Round 1

Reviewer 1 Report

The author presents a reasonably sized review of the usage of crystal plasticity theory in modelling irradiation effects. The paper presents an unbiased and rather comprehensive overview of the literature and is therefore an appropriate review article worth publishing in Crystals.

However, there are a few points why I think the paper needs a revision before publication. Besides some deficiencies in the quality of the English language to be discussed below, there are a few minor issues and two more substantial points. I'll begin with in the more substantial points.

That this is a review article is neither obvious from the title nor by its classification as "Article" in the MDPI-format (upper left corner). I would advise clarifying the nature of this publication as a review article since review articles are specifically searched for by the key audience; i.e. those who seek a quick overview of the state of the art in the field. It may be rather a matter of editorial policy how to classify the article, but I think it is in the interest of the author to have a clear classification. At least the title should contain the word "review".

My only concern about the content of the paper is section 5. Conclusions.  This is too short to be of any help. This can't be just a list of bullet points listing only the most basic differences between the reviewed models. Notably, the content of the first bullet point is not related to the actual topic of the review, i.e., CP-methods in irradiation research. The other points, especially when read without having gone through the paper before (which is what often happens in practice) seem to suggest, that crystal plasticity is not yet a helpful tool in modelling irradiation effects.  The fact that there are areas where no consensus has been reached in CP-modelling is exactly where one would expect guidance from a review article in whether the review suggests any variant to be superior or, if not, if this actually matters. I'd really consider the conclusions a core part of a review paper, which (the review) should be more than a collection of topical citations. It is only for this point that I classified the paper to require a major revision.

Not necessarily a minor issue is that I would not accept citing literature in the status of "in preperation", as is done with reference [104]. Unless the status of that work has changed to something more definitive, this reference shoud not be included.

One minor issue is that the abbrevations "SSD" and "GND" have not been introduced in the text nor included in the list of abbreviations.

The English is usually well intelligible but the usage of definite, indefinite or no articles is flawed. Most commonly the author uses to many definite articles (the) where no article would be necessary. But occasionally the author also leaves out an article where it would be necessary or at least common. The paper would strongly benefit from a thorough revision in this regard.

Author Response

Reviewer 1.

The author presents a reasonably sized review of the usage of crystal plasticity theory in modelling irradiation effects. The paper presents an unbiased and rather comprehensive overview of the literature and is therefore an appropriate review article worth publishing in Crystals.

>> I thank the reviewer for the time and effort spent on reviewing the article and the positive feedback.

However, there are a few points why I think the paper needs a revision before publication. Besides some deficiencies in the quality of the English language to be discussed below, there are a few minor issues and two more substantial points. I'll begin with in the more substantial points.

That this is a review article is neither obvious from the title nor by its classification as "Article" in the MDPI-format (upper left corner). I would advise clarifying the nature of this publication as a review article since review articles are specifically searched for by the key audience; i.e. those who seek a quick overview of the state of the art in the field. It may be rather a matter of editorial policy how to classify the article, but I think it is in the interest of the author to have a clear classification. At least the title should contain the word "review".

>> I am sorry for this omission and I am grateful for this valuable observation. I have modified the title and changed the manuscript type.

My only concern about the content of the paper is section 5. Conclusions.  This is too short to be of any help. This can't be just a list of bullet points listing only the most basic differences between the reviewed models. Notably, the content of the first bullet point is not related to the actual topic of the review, i.e., CP-methods in irradiation research. The other points, especially when read without having gone through the paper before (which is what often happens in practice) seem to suggest, that crystal plasticity is not yet a helpful tool in modelling irradiation effects.  The fact that there are areas where no consensus has been reached in CP-modelling is exactly where one would expect guidance from a review article in whether the review suggests any variant to be superior or, if not, if this actually matters. I'd really consider the conclusions a core part of a review paper, which (the review) should be more than a collection of topical citations. It is only for this point that I classified the paper to require a major revision.

>> According to the suggestion of both reviewers, I have removed the first bullet point from the conclusions. I have rewritten the conclusions and I hope they look better now. There are 4 paragraphs. First shows the strengths of the CP theory in modelling the irradiation effects. Second highlights the points one should be careful with. Third shows that CP is an optimal tool for modelling nanoindentation of ion-implanted materials. Fourth highlights the points one should be careful with in the case of nanoindentation.

Not necessarily a minor issue is that I would not accept citing literature in the status of "in preparation", as is done with reference [104]. Unless the status of that work has changed to something more definitive, this reference should not be included.

>> The citation has been removed.

One minor issue is that the abbreviations "SSD" and "GND" have not been introduced in the text nor included in the list of abbreviations.

>> This issue was corrected.

The English is usually well intelligible but the usage of definite, indefinite or no articles is flawed. Most commonly the author uses to many definite articles (the) where no article would be necessary. But occasionally the author also leaves out an article where it would be necessary or at least common. The paper would strongly benefit from a thorough revision in this regard.

>> I thoroughly checked the paper in this regard in order to make sure that the usage of articles conforms to the rules of the English language.

I once again thank the reviewer for the effort and time spent on reviewing my paper. I especially thank for the valuable comments. I am convinced that the paper is of much better quality now.

Reviewer 2 Report

The paper is interesting, the author made a good job to collect the literature on radiation damage modelling using crystal plasticity theory. This paper is a literature review.

The introduction about the necessity of nuclear and fusion power plant is true, however it widely known and not necessary to include a scientific review paper. It would be enough to write some sentence about the materials of which can be modelled using crystal plasticity theory, and explain, why this method of the radiation embrittlement modelling is useful.

The radiation embrittlement is the combined effect of three different mechanism: change of the dislocation structure, precipitations and segregations (e.g. Phosphorus) at the grains boundary. This last one may cause brittle fracture and missing from the review.

It would be good to separate the discussion of the different material groups. The ferrite-martensitic low alloyed steels (RPV steels) are damaged with high energy (fast) neutrons (over 0,1 or 0,5 or 1 MeV), and all the three damage mechanisms are typical. In case of austenitic steel, the dislocation structure change is the main ageing mechanism. In case of aluminium the dislocation structure change caused by fast neutrons and transmutation caused by thermal neutrons are the main ageing mechanisms. Consequently, the applied models may be different for the different materials or describe only some part for the embrittlement.

The lines 419-420 in conclusion should not be there. The necessity of new nuclear plants is economic, and political question, not to be concluded in a review paper on radiation embrittlement modelling.

The conclusion should give some highlight where (at which materials) can be  used the crystal plasticity theory, how are good the models, or how to develop them?

The EU recently financed 2 large Framework research projects on radiation embrittlement modelling : PERFECT, PERFORM 60. Are they missing from the review, or they not used crystal plasticity?

The selection of the topic of the paper is important, the number of processed literature papers is impressive. I recommend to rewrite the paper in more structured form. 

Author Response

Reviewer 2.

The paper is interesting, the author made a good job to collect the literature on radiation damage modelling using crystal plasticity theory. This paper is a literature review.

>> I thank the reviewer for the time and effort spent on reviewing the article and the positive feedback.

The introduction about the necessity of nuclear and fusion power plant is true, however it widely known and not necessary to include a scientific review paper. It would be enough to write some sentence about the materials of which can be modelled using crystal plasticity theory, and explain, why this method of the radiation embrittlement modelling is useful.

>> Thank you for this remark. I deleted the bullet points from this first part in order to make it look more compact. Still, I think that one paragraph highlighting the broader context is not too much for this review. Especially when we think that it can be useful to a person who has some background in CP but had nothing to do with irradiated materials nor nuclear power engineering in the past. The rest of the introduction is directly related to nuclear materials. Explanation why the CP theory is useful in the context of irradiation was added in the beginning of section 3.:

The CP theory is particularly useful in the context of modelling the effect of irradiation. First, it enables to reproduce experimentally observed irradiation hardening and post-yield softening by realistically accounting for dislocation-defect interactions \cite{Krishna2010}. Second, using CP one can directly compute stress distributions arising due to grain size, crystallographic orientation and other microstructural effects. These distributions can be then used to provide data for probabilistic assessment of brittle fracture \cite{Vincent2010,Singh2019}. Third, one can study the microcrack nucleation at intersections of grain boundaries and dislocation channels \cite{Evrard2010}. Fourth, it is possible to investigate in detail the effect of interactions on void growth and coalescence \cite{Ling2017}.

The radiation embrittlement is the combined effect of three different mechanism: change of the dislocation structure, precipitations and segregations (e.g. Phosphorus) at the grains boundary. This last one may cause brittle fracture and missing from the review.

>> Indeed, I did not mention radiation-induced grain boundary segregation in the originally submitted paper. I agree that this is an important phenomenon and I added a sentence:

Yet another important phenomenon is irradiation-induced grain boundary segregation \cite{Faulkner1997} which can lead to brittle fracture.

However, I did not found papers were this effect was included in the crystal plasticity framework.

