them on a hot press, initial polishing with 400-grit SiC abrasive paper, followed by finer grits up to 1200 grit SiC papers and 0.3 µm Alumina particles for final polishing. Subsequently, surfaces were etched using a 4% picral and 3% Nital solution for 4 seconds. Microstructural observations were conducted using Light Optical Microscopy (LOM) and scanning electron microscopy (SEM), focusing on the central region of the sample’s cross-sections. The initial microstructure of BS 080M46 medium carbon steel contains proeutectoid ferrite and pearlite, as depicted in Figure 2.

Table 1 Chemical compositions (wt%) of BS 080M46 medium carbon steel

Figure 2 Microstructure of BS 080M46 medium carbon steel by (a) LOM and (b) SEM showing proeutectoid ferrite and pearlite structure

3.1. Flow curve of BS 080M46 medium carbon steel

       The collected experimental data is employed to generate flow curves of BS 080M46 medium carbon steel, systematically plotted over a range of deformation temperatures spanning from 900 to 1200°C at 100°C intervals with constant strain rates of 0.1, 1, and 10 s^-1, as illustrated in Figure 1(c) to Figure 1(e). Flow curves represent the stress-strain relationship under well-defined deformation conditions. They often exhibit a characteristic behavior known as dynamic recrystallization (DRX), which starts with a peak stress and gradually declines towards a state of steady stress, as highlighted in Mirzadeh et al. (2012) and (Mirzadeh, 2015).

3.2. Establishment of DRX model of BS 080M46 medium carbon steel

3.2.1.  Determination of Critical Strain Model Parameters

       During the hot working process, the initial stage of compressive deformation shows a rapid rise to a peak in the experimental flow curves with an increase in true strain. This is subsequently followed by a gradual reduction, ultimately leading to a consistent, steady-state stress. The strain value associated with the peak stress () is commonly denoted as the peak strain ().

       The initiation of DRX is typically correlated with the dislocation accumulation, which may arise due to plastic deformation. DRX can be initiated when the dislocation density exceeds a certain critical point, commonly termed the critical strain () for DRX (Wu et al., 2018).  New grains can nucleate both at the pre-existing grain boundaries and within the grains that have undergone deformation, and these newly generated grains can grow into high-angle boundaries. The work hardening rate, denoted as (MPa), is expressed as the derivative of (Chen et al., 2021a; Shafiei and Ebrahimi, 2012; Najafizadeh and Jonas, 2006). In their findings, Poliak and Jonas (2003) proposed that the inflection observed in ln  plots can serve as a valuable indicator for identifying the initiation of DRX. The ln  analysis was effective in providing precise values for determining critical strain (Mirzadeh and Najafizadeh, 2010a; 2010b). Applying a third-order polynomial regression method to analyze the curve until it reaches its peak facilitates the identification of the inflection point, thereby allowing for the derivation of the critical strain () corresponding to the critical stress (). Figure 3(a) displays the ln  curves and their associated 3rd-order polynomial for a strain rate of 0.1 s^-1. The presented data in Table 2 exhibits the values for  and  under various deformation conditions. These values have been computed from the experimental stress-strain curves and work hardening rate curves. According to Figure 3(b), the normalized strain can is represented by the ratio  with a value of 0.478

Table 2 Values of   and  for BS 080M46 medium carbon steel 

Figure 3 (a) ln  curve of BS 080M46 medium carbon steel and their corresponding 3^rd order polynomial at a strain rate of 0.1 s^-1 and (b) 

Figure 4 Scatter plot and their linear regression of (a) 

Taking into consideration the initial grain size (), temperature (T), strain rate (), and the activation energy for deformation (Q), one can formulate the expression for  as follows (Chen et al., 2022; Wang et al., 2011): 

where the constants are associated with the material. With a value of 8.314 J×K^-1mol^-1, R represents the universal gas constant. All deformed samples share the same initial grain size. However, the influence of grain size is subsequently taken into consideration, resulting in  = 0. Obtaining the values of  involves applying the natural logarithm for both sides of Equation 1, yielding in Equation 2, as depicted below:

The material constant  is provided at a certain temperature  The fitted linear correlation with temperature variations between  and  is depicted in Figure 4(a). Consistent slopes across a range of temperatures result in  being computed as 0.189, obtained by averaging the slopes of the four fitted curves.  In accordance with the correlation between and 1000/T under varying strain rates, can be calculated at a certain strain rate The  could be obtained by linear fitting the data in Figure 4(b), and the average of the four slope values for  was found to be 29448.7 J×mol^-1. The value of was also computed as 0.012 by substituting the average of  into Equation 1. Hence, Equation 3 can be given as:

