# High temperature chromium coating cracking investigation during tensile tests monitored by acoustic emission

Yanis Taïbi, Ali Charbal, Jean-Christophe Brachet, Elodie Rouesne, Sergio

Sao Joao, Szilvia Kalácska, Morgan Rusinowicz, Guillaume Kermouche

► To cite this version:

Yanis Taïbi, Ali Charbal, Jean-Christophe Brachet, Elodie Rouesne, Sergio Sao Joao, et al. High tem-
perature chromium coating cracking investigation during tensile tests monitored by acoustic emission.
Journal of Nuclear Materials, 2025, 616, pp.156108. 10.1016/j.jnucmat.2025.156108. emse-05238666

HAL Id: emse-05238666

https://hal-emse.ccsd.cnrs.fr/emse-05238666v1

Submitted on 3 Sep 2025

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# High temperature chromium coating cracking investigation during tensile tests monitored by acoustic emission

Yanis Taïbi<sup>a,b,c</sup>, Ali Charbal<sup>a,∗</sup>, Jean-Christophe Brachet<sup>a,c</sup>, Elodie Rouesne<sup>a</sup>,
Sergio Sao-Joao<sup>b,d</sup>, Szilvia Kalacska<sup>b,d</sup>, Morgan Rusinowicz<sup>b,d</sup>, Guillaume Kermouche<sup>b,d</sup>

## ARTICLE INFO

### Keywords:

EATF
chromium coating
acoustic emission
cracking
tensile testing

## ABSTRACT

The present study focuses on in-situ measurements of crack initiation and propagation in first-generation PVD-HiPIMS chromium coatings on $M_5\text{Framatome}^1$ cladding substrates using an acoustic emission (AE) device and a tensile test machine. A key novelty of this work is the implementation of a temperature-controlled cracking monitoring system adapted to the cladding geometry under tensile loading. Post-mortem examinations (after different interrupted tensile tests) provide an evaluation of the in-situ method for determining the crack initiation threshold and crack density evolution. The critical strain to crack initiation increases exponentially from 0.4 % at room temperature to 3 % at 350 °C. Above 410 °C, the coating no longer exhibits brittle cracking until reaching high macroscopic imposed strain (up to 30-50 %). Additionally, the crack density decreases more or less linearly with the increasing testing temperature. At higher temperatures, the coating becomes highly ductile, consistently with the increased plasticity of pure chromium. SEM observations of the coating cross-section confirm that cracks do not propagate beyond the coating and that no delamination occurs. Thus, after rapidly reaching crack density saturation, the residual uncracked chromium coating exhibits significant plasticity and widening of the existing Cr cracks while providing slight mechanical reinforcement to the Zr-based cladding up to at least 400 °C.

## 1. Introduction

Nuclear fuel cladding tubes must meet specific design criteria for normal operation, anticipated operational occurrences, and hypothetical accidents [1–3]. For instance, during a Loss Of Coolant Accident (LOCA) postulated scenario, the zirconium alloy cladding tube can experience rapid thermomechanical transient induced by rapid heating and internal pressure increase, potentially causing ballooning and burst. Additionally, the cladding tubes may be exposed subsequently to a high-temperature steam environment, resulting in accelerated oxidation [3–9] and embrittlement. The exothermal reaction between water vapor and the zirconium alloy cladding results also in hydrogen gas production [3–5,7,8,10] that may cause an explosion in extreme (severe accident) conditions. To mitigate this risk and further enhance high-temperature oxidation resistance, many institutions and manufacturers are developing Enhanced Accident Tolerant Fuel (E-ATF) cladding (and/or fuel) technologies [1,5,10–14].

Short-term candidates consist of applying a thin (chromium) coating to the currently used zirconium-alloy cladding tubes. Therefore, these candidates represent an evolution of existing cladding materials with decades manufacturing and in-pile experience that provides a strong basis for their qualification with a coating [3,12,14,15]. Various techniques can be used to apply such coatings: cold spray [1,3,4,16], laser deposition (3D printing) [10,17], Arc ion plated deposition [18,19], and Physical Vapor Deposition (PVD) [3,4,14,20,21].

Separate case studies indicate clear improvements in corrosion resistance (single-face oxidation) and allow to claim some additional benefit in LOCA conditions [21–24]. It remains that a cladding should be able to withstand a Class 2 transient [25] and resume normal operation. This kind of transient generates a dilatation of the pellet as well as of the cladding where the cladding should be able to withstand a diametral/circumferential deformation up to 1 or 2 % at in-service temperature (300-350 °C). For coated cladding, the coating's capacity to tolerate such deformations without significant cracking needs investigation.

<footnote><sup>a</sup> Université Paris-Saclay, CEA, Service de Recherche en Matériaux et procédés Avancés, 91191, Gif-sur-Yvette, France</footnote>

<footnote><sup>b</sup> Mines Saint-Etienne, CNRS, UMR 5307 LGF, Centre SMS, F-42023 Saint-Etienne, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: ali.charbal@cea.fr (A. Charbal).</footnote>

<footnote n="1">¹ $M_5\text{Framatome}$ is a trademark or a registered trademark of Framatome or its affiliates in the USA or other countries.</footnote>
Coating cracking during a Class 2 transient would lead to corrosion of the zirconium alloy in the crack's vicinity during continued operation and would decrease their overall oxidation protectiveness in case of further hypothetical HT incursion. Consequently, an investigation of the coating's cracking resistance and crack density evolution as a function of temperature and deformation will provide important insight on the coated cladding's behavior in such scenarios.

In this work, chromium coating cracking initiation and evolution during mechanical loading at various temperatures is investigated. Previous studies have shown that chromium has low ductility at room temperature [21] leading to crack initiation at strain levels as low as 0.30-0.40 %. Roache et al. [23] studied crack initiation and propagation in cold-spray Cr coatings using acoustic emission coupled with digital image correlation at 20 and 315 °C. The deformation levels for coating crack initiation at room temperature (0.40 %) were comparable to coatings deposited using other techniques. Alakiozidis et al. [16] conducted in-situ SEM tensile tests on cladding tubes coated by cold spray at room temperature. The crack initiation and propagation appeared to be comparable with the observations of Roache et al. [23] (using same coating technology) and Nguyen et al. [21] (using PVD coating). Surprisingly Roache et al. [23] detected same strain levels for crack initiation at 315 °C. The results were different when the metallic coating deposited using magnetron sputtering was investigated by Jiang et al. [22]. From this last work, it appeared that the strain levels to reach cracking linearly increased (slow slope) with temperature up to ~450 °C. Above 450 °C, chromium's ductility rapidly increases suggesting a clear gain in cracking resistance. Note that the results from [22] and [21] were obtained on a different substrate geometries and alloys (Zircaloy 4 plate vs. $M_5\text{Framatome}$ cladding tubes), solicitation type and environment.

The current work provides a parametric study of crack initiation and evolution of a metallic chromium coating deposited by Physical Vapor Deposition-High Power Impulse Magnetron Sputtering (PVD-HiPIMS) on $M_5\text{Framatome}$ cladding tube during tensile testing carried out from ambient temperature to 540 °C. The only parameter that was varied is the temperature. The goal was to provide information on the strain level to crack initiation as performed by Jiang et al. on coated plate samples [22]. Working on the tube geometry constraints the instrumentation as, for instance, in-situ monitoring of cracking using an SEM was not possible. The geometrical aspects of the samples, however, could affect the coating's behavior and the study of tubular samples provides a more straightforward comparison basis for industrial products.

# 2. Materials and methods

## 2.1. Materials

The samples were as-received chromium coated $M_5\text{Framatome}$ zirconium alloy cladding tubes prototypes. The PVD-HiPIMS process generated two distinct types of grain microstructure along the coating thickness. Smaller and equiaxed grains near the interface between the coating and the substrate, followed by columnar grains. The average diameter of the equiaxed grains, located close to the interface, is 1 to 2 µm. The larger and elongated columnar grains, can be 6 µm high and less than 1 µm wide. A preferential [100] orientation along the radial direction is noted (see EBSD scans in Fig. 1). This deposition process produced a dense coating free from major defects with a very good Cr-Zr bounding strength [21].

In the prototypic deposition chamber, the coating was applied to 490 mm long cladding tubes. The resulting thickness varied along the cladding tube length. The tensile specimens with a 120 mm gauge length were selected from areas in which the measured chromium thicknesses varied from 15 to 18 µm. Zircaloy-4 plugs were machined and electron-beam welded as shown in the drawing in Fig. 2 to allow for mounting of the tubes in the tensile testing machine's grips.

