# Evolution of carbon distribution across meso-scale segregations in pressure vessel steel

M Bregeault, A Marceaux Dit Clément, B Le Gloannec, F Roch, M Véron, H

P van Landeghem

► To cite this version:

M Bregeault, A Marceaux Dit Clément, B Le Gloannec, F Roch, M Véron, et al., Evolution of carbon distribution across meso-scale segregations in pressure vessel steel. Materials Today Communications, 2025, 44, pp.112024. 10.1016/j.mtcomm.2025.112024. hal-04975662

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# Evolution of carbon distribution across meso-scale segregations in pressure vessel steel

M. Bregeault<sup>a,b</sup>, A. Marceaux Dit Clément<sup>b, c</sup>, B. Le Gloannec<sup>b</sup>, F. Roch<sup>b</sup>, M. Véron<sup>a</sup>, H.P. Van Landeghem<sup>a,*</sup>

## ARTICLE INFO

**Keywords:**

- Low alloy steel
- Carbon segregation
- Diffusion
- Thermodynamic modeling
- Heat treatment

## ABSTRACT

Carbon plays a major role in the microstructural evolution and associated mechanical properties of nuclear pressure vessel steel. Solidification conditions of large ingots lead to an inhomogeneous distribution of all elements in the microstructure. The standard thermal schedule for pressurized components was found to afford carbon enough mobility for complete meso-scale homogenization, while substitutional elements remain unaffected. Their inhomogeneous distribution negligibly changes the activity of carbon in austenite. Subsequent bainitic transformation causes redistribution of carbon at the scale of the parent austenite grain only. Tempering, however, leads to migration of carbon from solute-lean to solute-rich regions depending on its duration.

<figure><img src="image_2.png" /></figure>

CC-BY 4.0

https://creativecommons.org/licenses/by/4.0/

## 1. Introduction

Large pressurized components for the nuclear industry are widely made of low-alloy bainitic steel such as AFNOR 18MND5 or the equivalent ASME SA508 Gr3. The heavy section of these components requires them to be forged from very large ingots, commonly weighing more than 100 t. The solidification conditions in such large ingots are conducive to the segregation of the main alloying elements from the forming solid into the receding liquid at three different scales (micro, meso and macro) [1,2]. Macrosegregations have been thoroughly studied in terms of microstructural evolution and mechanical properties. Those ingot features are larger in scale and more positively segregated than mesoscale segregations, which result from segregation between grains during solidification. Thus, while macrosegregations can be cut out from the ingot, finer, ubiquitous mesosegregations must be worked with. Those mesosegregations are found in equiaxial solidification regions [3], which are difficult to prevent in large ingots. They are however

unwanted given their potential deleterious effect on toughness [3,4]. Given the mobility of substitutional elements, those meso-scale enrichments cannot be homogenized through practical heat-treatments, even after their sizes have been reduced by forming operations [5]. This can be understood by comparing the two characteristic sizes of the problem. First, the typical thickness of mesosegregation bands after forging is a few hundred micrometers [3]. Second, the order of magnitude of the diffusion distance of substitutional elements during industrial austenitization is around one micrometer [6]. This order of magnitude is the same for all substitutional elements as they share the same vacancy diffusion mechanism [7]. In contrast, carbon, being an interstitial element, enjoys a much greater mobility and is able to redistribute over large distances at standard heat-treatment temperatures. Additionally, while all alloying elements can alter the local microstructural evolution and the resulting mechanical properties such as fracture toughness, carbon is often found to have a dominating effect, notably through the formation of carbides [8–10].