The critical strain model was       

3.2.2.  Determination of DRX Kinetics Model Parameters

denotes the peak stress, and  represents the steady-state stress. The DRX kinetics model, based on the JMAK equation in alloys, has been widely adopted due to the findings of several studies (Zhang et al., 2022a; Joun et al., 2022; Ji et al., 2021; 2020; Sun et al., 2020; Zhang et al., 2020; 2019; Marques Ivaniski et al., 2019; Quan et al., 2019; Wang et al., 2016). At elevated temperatures, Equation 6 serves as a tool to observe the evolution of the DRX volume fraction.

where  represent material constants, while denotes the activation energy related to recrystallization. Additionally, are the material-specific constants in the JMAK equation. The initial grain size was not taken into account due to the observation that the average grain size of one specimen was found to be the same as that of the others, resulting in  Achieving Equation 9 involves the application of the natural logarithm to Equation 8 on both sides.

Equation 9 yield Additionally, Equation 5 allows the calculation of the stress at which 50% of the DRX volume fraction occurs. The associated strain,  can be calculated based on the experimental stress-strain data provided in Table 2. The plots representing can be illustrated in Figure 5(a) and Figure 5(b), respectively. Subsequent to the application of linear regression fitting, the computed average material constants are as follows:  and  By substituting into Equation 8, the average value of from twelve deformation conditions is 0.040. Equation 10 can be given as:

Figure 5 Scatter plot and their linear regression of (a) and (c) correlation of  and under a strain rate of 1 s^-1

     Upon performing the natural logarithm on both sides of Equation 10, the values of k_d and b_d, are obtained, as shown: 

  Under the conditions of 1100°C and a strain rate of 1 s^-1, the relationship between exhibited a nearly linear trend, as shown in Figure 5(c). Here  corresponds to the slope of the regression line and ln  indicates the regression intercept. The average calculated values for   are 5.070 and 2.404, respectively. Ultimately, the DRX kinetic model of BS 080M46 medium carbon steel can be written as follows:

    Considering Equation 12, Figure 6(a) and Figure 6(b) present the  under a deformation temperature of 1000°C and a strain rate of 1 s^-1, respectively.  According to the calculation from Equation 12, it becomes clear that an increase of the applied strain results in a proportional increase in the DRX volume fraction, ultimately nearing 1, or 100%. This observation strongly implies that the material undergoing deformation tends toward a complete DRX process. When applying a constant strain at a fixed strain rate of 1 s^-1, raising the deformation temperature accelerates the DRX phenomenon. The acceleration of this phenomenon arises from the increased mobility of grain boundaries in higher temperatures. This increased mobility promotes the initiation of new grains and facilitates the growth and merging of existing ones. This phenomenon enhances the nucleation and growth processes associated with DRX, ultimately leading to a higher DRX volume fraction. At a consistent deformation temperature of 1000°C, conversely, elevating the strain rate promotes grain boundary mobility. This increased mobility provides a longer duration for grain boundary migration, resulting in a delayed DRX. These findings suggest that the DRX volume fraction can be notably increased by elevating the deformation temperature and concurrently lowering the strain rate.

Figure 6  versus  curves at (a) 1 s^-1 and (b) 1000 °C; (c) Comparing computed and experimental  values for a specific deformation condition; (d) Correlation between computed and experimental  values

        The DRX kinetics model is applied to calculate the DRX volume fraction of BS 080M46 medium carbon steel within a range of deformation conditions. The plots in Figure 6(c) and Figure 6(d) illustrate the concordance between computed and experimental  values. In Figure 6(c), the comparison of the computed and experimental values of is depicted for the hot compression test of BS 080M46 medium carbon steel under specific conditions (1100°C and a strain rate of 1 s^-1). Meanwhile, Figure 6(d) displays a scatter plot illustrating the correlation analysis between experimental and calculated DRX volume fraction values across all deformation conditions. The high correlation coefficient (R = 0.949) and low root mean square error (RMSE = 0.113) confirm the accuracy and effectiveness of the DRX model in predicting  of BS 080M46 medium carbon steel during hot compression tests. 

3.2.3.  Determination of Grain size model parameters

where is the average DRX grain size,  are material constants. The initial grain size was ignored, so  By analysing  (Figure 8(a)) and  (Figure 8(b)) using linear regression, the values and were determined. The  was calculated as 7082.57 by averages of substituting into Equation 13. The expression representing the model for calculating the average DRX grain size of BS 080M46 medium carbon steel is presented below: