The Issues of the Radiation Hardening Determination of Steels After Ion Irradiation Using Instrumented Indentation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The presented paper by "The Issues of the Radiation Hardening Determination of Steels After Ion Irradiation Using Instrumented Indentation" by Boris Margolin, Lyubov Belyaeva, Alexander Sorokin and Ekaterina Gladkikh is devoted to an experimental investigation of the application of the instrumented indentation method for determining microhardness and radiation hardening in ion-irradiated steels. 

 

This is a good, solid experimental work with substantial experimental results that appear to be reliable, and there is little doubt that the presented results are credible and accurate. The subject of the paper is also of the highest importance for the industry and economy. 

Important and useful types of indent (Berkovich and Vickers) are considered and simple geometrical reasoning for the effect of which type is provided.  Therefore, this paper should be accepted for publication in Metals MDPI with only minor corrections.  My only suggestion would be to slightly extend the mathematical model and theoretical descriptions of the provided hardening processes,  specifically, you can discuss the geometrical properties like areas and depth of which type of indentation in more details, and what quantities they depend on. How does the model work for different types of metal and lattices? What is the temperature dependence of the considered phenomena and how will your result change if the temperatures are increased or decreased? 

 Finally,  since a radiation effect on a lattice is considered,  the presented manuscript would win and become more accessible for a broader readership if you also discuss many-body theory of proton-generated point defects for losses of electron energy and photons in quantum wells, defect capturing and charging dynamics, and their effects on magneto-transport of electrons in quantum wells.

Author Response

We are grateful to the Reviewer for the comments and remarks. We represent hereafter the detailed answers on all the comments. We tried our best to take into account all comments in the revised paper. We have provided additional clarifications and modifications according to the comments. All the changes in the revised manuscript are highlighted by yellow color.

Comment 1: Important and useful types of indent (Berkovich and Vickers) are considered and simple geometrical reasoning for the effect of which type is provided.  Therefore, this paper should be accepted for publication in Metals MDPI with only minor corrections.  My only suggestion would be to slightly extend the mathematical model and theoretical descriptions of the provided hardening processes, specifically, you can discuss the geometrical properties like areas and depth of which type of indentation in more details, and what quantities they depend on. How does the model work for different types of metal and lattices? What is the temperature dependence of the considered phenomena and how will your result change if the temperatures are increased or decreased? 

Response 1: According your recommendation we included the additional subsection in Discussion section with analysis of the mechanical properties effect on pile-ups formation, in particular, the temperature effect.

Comment 2: Finally, since a radiation effect on a lattice is considered, the presented manuscript would win and become more accessible for a broader readership if you also discuss many-body theory of proton-generated point defects for losses of electron energy and photons in quantum wells, defect capturing and charging dynamics, and their effects on magneto-transport of electrons in quantum wells.

Response 2: We added the results of calculations of the damage dose (point defects) distribution (See Fig.5) which were performed with taking into account the energy redistribution between heavy ions and lattice of the investigated material.

Reviewer 2 Report

Comments and Suggestions for Authors

MANUSCRIPT REVIEW

The manuscript entitled: "The Issues of the Radiation Hardening Determination of Steels After Ion Irradiation Using Instrumented Indentation" presents a study focused on the application of instrumented indentation method with a Berkovich pyramid is considered for determination of microhardness and radiation hardening of ion-irradiated steels. The authors have explained their claims based on experimental and theoretical foundations. According to this study, authors suggested method effectively eliminates the impact of indentation depth on microhardness of homogenous materials between 0.2 and 4 μm. It also provides accurate assessment of radiation hardening for a thin irradiated layer with a depth of around 2 μm. The pile-up effect is discussed, too.

Reviewer’s comments:

 

• Materials and Methods-It should specify the material being tested, briefly and clearly describe the methodology, and clearly and precisely define the devices used. Much of this section is intended for the Introduction (for example advantages and disadvantages Berkovich method vs. Vickers method). Lines 187-197 can be brought under the aim of research.
• Section three Equipment, Samples and Materials: The material is mentioned again. I also think the sections of the draft are not logically or clearly divided.
• Is there any reason for choosing the materials listed (austenitic steels-18Cr-10Ni-Ti, 16Cr-20Ni-2Mo-Ti and 16Cr-25Ni-2Mo-Ti and ferritic-martensitic steels -EP-823 and EP-450)? From Fig. 7 the growth rate of d_hp-up/d_hp for FMS is more than twice as high as for austenitic steel. Explanation, why?
• Line 17, please uniformed font.
• Berkovich pyramid indentation can reliably quantify radiation hardening in thin ion-irradiated layers, if microhardness is determined directly from the indent projection area. In contrast, using the Nix-Gao model, which calculates hardness based on indentation depth and assumes specific strain gradient behavior, can lead to significant errors. Substrate effects and irradiation-induced microstructural changes in this research are poorly discussed as an influential factor.
• Direct area-based measurements are preferable to depth-dependent modeling for accurately assessing radiation-induced hardening. Is this main conclusion of this study?
• It is advisable to update the list of references with more recent works, as most of the sources you mentioned are several decades old.
• The work is very impressive and ideologically interesting, but it is intended for a very narrow group of readers who are dedicated to this field.
• Technical requirements: Author Contributions, Funding, Conflicts of Interest...

