# Investigation of the influence of manganese on the dynamic strain ageing of ferritic steels – Part I: Model alloy

W. Mottay, D. Caillard, H. Idrissi, P. Maugis, A. Portavoce, F. Roch, C.

Perrin-Pellegrino, K. Hoummada

► To cite this version:

W. Mottay, D. Caillard, H. Idrissi, P. Maugis, A. Portavoce, et al. Investigation of the influence of manganese on the dynamic strain ageing of ferritic steels – Part I: Model alloy. Acta Materialia, 2025, 299, pp.121446. 10.1016/j.actamat.2025.121446. hal-05218692

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# Investigation of the influence of manganese on the dynamic strain ageing of ferritic steels – Part I: Model alloy

W. Mottay<sup>a,*</sup> <sup>●</sup>, D. Caillard<sup>b</sup>, H. Idrissi<sup>c,●</sup>, P. Maugis<sup>a,●</sup>, A. Portavoce<sup>a,●</sup>, F. Roch<sup>d</sup>, C. Perrin-Pellegrino<sup>a,●</sup>, K. Hoummada<sup>a,●</sup>

## ARTICLE INFO

### Keywords:

- Plastic deformation

- In-situ TEM

- Dynamic Strain-Aging

- Steel

- Dislocation dynamics

## ABSTRACT

Dislocation dynamics were studied in a ternary Fe-Mn-C model steel by in-situ tensile tests in a transmission electron microscope (TEM) at temperatures ranging from 300 K to 900 K. The influence of carbon and manganese on dynamic strain aging (DSA) is investigated, the latter being identified by a change in dislocation dynamics. In the DSA temperature range, plastic deformation proceeds by dislocation bursts or dislocation viscous glide. We measure dislocation glide velocities in the DSA regime to extract activation energies for dislocations glide. In Fe-C alloys, the activation energy for the so-called “high-temperature diffusion-controlled” (HTDC) Peierls glide of screw dislocations is close to the diffusion energy of carbon. Surprisingly, HTDC-Peierls glide of screw dislocations is not observed in Fe-Mn-C and viscous glide of mixed dislocations occurs at higher temperature with an activation energy close to that of Mn diffusion. We thus conclude that Mn addition hinders the HTDC-Peierls glide expected at about 500 K, and suggest that this may result from Mn being able to co-segregate with carbon on dislocations at temperatures as low as 500 K. In addition, Mn is responsible for DSA and controls dislocation viscous glide in the model Fe-Mn-C alloy. We propose a mechanism for Mn enrichment on mixed dislocations at such low temperatures, based on Mn pipe-diffuson. These findings shed new light on the elementary mechanisms controlling DSA in ferritic steels with a particular focus on the effect of C and Mn.

## 1. Introduction

The mechanical properties of steels, and especially their strength and ductility, are strongly influenced by the interactions between dislocations and the microstructural features of the material [1–4]. In this context, the phenomenon of dynamic strain aging (DSA) has long been recognized as a critical factor affecting those properties [5–12]. DSA refers to the transient increase in yield stress which occurs under certain conditions of temperature and strain rate, often associated with the interaction of dislocations with solute atoms, in particular carbon and nitrogen [13–18]. These interactions, in turn, affect the mobility of dislocations materials overall responses to deformation [19–25], potentially leading to the occurrence of serrated or jerky flow in the stress-strain curve [26–29], the so-called “Portevin – Le Châtelier” effect, accompanied by a minimum of strain rate sensitivity.

Historically, the role of carbon in promoting DSA has been well-

documented, with Cottrell’s seminal work [30] theorizing the pinning of dislocations by solute carbon atoms in iron. Numerous experimental findings highlight the modification of mechanical properties caused by carbon segregation on dislocations in steels [31–34]. The alloying element manganese, often found in combination with carbon, has also been recognized to play a critical role in modulating DSA sensitivity [15, 18,35–37]. While the influence of manganese on dislocation mobility has been studied in the context of both static and dynamic strain aging, the intricate mechanisms underlying these effects remain poorly understood at the atomic and nanoscale levels.

Theoretical and computational models have made significant strides in elucidating the mechanisms by which solute atoms interact with dislocations in steels. These models suggest that carbon atoms segregate both to dislocation cores [38,39] and in Cottrell atmospheres [40–43], creating localized strengthening effects that impede dislocation motion [44–46]. However, the role of manganese remains unclear. It was shown

<footnote><sup>a</sup> Aix Marseille Université, CNRS, IM2NP, 13397 Marseille, France</footnote>

<footnote><sup>b</sup> CEMES-CNRS, Université de Toulouse, 31055 Toulouse, France</footnote>

<footnote><sup>c</sup> IMMC, IMAP, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium</footnote>

<footnote><sup>d</sup> Framatome 92084 Paris la Défense Cedex, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: william.mottay@im2np.fr (W. Mottay).</footnote>
by Leslie [35] that Mn induces dynamic strain-aging in iron. Moreover, in a ternary Fe-Mn-C alloy, manganese modifies the DSA temperature range, compared to a binary Fe-C alloy, which might be explained by Mn-C interactions in BCC steels [47,48]. Although several experimental studies have attempted to observe and quantify the interaction effect of carbon and manganese on DSA [6,15,35,49], it has not been possible to draw clear conclusions on the underlying mechanisms. Discrepancies can be attributed to the complexity of these interactions at the nano-scale, where multitude of factors such as solute concentration, temperature, strain rate, and microstructural features complicate direct observation and interpretation.

Advancements in experimental techniques, in particular the development of in-situ transmission electron microscopy (TEM) coupled with tensile testing [50,51], have provided unprecedented insights into dislocation behavior under controlled deformation conditions [52,53]. These studies, conducted on a variety of alloy systems, have allowed for direct observation of dislocation motion and interactions at the nano-scale, complementing macroscopic mechanical testing data. Indeed, the experimental works from Caillard and collaborators [54,55] have provided significant contributions to understanding the interactions of substitutional and interstitial solutes with dislocations in iron. The work of these authors proposes a set of mechanisms by which these solutes affect dislocation motion and DSA in steels. On the one hand, the solutes-dislocations interaction in binary Fe-C alloy is rather clear [54]. At intermediate temperatures, between 400 K and 650 K, carbon is mobile enough to segregate on dislocations and induces DSA. This leads to dislocations being firmly locked and the appearance of dislocation avalanches. However, upon increasing temperatures, carbon can be dragged by dislocations, resulting in a “Peierls-like” glide motion of straight screw dislocations, hereafter called “high-temperature diffusion-controlled” (HTDC) Peierls glide. These experimental results are backed up by ab-initio modeling results [39,42,44]. On the other hand, the solutes-dislocations interactions in ternary Fe-M-C alloys (M = substitutional solute, such as Ni, Al, Cr, Si) are not so clear [55]. Notably, the proposed mechanisms for the interactions between substitutional and interstitial atoms are still not fully satisfactory, especially for the Fe-Al-C and Fe-Cr-C alloys. It is suggested that the substitutional solute might “have captured all free carbon atoms” [55], meaning that all the carbon in solid solution has been precipitated. This cannot be true as (i) it is thermodynamically impossible to fully deplete carbon from the solid solution, (ii) aluminum is not known to precipitate with C and (iii) the activation energy at the beginning of DSA is close to the one for carbon diffusion in ferrite, or slightly higher presumably because of interactions with substitutional solutes [55–57].

This study aims to shed new lights on the mechanisms of DSA in steels, with a particular focus on the effects of C and Mn. Indeed, Mn is one of the most common alloying elements in steels. Moreover, it was shown that Mn induces DSA in steels [58] and interacts with carbon in solid solution [47,48]. Using in-situ TEM tensile tests in an extended temperature range, we explore the role of C and Mn on dislocations motion, as well as the mutual interactions of these alloying elements. We seek to deepen our understanding of the mechanisms governing DSA in steels and provide new, valuable, insights on how Mn affects dislocation dynamics in the DSA temperature range. The present part of this study is devoted to a model Fe-Mn-C alloy and its comparison with several Fe-C alloys previously studied. In a second part, the present results will be compared to those obtained in an industrial alloy with somewhat similar composition but significantly different properties.

## 2. Experimental

A model material (Fe-3Mn-C) is investigated to better understand the effect of Mn on DSA and the complex C-Mn-dislocations interactions. The material, provided by Estelle Meslin from CEA Saclay, contains 2.75 wt% Mn (2.8 at %) and 3 wt.ppm C (16 at.ppm). Impurities are kept lower than 5 wt.ppm (S, N, Cr, O, P). The dislocation density is lower

than $10^{12} m^{-2}$. Macroscopic tensile tests could not be performed on these materials, but tensile experiments on similar materials are available in the literature, for Fe-C alloys [15,31] and Fe-Mn alloys [35,58,59]. These published researches will be discussed in lights of our new results.

In situ straining experiments have been carried out in a JEOL 2010HC TEM, using a Gatan low-temperature straining holder, and a high-temperature straining holder designed in CEMES. The movies have been recorded by a Megaview III video camera working at 25 images per second, and analyzed frame by frame. Images extracted from dynamic sequences are then subtracted in order to enhance corresponding tiny dislocation movements. Microsamples were rectangles with an electro-polished thin-edged hole, glued with a high-temperature cement on two rings adapted to the straining holder. Further details on the experimental setup can be found in references [54,55]. Videos are available as supplementary materials.

## 3. Results

In-situ straining experiments were performed on the model Fe-3Mn-C material at increasing temperatures in order to study the effect of Mn on dislocation dynamics in the DSA temperature range. The results were all obtained during a single experiment, in a single grain. The observed grain is oriented in the (211) plane. The tensile axis is vertical in all figures, along the [10-2] axis. The diffraction vector is $g = [01-1]$. The first experiment is performed at 293 K, Fig. 1. The screw direction of dislocations is represented by a black line, marked “screw”. This direction is the same for all figures. Dislocations with high screw components are curved between anchoring points on super-jogs caused by a cross-kink mechanism. These dislocations escape and glide rapidly to the next obstacle while forming dipoles by cross-slip. This corresponds to the athermal plasticity regime, which is also observed at 373 K, Fig. 2. These observations indicate that the material is in the plastic domain of the stress-strain curve. If dislocations had been previously anchored (static strain aging), this pinning has been erased and its effects are not being observed.

The DSA regime is reached at 473 K, Fig. 3. Plastic deformation proceeds by important dislocation bursts. After the burst, no individual movement of dislocations is observed during the following 56 s of the video. The same observations are made at 523 K and 573 K (not presented here). The occurrence of DSA at 473 K suggests that the traces of carbon present in the model alloy are responsible for DSA at this temperature range. However, the HTDC-Peierls mechanism on screw dislocations found in Fe-C alloys and described in introduction is not observed in this material. It is worth stating that the beginning of DSA is evidenced at 473 K, but it could have started at a lower temperature, between 373 K (Fig. 2) and 473 K (Fig. 3).

The DSA regime goes on at higher temperatures, such as 673 K, Fig. 4 and 773 K, Fig. 5. At 673 K and 773 K, most of the plastic deformation is controlled by dislocations bursts. In Fig. 4, no further movement of dislocation is observed during the 40 s after the burst, except for dislocation 1, which unlocks and re-locks in position 1'. At 773 K, Fig. 5, the unlocking and re-locking of a single dislocation is once again observed after the avalanche. Some very slow and viscous movements of dislocation are also observed, with average velocities of $0.8 \text{ nm.s}^{-1}$ for screw dislocations and $3 \text{ nm.s}^{-1}$ for edge dislocations. The emergence of fast viscous dislocation glide indicates the upper limit of DSA.

Dislocations bursts are no more observed once the tensile temperature reaches 823 K, Fig. 6a-b. The viscous glide of dislocations is faster and reaches $7 \text{ nm.s}^{-1}$. Some dislocations are still locked. At 873 K, Fig. 6c-d, dislocation dynamics is characteristic of the high-temperature viscous glide regime, with an average dislocation velocity of $240 \text{ nm.s}^{-1}$.

The results from in-situ TEM tensile tests at increasing temperatures in the model Fe-3Mn-C steel is dominated by the athermal regime near room temperature. A new regime of dislocation motion emerges around 450 K. From this temperature, dislocation motion is no more observed, as dislocations (mostly of mixed character) are firmly anchored. In these
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Athermal glide motion at 293 K in the model Fe-3Mn-C. Note the formation of the closed loop 2 and the rotation of dislocation 1 from 1 to 1', leading to a fast emission to the left (slip traces marked "tr").</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Avalanche of dislocations between images (a) and (b) at 373 K in the model Fe-3Mn-C. The DSA regime is however not yet attained because several dislocations (among which dislocation 1) have unlocked and glided further between images (b) and (c). TEM image at (t = 1.52 s) is not presented for clarity.</figcaption></figure>

conditions, plastic deformation relies on bursts of dislocations. This is characteristic of the DSA regime, where dislocations are firmly locked by segregated solute atoms.

These mixed dislocations are pinned, at temperatures up to about 800 K, in accordance with previous published results in models Fe-Cr-C and Fe-Al-C alloys [55]. However, the present observations differ from those previously made in binaries Fe-C. In the latter, mixed dislocations re-arrange as long straight screw dislocations at around 473 K, and then glide viscously above 523 K. This corresponds to the HTDC-Peierls mechanism, caused by carbon segregation into screw dislocation cores [38,54].

Then, it appears that the addition of a substitutional element (Mn in this study) suppresses the HTDC- Peierls mechanism expected at about 500 K. Two mechanisms can be proposed to explain such behaviour,

namely:

1. The substitutional atoms can fully precipitate carbon atoms present in solid solution. Without carbon in the matrix, high temperature Peierls glide cannot happen. It is the mechanism proposed for Fe-Cr-C and Fe-Al-C [55].

2. The substitutional atoms can co-segregate with carbon on mixed dislocations. The segregated substitutional, with limited mobility, hinders the re-arrangement as straight screw dislocations, and thus the Peierls mechanism.

These two mechanisms will be discussed in the following section.
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Dislocation avalanche at 473 K in the model Fe-3Mn-C. The DSA regime is considered to be attained because no further movement is observed during the following 56 s.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Dislocation avalanche at 673 K. The sample is still in the DSA regime because no further movement is observed during the following 40 s, except for the unlocking and re-locking of the sole screw dislocation 1 (from 1 to 1'). TEM images at (t = 0.8 s) and (t = 0.68 s) are not presented for clarity.</figcaption></figure>

# 4. Discussion

## 4.1. Dislocation motion and activation energies for DSA

In order to better understand the results from in-situ TEM tensile tests, the macroscopic tensile responses available in the literature will first be discussed. It is well-known that, in the presence of an interstitial solutes such as C or N, DSA will be first observed around 400 K, evidenced by an increase in flow stress and work-hardening rate [15,19].

PLC serrations might be observed at about 400–500 K, depending on the applied strain rate [60]. In binaries Fe-C and Fe-N alloys or in steels with sufficiently low substitutional content, the manifestations of DSA end around 600 K. The case of Fe-Mn alloys without interstitial solutes was studied by Leslie [35,58]. These authors have shown that without interstitial atoms Mn induces DSA, at strain rate from $3 \cdot 10^{-5} \text{ s}^{-1}$ to $1.5 \cdot 10^{-3} \text{ s}^{-1}$, from around 600 K. Then, assuming that these two DSA domains are additive, we could expect an extended DSA temperature range in a Fe-Mn-C alloy as the one studied in the present work.
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Small avalanche at 773 K, between images (a) and (b). The avalanche is followed by the fast unlocking and re-locking of dislocation 1 (from 1 to 1') similar to that observed in Fig. 3, and by the very slow and viscous movement of the same dislocation, from 1' to 1'' (at 0.8nm/s for screws, and 3nm/s for edges). Such a behavior corresponds to the upper limit of the DSA regime.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Steady glide motion at (a-b) 823 K and 7nm/s (from 1 to 1') and (c-d) 873 K and 240 nm/s (from 2 to 2'). Avalanches are no more observed.</figcaption></figure>

Let us now discuss the results from in-situ TEM tensile tests. Dislocation bursts and the DSA regime result from the segregation of solute atoms, which hinder dislocation motion. At increasing temperatures, the segregated atoms may become mobile enough to be dragged by dislocations. This leads to the appearance of dislocation viscous glide, this regime being controlled by the diffusion of the solute atoms segregated on dislocations. The dislocation velocity $v$ can be expressed as $v = v_0\tau\exp(-E_a/kT)$, where $\tau$ is the stress and $v_0$ the pre-exponential factor which depends on microstructural features [61]. In the case of viscous glide, the activation energy $E_a$ thus corresponds to that for the diffusion of the solute atom. The HTDC-Peierls glide, caused by the core segregation of C on screw dislocations, requires in addition the formation of a kink pair [44]. In this specific case, the activation energy $E_a$ corresponds

to the energy for C diffusion plus the energy for the formation of a critical kink-pair [54]. As a consequence, extracting activation energies for dislocation glide might allow for the determination of the nature of the segregated atoms on dislocations.

Fig. 7 shows the logarithm of the high-temperature viscous dislocations velocity $\ln(v)$ as a function of 1000/T for the model Fe-3Mn-C (yellow) and models Fe-C (red), which data are taken from [54,55]. As expected from a thermally activated process, $\ln(v)$ varies linearly with 1000/T. This allows for the determination of the viscous dislocation glide activation energy in each sample, which values are crucial to understand the underlying mechanisms of DSA. It could be argued that an error is introduced in the determination of activation energies, because the applied stress is not strictly constant. However, based on macroscopic tensile tests, the flow stress does not vary >10% when the
<figure><img src="image_9.png" /><figcaption>Fig. 7. Logarithm of the high-temperature viscous dislocation velocity, ln(v) (where v is in nm/s), as a function of 1000/T. Experimental data from the studied Fe-3Mn-C are the yellow circles. The values for the model Fe-C (red triangles) are taken from references [54,55]. Dashed lines are the linear fits of these data. Dotted horizontal lines are the DSA temperature ranges for each material.</figcaption></figure>

test temperature is increased [60]. It can be thus anticipated that the difference between the measured glide velocities do not vary much compared to those which would be obtained under strictly constant stress. In logarithmic scale, this leads to an uncertainty on the slope (thus on the activation energies) <10 %. Interestingly, the higher temperature limit of DSA is attained when the velocity of viscous glide reaches about 3 nm.s⁻¹ (≈ ln(v) = 1) a minimum value sufficient to accommodate the imposed strain rate, Fig. 7, independently of the elements contributing to DSA.

Dynamic strain aging sensitivity of model binary Fe-C alloys was studied in [54,55]. Three carbon contents were investigated, namely 1, 16 and 230 at.ppm, where the occurrence of HTDC-Peierls glide of dislocations was evidenced and discussed, as a result of carbon segregation on dislocation cores. Their experimental data are presented in Fig. 7, as red triangles for the three carbon contents. The linear fit of these data yields an activation energy of 1.0 eV for the glide of viscous straight screw dislocations, which corresponds to the sum of two activation energies: that for carbon diffusion (≈ 0.8 eV [16]) and that for the formation of a critical kink pair (≈ 0.2 eV [61]). It must be noted that slightly higher values were reported in theoretical investigations [44]. The low value of the critical kink-pair activation energy corresponds to a rather small difference between the respective velocities of screw and mixed parts of the same dislocations, the screws being clearly the slowest species. It can then be concluded that viscous dislocation glide, in the binary model Fe-C alloy, is controlled by the drag of segregated carbon on screw dislocation cores [44] and that DSA is also due to the diffusion of carbon. The whole mechanism is sketched in Fig. 8(a). Carbon atoms first pin mixed dislocations around 450 K. When temperature rises and reaches about 500 K, carbon atoms mobility increases and allows mixed dislocations to re-arrange as straight screw dislocations, leading to HTDC-Peierls glide. This is made possible because the mixed and edge parts surrounded by their Cottrell atmospheres trail behind them long screws with their reconstructed core moving at a substantially lower velocity.

Velocities of viscous glide in the model Fe-3Mn-C alloy, estimated in Figs. 5 and 6, are plotted as full yellow circles, Fig. 7. In this material, the linear fit of the experimental points leads to a higher activation energy, 2.8 eV, in good agreement with the activation energy for the diffusion of

substitutional solutes in alpha-iron [16] as well as the values reported for Mn diffusion in alpha-iron [62,63]. The viscous glide of dislocations above 750 K in this material is therefore controlled by Mn diffusion, in accordance with atom probe tomography (APT) results revealing Mn segregation on dislocations in model steels [59], ODS steels [64] low alloy steels [65,66] and C-Mn steels [37]. We can then conclude that dislocations are enriched in Mn in this material. At temperatures below 750 K, dislocations are anchored. As a result, deformation proceeds by dislocation bursts, meaning that Mn is also responsible for dislocations bursts in the model Fe-3Mn-C alloy. Besides, HTDC-Peierls glide of screw dislocations is not observed in the model Fe-3Mn-C around 500 K, contrary to what was observed in binaries Fe-C alloys. This suggests that Mn atoms are able to decorate mixed dislocations at temperatures as low as 500 K, thus hindering HTDC-Peierls glide.

## 4.2. Co-segregation of Mn and C on dislocations

In-situ TEM observations of the model Fe-3Mn-C during plastic deformation at elevated temperatures therefore reveal that, unexpectedly, Mn would be able to diffuse at temperatures as low as 500 K and anchor mixed dislocations. Indeed, at 500 K, the highest bulk diffusion coefficient available in the literature [63] for Mn yields a value of 5.9 × 10⁻²⁹ m².s⁻¹, corresponding to a diffusion length in the order of 6.10⁻⁵ nm in one minute. However, the presence of Mn atoms on mixed dislocations is all the more confirmed by the observations of some scarce unlocking events Figs. 4 and 5, at respectively 673 K and 773 K. These intriguing seldom-unlocking events probably correspond to anchored dislocations which are able to glide on a short distance before being anchored once again. Evidences of these unlocking events were also observed at 573 K and 623 K. The velocity of these unlocked screw dislocations was measured and reported in Fig. 7 as open yellow circles. These points fall in line with those obtained on the binary Fe-C alloy, meaning that the activation energy of the dislocation glide mechanism during the scarce unlocking events for the Fe-3Mn-C is the same as that for HTDC-Peierls glide in the binary Fe-C. In other words, these events are controlled by the diffusion of carbon as in the binary Fe-C alloy. They are expected to occur when dislocations can escape from their anchoring Mn atoms, and glide over short distances with their carbon atmosphere,
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Schematic representation of the effect of Mn addition on diffusion-controlled steady motion related to DSA. Short arrows indicate slow steady dislocation motion, and longer ones faster steady motion. (a) In binary Fe-C alloy, C segregates on mixed dislocations at the beginning of DSA. When the temperature becomes high enough, dislocations re-arrange as straight screw dislocations, giving rise to the HTDC-Peierls mechanism. (b) In ternary Fe-3Mn-C, C also segregates on mixed dislocations at the beginning of DSA. However, upon increasing temperatures, dislocations stay in their mixed character, because of Mn co-segregation, until viscous glide of Mn-segregated mixed dislocations becomes kinetically possible.</figcaption></figure>

until they are locked again by other Mn atoms. This confirms the existence of carbon segregation on dislocation cores in the model Fe-3Mn-C, but the additional presence of Mn atoms suppresses the characteristic features of C segregation to dislocations cores, namely the HTDC-Peierls glide.

We proposed two possible mechanisms for the suppression of the HTDC-Peierls glide in ternary model alloys (Fe-3Mn-C in this study, Fe-Cr-C and Fe-Al-C in a previous one [55]), namely the full precipitation of carbon atoms from the solid solution or the co-segregation of the substitutional atoms with carbon on dislocations. The observation of rare Peierls glide of screw dislocations in the model Fe-3Mn-C indicates that carbon is present in solid solution, thus invalidating the first proposed scenario (carbon in solid solution is fully precipitated by the substitutional atoms). This is all the more supported by the fact that aluminum is not a carbide former, once again invalidating the scenario based on the full precipitation of carbon atoms with the substitutional solute. Even in the presence of a strong carbide-former, such as Cr in Fe-Cr-C, it is thermodynamically impossible to fully deplete carbon from the solid solution. Consequently, we suggest that C and Mn both decorate mixed dislocations in the model Fe-3Mn-C at temperatures as low as 500 K. This mechanism is presented in Fig. 8(b). The beginning of DSA around 450 K relies on mixed dislocations pinning by carbon atoms. At 500 K, a temperature where Peierls glide is expected, Mn atoms have enriched the C-anchored mixed dislocations, because of the strong attraction between mixed dislocations and Mn (as well as Al, Cr and more generally substitutional atoms) [1,59], and hinder the Peierls glide. Mn and C

decorated dislocations will keep their mixed character up to elevated temperatures, about 800 K, where viscous glide of mixed dislocations will occur, controlled by Mn diffusion. It must be noted that Mn does not directly suppress HTDC-Peierls glide of screw dislocations, but rather hinders the possibility of mixed dislocations to re-arrange as screw dislocations (consequently hindering HTDC-Peierls glide as it concerns solely screw dislocations). In the Fe-3Mn-C alloy, HTDC-Peierls glide is purely suppressed and not shifted to higher temperatures. Then, it can be concluded that the effect of Mn is not kinetic, suggesting that the co-segregation of Mn and C on mixed dislocations is energetically more favorable than C-segregated screw dislocations with Mn remaining in solid solution.

However, it is not expected that viscous glide of mixed dislocations and HTDC-Peierls glide of screw dislocations produce differences on macroscopic tensile response. Both mechanisms are supposed to stabilize plastic flow, as will be presented in the second part of this work. The main difference relies on the intrinsic difference between the two mechanisms. HTDC-Peierls glide relies on carbon segregation to dislocation cores. It is then observed at a lower temperature than viscous glide of mixed dislocations, which relies on the segregation of substitutional atoms that are less mobile than carbon. Another significant difference is to be noted. If HTDC-Peierls glide is observed, it means that plasticity becomes controlled by gliding screw dislocations that will multiply as deformation proceeds. Substitutional atoms do not interact with screw dislocations (core segregation of substitutional atoms to screw dislocation has not been modeled or observed experimentally).
Then, HTDC-Peierls glide suppresses the possibility for substitutional
atoms to interact with dislocations at higher temperatures, meaning that
it hinders the possibility for substitutional atoms induced DSA to
happen.

4.3. Mechanisms for Mn diffusion

The presence of Mn on mixed dislocations at 500 K is highly unex-
pected due to its low diffusion kinetics, as was stated in the previous
paragraph, but Mn segregation on dislocations was already observed
using APT in a low-alloy steel after failure in tension at 573 K [37].
Moreover, experiments by Kuzmina [67] and Kwiatkowski da Silva [59]
revealed that important Mn-enrichment is observed at edge dislocations
in a model Fe-9Mn after heat treatments at 673 K (400 °C) and 723 K
(450 °C), the latter leading to a sufficient Mn segregation on dislocations
to induce static strain-aging on macroscopic tensile curves. Calculations
of diffusion length for the heat treatments performed in their work yield
theoretical values of 5–10 nm for both treatments. Then, even though it
is kinetically unexpected, important Mn segregation was observed in the
core of edge dislocations, up to 25 and 30 % at Interestingly, in refer-
ences [59,67], the model Fe-9Mn was cold rolled up to 50 % in order to
increase dislocation density and the model Fe-3Mn-C from the present
research is studied during a tensile test. It could then be proposed that
dislocation pipe diffusion accelerates Mn diffusion at rather low tem-
peratures, considering that Mn pipe diffusion has already been reported
in steels [68]. Based on Mehrer [62,69], the diffusion coefficient in
dislocation cores is about 5 orders of magnitude higher than in bulk, at
Tm/T = 2, i.e. about 900 K in steels, and this ratio tends to increase as
temperature decreases. The diffusion coefficient in grain boundaries is
even higher, about 3 orders of magnitude higher than in dislocation
cores. Moreover, whether we consider Peierls glide or viscous glide, both
mechanisms display an activation energy rather close to the bulk
diffusion of the solute. For mixed dislocations, this can be understood as
the necessity to drag the core-segregated Mn atoms as well as Mn atoms
in the Cottrell atmospheres and it can be expected that Mn diffusion in
the Cottrell atmosphere, far from the core, is rather close to that of bulk
diffusion. For HTDC-Peierls glide, this implies the formation of a critical
kink pair plus the diffusion of carbon. It was shown that dislocations are
anchored at temperatures lower than those at which viscous glide or
HTDC-Peierls glide are first observed. This means that the diffusion
mechanism, leading to dislocation pinning, is much faster than bulk
diffusion. These elements support our proposed mechanism. We assume
that carbon segregates first on mixed dislocations, temporarily stopped
on forest dislocations. Mn will then enrich the core of these C-pinned
dislocations, most probably because of diffusion short-circuits, such as
dislocations and grain boundaries. It could be expected that pipe diffu-
sion is affected by the nature of the dislocations (screw, edge, mixed),
but it will nevertheless be multiple orders of magnitude higher than bulk
diffusion. This mechanism could also be applied to the Fe-Cr-C and
Fe-Al-C model alloys from reference [55], since Cr segregation to the
core of edge dislocation was observed using APT by Medouni [66].
Similar conclusions were drawn in Al-Mg alloys, which exhibit PLC
serrations at room temperature [70], due to Mg segregation on dislo-
cations during tensile testing. Even though Mg diffusion is negligible at
room temperature, the authors evidence Mg segregation on dislocations
using APT. They propose that Mg diffusion is accelerated by
pipe-diffusion in the studied Al-Mg alloy, as we suggest for Mn in the
present Fe-Mn model material.

Short-range interactions between dislocations and Mn atoms could
also be proposed, as was done by Cuddy & Leslie [58]. Indeed, the mean
distance between Mn atoms in the Fe-3Mn-C material is 0.76 nm. This
leads to a maximal average distance between Mn atoms and dislocation
lines of one or two atomic jumps. However, it cannot be stated whether
Mn goes towards the dislocation in one or two atomic jumps or whether
the dislocations goes to the Mn atom, because of the applied stress and
the attraction between Mn atoms and dislocations. Upon increasing

temperatures, the increased mobility of Mn atoms will allow for its long
distance segregation on mixed dislocations, explaining the high tem-
perature DSA and the viscous glide of mixed dislocations at tempera-
tures around 800 K and higher.

