Swelling and He-Embrittlement of Austenitic Stainless Steels and Ni-Alloys in Nuclear Reactors
Round 1
Reviewer 1 Report
This manuscript presents an analysis of experimental data and develops a rate theory model to describe swelling and He embrittlement in reactor irradiated austenitic alloys. This topic is of importance for water-cooled nuclear reactors, and is also of potential importance for several proposed next generation (Gen-IV) reactor concepts. Several changes are recommended, as described in the following:
1. The introduction section should include some additional references that help to convey the underlying mechanisms responsible for the temperature-dependent He cavity evolution, including the well-cited review article by Trinkaus and Singh [R1]. In the introduction section, the current understanding of He-vacancy complex stability and migration should be more clearly conveyed, citing ref. [R1] and other relevant articles such as [R2, R3] that discuss the dependence of effective He migration energy on vacancy supersaturation level (two limiting conditions are observed for thermal equilibrium vs. high vacancy supersaturation conditions, with effective migration energies in Ni ranging from ~ 2.2 eV to ~~0.85 eV, respectively. He-vacancy clusters have been reported to migrate as V2He clusters, not as HeV [R3].
2. In section 1.1 (damage and gas atom production), the nonlinear accumulation of dpa and He associated with the thermal neutron two-step reaction involving 58Ni and 59Ni should be described. In several subsequent locations in the manuscript, the He/dpa for Ni-containing steels at a specific dose (e.g., 100 dpa) is mentioned without any mention of the dose dependence. The calculated time dependence of He and dpa accumulation for a thermalized reactor spectrum should be shown and/or summarized on pp. 5-6.
3. In the last sentence on p. 6, a few other elements with significant thermal neutron cross sections for He generation should be mentioned, e.g., Be and Li.
4. The section on freely migrating defects (pp. 7-11) needs significant revision. As noted by Trinkaus et al. [R4], the analysis used to extract “freely migrating defect” (FMD) fractions from experimental radiation enhanced diffusion and radiation induced solute segregation experiments does not adequately account for displacement cascade-induced sinks and therefore is a lower bound limit of the actual FMD fraction. The actual FMD fraction is considered to be ~0.05 to 0.10 relative to the NRT dpa value for energetic cascade conditions. Furthermore, the empirical fits to molecular dynamics (MD) and FMD experiments cannot be extrapolated to primary knock on atom (PKA) energies higher than the empirical database: the x-axis for Fig. 5 should be terminated below 0.1 MeV. It should also be noted that the Gao et al formula for MD overall defect production is only valid for energies below the subcascade breakup energy (~10-20 keV); this effect is noted in the ARC-DPA estimate of defect production efficiency Ref. 32).
5. Figure 7 should include some stainless steel experimental data for EBR-II and mixed spectrum reactors (e.g., HFIR, HFR) so that the reader can determine where or not the model predictions with respect to temperature dependence and relatively weak He/dpa dependence at intermediate temperatures is observed. There are numerous published reports on the temperature dependence of void swelling of 316SS up to high doses (~100 dpa) in fast and mixed spectrum reactors.
6. The theory section (2.2.1) is rather simplistic, which may introduce significant inaccuracies in the predicted behavior. For example, the cavity sink strength expression (eq. 4) on p. 15 is a simplified version of the general expression found in numerous review articles. In section 2.2.1.2 on p. 16, it is now recognized that small cavities are not neutral sinks (e.g., refs. R5, R6). Similarly, the effect of internal gas pressure on point defect absorption at cavities has been reported to be relatively weak for fission reactor-relevant conditions [e.g., R5]; the text in this section and Fig.11 should be revised. The full parameters used for the model presented in this manuscript should be provided in a table. For example, in section 2.2.2 it is stated that the bubble volume is assumed to evolve at a rate proportional to dpa, but the proportionality constant is not provided. What dislocation bias value was assumed?
7. The heading for Fig. 13 on p.21 needs correction for the typo (“Agorithm” should be “Algorithm”). The x-axis units for Fig. 14 are FPY whereas the figure caption states that this plot is as a function of dose (DPA); this needs to be revised to be consistent.
8. The predictive accuracy of the model results presented in Section 2.2.2 (pp. 22-24, Figs. 14, 15) is uncertain. Some experimental results should be included in these plots so the reader can assess the accuracy of the model. The sharp transition at 350C in Fig. 15 seems to be nonphysical and needs additional explanation/discussion. Overall, a major shortcoming of the model is the absence of applied stress. My understanding is that the failures in the CANDU Inconel components were associated with significant loading along with the generation of He and displacement damage. Most He embrittlement models evaluate stress-assisted migration of He-vacancy complexes to grain boundaries as a crucial feature in the embrittlement. Stress effects are well known to be of vital importance for inducing high temperature He embrittlement of grain boundaries, and are assumed to play a significant role at low temperatures as well.