## 2.2. Tensile tests

Tensile tests were systematically conducted on coated and uncoated tubes across a temperature range of 20 °C to 540 °C, at a strain rate of $2 \times 10^{-4} s^{-1}$, using an INSTRON 4507 tensile testing machine equipped with a 5800R load frame and a 20 kN force cell. Temperature control and homogeneity were ensured by an Instron® Environmental Chamber (3119-400 Series) working in air atmosphere, with heating monitored using two thermocouples positioned at the extremities of each sample. Samples were heated at rates varying between 15 °C/min and 21 °C/min, depending on the target temperature. The time required to reach the desired temperature ranged from 15 to 30 min, with a 30-minute dwell time applied uniformly to all samples to ensure thermal stabilization. During heating, the temperature was precisely controlled, with ranges recorded as follows: at 180 ± 2 °C, at 350 ± 2 °C, at 390 ± 2 °C, at 410 ± 2 °C, at 440 ± 2 °C, and at 540 ± 2 °C. The rational for this range of temperature is that they largely bound the cladding temperature during in-service conditions and upon a hypothetical class 2 transient. The thermal loading profiles (temperature vs. time) for representative target temperatures of 180 °C, 350 °C, and 540 °C are shown in Fig. 3(a), illustrating the consistency of the heating and stabilization process.

Fig. 3(b) illustrates the thermal and mechanical loading profiles applied during the tensile tests. The blue curve represents the temperature profile, showing the controlled heating phase, a dwell time of 30 min at the target temperature for thermal stabilization, and the subsequent cooling phase. The red curve corresponds to the mechanical loading applied after the thermal stabilization phase. The heating and cooling rates, as well as the thermal dwell time, are consistent with the process described above, ensuring uniform thermal conditions across the sample before the application of mechanical stress.

The tensile tests were performed in strain control loading (with a constant strain rate). This control is applied by calculating the equivalent tensile test machine jaws displacement speed. To determine precisely the effective gauge length<fnref n="2" />, a high-temperature un-cooled axial extensometer (epsilon's model 7642) capable of operating from ambient temperature up to 700 °C was mounted on the uncoated samples, which provided a calibration of the effective gauge length (in spite of the machine rigidity and plugs effects) for each test temperature. This calibration allowed tensile testing on the chromium coated samples without the extensometer, to ensure a clear and unpolluted AE signal. The coating cracking was monitored with AE Vallen system using a VS700-D piezoelectric sensor with a working frequency range from 150 kHz up to 800 kHz. The latter is placed outside the furnace chamber, approximately 60 cm away from the sample (see Fig. 4(a)), to ensure that the AE sensor is kept within its operating temperature specifications (temperature range from -20 to 70 °C). The system captures and converts the mechanical waves emitted during cracking into electrical signals, which are amplified and recorded by an AMSY-6 acquisition module.

To qualify and validate the AE results, an interrupted test is performed at 350 °C (see Table 1). For each strain level, the sample was unmounted and its external surface is imaged using an MCE Vertex three-dimensional measuring machine. This machine provides a precise motion (2 µm precision) to produce 9.35 × 7 mm<fnref n="2" /> maps with a 14 µm/pixel resolution. The crack quantification is performed using the Fiji software with the Weka Segmentation plugin. Based on machine learning algorithms, with a set of selected image features, it can detect the cracks feature on the maps. The obtained results are compared with the cumulative energy of AE.

<footnote n="2">² This calibration concerns the tubular geometry, where plugs inserted into the cladding make the calculation of the effective length indirect, so it focuses on correcting the deformation; whether the cladding is coated or not has no impact.</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 1. (a) EBSD map (IPF-Z) of the chromium coating surface and corresponding pole figures, (b) EBSD map (IPF-Y) of the chromium coating cross-section on the $M_5$Framatome substrate and corresponding pole figures.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. Geometry of tensile test specimens.</figcaption></figure>

# 3. Results

## 3.1. Tensile properties of temperature-coated claddings

The tensile tests conditions are applied to uncoated and coated claddings. The uncoated cladding tests provide a base-comparison for AE analyses and mechanical properties. The high temperature extensometer is used on uncoated samples to determine the effective applied strain. The calibration is determined in the elastic regime for each tested temperatures and the corrections are applied to the calculated strain using the crosshead displacements. The resulting stress-strain curves are provided with normalized stress in Fig. 5 (same value used to normalize all data) for coated and uncoated claddings from room temperature up to 540 °C. As expected, the flow stress decreases with temperature for both coated and uncoated sample.

