# Control of retained austenite stability during the heat treatment of the high performance steel Ferrium® M54®

Aurélien Mondière, V. Deneux, N. Binot, Denis Delagnes

► To cite this version:

Aurélien Mondière, V. Deneux, N. Binot, Denis Delagnes. Control of retained austenite stability during the heat treatment of the high performance steel Ferrium® M54®. Journal of Materials Research and Technology, 2025, 36, pp.2074-2082. 10.1016/j.jmrt.2025.03.230. hal-05007423

HAL Id: hal-05007423

https://imt-mines-albi.hal.science/hal-05007423v1

Submitted on 10 Apr 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

# Control of retained austenite stability during the heat treatment of the high performance steel Ferriuum® M54®

A. Mondiere<sup>a, *</sup>, V. Déneux<sup>b</sup>, N. Binot<sup>b</sup>, D. Delagnes<sup>a ID</sup>

## ARTICLE INFO

Handling Editor: P Rios

**Keywords:**

Ultra-high strength steel

Retained austenite

Heat treatment

Thermal stabilization of austenite

Yield strength

## ABSTRACT

Ferriuum® M54® ultra-high-strength steel is an excellent candidate for landing gear applications due to its balance of UTS, KIC, and KISCC properties, which is among the best compared to steels currently in use. The tensile strength of Ferriuum® M54® at room temperature is mainly provided by the martensitic structure formed during quenching and by the precipitation of molybdenum M₂C carbides during tempering. However, a significant amount of retained austenite may remain after heat treatment. This study demonstrates that both the temperature and the delay between quenching and cryogenic treatment are critical parameters. Specifically, carbon diffusion during this period, even at room temperature, contributes to stabilizing the retained austenite. Austenite stabilization is modelled using the Johnson-Mehl-Avrami-Kolmogorov law to determine the maximum allowable dwell time between quenching and cryogenic treatment. This important finding helps in stabilizing the yield strength and preventing the transformation of retained austenite into fresh martensite under load.

## 1. Introduction

Aeronautical structures subjected to high stresses, such as landing gear components, require materials with an optimal balance between ultimate tensile strength, fracture toughness, and the stress intensity threshold for stress corrosion cracking (UTS/KIC/KISCC) properties. Indeed, landing gear is exposed to high stresses while the aircraft is stationary, but it also experiences dynamic stresses during landing, taxiing, and take-off [1]. Ultra-high strength steels (UHSS) are used to achieve these mechanical properties and are widely used in landing gear applications. Very high strength is attained through martensitic transformation during quenching, while a balance with fracture toughness is achieved during tempering, during which hardening phases precipitate [2] and the martensitic matrix softens primarily due to a recovery mechanism [3,4]. For such critical applications, it is crucial to guarantee the balance of the properties defined above. Consequently, deviations from this compromise must be minimal between material batches from one treatment to the next, meaning the repeatability of treatments must be nearly perfect. Previous research on various UHSS has shown that austenitic grain size, as well as the potential presence of non-metallic inclusions or undissolved carbides during austenitization, significantly affect ductility, impact strength, and fracture toughness properties [5].

However, the stability of the retained austenite during the heat treatment, that also significantly influences these properties and yield strength, has not yet been explored. This is the focus of this work.

Even if a cryogenic treatment is performed after quenching and before tempering to achieve the highest martensite content, small amounts of retained austenite often remain, with a volume fraction typically reaching a few percent. Additionally, austenite can also form during tempering. This austenitic phase is referred to as reverted or precipitated austenite. The impact of retained austenite on yield strength is likely more significant in Ferriuum® M54® than in other UHSS, as UHSS generally contains both retained and reverted austenite. The reverted austenite content can be controlled by adapting the tempering conditions or by modifying the chemical composition, particularly the content of gamma-forming elements. Indeed, the tempering conditions for the Ferriuum® M54® steel adopted in this study [5,6] (section 2) result in the absence of reverted austenite formation. The research work presented is thus focused on the control of the retained austenite content during the final stages of the heat treatment.

The microstructure of Ferriuum® M54® steel at various observation scales was extensively described in a previous study [7]. The high yield strength can be attributed to the fine martensitic microstructure resulting from quenching, along with the uniform and finely distributed

<footnote><sup>a</sup> Institut Clément Ader (ICA), Université de Toulouse, CNRS, IMT Mines Albi, INSA, ISAE- SUPAERO, UPS, Campus Jarlard, F-81013, Albi, France</footnote>

<footnote><sup>b</sup> Safran Landing Systems, Bidos, F-64400, France</footnote>

<footnote>* Corresponding author. Aubert&Duval, France.</footnote>

<footnote>E-mail address: aurelien.mondiere@aubertduval.com (A. Mondiere).</footnote>
precipitation of $M_2C$ carbides during tempering. To achieve the desired microstructure and the corresponding optimal mechanical properties, the different stages of the heat treatment process are outlined as follows.

- Austenitization: The primary objectives of this stage are to nearly dissolve all remaining carbides from previous thermo-mechanical treatments into the austenitic phase and to achieve a chemically homogeneous austenite without excessive grain growth.

- Quenching: During this stage, austenite transforms into martensite. The martensite start temperature (Ms) is approximately 235 °C [9, 10], while the martensite finish temperature (Mf) lies well below room temperature.

- Cryogenic treatment: This treatment is carried out to complete the martensitic transformation. The objectives are twofold: firstly, to minimize the austenite content to achieve the highest mechanical strength, and secondly, to fully stabilize the microstructure.

