Comparative Theoretical Analysis of Halden Reactor Creep Tests on M5 Cladding Material

Abstract

This study provides a comparative analysis of two creep tests performed on M5 cladding material at the Halden reactor under different stress conditions in the IFA-617 and IFA-663 test rigs. The objective was to evaluate the creep behavior of the M5 cladding material, a crucial component in nuclear reactors, under both compressive and tensile stress environments. The data generated from these experiments were analyzed to assess the diameter changes in the cladding over time, considering factors such as stress, temperature, and neutron flux. The results revealed a significant difference in creep rates between the two tests, with IFA-663 showing a considerably higher rate. This disparity is attributed to the combined effects of creep and corrosion/crud deposition phenomena, which were more pronounced under tensile stress conditions. A model was developed to account for these factors, providing a better understanding of the M5 cladding behavior in different operational environments. These findings contribute to improving the predictive capabilities of the TRANSURANUS code for simulating M5 cladding creep, highlighting the need for further post-irradiation examinations to refine the understanding of corrosion and crud deposition effects.

1. Introduction

The cladding material in nuclear reactors plays a critical role in ensuring the structural integrity of fuel rods, which enclose the nuclear fuel during both regular operation and transient conditions. One of the most significant challenges faced by cladding materials is creep, a time-dependent deformation process accelerated by high temperature, stress, and fast neutron flux. In particular, the M5 alloy, a zirconium-based material, has emerged as a promising candidate for cladding in pressurized water reactors (PWRs) due to its superior corrosion resistance and reduced hydrogen uptake compared to traditional Zircaloy-4 [1,2]. Nevertheless, understanding its long-term creep behavior under both tensile and compressive stress conditions, as well as the impact of neutron irradiation, remain crucial for optimizing reactor safety and performance [3].

Recent studies have focused on the complex interaction between creep, irradiation, and corrosion phenomena, which can significantly alter the mechanical properties of cladding materials over time. For example, Adamson et al. [4] demonstrated that high neutron flux can accelerate the creep process, particularly in the presence of tensile stress, leading to greater cladding diameter changes. Similarly, Wang et al. [5] highlighted the exacerbating effects of localized corrosion, crud deposition, and surface oxidation, particularly under conditions of high surface temperatures, as experienced in nuclear reactors; in particular, Ref. [5] showed that crud deposition can induce a three-stage variation in cladding surface temperature, thus altering the corrosion mechanism and leading to a 9.5-fold increase in oxide layer thickness at the end of the fuel life. These findings underscore the necessity of considering both mechanical and chemical stressors in the analysis of in-reactor creep behavior.

Despite the extensive research on cladding materials, there remain diverging opinions regarding the primary contributors to cladding failure under extreme operating conditions. While some researchers argue that creep-induced failure is primarily a mechanical issue [6], others emphasize the role of corrosion, suggesting that surface degradation due to crud deposition can significantly weaken the cladding, contributing to premature failure [7]. This discrepancy highlights the need for a more comprehensive approach to studying the combined effects of mechanical stress, neutron flux, and chemical factors like corrosion and crud formation, especially in the analysis of the test results and in view of new dedicated experimental activities.

The present study aims to address these gaps by providing a detailed comparative analysis of the creep behavior of M5 cladding material under two distinct operational conditions: compressive stress in the IFA-617 test and tensile stress in the IFA-663 test, both conducted at the Halden reactor. By integrating experimental data with an analytical model, this work seeks to quantify the relative contributions of creep and corrosion in both environments. The findings of this study contribute to improving the predictive capabilities of codes such as TRANSURANUS, which are essential for simulating the long-term behavior of cladding materials in nuclear reactors. Additionally, this study provides insights that could inform future reactor designs and operational strategies aimed at mitigating cladding failure.