Interestingly, the coating exhibits a certain strengthening effect, as

illustrated in Fig. 6. This effect results in an increase of approximately 5 to 10 % in both the yield strength ($R_{p0.2}$) and ultimate strength ($R_m$) at varying temperatures. Specifically, at room temperature (20 °C), the yield strength is enhanced by 5–6 %, while the ultimate strength shows a smaller increase of 3–4 %. As the temperature rises to 180 °C, the yield strength gains are slightly higher, reaching 6–9 %, while the ultimate strength increases modestly by 2–4 %. At 350 °C, the coating's strengthening effect reaches its peak, with a 10 % improvement in yield strength and a 7 % boost in ultimate strength. However, as the temperature increases further, the strengthening effect diminishes. At 390 °C and 440 °C, the yield strength enhancement stabilizes at 8 %, with corresponding ultimate strength gains of 5 % and 10 %, respectively. Notably, at 540 °C, the coating's reinforcing effect significantly weakens, with only a 4 % improvement in yield strength and a quite negligible (~1 %) increase in ultimate strength. The evolution of the coating behavior toward cracking is investigated in the next sections.
<figure><img src="image_6.png" /><figcaption>Fig. 3. (a) Thermal loading profiles, (b) Diagram of thermal and mechanical loadings.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. (a) Experimental setup for high-temperature tensile testing with acoustic emission monitoring, (b) Mounted sample illustration with the high temperature extensometer (when used).</figcaption></figure>

<table><caption>**Table 1**
Experimental conditions of the tensile tests.</caption><thead><tr><th>Sample</th><th>Coating thickness (µm)</th><th>Strain rate (s<sup>-1</sup>)</th><th>Temperatures (°C)</th><th>Deformations at interruption (%)</th></tr></thead><tbody><tr><td>M5</td><td>-</td><td>2 × 10<sup>-4</sup></td><td>20, 180, 350, 390, 410, 440, 540</td><td>-</td></tr><tr><td>M5-Cr</td><td>15-18</td><td>2 × 10<sup>-4</sup></td><td>20, 180, 350, 390, 410, 440, 540</td><td>-</td></tr><tr><td>M5-Cr</td><td>15-17</td><td>2 × 10<sup>-4</sup></td><td>350</td><td>1, 3, 5, 6, 8, 10, 11, 15</td></tr></tbody></table>

## 3.2. AE cumulated energy vs. strain

Various AE signals can be exploited, the events count, the wave amplitude, the emission duration and frequency, and finally the energy. In this work, the integrated signal was used as it provides a quasi-straightforward interpretation. It remains to ensure the collected data correlates to the cracking formation. Indeed, AE could capture the elastic waves generated by various sources such as the plastic deformation of the substrate and/or coating, frictions of various machine parts and cracking itself. To eliminate the potential substrate plastic deformation effects (and other potential machine sources) on the cumulated energy, measurements are performed during tensile testing on uncoated samples. The measured cumulated energy is one to two decades lower than those obtained on coated samples (for the same

<figure><img src="image_8.png" /><figcaption>Fig. 5. Tensile stress-strain curves at 20 °C, 350 °C, and 540 °C.</figcaption></figure>

temperature). Fig. 7 shows a comparison of cumulated energy measured for coated and uncoated samples at 20 °C, 180 °C and 350 °C. This first comparison shows a clear difference between coated and uncoated, which indicates the possibility to depict a distinctive signal from the
<figure><img src="image_9.png" /><figcaption>Fig. 6. Tensile properties of uncoated and coated M5 claddings as a function of temperature: (a) evolution of Rp₀.₂, (b) evolution of Rₘ.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. Cumulated acoustic emission for uncoated and coated M5 claddings: (a) at 20 °C, (b) at 350 °C.</figcaption></figure>

coating response. The correlation between cumulative energy and cracking formation was already validated at room temperature using Digital Image Correlation (DIC) [21], having in mind that at room temperature, the AE sensor can be positioned near the sample (limiting potential parasitic effects induced by the machine's parts). Furthermore, images can be captured using an x1 lens, providing high spatial resolution images for cracks formation detection using DIC.

For higher temperatures, the AE sensor and camera needs to be placed further away from the sample. In order to validate the AE signal at higher temperature configurations, and confirm the correlation with cracking formation and cumulative energy signal, interrupted tests, for various strain levels, were performed at 350 °C. After each interruption, the surface of the cladding tube is mapped with a x23 magnification (Fig. 8(a)). The crack density was then measured for each strain level. The curve in Fig. 8(b) compares the evolution tendencies provided by optical imaging (in between interruptions) with the cumulative energy. Albeit a shift in strain, the correlation between the AE signal and crack formation is confirmed. The AE signal appear to provide “critical strain to cracking formation” earlier than the optical imaging approach. This difference could be interpreted as a delayed capture of cracking by optical imaging due to a lack of contrast and/or spatial resolution. It could also be due to cracking closing back after cooling the sample at room temperature, because, at the early stage of cracking, the crack opening

could be small enough to close-up after cooling. The determination of the critical strain to reach first cracks can be derived from the cumulative energy – strain curves. An automated method is proposed in the following subpart 3.3.

### 3.3. A method for critical strain determination using cumulative AE energy

To analyze and determine the critical strain for crack initiation, an automated method based on a sigmoidal fit of experimental data was used. The aim was to ensure the reproducibility and thus the reliability of the critical strain determination from several AE measurements. This method is discussed in detail in Appendix A. The critical strain $ε_c$ evolution<fnref n="3" /> with temperature is provided in Fig. 9. It increases from ~0.5 % at room temperature to ~1.8 at 180 °C. It further increases to ~3.5 % at 350 °C to reach nearly 4 % at 410 °C. Above 410 °C, the AE cumulative energy does not depict the crack signature up to 50 % of axial strain. For these cases, the cumulative energies are representative of the measured

<footnote n="3">³ The exponential fit, chosen for its ability to highlight a threshold around 410 °C beyond which no brittle cracking is observed, does not represent an intrinsic material law and is only valid within the 20 °C to 410 °C temperature range.</footnote>
<figure><img src="image_11.png" /><figcaption>Fig. 8. (a) Surface mapping of coated claddings (post tensile test at temperature), (b) Validation of AE device at 350 °C.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 9. Evolution of critical strain as a function of temperature.</figcaption></figure>

signal on the substrate only. These results, for 440 °C and 540 °C, are further supported by the post-mortem optical imaging performed on the top surface of the cladding tube (see subpart 3.4).

### 3.4. Post-mortem imaging and analyses: determination of the crack density

At 440 °C and 540 °C, the AE signals indicated no crack formation up

to 30-50 % of axial strain. In order to confirm such results, optical images were taken, along the sample length, and analyzed. The optical magnification x23 provides a spatial resolution of 14 µm/pixel. It was noticed that on both 440 °C and 540 °C samples, no cracks were detected but darker spots can be observed (Fig. 10). The spots are distributed in larger numbers on the samples tested at 440 °C than 540 °C. The resulting emitted signals are of lesser amplitudes, which explains the low cumulative energy levels. The observations thus confirm the results obtained on the cumulative energy – strain curve obtained for both temperatures.

The samples tested at lower temperatures show a clear cracks pattern. The pattern consists of parallel cracks formed perpendicularly to the loading direction (Fig. 11). For comparable axial strains, the crack density decreases with increasing testing temperature. This decrease confirms the chromium coating's ductility increases with temperature as expected.

The crack density is determined by image processing. The FIJI software [26] is used combined with the Trainable Weka Segmentation plugin [27]. The later provides machine-learning tools to automatically detect cracks. The used method for determining crack density is detailed in Appendix B. The Fig. 12 illustrates the evolution of the crack density as a function of temperature. The data points represent the values obtained after all post-processing steps, while the red dashed line indicates the linear trend obtained through regression analysis. The overall tendency shows a significant decrease in crack density with increasing temperature. At room temperature, the crack density is the highest, approximately 9 mm⁻¹, indicating a high level of coating cracking as shown in Fig. 11. As the temperature rises, the crack density gradually decreases. For instance, at 350 °C, the crack density drops to 2.3 mm⁻¹, representing a 75 % reduction compared with the room temperature density. The decreasing trend continues, reaching value as low as 0.4

<figure><img src="image_13.png" /><figcaption>Fig. 10. Surface mapping of coated claddings post tensile tests at 440 and 540 °C. No crack detected.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Fig. 11. Surface mapping of coated claddings post tensile tests at 20, 180, 350 and 410 °C.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 12. Evolution of crack density with temperature.</figcaption></figure>

mm⁻¹ at 410 °C, suggesting higher temperatures may contribute to a reduction in crack formation due to increased coating ductility. This trend is confirmed beyond 440 °C where no cracks appear. The coating ductility seems to accommodate the plastic deformation of the substrate. The damage observed on Fig. 10 are likely a signature of the underlying zirconium substrate, however further investigations are needed to support this hypothesis.

## 4. Discussions

The crack densities (as a function of the testing temperature) were obtained *post-mortem* with the MCE optical tools. The limited spatial resolution must be considered in the crack density calculations since cracks with too small openings may not be considered. An example is illustrated in Fig. 13 where the higher magnification SEM image reveals a crack with an opening lower than 1 µm while the MCE optical examination is not able to clearly detect the Cr-cracking at the equivalent location. Thus, the provided crack densities are to be considered only for cracks with an opening larger than ~1 µm. The failure to capture early-stage (incipient) cracks, with small openings, can explain the shift in Fig. 8-b between the AE cumulated energy and the MCE images analysis for crack density (during interrupted testing). AE appears to be sensitive enough to detect the early stages of Cr-cracking and thus seems to provide more accurate information – with less efforts - for measuring the critical strain for crack initiation.

The critical strain results, along with crack density evolution, highlight the impact of temperature on the mechanical behaviour of chromium coatings. A significant distinction appears beyond 410 °C, where no cracking is observed up to 50 % axial strain (Fig. 10). Similarly, the crack density follows a linear decreasing trend with temperature

<figure><img src="image_16.png" /><figcaption>Fig. 13. Surface mapping of the coated cladding post tensile tests.</figcaption></figure>

(Fig. 12), with noticeably fewer cracks forming at higher temperatures. These observations are qualitatively in good agreement with Jiang et al. [22], who conducted in-situ SEM tensile testing on chromium coated zirconium alloy plates. The PVD coating deposition techniques used in both studies seem to generate comparable microstructures: equiaxed grains form near the substrate/coating interface, while columnar grains are generated above. The critical strain for crack formation as a function of temperature, as reported by Jiang et al. in [22], follows a similar trend to the present work (see Fig. 14.a). Specifically, the authors distinguish two different chromium coatings behaviours: from room temperature up to 450 °C, the critical strain to crack formation increases linearly with a low slope value, while above 450 °C, the slope increases dramatically, confirming the enhancement of coating ductility with temperature. Likewise, Fig. 14.b shows that the crack density in both studies follows a decreasing trend with temperature. While no clear coating cracking were detected at 440 °C and above in the present work, Jiang et al. reported an axial strain limit of 7-8 % at 470 °C. At lower temperatures, some differences are also observed. For instance, at 400 °C, Jiang et al. measured an axial strain to first cracking below 2 %, whereas in the present study a higher value of ~4 % is observed at 410 °C.

Similarly, the crack density at a given temperature remains systematically lower in the present study (i.e., more or less half the values of Jiang et al.). Several factors may explain these discrepancies. First, due to the different deposition processes and parameters employed, the investigated coatings may not have identical properties, which may lead
<figure><img src="image_17.png" /><figcaption>Fig. 14. Comparison between current study and Jiang et al. [22]: (a) evolution of critical strain with temperature, (b) evolution of crack density with temperature.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 15. SEM images of cross section post tensile tests from 20 up to 540 °C.</figcaption></figure>
to variations in strain levels required for crack formation and differences in crack density. Second, the distinct specimen geometries used in both studies may influence the incipient Cr-cracking and further crack propagation and opening. Jiang et al. employed Zr-4 plates, whereas the present study used M5<sub>Framatome</sub> cladding tubular substrates, which represent the actual geometry of nuclear fuel cladding. The tubular geometry eliminates free edges, which are known to act as stress concentrators and facilitate crack initiation [28]. These concentrators could at least partially explain why fewer cracks were observed in the present study compared to Jiang et al. Furthermore, differences in crack detection methodologies may have contributed to the observed variations. In the present study, the critical strain was determined using AE cumulative energy analysis, while Jiang et al. relied on SEM observation. The higher spatial resolution of SEM could allow for earlier crack detection, which may partly explain the lower critical strain values in their work. However, compared to present study, this effect cannot fully explain the higher crack densities reported by Jiang et al. at significant strain, because it is likely that, after crack saturation occurrence, the important crack's opening makes the crack detection easier when using optical examination. Nevertheless, a major advantage of the AE method is its applicability to real industrial cladding tubes geometries and requiring minimal sample preparation. This technique is also well suited for industrial applications, including Post-Irradiation Examinations (PIEs), as it allows for comparative studies across different coatings and provides early indications of crack resistance as a function of coating microstructure, deposition technology, operating temperature, irradiation doses achieved, etc... However, the combination of sample geometry, deposition parameters, and detection methods must be carefully considered when comparing results derived from different studies, as they significantly affect both the critical strain and the crack density evolution.

In Jiang's study, the shear-lag model was used to predict the evolution of crack density during testing at room temperature, incorporating the effects of residual stress. This model successfully described crack propagation in their chromium coating. In our approach, we do not rely on this type of modeling, as acoustic emission provides a direct, in-situ method, for tracking crack density evolution in real-time during testing. This allows for continuous monitoring of crack growth without the need for further predictive models. In parallel, we use the Hutchinson model [29] to estimate the coating's toughness. This model assumes elastic behavior for the substrate-coating system, which is valid given the substrate thickness of 0.58 mm and the coating thickness of 15 µm. SEM cross-sectional observations presented in Fig. 15 of post-tensile test specimens confirm that, from room temperature to 410 °C, cracks do not penetrate the substrate, thus validating the assumption of channel cracking without substrate penetration and confirming the very good Cr-Zr bounding strength already observed on this type of Cr coating [21]. At higher temperatures (440 °C and 540 °C), the chromium appears to gain in ductility and can withhold higher strain levels prior to cracking. These observations are well illustrated with the necking like shape presented in Fig. 15.

