Modelling of Reversed Austenite Formation and its Effect on Performance of Stainless Steel Components

The kinetics of reversed austenite formation in 301 stainless steel and its effect on the deformation of an automobile front bumper beam are studied by using modelling approaches at different length scales. The diffusion-controlled reversed austenite formation is studied by using the JMAK model, based on the experimental data. The model can be used to predict the volume fraction of reversed austenite in a temperature range of 650 – 750 ◦C. A 3D elastoplastic phase-field model is used to study the diffusionless shear-type reversed austenite formation in 301 steel at 760 ◦C. The phase-field simulations show that reversion initiates at martensite lath boundaries and proceeds inwards of laths due to the high driving force at such high temperature. The effect of reversed austenite (RA) and martensite on the deformation of a bumper beam subjected to front and side impacts is studied by using finite element (FE) analysis. The FE simulations show that the presence of reversed austenite and martensite increased the critical speed at which the beam yielded and ∗Corresponding Author. E-mail: hemanth.yeddu@ncl.ac.uk Accepted for publication in Journal of Engineering Materials and Technology on 2 February 2021. doi: https://doi.org/10.1115/1.4050134 failed. RA fraction also affects the performance of the bumper beam.


Modelling of Reversed Austenite Formation and its Effect on Performance of Stainless Steel Components
Sadie Louise Green a , Hemantha Kumar Yeddu a, * a School of Engineering, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom.

Abstract
The and their ability to absorb energy during impact. Steel, however, is not lightweight and therefore in recent years, there has been an increase in the research into the possible use of stainless steel components in the automotive industry [1]. This growing interest is due to stainless steel being lightweight, which aids in fuel reduction and exhaust emissions that are important factors considered in the environmental and government regulations [2].
Austenitic stainless steels are mainly used for applications where it is important to have good corrosion resistance along with good aesthetic properties. Due to their low yield strength, austenitic stainless steels are not considered to be suitable for structural purposes [3]. As a result, there has been a lot of research conducted into heat treatments that could be used to improve the mechanical properties, e.g. high strength, good ductility and good corrosion resistance, of stainless steels that would allow them to be used in more applications, such as the automotive industry.
The formation of martensite can impart significant strength to steels. The yield strength of steels can also be significantly increased by grain refinement, due to Hall-Petch effect. Reversion annealing process, i.e. heat treatment to revert martensite to austenite, has proved to be successful in reducing the grain size and thereby in improving the mechanical properties of steels [4][5][6][7][8][9][10]. The improved strength of reversion annealed steel is also due to the high dislocation density of reversed austenite, inherited from martensite [11][12][13].
Reversed austenite has also been reported to improve corrosion resistance of stainless steel [14].
Earlier studies showed that reversion can take place at the austenitemartensite interfaces or inside the martensite laths [12,15]. The reversed austenite can grow by a diffusionless shear mechanism or by a diffusional mechanism, depending on the composition [12]. The reversion of martensite has been reported to occur by diffusional mechanism in Fe-18Cr-8.5Ni steel [16], Fe-18Cr-9Ni steel at 650 • C [13], 301 type steels up to the temperature of 750 • C [17] and in 301LN steel [18]. Reversion by shear mechanism has been reported to occur in Fe-16Cr-10Ni steel [13], 301 steels at 800 • C and possibly at 850 • C [17] as well as between 700-800 • C [9]. Thus it is essential to study both mechanisms in order to predict the transformation kinetics.
The Johnson-Mehl-Avrami-Kolmogorov (JMAK) model has been used to study austenite formation during intercritical as well as reversion annealing [19][20][21] and can be used to study the reversion kinetics of the diffusional phase transformation. The phase-field method [22,23] has been successfully used to study the microstructure evolution during martensitic transformations [24][25][26][27][28][29] and reverse transformation of martensite to austenite [30][31][32]. The effect of phase fractions on the mechanical properties and performance of the components can be studied by using macroscale finite element analysis.
In the present work, modelling approaches at different length scales are used to study the reversion kinetics in 301 stainless steel as well as its ef- i.e. martensite, and the rate of growth is the radial growth [33].
The JMAK equation in its simplest form is [20]: where V a is volume fraction of reversed austenite formed, k is constant related to the reversion temperature, t is time (seconds) and n is constant that depends on nucleation and growth mechanisms of the phase transformation.
Considering that there are only two phases, i.e. martensite and austenite, present in the microstructure, the martensite volume fraction (V m ) can be calculated using: In order to model the effect of annealing temperature and time on the reversed austenite formation, experimental data of the volume fraction of martensite reverted to austenite in 301 steels annealed at 650 • C, 700 • C and 750 • C was obtained from Ref. [6]. From the experimental data ( Fig. 1a), ) and ln(t) are calculated and then plotted (Fig. 1b). A line of best fit was applied to the straight line section of the graph. The equation of the line of best fit is: where n is gradient of the line of best fit and ln(k) is y-intercept, which are the required constants in JMAK equations (Eqs. (1) and (2)). Fig. 1b shows the plot for 650 • C. Similar analysis is performed for all the temperatures and the predicted values of k and n are shown in Table 1. Table 2 shows the established relationships to determine the constants k and n in different temperature ranges.
The calculated values of the constants (k and n) in Table 1 are used in JMAK equation and the volume fraction of martensite reverted to austenite is estimated. Fig. 2 shows the predicted volume fractions of reversed austenite at different temperatures compared to the experimental data. The predicted phase fractions are in agreement with the experimental data ( Fig. 2). Fig. 2 shows that there is a change in the transformation rate between the annealing temperatures of 700 • C and 750 • C. It is believed that this change in rate of transformation can be explained by a change in transformation mechanism, as supported by numerous studies. Johannsen et al. [17] studied the reversed austenite formation in 301 stainless steel annealed between 600-900 • C. They found that between 600-750 • C the stainless steel underwent a diffusional reversion mechanism from martensite to reversed austenite [17]. Diffusional reversion occurs by nucleation and growth of ultra-fine grains of austenite at martensite boundaries [34]. Another study by Lee et al. [15] confirmed the diffusional reversion mechanism in this transformation temperature range as they found reversed austenite, with a film-like structure and with a thickness of 1 µm, had formed along the martensite lath boundaries.
It was reported that by 800 • C the reversed austenite was formed by a shear reversion mechanism [17]. The shear reversion process involves the transformation of the strain-induced martensite, formed by cold rolling, into reversed austenite laths which have a high dislocation density [35]. The microstructure obtained at higher transformation temperatures, such as 750-1000 • C, is believed to consist of granular reversed austenite structure which existed inside the martensite laths as well as the film-like reversed austenite at the lath boundaries [15]. Another important feature that is noticeable in Fig.   2 is that the rate of transformation is significantly high in the initial stages of the annealing process. This can be attributed to the rapid grain growth which occurs due to the large amount of grain boundaries and therefore there is a large driving force for grain growth to occur [34].

Phase-field model
The diffusionless shear-type reversion mechanism and the microstructure evolution is studied by using the phase-field approach. The phase-field equation governing the microstructure evolution is given by [24,25]: where η q is the phase field variable that tracks the evolution of martensite, v is the total number of martensite variants and L pq is a matrix of kinetic parameters. In the present work three phase-field variables (η 1 , η 2 , η 3 ) that correspond to the three Bain variants, which form the basis for the Kurdjumov-Sachs (K-S) orientation relationship (OR) are considered [36].
The Gibbs energy of a system undergoing athermal martensitic transformation can be expressed as: where G chem v corresponds to the chemical part of the Gibbs energy density, G grad v is the gradient energy term, G el v is the elastic strain energy density.
G chem v is expressed as a Landau-type polynomial [24,25]: where V m is the molar volume and the coefficients A, B, C are expressed in terms of Gibbs energy barrier and the driving force [25].
G grad v is expressed as [24,25]: where r(x,y,z) is the position vector expressed in Cartesian coordinates. β ij is the gradient coefficient matrix expressed in terms of the interfacial energy, molar volume and the Gibbs energy barrier.
G el v can be expressed as: where σ ij (r) is the internal stress generated in the material due to martensite formation, c ijkl is the tensor of elastic constants and pl kl (r) is the plastic strain. ij (r) is the total strain, calculated by solving the mechanical equilibrium condition is the stress-free transformation strain. Bain strain tensors ( 00 ij (p)) of different variants are: where 3 and 1 are compressive and tensile transformation strains, respectively.
The material undergoes plastic deformation when the internal stress exceeds the yield limit. The evolution of plastic strain pl ij (r) is governed by [25,26]: where k ijkl is the plastic kinetic coefficient. G shear v is the shear energy density expressed as G shear v = c ijkl 1 2 e ij (r)e kl (r) + 1 2 e 0 ij (r)e 0 kl (r) − e ij (r)e 0 kl (r) , where e ij (r) is the deviatoric actual strain tensor and e 0 ij (r) is the deviatoric stressfree transformation strain tensor [25]. Linear isotropic strain hardening is considered by using the following expression [37]: where σ y is yield stress of the material that depends on plastic strain, σ 0 y is initial yield stress, H is hardening modulus and pl (r) is von Mises equivalent plastic strain.
The following input simulation data corresponding to stainless steels with a composition of Fe-17 wt %Cr-7 wt %Ni are acquired from different sources, such as CALPHAD, ab initio calculations and experiments [27,30] A single crystal of austenite of 1 µm grain size is subjected to quenching at -10 • C and subsequent isothermal annealing at 760 • C. Ref. [9] reported that shear-type reversion occurs in the range of 700 -800 • C, whereas Ref. [17] reported that shear-type reversion occurs at 800 • C and diffusional reversion occurs up to 750 • C in 301 stainless steels. In order to consider a temperature that is in agreement with both these experimental data as well as to study an annealing temperature that has not been studied before by the phase-field approach, 760 • C is considered as the annealing temperature to study the shear-type reversion mechanism in the present work. A preexisting martensite embryo is considered in the center of the grain. Dirichlet (clamped) boundary conditions are considered. Simulations are performed on a 50 x 50 x 50 mesh by using FemLego software [38]. Due to the lack of available experimental data on the kinetics of lath martensite, L pq in Eq.
(4) is considered to be unity and the microstructure evolution is discussed in terms of dimensionless time, t*.
A lath-type martensitic microstructure is obtained during quenching (Fig.   3), in agreement with the microstructure observed in 301-type stainless steels [39,40]. The simulation is started with one martensite variant and as it grows further, other martensite variants are formed due to autocatalysis such that the strain energy is minimized (Fig. 3)   The top view of the microstructure obtained at t*=80, shown in Fig. 3c, is shown in Fig. 4a. The microstructure evolution during annealing at 760 • C is shown in Fig. 4. Reversion initiates at martensite lath boundaries and proceeds inwards of laths (arrows in Fig. 4), which is in good agreement with Refs. [12,15]. The driving force for reversion of martensite is very high at such a high temperature and hence reversion can proceed inwards of laths, whereas at low temperatures reversion occurs only at lath boundaries due to low driving force [30]. Moreover, decrease in the internal stresses (