Finally, an interesting point to discuss concerns the amount of Mn
enrichment to attain on mixed dislocation cores, to effectively suppress
HTDC-Peierls glide. Kuzmina [67] and Kwiatkowski da Silva [59]
showed, in a Fe-9Mn alloy that Mn segregation reaching 25 % at in the
core of edge dislocations gave rise to static strain aging on macroscopic
tensile curves. Based on McLean theory [71], the equilibrium segregated
amount of Mn in the present work is three times lower, as nominal Mn
content is three times lower. Interestingly, we observed scarce unlocking
events of Mn-pinned dislocations, which gave rise to Peierls glide. The
existence of dislocations able to unlock from Mn anchoring suggests that
Mn dislocation-pinning strength is not that high. Considering a Gaussian
distribution of Mn segregation on dislocations, unlocked dislocations are
among those with the weakest Mn enrichment. We thus suppose that a
higher Mn content could fully suppress the possibility for dislocations to
unlock (such as in references [59,67]), and a lower Mn content could
prove insufficient to effectively lock mixed dislocations and suppress the
HTDC-Peierls mechanism. The suppression of HTDC-Peierls glide by Mn
addition (and possibly Cr, Al ...) could be linked to the suppression of
recovery after annealing of cold-rolled steels (so-called "back--
annealing" or "recovery-annealing" [72]). Indeed, it was shown in the
present work that Mn could strongly hinder dislocation motion, which
could explain the absence of recovery in "recovery-annealed" steels with
sufficient Mn content [73], or other substitutional atoms [74].

5. Conclusion

We studied the effect of Mn on DSA using *in-situ* TEM tensile tests at high temperatures in a model Fe-Mn-C alloy. The results were compared to those from a binary Fe-C alloy, with the same carbon content, 16 at. ppm. Our observations show that Mn addition suppresses the HTDC-Peierls mechanism on screw dislocations, expected around 500 K. Viscous glide is also observed at higher temperatures, around 800 K, on mixed dislocations. Activation energies for viscous glide were measured, based on dislocation velocities at approximately constant stress. These activation energies reveal that Mn is responsible for the viscous glide of mixed dislocations at high temperatures, and more generally that Mn is responsible for DSA in the Fe-3Mn-C model material. However, some scarce screw dislocations exhibit the HTDC-Peierls glide in the DSA regime of Fe-3Mn-C. Even though these dislocations are not representative of the plasticity regime, they point towards the presence of segregated carbon in dislocation cores. We conclude that Mn and C are co-segregated on dislocations, and that the presence of segregated Mn suppresses the HTDC-Peierls mechanism around 500 K. We then propose that Mn is able to decorate C-pinned mixed dislocations at temperatures as low as 500 K, even though this is kinetically highly unexpected. Mn diffusion is most probably accelerated by the applied stress as well as pipe diffusion along dislocation. This result is in line with previously published ones, which demonstrates important Mn enrichments on edge dislocations after heat treatments at rather low temperatures, around 700 K. These findings shed new light on the elementary mechanisms controlling DSA in ferritic steels with a particular focus on the effect of C and Mn. Further experiments performed on an industrial C-Mn steel will be presented in the second part of this research, in order to link the macroscopic mechanical response with the underlying mechanisms operating at the macro and nano scales. It will be shown that a reduced Mn content allows HTDC-Peierls to be preserved, the latter being linked to the disappearance of PLC serrations, giving rise to a smooth plastic flow.

Data availability

Videos of the *in-situ* TEM tensile tests are available as supplementary
## materials

### CRediT authorship contribution statement

**W. Mottay:** Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Data curation, Conceptualization.
**D. Caillard:** Writing – review & editing, Validation, Supervision, Methodology, Investigation, Data curation, Conceptualization.
**H. Idrissi:** Writing – review & editing, Visualization, Validation, Methodology, Conceptualization.
**P. Maugis:** Writing – review & editing, Validation, Supervision, Conceptualization.
**A. Portavoce:** Writing – review & editing, Validation, Supervision, Resources, Funding acquisition, Conceptualization.
**F. Roch:** Supervision, Resources, Project administration, Funding acquisition.
**C. Perrin-Pellegrino:** Writing – review & editing, Visualization, Validation, Supervision, Resources, Project administration, Funding acquisition.
**K. Hoummada:** Writing – review & editing, Validation, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization.

### 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 article.

### Acknowledgements

This project was supported by the National Association for Research and Technology, France (ANRT Project n° 2020/0883 and ANRT Project n° 2022/0152). This work was also supported by the European Union through the Program PIIEC ME/CT (project SCIRIUS, No. DOS0217953). H. Idrissi is mandated by the Belgian National Fund for Scientific Research (FSR-FNRS). The authors acknowledge financial support from the CNRS-CEA "METSA" French network (FR CNRS 3507) on the platforms CEMES and PACA.

### Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.actamat.2025.121446.

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