The majority of studies dealing with the consequences of segregation in pressure vessel steel were either conducted on as-cast ingots or on tempered components [8,9,11–13]. In both cases, carbon is observed to segregate along with the other elements [4,14]. Although it is not explicitly worded as such, it often seems assumed that the segregation during solidification seen in the former is the same as the segregation seen in the latter after thermomechanical processing. However, the

<footnote><sup>a</sup> Univ. Grenoble Alpes, CNRS, Grenoble INP, SIMAP, Grenoble F-38000, France</footnote>

<footnote><sup>b</sup> Materials Department (DTIMM) of Engineering & Design Authority, Framatome, 1, Place Jean Millier, Courbevoie 92400, France</footnote>

<footnote>* Corresponding author.
E-mail address: hugo.van-landeghem@grenoble-inp.fr (H.P. Van Landeghem).</footnote>
processing of forgings involves long intermediate stages at high temperature both in the austenitic and ferritic ranges, where carbon mobility is non-negligible. Basso et al. [15] suggest that carbon migrates towards Mn-rich zones in austenite before the bainitic transformation as a result of reduced carbon activity, but they do not show evidence of this mechanism. On the other hand, Yan et al. provide one of the rare examples of chemical analyses in pressure vessel right after fast continuous cooling, and show the absence of carbon enrichment in meso-scale segregated regions [16], suggesting that meso-scale carbon enrichment can be homogenized during processing and does not systematically reappear.

The objective of the present paper is to investigate both the thermodynamics and the kinetics of carbon redistribution in pressure vessel steel mesosegregations and clarify its evolution throughout the whole austenitization/quench/tempering sequence based on both experimental evidence and simulation results.

## 2. Materials and methods

### 2.1. 18MND5 low-alloy steel

The piece of 18MND5 low-alloy steel used in this study was provided by Framatome, France. This piece was cut from a thick-walled steam generator shell, forged from a 170 t ingot with a total strain of 4. Its nominal composition measured after ingot casting is listed in Table 1. After forging the part was reaustenitized at 875 °C for at least 5.5 h before being water quenched. It was then tempered for 5.5 h and submitted to a simulated stress-relief treatment at 640 °C, furnace cooled, then stress-relieved for 20 h at 615 °C. Although the segregation patterns in the equiaxed zone of the ingot do not present any privileged direction, the deformation imposed during forming operations creates a well-known sheet structure [17,18] where enriched zones appear in the form of sub-millimeter segregated bands (typical width around 300 µm, depending on the forging ratio) in a cross-section. A typical example of this band structure is shown in Fig. 1 with a low-magnification micrograph featuring vertical segregated bands. The position of chemical segregations is revealed by the heterogeneity they induce in the bainitic microstructure.

### 2.2. Heat treatments

Five specimens were machined out of the received piece of 18MND5. One was characterized as received and the other four were heat treated as listed in Table 2 in order to investigate carbon distribution in the intermediate stages.

### 2.3. Light microscopy

Samples for light microscopy were first ground with SiC paper then polished on polishing cloths with diamond pastes down to 1 µm diamond grain size. They were then etched with 3 % Nital before being thoroughly rinsed in ethanol. The observations were carried with an Olympus BX60 M light microscope.

### 2.4. Electron probe micro-analysis (EPMA)

Samples for EPMA were first prepared like for light microscopy and were then polished with an alumina colloidal suspension. For each sample, several chemical composition profiles were measured across segregated bands using EPMA with a step size of 5 µm. An accelerating

voltage of 15 kV and a current of 1 µA were used. The procedure detailed in [19] using standard calibration specimens was applied to obtain quantitative carbon measurements.

### 2.5. Thermodynamic and kinetic calculations

Thermodynamic and kinetic calculations were performed using Thermo-Calc with TCFE11 and MOB2 databases.

DICTRA simulations were conducted within a single region of 2125 µm with a linear grid and a 5 µm grid step. For simulations in austenitic conditions, FCC_A1 (austenite) was the only phase defined in the region. For simulations in ferritic conditions, BCC_A2 (ferrite), Cementite and HCP_A3 (Mo₂C) were defined in the region. Where necessary, experimental concentration profiles were extended so that the overall composition of the simulated region matches that of the bulk alloy.

## 3. Results

### 3.1. Space-resolved composition analyses

Fig. 2 shows a micrograph of a typical band measured in the final service-ready tempered and stress-relieved condition (sample S1-STREL) and the chemical analysis profile across it. The microstructure in the segregated band appears darker than the non-segregated region. This contrast stems from the difference between the upper bainite microstructure formed in the solute-lean zones and the lower bainite or martensite microstructure formed in the core of segregated bands [16]. The chemical profile shows that all the main substitutional elements (Mn, Ni, Mo, Si, Cr) segregate jointly, although with different partitioning coefficients. As those substitutional elements all display similarly slow solid-state diffusion rates, the enriched zones formed during solidification persist throughout the thermal sequence. In this condition, carbon is observed to have segregated to the same locations as the other elements.

Fig. 3 shows composition profiles across similar bands as the one shown in Fig. 2, after different stages of the typical heat treatment for mechanical properties. Fig. 3a shows carbon content is very homogeneous across the fully martensitic microstructure obtained after reaustenitization and water-quench (sample S2-AUST). In particular, it is the same inside and outside of meso-scale segregated bands. In this completely martensitic condition, the microstructure changes very little across the bands and produces little contrast in light microscopy. Their positions are still clearly revealed by the increase in substitutional element contents, whose distributions are not measurably affected by the austenitization treatment. Only molybdenum content is shown in the figure for clarity but its value can be used as a proxy for other substitutional element contents, as explained in the supplementary material. Fig. 3b presents the carbon distribution across a band after reaustenitization followed by controlled continuous cooling at 1000 °C. h-1 (sample S4-CC1000). Such a continuous cooling yields a bainitic microstructure. It is observed that carbon content is still homogeneous at the scale of the segregated bands at the end of this step, as its diffusion range remains quite limited during the transformation time span (≈ 50 min). However, micro-scale fluctuations, which are absent from the martensitic microstructure, can be seen outside of the meso-segregated band in this condition. Similar results were obtained for samples cooled at 200 °C.h⁻¹ (S3-CC200) and 3000 °C.h⁻¹ (S5-CC3000) as shown in the supplementary material, with the amplitude of the micro-scale fluctuations decreasing as the cooling rate increases.

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

Composition of the 18MND5 low-alloy steel piece used in this study (wt%).</caption><thead><tr><th>C</th><th>N</th><th>Al</th><th>Si</th><th>P</th><th>S</th><th>V</th><th>Cr</th><th>Mn</th><th>Ni</th><th>Cu</th><th>Mo</th></tr></thead><tbody><tr><td>0.18</td><td>0.0047</td><td>0.01</td><td>0.21</td><td>0.0043</td><td>0.0006</td><td>0.001</td><td>0.15</td><td>1.50</td><td>0.71</td><td>0.06</td><td>0.50</td></tr></tbody></table>
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Micrograph of a stress-relieved 18MND5 sample showing the meso-segregations in dark, arranged in a band structure. The micrograph was recorded after etching with 3 % Nital. The size difference between the Vickers indents reveals a higher hardness in the meso-segregated bands. S is the main upsetting direction of the forging operations.</figcaption></figure>

**Table 2**

Details of the sample heat treatments. The range of heat-treatment conditions is chosen to be representative of industrial conditions.

<table><thead><tr><th></th><th>Austenitization</th><th>Cooling</th><th>Microstructure</th></tr></thead><tbody><tr><td>S1-STREL</td><td>As-received (stress-relieved)</td><td></td><td>Tempered bainite / martensite</td></tr><tr><td>S2-AUST</td><td>870 °C, 1 h</td><td>Water quench</td><td>Fresh martensite</td></tr><tr><td>S3-CC200</td><td></td><td>200 °C.h<sup>-1</sup></td><td>Proeutec. ferrite / fresh bainite</td></tr><tr><td>S4-CC1000</td><td></td><td>1000 °C.h<sup>-1</sup></td><td>Fresh bainite / martensite</td></tr><tr><td>S5-CC3000</td><td></td><td>3000 °C.h<sup>-1</sup></td><td></td></tr></tbody></table>

## 3.2. Thermodynamic calculations

### 3.2.1. Carbon / substitutional interactions

The driving force for carbon segregation in the band during successive thermal stages can be assessed by calculating the chemical potential landscape created by the presence of substitutional elements. To this end, the chemical potential of carbon was calculated across the substitutional composition profile of the band seen in Fig. 2, while the carbon content is set constant at the bulk nominal value (0.18 wt%). Two conditions are investigated to depict the equilibrium thermodynamic situation during austenitization and tempering. For austenitization, the temperature is set to 870 °C and the only phase considered is the FCC austenite solid solution. For tempering, the temperature is 630 °C and the mixture of phases considered is BCC ferrite, cementite, and Mo2C carbides. Mo2C carbides are chosen as they are often reported in TEM observations of 18MND5 steels as small rods, although MoC are theoretically more stable but never observed in practice [9,20].

The results for tempering conditions in Fig. 4a show that the substitutional segregation profile in the band creates a strong potential well for carbon, plotted in solid black line. The individual contribution of each alloying element X is estimated separately by considering an Fe-X-C ternary alloy in the same manner and is plotted in dashed line. The sum of the individual effects amounts almost exactly to the overall profile, suggesting negligible interactions between substitutional elements. In the considered composition range, contributions to the potential well can be attributed to manganese, molybdenum and chromium, by

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Composition profile across a typical meso-scale segregated band in quenched, tempered and stress-relieved 18MND5 steel (S1-STREL). The light micrograph was recorded after etching with 3 % Nital. A plot of the relative enrichment based on this data can be found in the Supplementary Material. The micrograph is represented at the same distance scale as the corresponding composition profile.</figcaption></figure>

decreasing order of significance. Those three elements decrease the activity of carbon. Nickel and silicon actually have an opposite effect, but here their influence is of negligible magnitude in comparison. Fig. 4b
<figure><img src="image_5.png" /><figcaption>Fig. 3. Composition profiles across segregated bands a) after re-austenitization followed by water quench (S2-AUST) and b) after re-austenitization followed by continuous cooling at 1000 °C·h⁻¹ (S3-CC1000). The micrographs are represented at the same distance scale as the corresponding composition profiles.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Carbon chemical potential calculations in tempering (a,b) and austenitization (c,d) conditions. a,c) Potential well across a band resulting from the measured substitutional profile, highlighting the separate contribution of each element. b,d) Comparison of the effect of each element (X = Mn, Ni, Mo, Si, Cr) on carbon potential for a deviation from the nominal composition.</figcaption></figure>

shows the impact on carbon chemical potential of a deviation for each substitutional element from the nominal composition (0.5 wt% Mo), which lies at the intersection of all curves on the graph. Chromium has the strongest attractive interaction with carbon but this relative importance does not carry in terms of its effective impact on the chemical potential of carbon because of the higher bulk content and segregation tendency of manganese (see *supplementary material*). The

same analysis in stress-relief conditions shows very similar results, with the carbon potential well being only very slightly shallower.

The same analysis is conducted for austenitization conditions in Fig. 4c and Fig. 4d. The potential well is much less pronounced than in tempering conditions. Qualitatively, the interactions of all substitutional elements with carbon are the same in austenite as in ferrite. However, the repulsive effect of silicon is very strong relatively to the other
interactions and offsets the effect of manganese and molybdenum much more than it does in the ferritic microstructure. This calculated repulsive interaction between carbon and silicon is consistent with experimental observations by Darken [21].

### 3.2.2. Local equilibrium carbon concentrations

The dependance of carbon chemical potential on substitutional content in III.B.1 can be used to estimate local equilibrium carbon concentrations throughout the microstructure in both austenitization and tempering conditions. Substitutional elements diffuse much slower than interstitial ones such as carbon [22,23]. Thus, they are essentially immobile at the considered temperatures and timescale and only carbon content can adjust to reach local equilibrium. In Fig. 5, the carbon content leading to the same activity as that of the nominal composition is plotted as a function of the local substitutional content, for different conditions. The iso-activity lines corresponding to austenitization and tempering (blue and orange solid lines, respectively) conditions reveal a markedly different behavior. The predicted carbon enrichment in the bands is negligible (+ 0.003 wt%) in austenitization conditions (fully austenitic microstructure, 870 °C), while it is salient (+ 0.16 wt%) for tempering (carbide-containing ferritic microstructure, 630 °C). In the latter case, low molybdenum regions with local substitutional content slightly below the nominal composition display a carbon lean equilibrium composition compared to the nominal one. As these regions account for the majority of the total volume, a consistent global mass balance for carbon is ensured.

The iso-activity line corresponding to the hypothetic case of an austenite solid solution at the tempering temperature (630 °C) is also displayed (dashed line). Its low slope and reduced departure from the 870 °C case show that the temperature change plays a minor role in changing the activity of carbon compared to the phase transition.

### 3.2.3. Carbon diffusion kinetics

Thermodynamic calculations presented in III.B.2 show that local equilibrium carbon contents vary little in austenite regardless of temperature, while it will vary very substantially in a ferritic microstructure depending on the substitutional composition. The redistribution that will take place depends on the diffusion kinetics of carbon in those microstructures. Calculations of these kinetics were performed using the composition profile of the representative band shown in Fig. 2.

Fig. 6 shows the carbon profile obtained across the band after diffusion at 870°C while the microstructure is fully austenitic. The initial composition profile imposed is the one measured in the tempered and stress-relieved state in Fig. 2, already used for chemical potential wells calculations in III.B. The profile was extended on both sides such that the total amount of each element in the simulation cell matches the bulk

<figure><img src="image_7.png" /><figcaption>Fig. 5. Calculated carbon content in equilibrium with the nominal composition, at austenitization and tempering temperatures, as a function of substitutional content associated to a given Mo content.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. Simulation of carbon diffusion in austenite at 870 °C using ThermoCalc DICTRA with TCFE11 and MOB2 databases. The initial composition profile is adapted from the experimental data presented in Fig. 2.</figcaption></figure>

content. The carbon transport occurring after 1 h at this temperature is sufficient for its content across the band to homogenize substantially. The maximum carbon concentration in the band drops by 0.065 wt%. After 5.5 h, a typical duration for reaustenitization in industrial practice [24], carbon is almost fully homogenous as the peak content across the band drops below 0.2 wt%. The evolution of manganese and molybdenum composition profiles after such a treatment can be found in the supplementary material.

Fig. 7a presents the carbon profile obtained after 5.5 h at 630°C and after an extra 20 h at 610 °C, to simulate tempering and stress-relief treatments respectively. A flat carbon profile (0.18 wt%) is taken as initial condition. The segregation band becomes enriched with carbon from the non-segregated region, which becomes leaner as a result. Fig. 7b shows that tempering conditions are insufficient to attain the local equilibrium concentrations for the investigated heat treatments and that the predicted redistribution of carbon is also lower than that seen experimentally. In these simulations the microstructure is mostly ferritic but contains carbide precipitates as well, as explained in III.B.1. In the model used here, local equilibrium phase fractions are assumed at all times, while in reality secondary phases precipitate at a finite rate. This excess trapping of carbon in carbides artificially reduces its mobility and consequently, its redistribution for a given time and temperature.

## 4. Discussion

### 4.1. Homogeneity of carbon content after austenitization

Pressurized components undergo a complex thermal schedule after forging. The final microstructure is established during the final heat treatment, that imparts the piece its required mechanical properties. It includes four steps: austenitization, quenching, tempering and stress-relief, the latter being only applied to welded components in practice. Carbon can potentially redistribute throughout the microstructure during all these steps.

