Nattarawee Siripath, Surasak Suranuntchai, Sedthawatt Sucharitpwatskul

Corresponding email: surasak.sur@kmutt.ac.th

Corresponding email: surasak.sur@kmutt.ac.th

**Published at : ** 18 Sep 2024

**Volume :** **IJtech**
Vol 15, No 5 (2024)

**DOI :** https://doi.org/10.14716/ijtech.v15i5.6770

Siripath, N., Suranuntchai, S., Sucharitpwatskul, S., 2024. Modeling Dynamic Recrystallization Kinetics in BS 080M46 Medium Carbon Steel: Experimental Verification and Finite Element Simulation.

63

Nattarawee Siripath | Department of Tool and Materials Engineering, Faculty of Engineering, King Mongkut’s University of Technology, Thonburi, Bangkok, 10140, Thailand |

Surasak Suranuntchai | Department of Tool and Materials Engineering, Faculty of Engineering, King Mongkut’s University of Technology, Thonburi, Bangkok, 10140, Thailand |

Sedthawatt Sucharitpwatskul | National Science and Technology Development Agency (NSTDA), Thailand Science Park, Phahonyothin Road, Khlong Nueng, Khlong Luang, Pathum Thani, 12120, Thailand |

Abstract

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

Introduction

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.

Experimental Methods

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

C |
Si |
Mn |
P |
S |
Ni |
Cr |
Mo |
Cu |

0.467 |
0.194 |
0.673 |
0.027 |
0.021 |
0.068 |
0.110 |
0.016 |
0.178 |

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

Results and Discussion

*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).

In the beginning, stress starts to rise as the strain
continuously increases, which is governed by work hardening. The dislocations
within the material move and accumulate at the grain boundaries, leading to
deformation resistance and strengthening.
This
phenomenon is commonly referred to as work hardening, which makes the material
stronger and more resistant to deformation. At this point, the strain has not
yet reached its critical value. As dislocations accumulate and undergo
rearrangement, sub-boundaries are formed. These sub-boundaries play a role in
triggering the onset of DRX. DRX begins when the strain exceeds a critical
value, resulting in the softening mechanism, meaning the material becomes more
pliable and transforms from a previously strengthened state. This rapid
transformation gradually converts the accumulated energy at the grain
boundaries due to the work hardening process into activation energy for DRX,
facilitating the formation and growth of equiaxed grains and inducing a change
in the microstructure of the material. Nevertheless, with the increasing
strain, the dislocation density rises, and the softening effect tends to
gradually become higher. Consequently, the flow stress rises while the
increasing rate slightly continuously decreases. At the point of balance
between work hardening and softening mechanisms, driven by DRX, the stress
reaches its peak, and then exhibits a slight decline until it reaches
steady-state stress.

*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

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^{-1}mol^{-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__

Through the utilization of stress-strain
data from the experiment, cited in references (Joun *et al*.,
2022; Jantepa and Suranuntchai, 2021; Lv *et al*., 2018) one can directly compute the DRX
volume fraction (*X*_{d}) with the aid of Equation 5.

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.

In QForm software, the DRX volume
fraction is expressed as:

This equation, referred to as Equation 7, describes the evolution of the
DRX volume fraction as a function of strain. Furthermore, the strain required
to achieve a 50% DRX volume fraction, as calculated using Equation 8, can be
determined based on the existing literature.

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:

^{}

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__

The metallography method, in accordance
with the ASTM E1382 standard, was employed to determine the average DRX grain
size of BS 080M46 medium carbon steel. Figure 7 displays the optical
microstructures of the specimens subjected to compression under different
deformation conditions. The measured values obtained from the midpoint along
the cross-section aligned with the compression axis are presented in Table 2.
The average DRX grain size, as defined by Equation 13, is demonstrated in terms
of both deformation temperature and strain rate.

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: