# Dynamic strain-aging in C-Mn steel welds for nuclear power plants: a multi-scale investigation

W. MOTTAYª, D. CAILLARDᵇ, H. IDRISSIᶜ, M. GOUNEᵈ, V. MASSARDIERᵉ, M. JOUIADf, P. MAUGISª, F. ROCHg, C. PERRIN-PELLEGRINOª, K. HOUMMADAª

a. Aix Marseille Université, CNRS, IM2NP, 13397 Marseille, France

b. CEMES-CNRS, Université de Toulouse, 31055 Toulouse, France

c. IMMC, IMAP, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

d. ICMCB, University of Bordeaux, Pessac, 33600, France

e. Univ. Lyon, INSA Lyon, MATEIS – UMR CNRS 5510 F-69621 Villeurbanne Cedex, France

f. Laboratory of Physics of Condensed Matter, University of Picardie Jules Verne, Scientific Pole, 33 rue Saint-Leu, 80039 Amiens Cedex 1, France

g. Framatome, Développement (DTID) et Ingénierie Mécanique (DTIM), 92084 Paris la Défense Cedex, France

## Résumé

Les soudures en acier carbone-manganèse (C-Mn), couramment utilisées dans les circuits secondaires des centrales nucléaires, sont sensibles au vieillissement sous déformation (VSD). Ce phénomène, causé par les interactions entre les atomes interstitiels et les dislocations pendant la déformation plastique, peut affecter de manière significative les propriétés mécaniques des soudures en induisant un durcissement et une fragilisation. Il est essentiel de comprendre ces effets pour prédire le comportement à long terme des soudures et garantir la fiabilité des composants des centrales nucléaires. Dans cette étude, les mécanismes du VSD et leurs conséquences sont explorés à différentes échelles par le biais d'essais de traction macroscopiques, d'essais de traction in situ par microscopie électronique à transmission (MET) et d'analyses par sonde atomique tomographique (SAT), ce qui permet de comprendre l'influence de ces mécanismes sur les propriétés mécaniques des soudures.

Des essais de traction macroscopiques réalisés à 20°C et 300°C, analysés à l'aide du modèle de Kocks-Mecking, ont permis de faire deux constatations notables. Premièrement, malgré l'activation thermique, la restauration dynamique est réduite de manière inattendue à 300 °C. Cette réduction augmente le taux d'écrouissage et la résistance mécanique, contrairement aux observations habituelles en matière d'adoucissement thermique. Deuxièmement, l'allongement uniforme augmente de manière concomitante à la résistance mécanique à 300°C, comme le montre le critère de Considère. Les observations MET d'éprouvettes rompues en traction confirment ces résultats, révélant des densités de dislocation plus élevées à 300°C qu'à 20°C. Ces résultats établissent une corrélation directe entre la diminution de la restauration dynamique et l'augmentation observée non seulement de la résistance mécanique mais aussi de la ductilité.
Pour étudier plus en détails*/ les effets du VSD à l'échelle nanométrique, des essais de traction in-situ au MET ont été réalisés dans une plage de températures allant de la température ambiante à 600°C. Aux basses températures, le mouvement des dislocations est contrôlé par la friction de réseau. Avec l'augmentation de la température, la friction de réseau devient négligeable à partir de la température ambiante. Le mouvement des dislocations est alors athermique, contrôlé par les obstacles de la microstructure. Dans la plage de 150 à 350°C où le VSD est actif, la déformation plastique repose majoritairement sur des avalanches de dislocations au lieu d'un mouvement individuel continu, ce qui est caractéristique du VSD. Ce comportement est cohérent avec les observations macroscopiques, liant la diminution de la restauration dynamique à la ségrégation des atomes interstitiels sur les dislocations, ce qui entrave leur mouvement. Cette ségrégation sur les dislocations est mise en évidence par des mesures ex-situ de sonde atomique tomographique. Ces résultats démontrent comment les interactions entre les atomes interstitiels et les dislocations modifient les mécanismes de déformation plastique à l'échelle nanométrique, entraînant des modifications macroscopiques des propriétés mécaniques.

Enfin, un modèle quantitatif basé sur le modèle de Kocks-Mecking permet de décrire les effets combinés de la température et de la ségrégation des atomes interstitiels sur la restauration dynamique et l'écrouissage. Le modèle prédit une forte diminution de la restauration dynamique avec l'augmentation de la teneur en azote, mais une saturation au-delà d'une concentration critique. L'étude expérimentale d'échantillons traités thermiquement confirme ces prévisions : la réduction de la teneur en azote diminue de manière significative la sensibilité au VSD, tandis que des concentrations d'azote plus élevées ne produisent pas d'effets supplémentaires sur les propriétés de résistance à la traction.

Cette caractérisation multi-échelle fournit de nouvelles informations crucales sur les mécanismes qui contrôlent le VSD dans les soudures en acier C-Mn. Notamment, dans des conditions spécifiques, les atomes interstitiels peuvent améliorer les propriétés de traction à 300°C en augmentant simultanément la résistance et l'allongement. Ces résultats remettent en question les hypothèses traditionnelles selon lesquelles le VSD est purement délétère et révèlent une compréhension plus nuancée de son influence. Ce travail permet des prévisions plus précises du comportement mécanique des soudures dans le temps, contribuant directement à une exploitation plus sûre et plus fiable des centrales nucléaires.

## Abstract

Carbon-manganese (C-Mn) steel welds, commonly employed in the secondary circuits of nuclear power plants, are susceptible to Dynamic Strain Aging (DSA). This phenomenon, caused by interactions between interstitial atoms and dislocations during plastic deformation, may significantly affect mechanical properties by inducing hardening and embrittlement. Understanding these effects is critical for predicting long-term weld behavior and ensuring the reliability of nuclear power plant components. In this study, DSA mechanisms and their consequences are explored across various scales through macroscopic tensile testing, in-situ transmission electron microscopy (TEM) tensile experiments, and atom probe tomography (APT), offering a comprehensive understanding of its influence on weld performance.

Macroscopic tensile tests conducted at 20°C and 300°C, analyzed using the Kocks-Mecking framework, yield two notable findings. First, despite its thermal activation, dynamic recovery is
unexpectedly reduced at 300°C. This reduction enhances the work-hardening rate and mechanical strength, contrary to typical expectations of thermal softening. Second, uniform elongation improves concurrently with mechanical strength at 300°C, as evidenced by Considère's criterion. TEM observations of tensile-fractured specimens support these results, revealing more elevated dislocation densities at 300°C than at 20°C. These findings confirm a direct correlation between suppressed dynamic recovery and the observed increase not only in strength but also in ductility.

To further investigate DSA effects at the nanoscale, in-situ TEM tensile tests were conducted across a temperature range from room temperature to 600°C. The lattice-controlled dislocation motion observed at low temperature transitions progressively to the obstacle-controlled regime, near room temperature. Within the DSA-active range of 150–350°C, plastic deformation is dominated by dislocation bursts instead of continuous individual motion, a characteristic signature of DSA. This behavior aligns with macroscopic observations, linking reduced dynamic recovery to interstitial atom segregation, which hinders dislocation motion. Ex-situ measurements using atom probe tomography evidence the segregation of interstitial atoms to dislocations, in accordance with the in-situ TEM experiments. These results demonstrate how interstitial atoms interactions with dislocations tailor plastic deformation mechanisms at the nano-scale, leading to macroscopic changes in mechanical properties.

Finally, a quantitative model based on the Kocks-Mecking framework captures the combined effects of temperature and interstitial atom segregation on dynamic recovery and work hardening. The model predicts a sharp decline in dynamic recovery with increasing nitrogen content, which saturates beyond a critical concentration. Experimental validation through heat-treated samples confirms these predictions: reducing nitrogen content significantly decreases DSA sensitivity, while higher nitrogen concentrations do not produce additional effects on tensile properties.

This multi-scale characterization provides critical new insights into the mechanisms underlying DSA in C-Mn steel welds. Notably, under specific conditions, interstitial atoms can enhance tensile properties at 300°C by simultaneously increasing both strength and elongation. These findings challenge traditional assumptions about DSA as purely detrimental, revealing a nuanced understanding of its influence. This work enables more accurate predictions of weld performance over time, directly contributing to safer and more reliable operations of nuclear power plants.

## Keywords

## Nuclear power plant, Steel, Plasticity, Dislocation dynamics, In-situ TEM tensile tests

### 1 Introduction

C-Mn steel welds used in the secondary circuit of nuclear power plants might be susceptible to Dynamic Strain-Aging (DSA) at service temperature, around 250°C. This phenomenon is easily characterized by an increase in strength but is rather detrimental for structural applications as it alters ductility and fracture properties [1–4]. In C-Mn steels, the elementary mechanism of DSA can be explained by the interactions of diffusing interstitial atoms, carbon and nitrogen, with dislocations
during plastic deformation [5]. DSA is observed in a limited range of temperature and strain rate, typically between temperatures of 150 and 350°C and strain rates from 10⁻⁵ to 10⁻¹ s⁻¹ [6]. In this range of temperature and strain rate, carbon and nitrogen diffuse fast enough to anchor dislocations and to modify mechanical properties.

The consequences of DSA on steels' mechanical properties have been extensively studied [7–11] and discussed based on the interactions between interstitial atoms and dislocations [12]. However, despite these efforts, it appears still difficult to answer a simple question: what is DSA? Indeed, based on the researchers' expertise, DSA might refer to a modification of mechanical properties (hardening and embrittlement [13,14]), instabilities on tensile curves (serrated and jerky flow [15]), a change in dislocation dynamics (dislocation bursts [16,17]) or the segregation of solute atoms on dislocations [8,18]. Even though all the investigations agree on the fact that the interaction between solute atoms and dislocations is the governing mechanism, it remains complicated to link all of the phenomenon listed above.

In this work, we propose a multi-scale investigation approach which aims at a better understanding of the whole aspects of DSA, on an industrially relevant material. In Section 2, DSA is evidenced in a C-Mn steel weld from the secondary circuit of nuclear power plants using macroscopic tensile tests at 20°C and 300°C. The tensile properties are further investigated with the Kocks-Mecking model which provides insights on work-hardening rate and dislocation dynamics during 300°C tensile tests compared to room temperature ones. In Section 3, these theoretical results are consolidated by TEM observations on tensile tested samples. Dislocation dynamics are directly observed using in-situ TEM tensile tests at elevated temperatures. Atom probe tomography (APT) is used to directly evidence the interaction between solute atoms and dislocations. In Section 4, a quantitative model based on the Kocks-Mecking framework will be presented, allowing to capture the combined effects of temperature and solute segregation on dynamic recovery and overall tensile properties, taking into account nitrogen content in solid solution. Heat-treated samples are studied to experimentally investigate the effect of nitrogen content on DSA sensitivity.

The studied material is a C-Mn weld steel containing, in wt %, 0.065 C, 0.014 N, 1.37 Mn, 0.27 Si and 0.013 V. Welding was carried out by successive deposition of 36 consecutive passes using manual metal arc welding. Two different post weld heat-treatments (PWHT) were then carried out at 500 and 590 °C for 90 min. A third weld is studied in the as-welded condition to study the effect of PWHT. These three different materials are named AW (for As-Welded), PWHT500 and PWHT590, respectively.

# 2 Mechanical properties of the C-Mn weld

## 2.1 Tensile properties

DSA sensitivity of the C-Mn weld in the three conditions, AW, PWHT 500 and PWHT 590, is evidenced on true stress-strain curves, plotted in fig. 1. Tensile experiments at 20°C were performed at about 10⁻⁴ s⁻¹, in accordance with NF EN ISO 6892 [19,20], while at 300°C, a strain-rate increase from 7.5 x 10⁻⁵ to 5.4 x 10⁻⁴ s⁻¹ is achieved, resulting in a stress jump at 1.4% strain. Tensile curves are represented up to necking. The maximum stress σ<sub>m</sub> and uniform deformation ε<sub>u</sub> are defined based on Considere's criterion for necking [21]. Lüders peak and plateau at the elastic to plastic transition were
evidenced in all three samples at 20 °C, fig. 1a. These plastic instabilities rely on the anchoring of dislocations by interstitial atoms during natural aging. This phenomenon, originally highlighted by Piobert and Lüders [22,23], has been attributed by Cottrell and Bilby [5] to the pinning of dislocations by solute atoms.

<figure><img src="image_1.png" /><figcaption>Figure 1: True stress-strain curves obtained at (a) 20°C and (b) 300°C for the three samples</figcaption></figure>

At 300 °C, Lüders instabilities disappear and no Portevin – Le Châtelier (PLC) serrations are observed. For the three samples at 300 °C, we observed an increase in mechanical strength, characteristic of DSA. However, contrary to what is generally observed and discussed [24], this is accompanied by a significant increase in uniform elongation during tensile tests at 300 °C, compared to the ones at 20 °C (nearly 50 % for AW sample). The PWHT590 sample is less sensitive to DSA. However, and surprisingly, the PWHT500 sample has the same mechanical properties as the as-welded one. The tensile properties, and more specifically the increase in strength at 300°C, are further investigated using the Kocks-Mecking model in the next section.

## 2.2 Application of the Kocks-Mecking model

We propose to analyse the tensile properties of the as-welded sample using the Kocks-Mecking model, which describes the evolution of the dislocation density during plastic deformation and can be written as [25–28]:

$$ \frac{d\rho(\varepsilon)}{d\varepsilon} = M \left( \frac{k_1}{b} \sqrt{\rho(\varepsilon)} - K_2 \rho(\varepsilon) \right) \quad (1) $$

The first term in parentheses corresponds to the storage of dislocations that causes hardening. It is assumed that forest dislocations are likely to be strong barriers to dislocation glide. The second term in parentheses, corresponding to dynamic recovery, is obtained by reasoning that dislocations annihilate if the distance between two dislocations with opposite Burgers vectors is less than a critical distance. It is therefore related to the probability of two dislocations interacting and is proportional to the dislocation density via $K_2$, an efficiency factor. Using Taylor's law, $\sigma = \sigma_0 + M\alpha Gb\sqrt{\rho}$, it is then possible to calculate the experimental tensile curves as well as the work-hardening rate as a function of stress, using the parameters $K_1$ and $K_2$ as fitting parameters:
$$ \sqrt{\rho} = \left(\sqrt{\rho_0} - \frac{K_1}{bK_2}\right) * \exp\left(-\frac{MK_2\varepsilon}{2}\right) + \frac{K_1}{bK_2} \quad (2) $$

$$ \theta = \frac{d\sigma}{d\varepsilon} = \frac{-MK_2}{2} * (\sigma - \sigma_0) + \frac{M^2\alpha GK_1}{2} \quad (3) $$

Experimental and fitted tensile curves are presented in fig. 2a and 2c (as-welded and PWHT 590, respectively), while experimental and fitted work-hardening rate curves are presented in fig. 2b and 2d (as-welded and PWHT 590, respectively). G, M, α and ρ₀ are fixed parameters. The initial dislocation density ρ₀ was estimated using the line intercept method, based on 10 TEM micrographs on the as-welded sample. K₁, K₂ and σ₀ are the three fitting parameters. At a given temperature, they are kept constant on the tensile curves fit and the work-hardening fit.

<figure><img src="image_2.png" /><figcaption>Figure 2: Experimental and fitted data for (a) tensile curves, as-welded (b) work-hardening rate, as-welded (c) tensile curves, PWHT 590 (d) work-hardening rate, PWHT 590</figcaption></figure>

It appears from fig. 2a that the Kocks-Mecking model allows for a satisfactory fitting of the tensile curves both at 20°C and 300°C. K₁ is constant at both temperatures, as expected from a geometrical parameter and σ₀ decreases slightly as temperature increases. However, and unexpectedly, K₂ decreases at 300°C compared to 20°C. This is highly unexpected considering that K₂ is related to dynamic recovery, which is a thermally activated process [29]. This means that dynamic recovery is decreased while tensile temperature is increased. Moreover, as could be deduced from fig. 2a and is directly plotted in fig. 2b, work-hardening rate is increased at 300°C compared to 20°C, and the slope of the work hardening rate as a function of stress is increased. This is also explained by the reduction
of the parameter K₂, as work-hardening varies linearly with K₂ (see equation 3). It was shown in fig. 1 that the PWHT 590 sample is less sensitive to DSA. The Kocks-Mecking model reveals that this is explained by a lower reduction in dynamic recovery (K₂ parameter, fig. 2c) after PWHT 590, compared to the as-welded sample. This leads to a lower increase in work-hardening rate, fig. 2d, and ultimately a lower UTS at 300°C.

Then, analyses of the tensile curves from the as-welded sample using the Kocks-Mecking model yield important conclusions. DSA leads to a hardening of the material, but most importantly to an increase in work-hardening rate, experimentally observed, fig. 2b. This increase in work-hardening rate is the most important consequence of DSA on mechanical properties, as this leads to an increase in ultimate tensile strength but also a concomitant increase in uniform elongation. This surprising result is presented in fig. 3, which is a visual representation of Considere's criterion stating that uniform elongation is reached when θ = σ. In this particular case, the increase in work hardening rate is more important that the increase in stress, resulting in an increased uniform elongation. It appears that such results had already been observed, but were not discussed by the authors [1,6].

<figure><img src="image_3.png" /><figcaption>Figure 3 : Visual representation of Considere's criterion for the tensile tests at 20°C and 300°C</figcaption></figure>

The Kocks-Mecking model suggests that the modification of mechanical properties is due to a decrease in dynamic recovery, most probably caused by interstitial atoms segregation on dislocations. Moreover, the modified work-hardening rate at 300°C suggests that dislocation dynamics are modified. The next section is dedicated to microstructural characterizations of the C-Mn weld, in order to confirm the theoretical insights predicted by the Kocks-Mecking model. The investigations are focused on the as-welded sample, as it exhibits the maximum DSA sensitivity.
# 3 Microstructural characterizations

In this section, we will provide microstructural characterizations of the C-Mn weld in the as-welded state, in order to confirm the theoretical results presented in the previous section. First, TEM observations on tensile tested samples are presented, to estimate the difference in dislocation density between samples deformed at 20°C and 300°C. Then, *in-situ* TEM tensile tests are performed at different temperatures, to investigate dislocation dynamics during plastic deformation in the DSA temperature range. Finally, atom probe tomography (APT) is used to study the segregation of interstitial atoms on dislocations.

## 3.1 TEM observations on tensile tested samples

Analyses of the tensile curves using the Kocks-Mecking model showed that dynamic recovery decreases during tensile tests at 300°C, resulting in an increased work-hardening rate in ultimate tensile strength. As a consequence, it is expected that dislocation density would be more important after tensile tests at 300°C than at 20°C. This hypothesis is investigated by TEM observations on the as-welded material, after it failed during tensile tests at both 20°C and 300°C. Typical TEM micrographs are presented in fig. 4 (20°C) and 5 (300°C).

Despite the local character of TEM, the TEM micrographs presented in fig. 4 and fig. 5 suggest that dislocation density is more important after tensile testing at 300°C than at 20°C. Similar results were already published in the literature in similar steels [30]. These observations are in qualitative agreements with the analyses from the tensile curves: the strength and work-hardening rate increase evidenced at 300°C seems to be caused by a more important dislocation density than at 20°C.

<figure><img src="image_4.png" /><figcaption>Figure 4 : Typical TEM micrographs taken from the as-welded sample after it failed during tensile tests at 20°C</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 5 : Typical TEM micrographs taken from the as-welded sample after it failed during tensile tests at 300°C</figcaption></figure>

These observations provide interesting insights on dislocation dynamics during tensile tests of DSA-sensitive materials, but they do not allow understanding the mechanism responsible for the increase of dislocation density. To answer this question, in-situ TEM tensile tests were performed at increasing temperatures, from room temperature to 600°C, on the as-welded sample, in order to directly observe dislocation dynamics in the DSA temperature range.

## 3.2 In-situ TEM tensile tests

In-situ TEM tensile tests were performed at CEMES, 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. Samples were rectangles with an electro-polished thin-edged hole, glued with a high-temperature cement on two rings adapted to the straining holder. Straining experiments were performed at 40°C, fig. 6, 280°C, fig.7 and 400°C, fig. 8. For each figure, frames of the video at different times are presented, as well as differential images between two frames of the video.

During straining at 40°C, fig. 6, we observe individual movements of two families whose screw directions are at 45°. The dislocations exhibit dominant screw character and are often anchored on macro-kinks. The slip traces are sinuous, consistent with a marked cross-slip. This corresponds to the athermal glide regime of dislocations, meaning that DSA has not yet been reached. At 280°C, fig. 7, dislocation dynamics are modified. At this temperature, dislocations glide at high speed over important distances, before being firmly anchored on obstacles. Once the slip bands appear, in less than one frame of the video, no further individual, slow motion of dislocation is observed. This regime of dislocation motion, by bursts or avalanches, is characteristic of DSA [16,17]. Most of the plasticity is controlled by these dislocations bursts, even though some anchored dislocations might glide slowly and viscously. At 400°C, fig. 8, evidences of DSA can hardly be detected. Very few dislocation bursts remain and most of the plasticity is achieved by viscous glide of faster screw dislocations. This
indicates a progressive transition to homogeneous and steady glide plasticity, as is confirmed by
straining at higher temperatures, not presented here.

<figure><img src="image_6.png" /><figcaption>Figure 6 : "Athermal" glide motion of dislocations at 40°C. The motion is called "athermal" as it is highly discontinuous. Locking and unlocking from various obstacles are frequently observed.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 7 : Rapid slip and cross-slip event, in less than 0.16s, of a dislocation coming from a grain boundary noted GB, at 280°C. During the 23s following this event, no other motion can be observed</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 8 : Steady motion of a screw dislocation from 1 to 1' and 1" at 400°C</figcaption></figure>

The results from *in-situ* TEM tensile tests on the as-welded sample reveal different mechanisms of plasticity at increasing temperatures. Around room temperature, plasticity is athermal, obstacle-controlled, as evidenced by fast and curved dislocations [31]. Another regime of dislocation motion is observed at 280°C, in the macroscopic DSA temperature range. At this temperature, no slow dislocation motion is observed. Plastic deformation relies on bursts of individual or small groups of dislocations. This is characteristic of the DSA regime, where dislocations are firmly locked, most probably by segregated solute atoms. At higher temperatures, 400°C, dislocations are able to drag the segregated carbon, marking the end of the DSA regime.

These new results are in qualitative agreement with the theoretical ones provided by the Kock-Mecking model. No slow dislocation motion is observed in the DSA temperature range, confirming the decreased dynamic recovery predicted by the Kocks-Mecking analysis. Deformation relies on bursts of “fresh” dislocations, because of local stress concentrations. Due to the decreased dynamic recovery, the overall dislocation density increases much more in the DSA temperature range, as new dislocations are emitted by dislocation bursts. This finally leads to an increased work-hardening rate.

## 3.3 Atom probe tomography (APT)

*In-situ* TEM tensile tests evidence a change in dislocation dynamics in the DSA temperature range, leading to modified mechanical properties. In order to unravel the origin of such feature, atom probe tomography (APT) was used to evidence solute atoms enrichment along dislocation lines, which could be responsible for dislocations anchoring during plastic deformation.

An APT volume from the as-welded sample is presented in fig. 9a, where each colored dot is an atom. A 1% iso-concentration of C is plotted. It forms a rather cylindrical line crossing the specimen. This is interpreted as C enrichment along a dislocation line. The excess of solute atom along this line is plotted in fig. 9b. This graph shows that carbon segregation on the dislocations is extremely high, up to 125 at.nm⁻¹. Nitrogen and manganese also segregates on this dislocation, with excess values reaching 10 and 20 at.nm⁻¹, respectively. More details are found in reference [18]. Note that another dislocation segregated by C and N was also evidenced in this material [32].
<figure><img src="image_9.png" /><figcaption>Figure 9 : APT analysis performed on the as-welded sample, evidencing C, N and Mn segregation on a dislocation line</figcaption></figure>

Thus, APT analyses confirm C, N and Mn segregation on dislocations. All these elements might pin dislocations prior to plastic deformation, thus inducing static strain-aging. Due to Mn negligible diffusion at 300°C, only interstitial atoms are responsible for dislocations anchoring during plastic deformation in the DSA temperature range, leading to a modified dislocation dynamics, as evidenced by *in-situ* TEM tensile tests. Dislocations being pinned by C and N, the probability for two dislocations to annihilate is then reduced, thus explaining the decrease in dynamic recovery predicted by the Kocks-Mecking model. Finally, the decreased dynamic recovery is responsible for the increase in work-hardening rate, and overall modified mechanical properties.

# 4 Interstitial atoms content effect on DSA sensitivity

The previous section evidenced that interstitial atoms are responsible for DSA sensitivity, as they are able to segregate on dislocations during plastic deformation. In this section, we will focus on quantifying the effect on interstitial atom content on DSA sensitivity of the C-Mn weld, i.e. the modification of mechanical properties. First, the variation in interstitial atoms content in solid solution is studied by internal friction experiments and linked to mechanical properties. Then, a quantitative model based on the Kocks-Mecking framework will be presented, allowing to capture the combined effects of temperature and solute segregation on dynamic recovery and overall tensile properties, taking into account nitrogen content in solid solution.

## 4.1 Interstitial atoms content in solid solution

The as-welded sample was heat-treated at 500 and 590°C in order to vary interstitial atoms content in solid solution and to investigate the effect on mechanical properties and DSA-sensitivity. The heat-treated samples are named PWHT 500 and PWHT 590, respectively. As was shown on the tensile curves from fig. 1, section 2.1, PWHT 500 did not modify mechanical properties and DSA sensitivity, whereas PWHT 590 decreased DSA sensitivity and softened the material.

Internal friction experiments performed on an inverted torsion pendulum at 1 Hz were used to compare the free carbon and nitrogen concentrations in the lattice of the three samples [33]. This technique is able to detect low concentrations of solutes in macroscopic specimens and is commonly used to
measure DSA sensitivity [24]. The results are presented in fig. 10. The internal friction spectra present a broad peak over a wide temperature range with a maximum around 285 K, attributed to the presence of N in solid solution, for the three samples [34,35]. The PWHT590 reduces N content in solid solution, making it less sensitive to DSA. Due to the dissolution of metastable nitrides formed after welding [32], PWHT500 sample has a nitrogen concentration in solid solution estimated to be three times that of the AW sample, as estimated from the peak height in the IF spectra. Surprisingly, PWHT 500 and AW exhibit similar mechanical properties and sensitivity to DSA but very different free nitrogen contents. In the following section, we seek to explain this observation by developing a model based on the Kocks-Mecking framework, allowing to capture the combined effects of temperature and solute segregation on dynamic recovery and overall tensile properties, taking into account nitrogen content in solid solution.

<figure><img src="image_10.png" /><figcaption>Figure 10: Internal friction experiments performed on the three samples of the study, AW (black), PWHT 500 (blue) and PWHT 590 (red)</figcaption></figure>

## 4.2 Modeling

The following approach is used to study the obtained results. Details of the calculations can be found in reference [36]. The stress is first decomposed into an athermal (square brackets) and a thermal contribution [37], such as:

$$ \sigma = [\sigma_0 + \sigma_d^0 \phi(t_a)] + \frac{\mu}{\mu_0} s(\dot{\epsilon}, T) \hat{\sigma}_f \quad (4) $$

Where :

- $\sigma_0$ is a contribution to yield stress and for simplicity includes the lattice friction stress, solid solution and precipitation hardening,
- $\sigma_d^0 \phi(t_a)$ corresponds to the extra resistance stress exerted by the diffusing solute atoms on the dislocation motion and $\sigma_d^0$ is the maximum stress when dislocations are fully pinned.

- $\hat{\sigma}_f$ is the critical forest hardening which is controlled by dislocation-dislocation interactions, expressed from the well-known Taylor relation

We do not distinguish between forest and mobile dislocation densities. The strain rate and temperature dependent pre-factor $s(\dot{\epsilon}, T)$ depicts the obstacle profile of short-range temperature-dependant thermal barrier [37]. The temperature dependent shear modulus was defined according to a correlation proposed by Varshni [38]. $\phi(t_a)$, the relative concentration of solute atoms pinning the dislocations, varies between 0 (unpinned dislocations) and 1 (fully pinned dislocations) and is a function of the ratio between the ageing time $t_a$ and the characteristic diffusion time $t_d$ [39–41] :

$$ \phi(t_a) = \left(1 - \exp\left(-\left(\frac{t_a}{t_d}\right)^n\right)\right) \qquad (5) $$

Expressions for the ageing time $t_a$ and the characteristic diffusion time $t_d$ are found in the literature [42–44]. The Kocks-Mecking model, equation (1) is modified as to take into account the effect of DSA on dynamic recovery. We then write [43]:

$$ K_2^{DSA} = k_2[1 - \xi\phi(t_a)] \qquad (9) $$

The parameter $\xi$ ($0 \le \xi \le 1$) which controls the level of influence of strain ageing on strain hardening has to be determined.

Finally, the flow stress was obtained by solving the following system:

$$ \left\{ \begin{aligned} \sigma(\varepsilon) &= \sigma_0 + \sigma_d^0 \left[ \left( 1 - \exp\left(-\frac{3|E_s|D\omega(\pi X_s)^{\frac{3}{2}}}{\dot{\epsilon}k_B T b^2}\right)^{\frac{1}{3}} \right)^{\frac{1}{3}} \right] + \alpha M \mu b s(\dot{\epsilon}, T) \sqrt{\rho(\varepsilon)} \\ \frac{d\rho(\varepsilon)}{d\varepsilon} &= M \left( \frac{k_1}{b} \sqrt{\rho(\varepsilon)} - k_2 \left[ 1 - \xi \left( 1 - \exp\left(-\frac{3|E_s|D\omega(\pi X_s)^{\frac{3}{2}}}{\dot{\epsilon}k_B T b^2}\right)^{\frac{1}{3}} \right) \right] \right) \rho(\varepsilon) \end{aligned} \right. \qquad (10) $$

The values of the parameters used in the calculations are available in Table 1.

<table><caption>Table 1: Values of the parameters used in the calculations</caption><thead><tr><th></th><th colspan="7">Parameters used in the calculations</th></tr><tr><th></th><th>α</th><th>b</th><th>ρ<sub>0</sub></th><th>g<sub>0</sub></th><th>k</th><th>ε̇<sub>0</sub></th><th>p</th><th>q</th></tr></thead><tbody><tr><th>Value</th><td>0.33</td><td>2.5 x 10<sup>-10</sup></td><td>10<sup>14</sup></td><td>1.34</td><td>1.38 x 10<sup>-23</sup></td><td>3 x 10<sup>6</sup></td><td>2/3</td><td>1</td></tr><tr><th>Unit</th><td>-</td><td>m</td><td>m<sup>-2</sup></td><td>-</td><td>J.K<sup>-1</sup></td><td>s<sup>-1</sup></td><td>-</td><td>-</td></tr><tr><th></th><th>μ<sub>0</sub></th><th>D<sub>0</sub></th><th>T<sub>0</sub></th><th>n</th><th>ω</th><th>E<sub>s</sub></th><th>M</th><td></td></tr><tr><th>Value</th><td>81.5</td><td>9128</td><td>215</td><td>1/3</td><td>2 x 10<sup>-4</sup></td><td>0.5</td><td>3</td><td></td></tr><tr><th>Unit</th><td>GPa</td><td>MPa</td><td>K</td><td>-</td><td>-</td><td>eV</td><td>-</td><td></td></tr></tbody></table>
The model has been calibrated to accurately reproduce the tensile curves and the evolution of the strain hardening rate at 20°C and 300°C, after the strain rate increase at 1.4% strain. The results of the model are in line with the measured tensile curves and strain hardening rates. The procedure used consists of considering four fitting parameters: $\sigma_0$, $\sigma_d^0\phi(t_a)$, $k_1$ and $K_2^{DSA}$, which values are presented in Table 22. The concomitant increase in strength and uniform elongation is well reproduced by the calculations.

<table><caption>Table 2 : Parameters determined for the calculations, at 20°C and 300°C</caption><thead><tr><th rowspan="3"></th><th colspan="4">Parameters determined</th><th colspan="4">Parameters determined</th></tr><tr><th colspan="4">20°C</th><th colspan="4">300°C</th></tr><tr><th>σ<sub>0</sub><br>(MPa)</th><th>σ<sub>d</sub><sup>0</sup>φ(t<sub>a</sub>)<br>(MPa)</th><th>k<sub>1</sub></th><th>K<sub>2</sub><sup>DSA</sup></th><th>σ<sub>0</sub><br>(MPa)</th><th>σ<sub>d</sub><sup>0</sup>φ(t<sub>a</sub>)<br>(MPa)</th><th>k<sub>1</sub></th><th>K<sub>2</sub><sup>DSA</sup></th></tr></thead><tbody><tr><td>AW</td><td>274</td><td>0.70</td><td>0.065</td><td>11.0</td><td>257</td><td>38.0</td><td>0.07</td><td>8.1</td></tr><tr><td>PWHT500</td><td>259</td><td>0.50</td><td>0.065</td><td>10.85</td><td>271</td><td>34.0</td><td>0.07</td><td>8.4</td></tr><tr><td>PWHT590</td><td>215</td><td>0.09</td><td>0.065</td><td>10.85</td><td>238</td><td>12.0</td><td>0.07</td><td>10.1</td></tr></tbody></table>

Table 2 shows that the AW and PWHT500 samples, which have different concentrations of free nitrogen in the lattice, have very similar $K_2^{DSA}$ values, whereas the PWHT590 sample has a significantly different $K_2^{DSA}$ value. To understand this, we can express $K_2^{DSA}$ as a function of free nitrogen content in the lattice $X_s$:

$$K_2^{DSA} = k_2 \left[ 1 - \xi \left( 1 - \exp \left( - \frac{3|E_s|D\omega(\pi X_s)^{\frac{3}{2}}}{\dot{\epsilon}k_B T b^2} \right) \right)^n \right] \quad (12)$$

<figure><img src="image_11.png" /><figcaption>Figure 11 : Evolution of $K_2^{DSA}$ as a function of nitrogen concentration for different values of $\xi$ at two strain rates ($10^{-4}$ and $10^{-2}$ s$^{-1}$). The red dots represent the $K_2^{DSA}$ values determined and the associated free nitrogen content.</figcaption></figure>

In the absence of DSA, it is reasonable to assume that the value of $k_2$ at 300°C is at least greater than that at 20°C. For the sake of simplicity, let us assume that the value of $k_2$ at 300°C is the same as that at 20°C. In any case, this hypothesis does not change the conclusions of our study. The plot of $K_2^{DSA}$ as a function of $X_s$ decreases exponentially with the nitrogen concentration and tends asymptotically to
a value of $K_2^{DSA}$ fixed by the value of $\xi$. Consequently, this regime operates at very low solute concentrations and saturates above a critical solute concentration. The evolution shown in fig. 11 is very sensitive to any variation in $\xi$, passing through the values of $K_2^{DSA}$ determined for a value of $\xi \approx 0.27$. This value is close to that recommended in [43] for a C-Mn steel. We show a plateau where $K_2^{DSA}$ varies little as the nitrogen content in the solid solution increases. This may explain why the AW and PWHT 500 samples have identical $K_2^{DSA}$ and mechanical properties at 300°C although their free nitrogen content in the lattice is very different.

## 5 Conclusion

This study investigated the multiscale consequences of dynamic strain aging (DSA) in a C-Mn weld steel. At the macroscopic level, DSA manifests as an increase in mechanical strength at 300 °C compared to 20 °C. Interestingly, under these conditions, uniform elongation also increases alongside the ultimate tensile strength. Analysis of the tensile curves using the Kocks-Mecking model reveals a significant increase in work-hardening rate within the DSA temperature range, attributed to a reduced dynamic recovery during plastic deformation.

This reduction in dynamic recovery is supported by *in-situ* TEM tensile tests, which show that dislocation motion is hindered in the DSA regime, with plastic deformation occurring through intermittent dislocation bursts. Atom probe tomography confirms the segregation of carbon and nitrogen to dislocations, providing direct evidence of dislocation pinning. Heat treatments that reduce interstitial solute content in solid solution consequently diminish DSA sensitivity.

These observations lead us to a clear interpretation of DSA: it originates from the segregation of interstitial atoms (C and N) to dislocations during plastic deformation. Within specific temperature and strain rate windows, these atoms diffuse fast enough to pin dislocations during plastic deformation, altering their dynamics and reducing their mutual annihilation. This diminished dynamic recovery increases dislocation density and thus enhances work-hardening and mechanical strength. Phenomena such as the Portevin–Le Chatelier (PLC) effect or the simultaneous increase in strength and ductility, as observed in this study, are macroscopic manifestations of these fundamental mechanisms observed in specific experimental conditions.

Ultimately, this work contributes to a deeper understanding of DSA across scales, linking atomic-scale processes to macroscopic mechanical behavior. Future studies should aim to quantify the scaling transitions—specifically, how microstructural events translate into observable macroscopic effects.

## Références

[1] D. Wagner, J.C. Moreno, C. Prioul, Influence of Post Weld Heat Treatment on the Dynamic Strain Aging of C-Mn Steels, J. Phys. IV France 06 (1996) C8-159-C8-162.
https://doi.org/10.1051/jp4:1996833.

[2] B.J. Brindley, J.T. Barnby, Dynamic strain ageing in mild steel, Acta Metallurgica 14 (1966) 1765-1780.
https://doi.org/10.1016/0001-6160(66)90028-9.

[3] B. Houssin, Strain ageing sensitivity of pressure vessel steels and welds of nuclear reactor components, in: Berlin, 1979.
[4] M. Grumbach, Vieillissement des aciers, Techniques de l'ingénieur Etude et propriétés des matériaux (1993). https://doi.org/10.51257/a-v1-m235.

[5] A.H. Cottrell, B.A. Bilby, Dislocation Theory of Yielding and Strain Ageing of Iron, Proc. Phys. Soc. A 62 (1949) 49–62. https://doi.org/10.1088/0370-1298/62/1/308.

[6] J. Belotteau, Comportement et rupture d'un acier au C-Mn en présence de vieillissement sous déformation, 2009. https://tel.archives-ouvertes.fr/tel-01081269.

[7] J.D. Baird, The effects of strain-ageing due to interstitial solutes on the mechanical properties of metals, Metallurgical Reviews 16 (1971) 1–18. https://doi.org/10.1179/mtlr.1971.16.1.1.

[8] E. Pereloma, I. Timokhina, Bake hardening of automotive steels, in: Automotive Steels, Woodhead Publishing, Elsevier, 2017: pp. 259–288. https://doi.org/10.1016/B978-0-08-100638-2.00009-2.

[9] P. Elsen, H.P. Hougardy, On the mechanism of bake-hardening, Steel Research 64 (1993) 431–436. https://doi.org/10.1002/srin.199301049.

[10] A. Okamoto, K. Tdkeuchi, M. Tahagi, A Mechanism of Paint Bake-hardening, The Sumitomo Search (1989) 13.

[11] D.R.G. Achar, M. Koçak, G.M. Evans, Effect of nitrogen on toughness and strain age embrittlement of ferritic steel weld metal, Science and Technology of Welding and Joining 3 (1998) 233–243. https://doi.org/10.1179/stw.1998.3.5.233.

[12] D. Wagner, J.C. Moreno, C. Prioul, Dynamic strain aging sensitivity of heat affected zones in C–Mn steels, Journal of Nuclear Materials 252 (1998) 257–265. https://doi.org/10.1016/S0022-3115(97)00279-1.

[13] K.C. Kim, J.T. Kim, J.I. Suk, U.H. Sung, H.K. Kwon, Influences of the dynamic strain aging on the J–R fracture characteristics of the ferritic steels for reactor coolant piping system, Nuclear Engineering and Design 228 (2004) 151–159. https://doi.org/10.1016/j.nucengdes.2003.06.014.

[14] C.W. Marschall, R. Mohan, P. Krishnaswamy, G.M. Wilkowski, Effect of dynamic strain aging on the strength and toughness of nuclear ferritic piping at LWR temperatures, 1994. https://doi.org/10.2172/10193189.

[15] A. Yilmaz, The Portevin–Le Chatelier effect: a review of experimental findings, Science and Technology of Advanced Materials 12 (2011) 063001. https://doi.org/10.1088/1468-6996/12/6/063001.

[16] D. Caillard, Dynamic strain ageing in iron alloys: The shielding effect of carbon, Acta Materialia 112 (2016) 273–284. https://doi.org/10.1016/j.actamat.2016.04.018.

[17] D. Caillard, J. Bonneville, Dynamic strain aging caused by a new Peierls mechanism at high-temperature in iron, Scripta Materialia 95 (2015) 15–18. https://doi.org/10.1016/j.scriptamat.2014.09.019.

[18] W. Mottay, P. Maugis, M. Jouiad, F. Roch, C. Perrin-Pellegrino, K. Hoummada, Effect of dislocation density on competitive segregation of solute atoms to dislocations, Materials Science and Engineering: A 881 (2023) 145380. https://doi.org/10.1016/j.msea.2023.145380.

[19] Norme NF EN ISO 6892-1, International Organization for Standardization (2019). https://www.iso.org/fr/standard/78322.html.