The present paper specifically addresses two M5 cladding creep tests performed at the Halden reactor in the IFA-617 and IFA-663 test rigs, as reported in Halden reports HWR-658 [8] and HWR-755 [9]. These tests were conducted under different cladding stress conditions: the M5 cladding operated under compressive stress in the IFA-617 test, while, in IFA-663, the cladding was subjected to tensile stress. The primary objective of this analysis is to evaluate the creep behavior of the M5 cladding material in these contrasting environments, drawing conclusions from the test results. Moreover, this work represents a preliminary task in assessing the capability of the TRANSURANUS code to simulate the creep behavior of M5 cladding.

In the following sections, a detailed discussion of the experimental conditions, results, and their implications will be presented, followed by an analysis of the effects of corrosion and crud deposition on the M5 cladding’s creep behavior. Finally, the results will be used to propose a refined model that captures the observed creep behavior under different operational stresses.

2. The TRANSURANUS Code

The TRANSURANUS code [10,11,12,13] is a widely used computational tool developed for the analysis of fuel behavior in nuclear reactors. It was initially designed to predict the thermal and mechanical behavior of fuel rods in light water reactors (LWRs) under both normal operation and transient conditions. Over the years, its scope has expanded to encompass various types of fuel and cladding materials, as well as different reactor designs, including fast reactors and experimental setups like those at the Halden reactor. The code provides detailed simulations of fuel rod performance by accounting for a wide range of physical processes, including fuel swelling, fission gas release, creep, and mechanical interactions between the fuel and cladding.

One of the key strengths of TRANSURANUS lies in its ability to simulate complex time-dependent phenomena, such as the in-reactor creep behavior of cladding materials under varying stress, temperature, and irradiation conditions. This makes it particularly useful for assessing the long-term structural integrity of cladding materials like M5, which are subjected to high neutron flux and mechanical stress during reactor operation. The code is frequently updated to incorporate the latest experimental data and to improve its predictive capabilities, which are essential for ensuring the safety and efficiency of nuclear reactors. In the present study, TRANSURANUS is employed to simulate the creep behavior of M5 cladding material under the specific operational conditions of the IFA-617 test, enabling a detailed evaluation of the combined effects of stress, temperature, and neutron flux on the cladding’s performance. For the present work, the v1m1j23 version of the code was used.

3. Experimental Results and Discussion

The best fit of the results shown in Figure 18 of the HWR-658 report, which depicts the details of the IFA-617 test, is presented in the plot of Figure 1. This shows that, after an initial phase of rapid diameter decrease (mentioned in both reports as ‘primary creep’), a linear decline follows beyond a time of 500 h (reported as ‘secondary creep’). In the first 500 h period, a ΔD of ca. −2.8 µm was detected, whereas, in the following phase, a linear trend was observed with a diameter change of −2.8 µm in a time-period of 2800 h.

The models available in the previous versions of TRANSURANUS for M5 were not able to satisfactorily reproduce the experimental data described below, and this triggered interest in a more thorough examination of the experimental data and conditions.

Regarding the IFA-663 test data [9], Halden report HWR-755 mentions that some problems arose during the early phase of the experiment; hence, what can be considered reliable is the rate of diameter increase—i.e., the slope of the solid line in Figure 9 of the HWR-755 report—in the time interval between 3800 and 5600 full power hours. The M5 diameter change rate between these two points in time, as inferred from the data presented in that report, is 14 µm/1800 h. As an additional note, the diameter increase rate as depicted in Figure 9 of the same report is similar for the three alloys studied, i.e., Zirlo, M5, and VVER (E110). However, the absolute ΔD values for M5 and Zirlo are quite larger than for the VVER cladding (which was unfueled). The HWR-755 report does not address the reason for this behavior, which nevertheless does not interfere with the present analysis as this builds on the rate of ΔD vs. time (and not on ΔD absolute values).

The experimental diameter change rate was therefore −1 µm/1000 h in IFA-617 and 7.7 µm/1000 h in IFA-663.

Considering the experimental conditions in which the tests were conducted (see

Table 1. Comparison of the experimental conditions for tests IFA-617 and IFA-663 concerning the M5 cladding rod [8,9].

	IFA-617	IFA-663
Φ (n/cm2·s)	2.9 × 1013	2.8 × 1013
T (°C)	375	359
σ (MPa)	−75	64

below)—and in particular considering that IFA-617 was run at somewhat more demanding conditions than IFA-663—a slight correction is needed in order to make the results of the two tests directly comparable.

The Franklin model (which strictly applies to Zr-4) has been used here for the purpose of completing the small correction mentioned above, which arises from the slight differences in fast neutron flux, average cladding temperature, and cladding stress in the two experiments. The Franklin model is as follows (Equation (1)):

$${\displaystyle \frac{∆\mathrm{D}}{\mathrm{D}}}=\mathrm{A}·{\mathrm{t}}^{\mathrm{m}}·{\mathsf{\Phi }}^{\mathrm{p}}·{\mathsf{\sigma }}_{\mathsf{\theta }}^{\mathrm{n}}·{\mathrm{e}}^{\left(-{\displaystyle \frac{\mathrm{Q}}{\mathrm{R}\mathrm{T}}}\right)}$$

(1)

where A = 1.11 × 10⁻¹³, m = 0.682, p = 0.550, n = 0.579, and Q/R = 1173.

In the equation above, D is the initial diameter, ∆D is the change in rod diameter (absolute value) at time t (hours), φ is the neutron flux (n/cm²⋅s), σ_θ is the hoop stress (MPa), T is the temperature (K), and Q is the activation energy (cal/mole⋅K). The time factor is irrelevant in this particular context since the aim here is to assess how the test conditions (i.e., neutron flux, stress, and temperature) affect the diameter change rate. Applying Equation (1), one obtains the factors of 1.019, 1.096, and 1.047 for, respectively, the differences in neutron flux, hoop stress, and temperature between IFA-617 and IFA-663—the product of these factors being 1.17. This is the (rather small) scaling factor for the creep rates expected in the two tests.

One should note that the absolute ΔD rate as measured in the two IFA tests is, in the linear part, almost eight times larger in IFA-663 as compared with IFA-617. The only possible explanation found for this very large difference is that there can be phenomena in the rig that affect the diameter in opposite ways in the two tests. This may occur if corrosion and/or crud deposition on cladding occur during the rod in-pile operation. In fact, corrosion and crud (C&C in the following) in IFA-617 would cause a cladding diameter increase, which is opposite to creep, since this rig operates the rod at under-pressure conditions, whereas, in IFA-663, creep and C&C will contribute to diameter change in the same direction; i.e., they will both cause a diameter increase.

Regarding C&C during the test, the HWR-658 report states that “at each traverse, the gauges were effectively re-calibrated due to the presence of machined steps of known magnitude (approximately 50 µm) on the end and mid-plugs. These calibration steps compensate for clad diameter changes arising from the growth of surface oxide layers”. However, one should note that, because corrosion would not affect the calibration step size, which remains at 50 µm with or without corrosion, the step itself would not provide any correction for corrosion (or crud). Further, any C&C occurring in the unfueled zone of the rod (where the calibration steps are located), if existent at all, would be far lower than the C&C occurring in the fueled region due to the higher temperature (+40–50 °C) and the presence of surface boiling.

Unfortunately, the Halden reports [8,9] do not provide any information about C&C aspects and their possible influence on ΔD evolution vs. time. In order to address this point and reach practical conclusions, the following two equations with two unknowns (2) have been considered for the two tests:

$$\begin{gathered} \left\{\begin{array}{c}-1.17·{\dot{D}}_{creep}+K·{\dot{D}}_{C\&C}=-1\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \left[IFA617\right] \\ {\dot{D}}_{creep}+{\dot{D}}_{C\&C}=7.7\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \left[IFA663\right]\end{array}\right. \end{gathered}$$

(2)

In the above, ${\dot{D}}_{creep}$ and −1.17·${\dot{D}}_{creep}$ are the M5 creep rates in IFA-663 and IFA 617, respectively, while ${\dot{D}}_{C\&C}$ is the corrosion + crud deposition rate during the test. The term K is the ratio of C&C deposition rate between the two experiments (i.e., IFA-617/IFA-663).