9. In the first line of the discussion (p. 24) some additional citations besides those of the authors [13, 24, 25] should be included.
10. Much of the conclusions section (pp. 28-29) should be rewritten. The first two paragraphs of the conclusions are not actually conclusions and would be better placed in the introduction and discussion sections, respectively. Also, the statement in the 2nd paragraph that grain boundaries are normally the strongest part of any material is incorrect. Grain boundaries are a strong obstacle to dislocation motion, but there are numerous materials where failure occurs intergranularly even in the absence of irradiation.
References
[R1] Helium accumulation in metals during irradiation–Where do we stand?, J. Nucl. Mater. 323 (2003) 229-242.
[R2] On the diffusion mechanisms of helium in nickel, J. Nucl. Mater. 158 (1988) 25-29.
[R3] First-principles study of helium, carbon, and nitrogen in austenite, dilute austenitic iron alloys, and nickel, Phys. Rev. B 88 (2013) 024115
[R4] On the experimental-determination of the migrating defect fraction under cascade damage conditions, J. Nucl. Mater. 210 (1994) 244-253.
[R5] Molecular statics calculations of the biases and point defect capture volumes of small cavities, J. Nucl. Mater. 499 (2018) 480-489.
[R6] Formulation of voids and bubbles as biased sinks to crystalline point defects, Scripta Mater. 197 (2021) 113806
Author Response
Please see attachment
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this paper, authors described a rate theory model to calculate the GB coverage, swelling and He-embrittlement of austenitic stainless steels and Ni-alloys in reactors. From my viewpoints, this paper includes enough related information and knowledge, resulting in a very long article. For a reviewing paper, it is perfect. For a normal paper, focusing on the main topic would be welcome. I have several questions, which may be helpful to further improve this paper.
(1) authors considered the effects of helium on properties of cavities or bubbles by considering the contribution from free defects, for example, interstitials and single vacancies. After the absorption of helium atoms by vacancies or vacancy-clusters, authors assume the immobility of these helium-defect clusters. However, in fact, previous MD studies have reported that these clusters could also diffuse with energy barrier around 0.8-1.2 eV in Fe-based alloys. In previous papers published by authors, only He interstitial clusters were considered. In this paper, I suggest authors also considered the He-V cluster contributions to GB coverage, swelling and He-embrittlement.
(2) When authors considered sink strength of different defects, I notice only the 1st approximation is made for simple defect sink. However, in real experiments, voids, dislocation loops or precipitates would also be formed. It would be better to include the contributions from these defects.
(3) As stated by authors, rate theory is mean-field approach. A discussion about the effect of mean-field on these results is welcome.
Author Response
Please see attachment
Author Response File: Author Response.pdf
Reviewer 3 Report
A review is like a cover of a famous song. If you cannot do it better than the original one – do not even try. That is why I am not going to interfere with the original text. The manuscript presented by M. Griffiths, S. Xu and J. Ramos-Nervi was prepared according to all the guidelines for writing articles. The problem described is worth studying, is actual, the obtained results about the accumulation of cavities on grain boundaries are interesting for a reader and they are presented in a clear way (maybe paper is slightly too long, but it is only my opinion, not an objection). As a reviewer I can only recommend publishing the manuscript as soon as it is possible.
Author Response
Reviewer #3
A review is like a cover of a famous song. If you cannot do it better than the original one – do not even try. That is why I am not going to interfere with the original text. The manuscript presented by M. Griffiths, S. Xu and J. Ramos-Nervi was prepared according to all the guidelines for writing articles. The problem described is worth studying, is actual, the obtained results about the accumulation of cavities on grain boundaries are interesting for a reader and they are presented in a clear way (maybe paper is slightly too long, but it is only my opinion, not an objection). As a reviewer I can only recommend publishing the manuscript as soon as it is possible.
This is a very kind and generous review comment. We are very grateful to the reviewer, someone who clearly understands that any paper can be adjusted to suit different sensibilities but so long as it is technically sound enough (albeit with stated assumptions and approximations), it can be left untouched. Thank you!
Reviewer 4 Report
Very god work.
Author Response
Reviewer #4
Very good work.
Thank you.