- Tempering: By carefully adjusting the temperature and duration, this final stage is designed to achieve the optimal balance of properties. It enhances fracture toughness with a limited reduction in ultimate tensile strength (UTS) through the precipitation of nanometer-sized $M_2C$ carbides [8] and the softening of the martensitic phase due to the reduction in dislocation density inherited from the quenching process [3,9–11].

The evolution of the microstructure at each stage of heat treatment and its effect on the mechanical properties have been extensively documented in the literature (see Refs. [12–15]). However, the effect of a cryogenic treatment has been less frequently studied [16,17]. Achieving complete martensitic transformation with excellent repeatability requires a thorough investigation of the duration and temperature conditions of cryogenic treatment. Specifically, when cryogenic treatment is performed almost immediately after quenching, the Koistinen and Marburger equation [18] can generally be used to predict the proportion of transformed phase with fairly good accuracy. However, this approach is not always applicable in industrial heat treatment processes. Therefore, less intuitively, the time interval between the end of quenching and the start of cryogenic treatment must also be considered. Indeed, during quenching, the carbon supersaturated solid solution in the freshly formed martensite and the spatial distribution of the carbon atoms dictates the kinetics of the subsequent transformation and, consequently, the steel final microstructure and associated properties. Carbon partitioning at the transformation front, which has a major influence on the mobility of the interface and diffusion kinetics within the austenite and martensite on either side of the interface are phenomena that are not yet fully understood at the atomic scale, partly due to experimental difficulties at this scale of observation. However, improved knowledge would be highly beneficial for the design of martensitic steels with precisely controlled mechanical properties. The main objective of this work is to investigate the effects of the inter-processing time and temperature between quenching and cryogenic treatment on the retained austenite content and the corresponding yield strength.

The metallurgical mechanisms that influence the retained austenite content have been well documented and can be summarized as follows.

- The evolution of the chemical composition of the retained austenite during heat treatment. In particular, the carbon enrichment of the austenite lowers the Ms temperature thereby stabilizing the austenitic phase [19–24]. This enrichment is linked in particular to a phenomenon of carbon partitioning from martensite to austenite, which occurs throughout the transformation below Ms. Other authors have shown that carbon is not uniformly distributed within austenite but remains locally in high concentration near the martensite/austenite interface [25]. This localized high carbon concentration, which is fairly stable during cooling, tends to reduce the

mobility of the interface and slows the progression of the transformation.

- In addition to these chemical considerations, retained austenite is also influenced by the mechanical stresses that develop throughout the martensitic transformation [26]. The volume change associated with the transition from a face-centered cubic structure to a body-centered tetragonal structure induces internal stresses within the austenite phase, which is considerably softer than the martensite. The effects of these stresses on the stability of austenite are already well documented in the literature [27].

Finally, the martensitic transformation that occurs at room temperature following quenching is influenced by diffusion phenomena within both the already-formed martensite and the retained austenite phase. These diffusive processes continue as long as the carbon in the martensitic matrix remains supersaturated and the partitioning mechanisms at the martensite/austenite interface remain active. Such a stabilization of retained austenite is therefore a very important phenomenon that must be carefully considered. The primary objectives of this study are, first, to demonstrate the significant impact of austenite content on the mechanical properties of Ferrium® M54® steel, and second, to develop a method for controlling the retained austenite content after heat treatment in order to prevent any undesirable degradation of mechanical properties.

## 2. Investigated steel and experiments

### 2.1. Materials and heat treatment

The chemical composition of the studied Ferrium® M54® steel is given in Table 1:

The steel was received in a normalized and annealed condition. Samples for microstructural analysis (in particular for measuring the retained austenite content) and specimens for tensile testing were taken at the mid-radius of a 10.25 cm diameter bar, in the longitudinal direction. The first set of samples and test specimen blanks underwent heat treatment in the laboratory to achieve the desired final properties, as described in the following paragraph. A second set of samples and specimen blanks was subjected to the same heat treatment process, including identical temperatures and times, but under industrial conditions. These samples were then returned to the laboratory for the same characterization as the first batch.

The heat treatments performed were in agreement with the Questek's recommendations [28] and consisted of a preheating treatment at 315 °C for 1h, a solutionizing at 1060 °C for 1h, followed by oil quenching, cryogenic treatment at -75 °C for 2h, and tempering at 516 °C for 10h.

The time and temperature between quenching and cryogenic treatment (inter-processing time and temperature) were varied to study their effects on the retained austenite content. The first parameter pertains to the fact that the time between quenching and cryogenic treatment can vary under industrial conditions. The second parameter relates to the temperature of the quenching oil, which can fluctuate between batches. For laboratory treatments, a constant holding temperature was maintained for 2 h. However, under industrial conditions, the temperature evolution of the specimen blank once immersed in the oil is not precisely known and the temperature may very slightly between different treatments. In addition, thermal gradients are also more pronounced in industrial furnaces compared to laboratory furnaces (with a few degrees of difference), though this remains difficult to quantify precisely. For

<table><caption>**Table 1**

Chemical composition (wt%) of the Ferrium® M54® steel.</caption><thead><tr><th>Element</th><th>C</th><th>Cr</th><th>Ni</th><th>Co</th><th>Mo</th><th>W</th><th>V</th></tr></thead><tbody><tr><td>Wt%</td><td>0.31</td><td>0.99</td><td>10.30</td><td>7.44</td><td>2.20</td><td>1.40</td><td>0.10</td></tr></tbody></table>
industrial treatments, it is assumed that the inter-processing temperature is an average value between the temperature measured at the end of the quench and at the beginning of the cryogenic treatment. Furthermore, the geometries of the test specimen blanks were strictly identical in both the industrial and laboratory cases. In the case of larger industrial parts, it will be important to carefully monitor (for example, through calculation) the temperature distribution within the volume.