It would be good to separate the discussion of the different material groups. The ferrite-martensitic low alloyed steels (RPV steels) are damaged with high energy (fast) neutrons (over 0,1 or 0,5 or 1 MeV), and all the three damage mechanisms are typical. In case of austenitic steel, the dislocation structure change is the main ageing mechanism. In case of aluminium the dislocation structure change caused by fast neutrons and transmutation caused by thermal neutrons are the main ageing mechanisms. Consequently, the applied models may be different for the different materials or describe only some part for the embrittlement.

>> Thank you for that remark. In fact, I was considering to divide the literature according to materials but I did not do it in the originally submitted paper as some authors translate their model from one material to the other and separation is difficult. I have now restructured section 3 and it contains 4 sections: materials for fuel cladding, model FCC materials, materials for reactor internals and materials for RPV. I agree that this structure makes much more sense. The review will be also more useful as the person interested in a particular material will be able to focus only on the selected section.

The lines 419-420 in conclusion should not be there. The necessity of new nuclear plants is economic, and political question, not to be concluded in a review paper on radiation embrittlement modelling.

>> According to the suggestion of both reviewers, I have removed the first bullet point from the conclusions

The conclusion should give some highlight where (at which materials) can be  used the crystal plasticity theory, how are good the models, or how to develop them?

>> I have rewritten the conclusions and I hope they look better now. There are 4 paragraphs. First shows the strengths of the CP theory in modelling the irradiation effects. Second highlights the points one should be careful with. Third shows that CP is an optimal tool for modelling nanoindentation of ion-implanted materials. Fourth highlights the the points one should be careful with in the case of nanoindentation.

The EU recently financed 2 large Framework research projects on radiation embrittlement modelling : PERFECT, PERFORM 60. Are they missing from the review, or they not used crystal plasticity?

>> If the question is about mentioning projects explicitly, I did not do it as this is a review of research papers rather than projects. Mentioning EU projects would oblige me to mention also analogous projects funded in US and possibly other countries. If the question is about papers published as a result of those projects, I have checked the list of papers provided in the reports of the PERFECT and PERFORM-60 projects. I have found several papers related to crystal plasticity:

• Queyreau, Monnet, Devincre, Slip systems interactions in a-iron determined by dislocation dynamics simulations, IJP, 2009,
• Monnet, Domain, Queyreau, Naamane, Devincre, Atomic and dislocation dynamics simulations of plastic deformation in reactor pressure vessel steel, JNM, 2009,
• Evrard, Sauzay, Modelling of the effect of dislocation channel on intergranular microcrack nucleation in pre-irradiated austenitic stainless steels during low strain rate tensile loading, JNM, 2010
• Vincent, Libert, Marini, Rey, Towards a modelling of RPV steel brittle fracture using crystal plasticity computations on polycrystalline aggregates, JNM, 2010
• Monnet, Vincent, Loi de comportement en plasticite cristalline pour acier a basse temperature, Mecanique et Industries, 2011
• Monnet, Vincent, Devincre, Dislocation-dynamics based crystal plasticity law for the low- and

high-temperature deformation regimes of bcc crystal, Acta Mat., 2013.

The title of my paper is: Modelling irradiation effects in metallic materials using the crystal plasticity theory – a review. Papers [1] and [2] are very interesting studies reporting establishment of latent hardening coefficients in BCC iron and steel using DDD simulations. However, they don’t contain any CP simulations nor irradiation effects and that’s why I don’t think they suit the review. The paper [3] was indeed missing from the review (eventhough it does not contain any constitutive law for irradiation defects) and is included in the revised version:

In the case of PWR reactor internals made of austenitic stainless steel, the intergranular stress corrosion cracking (IGSCC) and irradiation assisted stress corrosion cracking (IASCC) are of major importance. Therefore, in \cite{Evrard2010} a single dislocation channel (DC) interfacing a grain boundary was analyzed using CPFEM simulation. Irradiation was not taken into account directly as the DC was considered to be free of irradiation defects (note however, that DC itself is a result of irradiation followed by mechanical deformation). The results were used to build an analytical model and deduce a microcrack nucleation criterion.

Paper [4] was already cited in the original version of the submitted manuscript.

Papers [5,6] did not concern the irradiation effects and that’s why I do not describe them in the review.

The selection of the topic of the paper is important, the number of processed literature papers is impressive. I recommend to rewrite the paper in more structured form. 

>> I have modified section 3 so that each material is treated separately. I have also rewritten the conclusions. I hope the structure of the paper looks better now.

I thank the reviewer for the time and effort spent reviewing my paper and all the comments. They really helped me to improve the review paper.

Round 2

Reviewer 1 Report

The authors have adopted the changes as required.

The English has been improved and any further language issues are a matter of editorial policy.

Reviewer 2 Report

The extensions of the paper helps the understanding. The paper can be published in present form.