By assuming K = 1, i.e., by assuming the same C&C deposition rate in the two tests, Equation (2) results in

$${\dot{D}}_{\begin{array}{c}creep\\ IFA-617\end{array}}=4.73{\displaystyle \frac{\mu m}{1000hr}},{\dot{D}}_{\begin{array}{c}creep\\ IFA-663\end{array}}=4.05{\displaystyle \frac{\mu m}{1000hr}},{\dot{D}}_{C\&C}=3.73{\displaystyle \frac{\mu m}{1000hr}}$$

(3)

As noted earlier, the difference in secondary creep arises from the difference between the operating conditions in the two rigs (resulting in the factor 1.17 mentioned earlier). Figure 2 below shows the resulting values of the diameter changes in the IFA-617 test, split by the contribution of creep and C&C.

A similar split can also be obtained for IFA-663, provided that the drift of 57 µm reported at time 3000 h—i.e., at the time when stress was applied—is accounted for. This drift is clearly visible in Figure 9 of HWR-755 [9].

For an M5 cladding, the C&C rate of 3.7 µm/1000 h mentioned above may be considered as rather high if compared with the power plant data, which, for M5, show a corrosion normally below 10 µm/year (order of 1–1.5 µm/1000 h). However, one should bear in mind that the test conditions in the two rigs were more severe than in the power plants since the average cladding wall temperature was as high as 375 °C in IFA-617 and 359 °C in IFA-663. This corresponds to cladding outer surface temperatures of about 395 °C and 380 °C, respectively, which are very high temperatures compared with the operating temperature in power plants, where the cladding surface temperature is normally below 350 °C. Further, the very high cladding temperature created nucleate boiling conditions at the cladding surface in both rigs. Boiling may alter the local water chemistry and may cause accelerated corrosion (in fact, both HWRs report severe corrosion problems). Because of the very high temperature and because details of the water chemistry test condition are not reported, the extent of corrosion in the two tests may have been considerably larger as compared with the power reactor conditions.

The above aspects regarding cladding corrosion also apply to crud deposition, especially concerning the effects of high surface temperature and surface boiling conditions. Hence, a C&C of about 3.7 µm/1000 h may be on the high side as compared to power plants but not unrealistic for the conditions at which the two rigs were operated in the two mentioned experiments.

The above results are based on the assumption that the C&C deposition rate is the same in the two tests (i.e., K = 1 in Equation (2)). A sensitivity assessment was conducted by varying parameter K up to ±30%, i.e., from K = 0.7 to K = 1.3. The results show that such a variation results in a creep rate variation of about 10–15% (Figure 3), which implies that the creep rate is only moderately sensitive to the differences in C&C in the two tests. Because of the higher temperature in IFA-617, an increasing K in the range 1 < K < 1.3 would be more likely than a K lower than 1.

4. Effects of Corrosion and Crud Deposition on Cladding Temperature and Comparative Material Analysis

4.1. Effect of C&C and Resulting Temperature Increment

Because of C&C, one expects the cladding temperature to increase as the C&C progresses. In IFA-663, the time-period under stress is 2700 h (see Figure 9 in HWR-755). Considering that we found a C&C of 3.73 µm/1000 h (see Equation (3)), the expected C&C would amount to 3.73 × 2.700 = 10 µm. With a Zr C&C conductivity of 0.02 W/cm °C and a fuel LHR of 40 kW/m (indicative value for an 8% enriched fuel in the HBWR), this would result in a cladding temperature increment of 8 °C. A similar result applies to IFA-617 (see Figure 18 in HWR-658). One should note that, here, one assumes that crud and oxide have similar thermal conductivity, which requires further assessment when a complete model is developed.

The 8 °C temperature increment caused by corrosion and crud (C&C) deposition corresponds to the maximum value reached at the end of the creep period as the deposition progresses over time. To account for this gradual buildup, a simplified approach assumes an average increment of 4 °C over the 2700 h of the test. This approximation is based on the following rationale:

• Gradual Progression of C&C Deposition: the deposition and associated temperature effects develop progressively, starting from negligible levels at the beginning of the test. Using half the maximum increment reflects this time-dependent growth without overestimating the impact;
• Conservative and Realistic Simplification: By averaging the temperature increment, the model avoids overstating the effects while maintaining a reasonable approximation;
• Limited Impact on Results: Sensitivity analysis demonstrates that variations in C&C deposition rates have only a moderate influence on creep rates, making this simplification adequate for capturing overall trends;
• Established Methodology: Averaging temperature increments over time is a practical and commonly adopted approach in cladding studies when detailed time-dependent data are unavailable.

This approach strikes a balance between simplicity and accuracy, ensuring that the earlier results remain valid. A more detailed time-dependent correction would likely yield similar conclusions.

4.2. M5, Zirlo, and E-110 Rod Comparison in IFA-663 Test

Figure 9 in HWR-755 (IFA-663) shows a peculiarity of the M5 (and Zirlo) rod as compared with the VVER rod. That is, the M5 and Zirlo rods exhibit a significant ΔD at the start of pressurization, amounting to approximately 60 µm, whereas, for the VVER cladding, the ΔD at the same point in time is negligible. This is likely related to the fact that both the M5 and Zirlo test rods were fueled (with 8% enriched UO₂ fuel), whereas the VVER cladding tube was unfueled. In combination with other operational factors, this could have favored a large C&C during the early phase of the irradiation for the M5 and Zirlo rods. The VVER cladding, instead, did not experience any C&C because there was no heat generation in the test tube and hence the cladding temperature remained low—and surface boiling absent.

4.3. Comment on Data Reported from Technical Literature [14]

Ref. [8] states that the creep rate observed in IFA-617 was 2.3 times larger in Zr-4 as compared with M5, “in accordance with published data” from Mardon et al. [14]. However, the evidence shown in [14] does not support the above conclusion because of the following:

• Mardon et al. ii [14] refer to a ‘high fuel rod operation (>65 GWd/tU)’, while the rod tested by McGrath and Bennett [1] in HWR-658 was irradiated up to a burnup of 20 GWd/t;
• Very large M5 creep variations are reported in Figure 14 of Ref. [14] depending on the M5 sulfur content;
• Mardon et al. ii [14] clearly stress in their text that the annealing sequence has a deep impact on the mechanical performance of the material, while McGrath and Bennett [8] mention in their report just the ‘final anneal’ temperature of 580 °C, not providing any information about the annealing sequence;
• The cladding stress was up to a factor of ~2 larger in Zr-4 clad as compared with that of the M5 cladding;
• The test conditions, such temperature, fast neutron flux, and pre-test fast neutron dose, are not provided;
• Individual data points are not shown; hence, data scatter and repeatability cannot be determined;
• Zr-4 and M5 data derive from tests conducted at different points in time, possibly in different experimental setups.

5. Proposed M5 Creep Model

The above results have been used for comparing the creep rate obtained here for M5 with the one expected for Zr-4 run with the same conditions as M5 in IFA-617 and IFA-663. The expected creep for Zr-4 has been calculated with the Franklin correlation mentioned earlier, while the secondary creep rate values obtained in this work have been used for M5. The results are shown in Figure 4 and Figure 5. Based on the above arguments, an attempt at deriving an overall M5 creep model has been made by combining the Franklin model for the primary creep, which seems to also reproduce the primary creep phase in IFA-617 reasonably well, with the slope of the secondary creep obtained here, which appears to linearly evolve with time. The proposed model is as follows:

• At the start, the primary creep evolves in accordance with the Franklin equation.
• At some point, the secondary creep will start, evolving linearly with a slope provided by the following equation:

$${\displaystyle \frac{\mathrm{d}\mathrm{D}}{\mathrm{d}\mathsf{\tau }}}=4.48·{\left({\displaystyle \frac{\mathsf{\Phi }}{2.8\times {10}^{13}}}\right)}^{0.55}·{\left({\displaystyle \frac{\mathsf{\sigma }}{64}}\right)}^{0.579}·{\mathrm{e}}^{-{\displaystyle \frac{\mathrm{Q}}{\mathrm{R}}}·\left({\displaystyle \frac{1}{\mathrm{T}}}-{\displaystyle \frac{1}{632}}\right)}$$

where 4.48 is in µm/1000 h and provides the slope of the IFA-663 secondary creep (see Figure 4 with K = 1.3), which is a realistic value considering the temperature difference in IFA-663 and IFA-617. The values 2.8 × 10¹³, 64, and 632 are the fast neutron flux in n/cm²·s, the cladding hoop stress in MPa, and the cladding mean temperature in K in IFA-663; τ represents the time variable in this equation.

The creep will then start and proceed according to (a) as long as the creep rate (i.e., the time derivative of the Franklin equation) remains higher than the creep rate provided by Equation (4). Calculations show that this transition occurs at about 500 h. After that, the creep will proceed linearly with time, with a derivative provided by Equation (4).

The findings from this study align with recent research on creep behavior in zirconium-based cladding materials, particularly those investigating the role of stress and environmental factors such as corrosion and neutron flux. For instance, Adamson et al. [4] demonstrated that elevated neutron flux accelerates creep deformation in zirconium alloys, particularly under tensile stress. This is consistent with the higher creep rates observed in the IFA-663 test, where tensile stress played a significant role in enhancing deformation. Similarly, Wang et al. [5] highlighted the exacerbating effects of localized corrosion and crud deposition on cladding materials, suggesting that surface oxidation and corrosion contribute to weakening the structural integrity of fuel rods. Our study’s inclusion of corrosion and crud effects in the mathematical model corroborates their findings, emphasizing the necessity of accounting for these phenomena when evaluating long-term cladding performance.

However, while previous studies have generally focused on the primary effects of mechanical stress and neutron flux, the present study goes further by integrating the impact of corrosion and crud deposition into a comprehensive model. This model provides a more accurate prediction of M5 cladding behavior under complex operational conditions. The sensitivity analysis performed here offers a deeper understanding of the relative importance of these phenomena, suggesting that, while creep rates are moderately affected by corrosion, their primary driver remains the mechanical stress environment.

These results differ from some earlier studies, such as those by Jeong et al. [6], which placed a stronger emphasis on radiation damage as the principal factor governing cladding degradation. In contrast, our findings suggest that, while radiation effects are critical, corrosion and crud deposition play an equally significant role, particularly under extreme operational conditions like those simulated in IFA-617 and IFA-663.

6. The TRANSURANUS Simulations of the Tests: Preliminary Results

The M5 creep tests mentioned above were reproduced with the TRANSURANUS code in order to test its capability and accuracy to reproduce experimental results. The adopted input data were the following:

• a PWR-type reactor, with a thermal spectrum, oxide fuel, and an M5 cladding (PINCHA card);
• the rod was subdivided in 10 axial slices;
• small-strain approximation concerning the cladding mechanical treatment was applied (ITEOMEC = 1);
• fission gas release was not considered (i.e., FGDIFF = 0);
• the empirical model for LWRs was selected for the fuel densification model (IDENSI = 2);
• Modified FRAPCON-3 model relocation was applied (IRELOC = 8);
• the analysis included both thermal and mechanical analysis (ITEMTE = 0);
• the applied M5 corrosion model was the JRC’s by A. Kecek and Alii [15] (ICORRO = 39);

The applied creep model was the JRC’s by A. Kecek and Alii [14], modification 02, date 22 May 2020 (ModClad (7) = 21);

• the cladding failure criterion was based on both cladding instability and overstress criteria (ICLFAIL = 3);
• the assumed initial enrichment of the fuel was 9% and its assumed porosity 5.0%;
  Initial fuel gap is 225 μm.

The simulated hoop stress in the cladding over time was designed to replicate the experimental values according to Ref. [8] and is shown in Figure 6.