The experimental schedule can be summarized as follows (Tables 2 and 3):

Numerous additional samples and specimen blanks were heat treated under the same conditions with varying inter-processing times and temperatures (within the range specified in Tables 2 and 3) in order to complete the database, which includes tensile test results and retained austenite content (see section 3.1).

## 2.2. Experimental techniques

Tensile tests were conducted in accordance with ASTM E8-M standard on cylindrical specimens. The test was performed at room temperature with total strain control at a strain rate of 0.005 min⁻¹ up to 1.3 % strain, followed by 0.05 min⁻¹ until fracture. Three tests were performed for each experimental condition.

The retained austenite content was determined through saturation magnetization measurements, using a Setaram sigmameter within the facilities of the EDF (Electricité De France) laboratories. The evaluation of retained austenite volume fraction by magnetic measurements has been extensively documented in the literature [29]. The ferromagnetic sample is positioned between two electromagnets strong enough to reach the saturation magnetization. The sample is then rapidly removed, resulting in a variation in magnetic flux that is detected by coils. The variation of the magnetic flux is contingent upon the magnetization of the sample, exhibiting greater or lesser significance accordingly. As the martensitic phase is ferromagnetic, while austenite is paramagnetic (and thus considered non-magnetic due to its very small susceptibility), only the martensitic phase contributes to the signal. Consequently, the saturation magnetization is assumed to be directly proportional to the content of the ferromagnetic phase (and by extension, the austenite content) in the steel.

The retained austenite content was calculated using the following equation:

$$f_{V_r}^{sample} = 1 - \left( \frac{M_{sat}^{sample} \times f_{V'\alpha}^{ref}}{M_{sat}^{ref}} \right) \quad (1)$$

Where $f_{V_r}^{sample}$ is the volume fraction of austenite in the analysed sample, $M_{sat}^{sample}$ and $M_{sat}^{ref}$, respectively the saturation magnetization of the analysed sample and the reference, and $f_{V'\alpha}^{ref}$, the volume fraction of martensite in the reference.

It is therefore necessary to estimate the volume fraction of austenite or martensite in a reference sample using an alternative technique. Energy dispersive X-ray diffraction (XRD) experiments were carried out to estimate the austenite content in several samples that had been previously electrolytically polished to minimize the effect of residual stresses. The recorded diffraction patterns obtained using this technique exhibit a considerable number of diffraction lines (16–18 lines for each of the iron

<table><caption>**Table 2**
Experimental schedule for laboratory conditions heat treated samples (10 samples).</caption><thead><tr><th>Parameter</th><th>Inter-processing time at room temperature (h)</th><th>Inter-processing temperature for a 2h holding time (°C)</th></tr></thead><tbody><tr><td>Samples prepared (laboratory conditions)</td><td>0,1 ; 2 ; 8 ; 24 ; 48 ; 336</td><td>20 ; 50 ; 75 ; 100</td></tr></tbody></table>

<table><caption>**Table 3**
Experimental schedule for industrial conditions heat treated samples (6 samples).</caption><thead><tr><th>Parameter</th><th>Inter-processing time (h)</th><th>Inter-processing temperature (°C)</th></tr></thead><tbody><tr><td rowspan="5">Samples prepared (industrial conditions)</td><td>2</td><td>28</td></tr><tr><td>1</td><td>35</td></tr><tr><td>1.5</td><td>50</td></tr><tr><td>0.75</td><td>37</td></tr><tr><td>1.33</td><td>97</td></tr><tr><td></td><td>3.5</td><td>24</td></tr></tbody></table>

phases), which helps reduce the influence of textural effects on the determination of retained austenite content. Phase identification and lattice measurements were performed by comparing the experimental diffraction patterns with reference JCPDS patterns. The Rietveld refinement method was used to determine the volume fraction of the austenitic phase. The uncertainty in the measurements was estimated by conducting measurements on different samples that underwent identical heat treatments as well as by performing repeated measurements on the same samples. The estimated uncertainty is ±1 % in absolute value around the mean value. Furthermore, after selecting a reference state and determining the two values required for the application of equation (1), several XRD measurements of the austenite content were compared with the values obtained from the saturation field determination and equation (1). The differences observed were well below the measurement uncertainty, thus validating the experimental protocol for estimating the volume fraction of retained austenite by magnetic measurement.

Finally, the austenite content was measured on the same specimens both after cryogenic treatment and after tempering. These measurements demonstrated that the austenite content remains unchanged during tempering. It can therefore be concluded that, for the tempering conditions studied, the retained austenite is stable during tempering and no reverted austenite is formed. The absence of reverted austenite may be attributed to a higher AC1 critical temperature for Ferrium® M54® (800 °C according to the Carpenter data sheet [30]) compared to other UHSS in the same family, which is due to its lower cobalt content. Therefore, although carbide precipitation during tempering can locally modify the matrix composition and lower the AC1 point, the difference between the tempering temperature and the AC1 temperature is sufficiently large to prevent the formation of reverted austenite. All the results presented in the following section, including austenite content measurements and tensile tests, were obtained after tempering.

# 3. Results and discussion

## 3.1. Influence of retained austenite content on tensile mechanical properties

As the retained austenite content increases, a loss of linearity in the stress-strain curve is observed at lower stresses (see Fig. 1). As the conventional yield strength (YS) of austenite is considerably lower than that of martensite, this result was expected. An increase in austenite content consequently affects tensile properties, resulting in a decline in conventional yield strength (see Fig. 2). The correlation between the two is nearly linear within the limited range of austenite content examined:

$$YS = 1978 - 68\%\gamma \quad (2)$$

Where %γ is the retained austenite volume fraction (in percent).

The impact of increased retained austenite content on yield strength is thus very significant, with a reduction of 68 MPa per percentage point of austenite observed across the studied range. This initial result is consistent with findings reported by Sato et al. [31], who examined the impact of heat treatment on the mechanical properties of AerMet®100
<figure><img src="image_4.png" /><figcaption>Fig. 1. Experimental tensile curves for different retained austenite contents.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. Effect of increasing retained austenite content on yield strength.</figcaption></figure>

steel (0.23 %C, 13.4 %Co, 3.1 % Cr, 11.1 %Ni, 1.2 %Mo). According to these authors, increasing the retained austenite rate from 1.2 % to 5.7 % results in a 200 MPa loss in yield strength. Nevertheless, the linear law given by equation (2) should not be extrapolated to higher retained austenite contents. The slope of the line is steep, and extrapolating it would lead to an unreasonably rapid decrease in yield strength, ultimately approaching the yield strength of austenite, which Wang et al. estimated at 380 MPa for AerMet®100 steel [32] at room temperature.

Conversely, as shown in Fig. 1, the UTS remains constant at approximately 2020 MPa as the retained austenite content increases. Similarly, the elongation at fracture A (%), as illustrated in Fig. 3, does not appear to depend on the austenite content. Furthermore, an enhanced strain hardening of the austenitic phase is observed in comparison to martensite, along with an apparent convergence in the mechanical response as the total strain increases.

To explain this similar mechanical behaviour at elevated total strains (Fig. 1), measurements of the retained austenite content were conducted on the deformed portion of the fractured specimens. To this end, samples were cut from an area beneath the necking zone (see Fig. 4) and the retained austenite content of these samples was determined using the sigmometer.

The results indicate that the retained austenite rates did not exceed 1 % in any of the 15 tensile specimens examined after rupture. XRD analysis (see Fig. 5) definitively supports this result, showing the absence of an austenitic phase after the loading process. The

<figure><img src="image_6.png" /><figcaption>Fig. 3. Graph showing a constant elongation at rupture as the retained austenite content is increased.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. Cutting out of a deformed zone in a broken specimen after the tensile test.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 5. XRD pattern showing the absence of an austenitic phase in the Ferrium® M54® steel after a tensile test.</figcaption></figure>
transformation of austenite into fresh martensite under loading, as previously observed by Sato [31], is therefore the mechanism that leads to stress convergence at high total strains, regardless of the retained austenite contents prior to loading.

Consequently, the first major conclusion that can be drawn from these results is as follows: the instability of the retained austenite under mechanical loading and its significant effect on yield strength require very precise control of its content throughout the heat treatment process.

## 3.2. Cryogenic treatment to reduce retained austenite content

The effect of varying cryogenic treatment temperatures on the transformation of retained austenite into fresh martensite was investigated. As illustrated in Fig. 6, a reduction in the temperature of the cryogenic treatment results in a significant decrease in the austenite content. The experiments were carried out for a 2-h cryogenic treatment, with an inter-processing time of approximately 2 h.

The well-known Koistinen and Marburger law [18] is generally used to describe the martensitic transformation as a function of the final cryogenic temperature $T_c$ (see equation (3)):

$$p = 1 - \exp[-0.011(M_s - T_c)] \quad (3)$$

$p$ is the proportion of the transformed phase (the volume fraction of martensite). The theoretical values derived from Formula (3) are calculated with the experimental $M_s$ temperature, determined by conventional dilatometry in a previous study [7]. The discrepancy between the experimental and calculated austenite contents is less than 1 % (or close to 1 % at room temperature) over the entire temperature range covered by the experimentally determined austenite content (see Table 4). The austenite content is thus found to be highly sensitive to cryogenic treatment temperature, showing a fairly good agreement with the Koistinen and Marburger law. To achieve a reduced austenite content, a treatment at -75 °C with dry ice is selected and carried out. However, the effects of time and temperature conditions between the end of quenching and the start of cryogenic treatment (conditions rarely precisely measured and controlled during industrial treatments) are studied in the next section.

## 3.3. Influence of inter-processing time and temperature on the retained austenite stabilization

As the inter-processing time increases, the retained austenite content also increases (see Fig. 7). This indicates that the transformation of austenite to martensite during cryogenic treatment following oil quench is reduced.

In addition, an increase in inter-processing temperature results in an

<figure><img src="image_9.png" /><figcaption>Fig. 6. Retained austenite content according to the cryogenic temperature.</figcaption></figure>

<caption>Table 4</caption>

Comparison of the experimental retained austenite rates and those calculated using the Koistinen and Marburger equation.

<table><thead><tr><th></th><th>20 °C</th><th>-40 °C</th><th>-60 °C</th><th>-75 °C</th><th>-90 °C</th></tr></thead><tbody><tr><td>Experimental austenite contents (%)</td><td>10.0</td><td>5.2</td><td>4.7</td><td>4.1</td><td>3.9</td></tr><tr><td>Austenite contents derived by equation (3) (%)</td><td>11.3</td><td>6.2</td><td>5.3</td><td>4.7</td><td>3.8</td></tr></tbody></table>

<figure><img src="image_10.png" /><figcaption>Fig. 7. Evolution of retained austenite content as a function of inter-processing time at room temperature.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 8. Evolution of austenite content as a function of inter-processing temperature for an inter-processing time of 2h</figcaption></figure>

increase in the retained austenite content (see Fig. 8). It can be concluded that both the temperature of the quenching oil and the quenching time in oil prior to cryogenic treatment are critical parameters that must be carefully controlled under industrial conditions. These variations in the retained austenite content are not predicted by equation (3) but the significant effect on yield strength is described by equation (2). Therefore, precise control of the inter-processing time and temperature is essential to achieve repeatable tensile properties.

As mentioned in the introduction, one of the main mechanisms for austenite stabilization is carbon diffusion during the dwell time between oil quenching and cryogenic treatment. In more detail, several authors have already observed the stabilization of austenite during the time delay between $M_s$ and $M_f$ [33-43]. According to Kinsman and Shyne [37, 38], thermal stabilization is a consequence of carbon diffusion in supersaturated martensite, leading to a high concentration of carbon at the austenite/martensite interfaces. Indeed, Gouné et al. [44] observed this
high content of carbon near interfaces (nearly 5 at% over a few nano-meters) using atom probe tomography following a waiting period at 75 °C. The stabilization of austenite is a consequence of the pinning of the interface between the martensite nucleus and the austenite, which is achieved by the segregation of interstitial atoms, such as carbon, in the lattice. This phenomenon leads to the fixation of dislocation entanglements which significantly hinder martensite growth due to the reduced mobility of the dislocations. The degree of austenite stabilization is therefore linked to the anchoring strength of the interface.

Furthermore, the comparison between the austenite stabilization phenomenon in Ferrium M54® steel and that observed by Mohanty [40] in a 1.33 %C-0.25 %Si-0.23 %Mn-0.01 %P-0.019 %S-0.08 %Cr-0.019 %Al steel shows comparable behaviour (see Fig. 9). In this figure, the degree of austenite stabilization is estimated by measuring the shift in the martensitic transformation temperature (Y-axis). Upon quenching, austenite begins its transformation into martensite at the Ms temperature. Following a dwell time at a temperature below Ms, the martensitic transformation will restart at a lower temperature, Ms'. The difference between Ms and Ms' indicates the degree of stabilization, θ, of the austenite.

In order to test the validity of the hypothesis of carbon diffusion within supersaturated martensite mentioned in the literature, the diffusion coefficient of carbon in martensite $D'_C$ close to room temperature can be estimated using the following equation, as proposed by Allain et al. [25]:

$$D'_C = 2 \times 10^{-6} \exp\left(\frac{-84.100}{RT}\right) \quad (4)$$

The diffusion length $l_c$ can be estimated using the following equation (5):

$$l_c = \sqrt{D'_C t} \quad (5)$$

From equations (4) and (5), the carbon diffusion length can be calculated for a range of inter-processing time and temperature conditions (see Fig. 10). As previously noted by Ref. [25], the results show that the carbon diffusivity in martensite is indeed significant at room temperature.

The estimated carbon diffusion distance is several tens of nanometers at room temperature, increasing to more than 100 nm as the inter-processing temperature rises. Given the range of lath sizes observed in Ferrium® M54® (50 nm to a few hundred nanometers), as reported in Refs. [32,45], the carbon diffusion distance in supersaturated martensite appears sufficient to facilitate an increase in its content at the martensite/austenite interfaces. Indeed, as the precipitation of transition

<figure><img src="image_12.png" /><figcaption>Fig. 9. Comparison of retained austenite stabilization in Ferrium® M54® steel and the steel investigated by Mohanty [40].</figcaption></figure>

carbides at these low temperatures is highly unlikely, and impossible at room temperature, it can be concluded that a large proportion of the supersaturated carbon in the martensite can diffuse towards the lath boundaries. This process would result in the pinning of the austenite/-martensite interface, as described in Ref. [44]. This analysis is highly consistent with the previously described mechanisms, even at temperatures approaching 20 °C.

Furthermore, the crystal lattice parameter of martensite was estimated from XRD experiments. The crystal structure of martensite formed during quenching can be interpreted as a deformed ferrite with a slightly body-centered tetragonal structure, where the ratio of crystal parameters c/a varies with carbon content. This metastable structure tends to revert to a body-centered cubic structure when a fraction of the carbon atoms initially positioned at the center of the edges of the tetragonal structure recover some mobility. However, the tetragonal structure of martensite cannot be detected with sufficient accuracy using our XRD measurements with a conventional X-ray source. In other words, the slightly higher value of the crystalline parameter along the [001] axis cannot be measured. Nevertheless, as a preliminary approach, if we consider a single diffraction peak for all crystallographic directions of type <001> (cubic structure), a slight decrease in the average lattice parameter as a function of the inter-processing time is observed, as shown in Fig. 11. At such a low temperature, the precipitation of iron carbides is not possible. Conversely, the trend observed in Fig. 11, which shows a slight tendency towards reversion to the stable body-centered cubic structure of α-ferrite, is consistent with a carbon diffusion mechanism occurring within the martensite.

### Austenite stabilization modelling

In relation to the previously described phenomena, a framework is required to predict the rate of retained austenite as a function of time and temperature. As proposed by Edmonson [36] and Mohanty [40], the variation of retained austenite content with time and temperature can be described thanks to the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation [46-48]:

$$f = 1 - \exp(-kt^n) \quad (6)$$

The fraction of retained austenite, f, is a function of the temperature-dependent parameter, k, and the temperature-independent exponent, n. The value of n is determined using the measured experimental austenite contents for inter-processing times listed in Table 2 (see Fig. 12). Two values of n can be estimated depending on the temperature: 0.134 at 50 °C and 0.094 at 20 °C. These values are generally lower than those reported in the literature, but still fall within the range of the lowest values reported in previous studies [36,40]. The average of these two values will be considered, namely n = 0.11395. The parameter k is then calculated as a function of temperature for an inter-processing time of 2h (see Table 2) and experimental austenite rates, using the least squares method. The temperature dependence of k is then calculated (see Fig. 13).

From n and k parameters, the retained austenite content (expressed as a percentage, see equation (2)) after tempering can be estimated as a function of inter-processing time and temperature using the following relationship:

$$\%\gamma = (1 - \exp(-0.0311 + 1.783 \times 10^{-4}T)t^{0.11395}) \times 100 \quad (7)$$

In equation (7), T and t are respectively the average inter-processing temperature (°C) and time (in hours). From this equation, a 1 % increase in the retained austenite content, which has a very significant impact on the yield strength (see equation (2)), corresponds roughly to an increase in the inter-processing temperature of about 30 °C for a fixed duration of 5 h and an increase in the inter-processing duration of approximately 10 h for a fixed temperature. For this latter case, it means that the cryogenic treatment is performed the day after the quenching.
<figure><img src="image_13.png" /><figcaption>Fig. 10. Effect of inter-processing time at room temperature (a) and inter-processing temperature for a dwell time of 2 h (b) on the carbon diffusion length in martensite.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 11. Evolution of ferrite lattice parameter in function of inter-processing time at room temperature.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 13. Thermal dependence of the parameter *k* in the JMAK equation.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 12. Determination JMAK parameters *n* and *k*, from experimental retained austenite contents.</figcaption></figure>

The retained austenite rates, as calculated using equation (7), are compared with the laboratory experimental rates in Fig. 14. These experimental values were used to identify the *k* and *n* parameters (conditions reported in Table 2). The discrepancy between the two rates remains fairly limited. Furthermore, this preliminary comparison delineates the validity range of the proposed model in terms of inter-

<figure><img src="image_17.png" /><figcaption>Fig. 14. Comparison between the retained austenite content calculated from equation (7) and the experimental retained austenite content obtained from laboratory samples (Table 2) and industrial samples (Table 3).</figcaption></figure>

processing time (between 5 min to two weeks) and temperature (from 20 °C to 100 °C). The same figure also shows the retained austenite content measured following industrial heat treatments (conditions reported in Table 3). The discrepancies between the calculated and the measured values are more pronounced than those observed for
laboratory heat treatments. However, these differences remain within 1.5 % in absolute value over the six experimental values, which is a satisfactory outcome, particularly in light of the approximation made for the inter-processing temperature that has already been mentioned in section 2.1.

- Critical inter-processing time and temperature

The two critical parameters for the regulation of retained austenite content are undoubtedly the time and temperature (which can be difficult to assess if not constant) between quenching and cryogenic treatment. In contrast, the cryogenic treatment temperature is reproducible and does not require any particular attention, provided that the temperature reached is well controlled. Conversely, oil quenching can have a more significant impact on austenite content due to the inherent challenges in achieving reproducibility in an industrial setting when processing a large volume of parts or large-sized components. It is imperative that oil-quenched parts are removed from the bath when they have reached a sufficiently low and fixed temperature. If the temperature of the parts is excessive, even by just a few Celsius degrees, and the cryogenic treatment is not initiated immediately, the retained austenite may become stabilized. The same effects occurs if components are left in the oil for an extended period.

To assist in establishing optimal operating conditions during the heat treatment process, the relationship identified in this study between yield strength and retained austenite content can be applied. Using equations (2) and (7), an abacus can be constructed to determine the critical inter-processing conditions (which must not be exceeded) to achieve the required yield strength (see Fig. 15).

This abacus will also be very useful in the event of deviations in the heat treatment process, such as excessive inter-processing delays and/or temperature between quenching and cryogenic treatment. Using this tool, the manufacturer will be able to estimate the impact on the yield strength and determine whether the heat treatment needs to be repeated.

## 4. Conclusion

The ultra-high-strength steel Ferrium® M54® offers an optimal balance between strength, fracture toughness, and stress corrosion cracking resistance. The objective of this study was to demonstrate the high sensitivity of Ferrium® M54® to retained austenite content and to develop a comprehensive methodology for controlling this content during the final stages of the heat treatment process, thereby preventing a reduction in mechanical properties. Tensile tests and measurements of retained austenite content were carried out over a wide range of time and temperature conditions from the end of the quenching stage to the initiation of cryogenic treatment. The main results can be summarized as follows.

- Ferrium® M54® is highly sensitive to retained austenite content, exhibiting a linear decrease in yield strength as the retained austenite content increases. Additionally, no evidence of reverted austenite formation was observed. The austenite content measured after the quenching and tempering corresponds exclusively to the retained austenite content.

- The progress of martensitic transformation during quenching is in good agreement with the Koistinen and Marburger law. Cryogenic treatment below -75 °C results in a retained austenite volume fraction close to 4 %. It was shown that the time and temperature between quenching and cryogenic treatment are crucial parameters. Specifically, carbon atom mobility during this period is sufficient to stabilize austenite, underscoring the importance of precise control over the inter-treatment time and temperature to control the retained austenite content.

<figure><img src="image_18.png" /><figcaption>Fig. 15. Abacus giving the critical inter-processing time and temperature to meet the required yield strength.</figcaption></figure>

- The stabilization of retained austenite is described by the Johnson-Mehl-Avrami-Kolmogorov law. The parameters of this law were identified using instrumented treatments conducted in laboratory furnaces. The results show a high level of agreement between the calculated retained austenite content using this model and the austenite content measured after heat treatments under industrial conditions.