The critical energy release G<sub>c</sub> rate can therefore be estimated from room temperature up to 410 °C using the following formula:

$$G_c = Z e_c^2 h_{Cr} \cdot \frac{E_{Cr}}{1 - \nu_{Cr}} \qquad (1)$$

In this Eq. (1), Z = 1.976 is a dimensionless factor specific to channel cracking [29]. This factor Z accounts for the nature of the observed cracking phenomenon. e<sub>c</sub> represents the critical strain, h<sub>Cr</sub> is the thickness of the chromium coating, E<sub>Cr</sub> its Young's modulus, and ν<sub>Cr</sub> is the Poisson's ratio. Once the energy release rate is determined, the stress intensity factor K<sub>IC</sub> can be calculated using the related Eq. (2):

$$K_{IC} = \sqrt{\frac{E_{Cr}}{1 - \nu_{Cr}}} \cdot G_c \qquad (2)$$

By applying this formula along with the critical strain values

obtained in section 3.3, we can estimate the evolution of the stress intensity factor as a function of temperature. Fig. 16 highlights an exponential increase in fracture toughness K<sub>IC</sub> with temperature, rising from 7 MPa m<sup>1/2</sup> at ambient temperature to 46 ± 2 MPa m<sup>1/2</sup> at 350 °C, and reaching 66 ± 2 MPa·m<sup>1/2</sup> at 410 °C. This trend, consistent with literature data [30], confirms the reliability of the results. It also reflects an improved resistance to crack propagation and a significant increase in the coating's ductility with rising temperature.

## 5. Conclusions and perspectives

This study has provided a detailed investigation of the mechanical behaviour of Cr-coated M5<sub>Framatome</sub> cladding at elevated temperatures, focusing on crack initiation and coating performance. The main results are as follows:

* A system for monitoring cracking using acoustic emissions was developed and successfully implemented in-situ during tensile tests at temperatures up to 540 °C.

* A critical strain threshold was established for the Cr coating, increasing exponentially from 0.4 % at room temperature to 4 % at 410 °C. Cracking was not detected at 440 °C and 540 °C.

* The saturation crack density of the Cr coating decreased linearly with temperature, from 8.9 mm<sup>-1</sup> at room temperature to 0.4 mm<sup>-1</sup> at 410 °C.

* Calculated fracture toughness – using “Hutchinson model” – increased exponentially with temperature, from ~7 MPa m<sup>1/2</sup> at ambient temperature to ~66 MPa m<sup>1/2</sup> at 410 °C.

* Above 440 °C, the Cr coating becomes more ductile, and crack formation was related to the Zr-based substrate plastic deformation.

* SEM post-test observations showed that cracking did not propagate beyond the coating, with no sign of coating delamination, confirming excellent coating-substrate interface resistance.

Future research will focus on exploring the internal stress states within the coating using X-ray diffraction (XRD) and focused ion beam digital image correlation (FIB-DIC). Moreover, micromechanical testing (such as micropillar compression and microcantilever bending) will be conducted at elevated temperatures to further understand the evolution of mechanical properties and toughness. Additionally, to link microscale mechanics and macroscopic observations heat treatments should be studied to investigate their effects on the microstructure, internal stresses, and mechanical properties of the chromium coating. Finally, such approach should be further extended to PIEs following in-reactor neutron irradiation.

<figure><img src="image_19.png" /><figcaption>Fig. 16. Evolution of chromium fracture toughness with temperature.</figcaption></figure>
Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the author used ChatGPT in order to enhance the clarity of the text. After using this tool/service, the author reviewed and edited the content as needed and takes full responsibility for the content of the publication.

CRediT authorship contribution statement

Yanis Taïbi: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Ali Charbal: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization. Jean-Christophe Brachet: Writing – review & editing, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization. Elodie Rouesne: Methodology, Investigation, Data curation. Sergio Sao-Joao: Writing – review & editing, Investigation, Formal analysis. Szilvia Kalacska: Writing – review & editing,

Investigation, Formal analysis. Morgan Rusinowicz: Writing – review & editing, Formal analysis, Data curation, Conceptualization. Guillaume Kermouche: Writing – review & editing, Project administration, Methodology, Investigation, Formal analysis, 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 paper.

Acknowledgements

Numerous people took part in this study at CEA and the authors want to thank them all. Special thanks to: E. Pons, A. Sarrazin and C. Oliveira Rodrigues for providing training and support in the use of the tensile testing machine and MCE. The presented work was supported by the CEA-EDF-FRAMATOME “Innovation COMBustible” project. Special thanks to E. Pouillier & A. Ambard (EDF), T. Garnier and K. Buchanan (FRAMATOME) for their fruitful feedbacks and corrections.

Appendix A

To analyze and determine the critical strain for crack initiation, we propose fitting the experimental data with a mathematical function to ensure the analysis is both reproducible and more reliable. Initially, the data will be matched using a sigmoidal function (Eq. (3)):

$$Ec = \frac{L}{1 + e^{-k(\epsilon - \epsilon_0)}} \qquad (3)$$

where L is the amplitude of the sigmoidal part, k the slope of the sigmoidal part, and $\epsilon_0$ the inflection point. Although the trend is well captured, the sigmoid asymptotically approaches a finite value, unlike the experimental data, which shows a slight increase beyond saturation (see Fig. 17). This increase can be attributed to acoustic emissions generated by the substrate and the testing machine (previously shown to be negligible compared to coating cracking but still present). To address this, an adjustment of the sigmoidal function by multiplying it with a linear function (ax+b) is proposed (Eq. (4)):

$$Ec = \frac{L}{1 + e^{-k(\epsilon - \epsilon_0)}} \cdot (a \cdot \epsilon + b) \qquad (4)$$

This adjustment provides a better fit to the data, allowing for a more accurate determination of the critical strain.

<figure><img src="image_20.png" /><figcaption>Fig. 17. Fitting of experimental AE data at: (a) 180 °C, (b) 390 °C.</figcaption></figure>

To estimate the critical strain $\epsilon_c$, the intersection between the curve and its tangent at the inflection point is calculated, where the slope is maximal. This intersection occurs with the X-axis, and it represents the critical strain. The Eq. (5) is used for determining $\epsilon_c$:

$$\epsilon_c = \epsilon_1 - \frac{Ec(\epsilon_1)}{Ec'(\epsilon_1)} \qquad (5)$$
where $ε_1$ is the point where the derivative $Ec'(ε)$ is maximized: the point where the tangent to the curve at the inflection point has the steepest slope (see Fig. 18). The derivative $Ec'(ε)$ is obtained by differentiating the product of the sigmoidal and linear terms. Once $ε_1$ is found, the critical strain $ε_c$ can be computed using the formula above, representing the intersection with the X-axis.

<figure><img src="image_21.png" /><figcaption>Fig. 18. Diagram for assessing critical deformation.</figcaption></figure>

## Appendix B

The crack density is determined by image processing. The FIJI software [26] is used combined with the Trainable Weka Segmentation plugin [27]. The later provides machine-learning tools to automatically detect cracks. Two classes are generated: the background, representing the uncracked coating surface, and a second class corresponding to the detected cracks. A model is trained on these classes and then applied to surface maps obtained after tensile tests. These maps are taken from the central part of the coated sheath, which measures 29 × 2 mm². This model produces a black-and-white image (Fig. 19(b)), where: black represents the uncracked coating and white corresponds to the detected cracks. The cracks have a width ranging from 1 to 3 pixels, which may depend on the crack opening and/or the interruption strain. To ensure an accurate measurement of the crack density and to avoid any influence of crack width on the results, the image is processed in MATLAB to refine all cracks to a single-pixel width. The density of white pixels in the processed image then directly represents the linear crack density. Another important aspect is that the surface maps were captured after the tensile tests, with applied strain levels ranging from 13 % to 20 %. To account for this deformation and adjust the measured crack density accordingly, a correction factor is applied using the Eq. (6):

$$ \rho_{corr} = \rho(1 + \varepsilon) \qquad (6) $$

- $ρ_{corr}$ is the corrected crack density,

- $ρ$ is the measured density from the processed image,

- $ε$ is the applied strain level when the test was interrupted.

The different steps of this process are illustrated in Fig. 19.

<figure><img src="image_22.png" /><figcaption>Fig. 19. Crack density measurement: (a) raw surface mapping, (b) crack determination by FIJI- Weka plugin, (c) linear crack obtained by Matlab.</figcaption></figure>

## Data availability

Data will be made available on request.

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