Macroscopic FEA
A front bumper beam of an Audi A1 with dimensions of 1750 mm length x 200 mm height x 100 mm width x 10 mm thickness was designed using Autodesk Inventor [41]. Fig. 6 shows the bumper beam, energy absorber and the back plates. Finite element analysis, using ANSYS software [42] with rectangular finite elements, is performed to study the effect of reversed austenite on the mechanical behaviour of the bumper beam under the following loading conditions.
(a) Loading condition 1: The beam was subjected to a frontal impact with a stationary object. The impact force associated with the collision at speeds between 20-70 miles per hour (mph) were calculated using F max = mv 2 2d , where m is mass of Audi A1 car, d is distance travelled during collision, v is speed (m/s) of the car before collision and F max is impact force (kN).
(b) Loading condition 2: In this loading type, tension caused by a side impact of the bumper beam was investigated. It was assumed that the bumper beam was stationary and was impacted at an angle of 45 • by another vehicle travelling at a given speed (v). The impact forces can be calculated using , where θ is angle of impact.   Table 3. When the front bumper beam was subjected to compression due to front impact, i.e. loading condition 1, the presence of martensite and reversed austenite in steels increased the force required to yield the bumper beam by a factor of 3 and the force required to failure by a factor of 1.5 (Table 3 and Fig. 7). The critical speed at which the beam yielded and failed has increased by 20 mph and 12 mph, respectively.
A similar increase in performance was observed when the bumper beam was subjected to tension due to side impact, i.e. loading condition 2 (Fig. 8).
The presence of martensite and reversed austenite increased the critical speed at which the beam yielded and failed by 22 mph and 10 mph, respectively.
The effect of reversed austenite (RA) content on deformation of the bumper beam during front impact was studied by considering (i) 40% RA with σ yield = 1223 MPa [34] and (ii) 95% RA with σ yield = 758 MPa [34].
The simulations show that the bumper beam would yield at 70 mph in the case of 40% RA (Fig. 9a) and 50 mph in the case of 95% RA (Fig. 9b). An excessive amount of RA leads to reduced strength, despite giving rise to an increase in ductility. Therefore, a reduced performance of the bumper beam with a very high RA is observed. Nevertheless, the bumper beam with 95% RA performed better (50 mph, Fig. 9b) compared to that without RA (28 mph, Fig. 7b).
The choice of a static component reduced the variables involved in analysing the yield and failure points. Consequently, the mechanical properties and changes in performance were analysed more accurately. In reality, however, the bumper beam with reversed austenite would have absorbed more energy as the applied compressive load coupled with the compressive internal residual stresses (Fig. 5) could transform the reversed austenite to martensite during front impact [27]. During the side impact, the applied tensile load would first need to overcome the compressive internal residual stresses and hence the beam would have tolerated slightly higher loads.
The above results show that the presence of martensite and reversed austenite has significantly improved the performance of the front bumper beam. Earlier research has showed that the steel composition, martensite and reversed austenite phase fractions, percentage of cold rolling and grain size can significantly affect the mechanical properties [34,44]. By a careful selection of heat treatment temperature, time and percentage of cold rolling the martensite and reversed austenite phase fractions can be tailored to improve the performance of bumper beams and other stainless steel components.