- The model can be used to define the critical time-temperature conditions that will ensure the retained austenite content remains below a specified threshold.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

The authors wish to thank the MMC EDF laboratory in Renardière for the use of the sigmameter, which permitted accurate austenite content measurements.

## References

[1] Flower HM. High performance materials in aerospace. Dordrecht: Springer Netherlands; 1995. https://doi.org/10.1007/978-94-011-0685-6.

[2] Li J, Zhan D, Jiang Z, Zhang H, Yang Y, Zhang Y. Progress on improving strength-toughness of ultra-high strength martensitic steels for aerospace applications: a review. J Mater Res Technol 2023;23:172–90. https://doi.org/10.1016/j.jmrt.2022.12.177.

[3] Galindo-Nava EI, Rivera-Díaz-del-Castillo PEJ. A model for the microstructure behaviour and strength evolution in lath martensite. Acta Mater 2015;98:81–93. https://doi.org/10.1016/j.actamat.2015.07.018.

[4] Kennett SC, Krauss G, Findley KO. Prior austenite grain size and tempering effects on the dislocation density of low-C Nb–Ti microalloyed lath martensite. Scr Mater 2015;107:123–6. https://doi.org/10.1016/j scriptamat.2015.05.036.

[5] Sun Y, Quan J, Salvador H, Edwards J, Lin J, Kozmel T, et al. Ausforming and tempering of a novel ultra-high strength steel. Mater Sci Eng, A 2022;838:142750. https://doi.org/10.1016/j.msea.2022.142750.

[6] Li X-Y, Zhang Z-H, Cheng X-W, Wang Q, Hao G-L. A rapid route to improve the mechanical properties of the aged high Co–Ni steel. Mater Sci Eng, A 2022;834: 142612. https://doi.org/10.1016/j.msea.2022.142612.

[7] Aurélien Mondiere. Control of Ferrium® M54® steel mechanical properties by the control of its microstructure during heat treatment to aeronautical applications. Toulouse: University of; 2018.

[8] Mondiere A, Dêneux V, Binot N, Delagnes D. Controlling the MC and M2C carbide precipitation in Ferrium® M54® steel to achieve optimum ultimate tensile strength/fracture toughness balance. Mater Char 2018;140:103–12. https://doi.org/10.1016/j.matchar.2018.03.041.
[9] Mebarki N, Delagnes D, Lamesle P, Delmas F, Levaillant C. Relationship between microstructure and mechanical properties of a 5% Cr tempered martensitic tool steel. Mater Sci Eng, A 2004;387-389:171-5. https://doi.org/10.1016/j.msea.2004.02.073.

[10] Saha DC, Biro E, Gerlich AP, Zhou Y. Effects of tempering mode on the structural changes of martensite. Mater Sci Eng, A 2016;673:467-75. https://doi.org/10.1016/j.msea.2016.07.092.

[11] Li Z, Xiao N, Li D, Zhang J, Luo Y, Zhang R. Effect of microstructure evolution on strength and impact toughness of G18CrMo2-6 heat-resistant steel during tempering. Mater Sci Eng, A 2014;604:103-10. https://doi.org/10.1016/j.msea.2014.03.013.

[12] Bhareshia H, Honeycombe R. Steels: microstructure and properties. Elsevier; 2017.

[13] Krauss G. Steels. ASM International; 2015. https://doi.org/10.31399/asm.tb.spsp2.9781627082655.

[14] Jiang B, Wu M, Zhang M, Zhao F, Zhao Z, Liu Y. Microstructural characterization, strengthening and toughening mechanisms of a quenched and tempered steel: effect of heat treatment parameters. Mater Sci Eng, A 2017;707:306-14. https://doi.org/10.1016/j.msea.2017.09.062.

[15] Zhu C, Xu L, Xie H, Shi R, Yin L, Wei S. Effect of heat treatment processes on the microstructure and mechanical properties of 00Cr13Ni5Mo super martensitic stainless steel (SMSS). J Mater Res Technol 2024;32:2006-21. https://doi.org/10.1016/j.jmrt.2024.08.030.

[16] Zhang H, Zhang G, Zhou H, Liu Z, Xu B, Hao L, et al. Influence of cooling rate during cryogenic treatment on the hierarchical microstructure and mechanical properties of M54 secondary hardening steel. Mater Sci Eng, A 2022;851:143659. https://doi.org/10.1016/j.msea.2022.143659.

[17] Kumar TV, Thirumurugan R, Viswanath B. Influence of cryogenic treatment on the metallurgy of ferrous alloys: a review. Mater Manuf Process 2017;32:1789-805. https://doi.org/10.1080/10426914.2017.1317790.

[18] Koistinen DP, Marburger RE. A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels. Acta Metall 1959;7:59-60. https://doi.org/10.1016/0001-6160(59)90170-1.

[19] Liu JH, Binot N, Delagnes D, Jahazi M. Influence of the cooling rate below Ms on the martensitic transformation in a low alloy medium-carbon steel. J Mater Res Technol 2021;12:234-42. https://doi.org/10.1016/j.jmrt.2021.02.075.

[20] Allain SYP, Gaudez S, Geandier G, Hell J-C, Gouné M, Danoix F, et al. Internal stresses and carbon enrichment in austenite of Quenching and Partitioning steels from high energy X-ray diffraction experiments. Mater Sci Eng, A 2018;710:245-50. https://doi.org/10.1016/j.msea.2017.10.105.

[21] Speer J, Matlock DK, De Cooman BC, Schroth JG. Carbon partitioning into austenite after martensite transformation. Acta Mater 2003;51:2611-22. https://doi.org/10.1016/S1359-6454(03)00059-4.