The TRANSURANUS simulation was performed after changing the ‘thinning increment’ from 2 to 0.1 μm in the routine ‘WeakeningOfClad’ as the original version provided some non-physical jumps in the diameter displacement. The simulation results, compared with the experimental data from the HWR-658 test and the described model, are shown in Figure 7.

The comparison in Figure 7 highlights notable differences between the experimental data, the developed creep model, and the predictions from TRANSURANUS. While the experimental results from the HWR-658 and HWR-755 tests [8,9] serve as important benchmarks, their reliability is compromised by uncertainties related to instrumentation issues and potential misrepresentation of oxide growth and crud deposition effects. Such limitations, as detailed by McGrath [8] and Horn [9], necessitate cautious interpretation of the experimental trends.

The developed model, which incorporates mechanisms such as secondary creep and the influence of surface oxidation, provides a more comprehensive framework for predicting cladding behavior. Its alignment with steady-state creep trends supports its validity under typical PWR operating conditions. Nonetheless, the slight overestimation of creep deformation in the early stages suggests that refinements may be needed for more accurate modeling of primary creep effects.

In contrast, the TRANSURANUS predictions underpredict creep deformation, particularly under conditions of elevated temperatures and high neutron flux. While the code offers conservative estimates that are suitable for bounding analyses, it falls short in capturing the nuanced interplay of the factors observed in M5 cladding behavior. Enhancing its creep modeling framework would improve its applicability for precise evaluations of advanced materials like M5.

Overall, the findings underscore the value of the developed model as a reliable tool for understanding M5 cladding creep behavior under in-pile conditions. They also point to the need for refined experimental methodologies and further development of simulation codes to address gaps in predictive capability.

7. Conclusions

This study evaluated the creep behavior of M5 cladding under in-reactor conditions by comparing experimental data from the HWR-658 and HWR-755 reports with two predictive approaches. While the experimental results provide valuable benchmarks, their reliability is limited by uncertainties related to instrumentation and environmental factors such as oxide growth and crud deposition. This underlines the need for caution when using these data as a sole reference.

The model developed in this work, based on Franklin’s primary creep formulation and expanded to include secondary creep and corrosion effects, demonstrates good agreement with steady-state trends under typical PWR conditions. Its performance suggests that it is a useful tool for interpreting cladding behavior in scenarios where experimental data may lack precision. However, some overestimation of deformation in the early phases highlights the need for further refinements to better account for primary creep transitions and other potential influences, such as anisotropy in material behavior.

TRANSURANUS, while providing a conservative and widely used approach, tends to underpredict creep deformation in the studied conditions. This is consistent with its current implementation, which does not fully capture complex phenomena such as stress anisotropy or detailed secondary creep mechanics. Future updates to the code could enhance its applicability for advanced materials like M5.

As a final remark, it would be highly beneficial if post-irradiation examinations (PIEs) were conducted on these rods. Non-destructive PIEs, including dimensional measurements and oxide/crud analysis, would provide a valuable complement to the in-pile data at a practically negligible cost compared to the fabrication and operation of rods and rigs. This is particularly relevant given the diameter gauge setup, which enables precise evaluation of cladding behavior under operational conditions.

An additional point of consideration includes the higher creep rates observed under tensile stress compared to compressive stress in the Halden experiments. This asymmetry, while not fully explained in the reports, may be influenced by creep and corrosion (C&C) effects, such as accelerated oxidation and hydrogen pickup under tensile loading. Incorporating stress-dependent terms to account for these effects could improve the predictive accuracy of the Romanello model and align it more closely with experimental data. Addressing this phenomenon through targeted experiments and PIEs would further enhance the understanding of M5’s performance.

In conclusion, this work demonstrates the value of integrating robust physics-based modeling approaches with experimental benchmarks to analyze M5 creep behavior. Continued refinement of both models and experimental methodologies, alongside targeted PIEs, will be essential to advancing the understanding and prediction of cladding performance under reactor conditions.