[20] Norme NF EN ISO 6892-2, International Organization for Standardization (2018). https://www.iso.org/fr/standard/78322.html.

[21] A. Considère, Mémoire sur l'emploi du fer et de l'acier dans les constructions, Annales Des Ponts et Chaussées 9 (1885) 574.

[22] G. Piobert, Expérience sur la pénétration des projectiles dans le fer forgé, Mémoire de l'Artillerie (1842).

[23] W. Lüders, Über die äusserung der elasticität an stahlartigen eisenstäben und stahlstäben, und über eine beim biegen solcher stäbe beobachtete molecularbewegung, Dinglers Polytech J (1860).

[24] D. Wagner, N. Roubier, C. Prioul, Measurement of sensitivity to dynamic strain aging in C–Mn steels by internal friction experiments, Materials Science and Technology 22 (2006) 301–307. https://doi.org/10.1179/174328406X86155.

[25] U.F. Kocks, Laws for Work-Hardening and Low-Temperature Creep, Journal of Engineering Materials and Technology 98 (1976) 76–85. https://doi.org/10.1115/1.3443340.
[26] U.F. Kocks, H. Mecking, Dislocation kinetics at not-so-constant structure, in: Dislocation Modelling of Physical Systems, Elsevier, 1981: pp. 173–192. https://doi.org/10.1016/B978-0-08-026724-1.50024-8.

[27] Y. Estrin, H. Mecking, A unified phenomenological description of work hardening and creep based on one-parameter models, Acta Metallurgica 32 (1984) 57–70.
https://doi.org/10.1016/0001-6160(84)90202-5.

[28] L.P. Kubin, Y. Estrin, Dynamic strain ageing and the mechanical response of alloys, J. Phys. III France 1 (1991) 929–943. https://doi.org/10.1051/jp3:1991166.

[29] U.F. Kocks, H. Mecking, Physics and phenomenology of strain hardening: the FCC case, Progress in Materials Science (2003) 103.

[30] A.S. Keh, W.C. Leslie, Recent Observations on Quench-Aging and Strain-Aging of Iron and Steel, in: H.H. Stadelmaier, W.W. Austin (Eds.), Materials Science Research, Springer US, Boston, MA, 1963: pp. 208–250. https://doi.org/10.1007/978-1-4899-5537-1_12.

[31] U. Messerschmidt, Dislocation Dynamics During Plastic Deformation, Springer Berlin Heidelberg, Berlin, Heidelberg, 2010. https://doi.org/10.1007/978-3-642-03177-9.

[32] J. Landes, W. Mottay, K. Hoummada, C. Perrin, V. Massardier, M. Jouiad, N. Hervé, A. Marceaux Dit Clément, P. Maugis, Precipitation of Manganese Nitride During Post-Weld Heat Treatment in C-Mn and Low-Alloy Steel Welds, Metall Mater Trans A (2025).
https://doi.org/10.1007/s11661-025-07694-8.

[33] M.S. Blanter, I.S. Golovin, H. Neuhäuser, H.-R. Sinning, Internal Friction in Metallic Materials: A Handbook, Springer Berlin Heidelberg, Berlin, Heidelberg, 2007. https://doi.org/10.1007/978-3-540-68758-0.

[34] T. Gladman, R.L. Barker, Internal friction characteristics of interstitial carbon and nitrogen in α-iron, J. Phys. Colloques 32 (1971) C2-57-C2-58. https://doi.org/10.1051/jphyscol:1971211.

[35] A. Kruk, J. Pietrzyk, C. Kapusta, The influence of manganese on internal friction spectra in Fe-Mn-N alloys, Scripta Metallurgica et Materialia 31 (1994) 1679–1683.
https://doi.org/10.1016/0956-716X(94)90463-4.

[36] W. Mottay, K. Hoummada, Y. Bréchet, V. Massardier, C. Perrin-Pellegrino, P. Maugis, F. Roch, M. Gouné, Identification and analysis of a reverse dynamic strain ageing in welded joints of C-Mn steels in the secondary circuit welds of nuclear power plants, Scripta Materialia 247 (2024) 116099. https://doi.org/10.1016/j.scriptamat.2024.116099.

[37] P.S. Follansbee, U.F. Kocks, A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable, Acta Metallurgica 36 (1988) 81–93. https://doi.org/10.1016/0001-6160(88)90030-2.

[38] Y.P. Varshni, Temperature Dependence of the Elastic Constants, Phys. Rev. B 2 (1970) 3952–3958. https://doi.org/10.1103/PhysRevB.2.3952.

[39] H.D. Wang, C. Berdin, M. Mazière, S. Forest, C. Prioul, A. Parrot, P. Le-Delliou, Experimental and numerical study of dynamic strain ageing and its relation to ductile fracture of a C–Mn steel, Materials Science and Engineering: A 547 (2012) 19–31.
https://doi.org/10.1016/j.msea.2012.03.069.

[40] F. Springer, Ch. Schwink, Quantitative investigations on dynamic strain ageing in polycrystalline CuMn alloys, Scripta Metallurgica et Materialia 25 (1991) 2739–2744.
https://doi.org/10.1016/0956-716X(91)90149-U.

[41] N. Louat, On the theory of the portevin-le chatelier effect, Scripta Metallurgica 15 (1981) 1167–1170. https://doi.org/10.1016/0036-9748(81)90290-8.

[42] P.G. McCormick, Theory of flow localisation due to dynamic strain ageing, Acta Metallurgica 36 (1988) 3061–3067. https://doi.org/10.1016/0001-6160(88)90043-0.

[43] S. Ren, M. Mazière, S. Forest, T.F. Morgeneyer, G. Rousselier, A constitutive model accounting for strain ageing effects on work-hardening. Application to a C–Mn steel, Comptes Rendus Mécanique 345 (2017) 908–921. https://doi.org/10.1016/j.crme.2017.09.005.

[44] J. Friedel, Dislocations: International Series of Monographs on Solid State Physics, Pergamon, Amsterdam, 2013.