[22] Choi KS, Zhu Z, Sun X, De Moor E, Taylor MD, Speer JG, et al. Determination of carbon distributions in quenched and partitioned microstructures using nanoscale secondary ion mass spectroscopy. Scr Mater 2015;104:79-82. https://doi.org/10.1016/j scriptamat.2015.03.027.

[23] Lerchbacher C, Zinner S, Leitner H. Atom probe study of the carbon distribution in a hardened martensitic hot-work tool steel X38CrMoV5-1. Micron 2012;43:818-26. https://doi.org/10.1016/j.micron.2012.02.005.

[24] Pickering EJ, Collins J, Stark A, Connor LD, Kiely AA, Stone HJ. In situ observations of continuous cooling transformations in low alloy steels. Mater Char 2020;165:110355. https://doi.org/10.1016/j.matchar.2020.110355.

[25] Allain S, Danoix F, Goune M, Hoummada K, Mangelinck D. Static and dynamical ageing processes at room temperature in a Fe25Ni0.4C virgin martensite: effect of C redistribution at the nanoscale. Philos Mag Lett 2013;93:68-76. https://doi.org/10.1080/09500839.2012.742590.

[26] Lavakumar A, Park M, Hwang S, Adachi H, Sato M, Ray RK, et al. Role of surrounding phases on deformation-induced martensitic transformation of retained austenite in multi-phase TRIP steel. Mater Sci Eng, A 2023;874:145089. https://doi.org/10.1016/j.msea.2023.145089.

[27] Nakada N, Ishibashi Y, Tsuchiyama T, Takaki S. Self-stabilization of untransformed austenite by hydrostatic pressure via martensitic transformation. Acta Mater 2016; 110:95-102. https://doi.org/10.1016/j.actamat.2016.03.048.

[28] QuesTek. Processing information QPI-M54. 2012.

[29] Zhao L, van Dijk NH, Brück E, Sietsma J, van der Zwaag S. Magnetic and X-ray diffraction measurements for the determination of retained austenite in TRIP steels. Mater Sci Eng, A 2001;313:145-52. https://doi.org/10.1016/S0921-5093 (01)00965-0.

[30] Carpenter. Carpenter Ferrium M54 datasheet n.d.

[31] Sato K. Improving the toughness of ultrahigh strength steel. University of California; 2002.

[32] Wang C, Zhang C, Yang Z. Austenite layer and precipitation in high Co-Ni maraging steel. Micron 2014;67:112-6. https://doi.org/10.1016/j.micron.2014.07.008.

[33] Blanter ME, Serebrennikova BG. The nature of thermal stabilization of austenite. Met Sci Heat Treat 1972;14:567-70. https://doi.org/10.1007/BF00647864.

[34] Blanter ME. Thermal stabilization of austenite. Met Sci Heat Treat 1972;14:439-40. https://doi.org/10.1007/BF00649831.

[35] Brook R, Sanyal TK, White G. Thermal stabilization of austenite in a high-nickel steel. Metall Trans A 1977;8:1449-52. https://doi.org/10.1007/BF02642858.

[36] Edmondson B. Thermal stabilization of austenite in a 10% Ni, 1% C steel. Acta Metall 1957;5:208-15. https://doi.org/10.1016/0001-6160(57)90167-0.

[37] Kinsman KR, Shyne JC. The thermal stabilization of austenite. Acta Metall 1966; 14:1063-72. https://doi.org/10.1016/0001-6160(66)90194-5.

[38] Kinsman KR, Shyne JG. Thermal stabilization of austenite in iron-nickel-carbon alloys. Acta Metall 1967;15:1527-43. https://doi.org/10.1016/0001-6160(67)90184-8.

[39] Ko T, Edmondson B. Thermal stabilization of austenite in nickel steels. Acta Metall 1953;1:466-7. https://doi.org/10.1016/0001-6160(53)90135-7.

[40] Mohanty ON. On the stabilization of retained austenite: mechanism and kinetics. Mater Sci Eng, B 1995;32:267-78. https://doi.org/10.1016/0921-5107(95)03017-4.

[41] Morgan ER, Ko T. Thermal stabilization of austenite in iron-carbon-nickel alloys. Acta Metall 1953;1:36-48. https://doi.org/10.1016/0001-6160(53)90008-X.

[42] Popandopulo AN, Zhukova LT. Thermal stabilization and destabilization of austenite in tungsten-molybdenum high-speed steels. Met Sci Heat Treat 1984;26:599-603. https://doi.org/10.1007/BF00707799.

[43] Imai Y, Izumiyama M. Sub-zero treatment of quenched steel (4th report). Control of stabilization of retained austenite. J Jpn Inst Metals 1958;22:7-11. https://doi.org/10.2320/jinstmet1952.22.1.7.

[44] Gouné M, Danoix F, Allain S, Bouaziz O. Unambiguous carbon partitioning from martensite to austenite in Fe-C-Ni alloys during quenching and partitioning. Scr Mater 2013;68:1004-7. https://doi.org/10.1016/j.scriptamat.2013.02.058.

[45] Pioszak GL. Hydrogen assisted cracking of ultra-high strength steels. University of Virginia; 2015.

[46] Kolmogorov AN. On the statistical theory of the crystallization of metals. 1937.

[47] Johnson WA, Mehl KE. Reaction kinetics in processes of nucleation and growth. Transactions of the American institute of mining. Metallurgical and Petroleum Engineers 1939;195.

[48] Avrami M. Kinetics of phase change. I general theory. J Chem Phys 1939;7:1103-12. https://doi.org/10.1063/1.1750380.