Composition measurements in the sample reaustenitized and quenched provide with a snapshot of elemental distributions at the end of an austenitization treatment at 870 °C for 1 h. The observed flat carbon content profile indicates that this treatment provides sufficient thermal activation for an almost complete homogenization of carbon content across a segregation band. Thermodynamic calculations support that the distribution of local substitutional contents encountered in 18MND5 meso-scale segregations do not create chemical potential gradients for carbon and result in identical equilibrium carbon contents at 870 °C. This implies that reaustenitizing tempered components containing bands such as the one shown in Fig. 2 does result in a driving
<figure><img src="image_9.png" /><figcaption>Fig. 7. a) Calculated carbon profiles across a segregated band after diffusion during tempering (5.5 h at 630 °C) and stress-relief heat treatments (20 h at 610 °C), starting from the as-quenched condition. b) Comparison of diffusion simulation result, equilibrium profile and measured carbon profile presented in Fig. 2.</figcaption></figure>

force for the homogenization of carbon content. It should be noted that this almost perfect evenness of carbon chemical potential across segregation bands is a feature specific to the 18MND5 composition. Due to its strong repulsive interaction with carbon, silicon plays a key role in balancing the attractive interactions of the carbon-attractive elements (Cr, Mn, Mo). In Fig. 6, kinetic simulations of the treatment show a substantial redistribution of carbon at 870 °C given a band thickness of 250–300 µm commonly found in 18MND5 forgings. After only 1 h, the homogenization is less advanced than observed experimentally. However, after a duration 5.5 h, closer to industrial practice, the simulated carbon profile is found to be almost homogeneous too. This result shows that the thermal schedule typically used to process 18MND5 leads to homogeneous carbon content in the workpiece after austenitization.

Samples continuously cooled after austenitization at rates between 200 °C·h⁻¹ and 3000 °C·h⁻¹, typically encountered during water quench of thick-section components, show that the homogeneous carbon content established during austenitization is preserved at the scale of the meso-segregations. However, some micro-scale redistribution takes place at such continuous cooling rates, as evidenced by a local scatter in the carbon profiles shown in Fig. 3b and in the supplementary material. This local redistribution is due to the phase transformation and corresponds to carbon partitioning from transformed ferritic regions towards neighboring un-transformed austenite in the two-phase microstructure. The slower the cooling rate, the more pronounced this redistribution is as evidenced by the increasing amplitude of the scatter. It is also more pronounced in non-segregated regions. Both observations are related to the time necessary for carbon redistribution. The explanation for the former is straightforward: a slower cooling rate means a longer time spent in any given temperature range thus facilitating diffusion. For the latter, it is necessary to consider the onset of the phase transformation of austenite into ferritic products (proeutectoid ferrite, bainite, martensite). Higher alloy content delays the transformation to lower temperature ranges, thus reducing the time/temperature budget available for posterior diffusion from the ferritic products to the remaining parent austenite. This result indicates that as-quenched forgings should display a homogeneous carbon content at the meso-scale and limited redistribution at the micro-scale. A similar result is obtained by Yan et al. [16] after continuous cooling at 2700 °C·h⁻¹ ("as-quenched" in the reference), with no carbon segregation observed across 300 µm wide bands while local fluctuations due to carbon partitioning during upper bainite formation is observed in low-alloyed regions.

## 4.2. Carbon segregation during tempering

The carbon profile in the final service-ready component shown in Fig. 2 shows carbon to be strongly segregated in meso-scale bands in this condition. Since it is now established that carbon content is constant at

the meso-scale in components after austenitization and quench, this observed segregation must develop during the remaining heat treatment: tempering. In tempering conditions, the microstructure in the material is fully ferritic and contains carbide: cementite in all locations and MoC₂ carbides in Mo-rich meso-scale bands. In such a microstructure, there is a pronounced carbon chemical potential gradient across the band as shown in Fig. 4, thus providing the driving force for the enrichment of the band. Kinetic simulation of a representative tempering treatment shows that the mobility of carbon in the ferritic microstructure leads to a significant enrichment of the band, as displayed in Fig. 7. However, the enrichment predicted by the kinetic simulation is lower than that found experimentally, which is closer to equilibrium values. A potential explanation for this underestimation of the carbon enrichment is the assumption of the model that secondary phases (cementite, Mo₂C) form instantaneously at equilibrium fractions. Those fractions are higher in solute rich regions. The model assumes that the carbon atoms included in those phases, whose amounts increase in the segregated band, do not participate in diffusion. Experimental observations support an increase of the amounts of secondary phases in segregated bands [9]. Nevertheless, the finite mobility of carbon also leads to a finite precipitation rate of carbides, keeping more of it available for long range diffusion in the solid solution.

Stress relief is carried out at a slightly lower temperature than tempering as a standard practice. The chemical potential well is almost identical at 610°C to the one at 630°C, and the maximal equilibrium carbon concentration predicted is only lower by 0.01 wt% than the value at 630°C. As the treatment is much longer, and carbon mobility is still high enough for additional carbon redistribution to happen, this treatment exacerbates carbon migration towards the bands.

## 5. Conclusion

Meso-scale heterogeneities in substitutional contents inherited from 18MND5 ingot solidification persist through all the standard thermal schedule. The corresponding alternance between segregated and non-segregated regions constitutes the thermodynamic background for both microstructure formation and carbon redistribution. The latter was investigated through both experiments and simulation, resulting in the following findings:

* Local substitutional enrichment causes a significant decrease of carbon potential in the ferritic range. In contrast, the sum of repulsive and attractive interactions leads to a negligible effect in austenite where carbon chemical potential is practically unaffected. This negligible net effect is a feature of 18MND5 elemental ratios.
* Carbon tends to homogenize during austenitization. Carbon diffusion kinetics allow this homogenization to be almost complete in typical austenitization conditions.

* Continuous cooling after austenitization causes the decomposition of austenite into a ferritic microstructure. However, industrially relevant cooling rates do not provide time/temperature combinations sufficient for its segregation back into substitutionally segregated regions.

* The temperatures and durations of the tempering and stress relief treatments are, however, conducive to this carbon redistribution. Experimentally, the obtained carbon profile after tempering is close to that of local equilibrium.

### CRediT authorship contribution statement

**Bregeault M.:** Writing – original draft, Visualization, Investigation.
**Van Landeghem H.P.:** Writing – original draft, Supervision, Conceptualization.
**Véron M.:** Writing – review & editing, Supervision.
**Roch F.:** Writing – review & editing, Resources, Project administration.
**Le Gloannec B.:** Writing – review & editing, Resources, Project administration.
**Marceaux Dit Clément A.:** Writing – review & editing, Resources, Project administration.

### Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: H. P. Van Landeghem reports financial support was provided by Framatome. H. P. Van Landeghem reports financial support was provided by Carnot Institute Energies du Futur. A. Marceaux Dit Clément reports a relationship with Framatome that includes: employment. B. Le Gloannec reports a relationship with Framatome that includes: employment. F. Roch reports a relationship with Framatome that includes: employment. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

This work was supported by the Carnot Institute "Energies du Futur" under reference 22T38 - MAXIME. Marion Bregeault: Investigation, Visualization, Writing - Original Draft. Arthur Marceaux Dit Clément, Brendan Le Gloannec, François Roch: Resources, Project administration, Writing - Review & Editing. Muriel Véron: Supervision, Writing - Review & Editing. Hugo Paul Van Landeghem: Conceptualization, Supervision, Writing - Original Draft.

### Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.mtcomm.2025.112024.

### Data availability

Data will be made available on request.

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