However, addressing the minor concerns outlined below is crucial for improving the manuscript's quality and clarity. Thus, Minor Revisions are recommended.

 

     

Comments for author File: Comments.pdf

Author Response

We are grateful to the Reviewer for the comments and remarks. We represent hereafter the detailed answers on all the comments. We tried our best to take into account all comments in the revised paper. We have provided additional clarifications and modifications according to the comments. All the changes in the revised manuscript are highlighted by yellow color.

Comment 1: Materials and Methods: It should specify the material being tested, briefly and clearly describe the methodology, and clearly and precisely define the devices used. Much of this section is intended for the Introduction (for example advantages and disadvantages Berkovich method vs. Vickers method). Lines 187-197 can be brought under the aim of research.

Response 1: The title of the section 2 has been corrected and the word “Materials” has been removed. Materials and devices are described in section 3. We believe that Lines 187-197 correspond to “2.1 Methodology…” subsection more than “1. Introduction” section.

 

Comment 2: Section three Equipment, Samples and Materials: The material is mentioned again. I also think the sections of the draft are not logically or clearly divided.

Response 2: We have corrected the title of Section 2 and removed the word “Materials” from it. Investigated materials are described in Section 3 only.

 

Comment 3: Is there any reason for choosing the materials listed (austenitic steels-18Cr-10Ni-Ti, 16Cr-20Ni-2Mo-Ti and 16Cr-25Ni-2Mo-Ti and ferritic-martensitic steels -EP-823 and EP-450)? From Fig. 7 the growth rate of d_hp-up/d_hp for FMS is more than twice as high as for austenitic steel. Explanation, why?

Response 3: The investigated materials are chosen as typical steels with FCC (austenitic steels) and BCC (ferritic-martensitic steels) lattices used as materials for reactor components under irradiation. Chemical compositions of the studied materials were added in articles (See Tables). Concerning explanation of the growth rate d_hp-up/d_hp for FMS and for austenitic steel it should be noted that austenitic steel has higher the strain hardening than FMS that results in higher pile-ups in FMS. To clarify this issue, we have added additional subsection in Discussion.

 

Comment 4: Line 17, please uniformed font.

Response 4: The font has been corrected

 

Comment 5: Berkovich pyramid indentation can reliably quantify radiation hardening in thin ion-irradiated layers, if microhardness is determined directly from the indent projection area. In contrast, using the Nix-Gao model, which calculates hardness based on indentation depth and assumes specific strain gradient behavior, can lead to significant errors. Substrate effects and irradiation-induced microstructural changes in this research are poorly discussed as an influential factor.

Response 5: From mechanical point of view irradiation induced microstructural changes affect the localization of deformation. When neutron fluence increases the yield strength increases also but deformation hardening decreases. As a result, strain corresponding to localization of deformation decreases. Such trends are described in the corrected paper (See pages …).

The effect of substrate on microhardness determination was described in detail in paper  

“Margolin, B.; Sorokin, A.; Belyaeva, L. A Link between Neutron and Ion Irradiation Hardening for Stainless Austenitic and Ferritic-Martensitic Steels. Metals 2024, 14, 99. https://doi.org/10.3390/met14010099”

and also in standard

“ISO 14577-4:2016 (E); Metallic Materials—Instrumented Indentation Test for Hardness and Materials Parameters—Part 4: Test Method for Metallic and Nonmetallic Coatings. ISO: Geneva, Switzerland, 2016”.

In the reviewed paper the effect of substrate described in lines 52-59 and lines 84-95 (page 2).

 

Comment 6: Direct area-based measurements are preferable to depth-dependent modeling for accurately assessing radiation-induced hardening. Is this main conclusion of this study?

Response 6: Yes, the direct area-based measures with account taken of pile-ups maintain the independence of the microhardness on indentation depth. This is the main conclusion of this study.

 

Comment 7: It is advisable to update the list of references with more recent works, as most of the sources you mentioned are several decades old.

Response 7: Indeed, we referenced, first of all, the fundamental works and reviews concerning microhardness measurements which are published several decades ago. In addition, we referenced the relatively fresh papers concerning microhardness measurement of the material after ion irradiation. Taking into account your comment we have extended the list of reference with more recent works.

 

Comment 8: The work is very impressive and ideologically interesting, but it is intended for a very narrow group of readers who are dedicated to this field.

Response 8: We agree with you. Indeed, not many readers are currently dedicated to this field. At the same time, this field is very promising for express estimation of radiation hardening of structural materials. Therefore, we hope the obtained results are important both for researchers and engineers.

 

Comment 9: Technical requirements: Author Contributions, Funding, Conflicts of Interest...

Response 9: These sections have been added to the article.

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript is interesting and valuable, but methodological details, some claims, and presentation/referencing issues need to be addressed before publication.

Major comments and questions:

1. It is necessary to note that in the world literature, 'Berkovich indenter' is more commonly used instead of 'pyramid'. The Berkovich surname is missing from the reference list. It would be helpful to provide a few general references on this topic. One of the most frequently cited works here is: Chudoba, T., Schwaller, P., Rabe, R., Breguet, J. M., & Michler, J. (2006). Comparison of nanoindentation results obtained with Berkovich and cube-corner indenters. Philosophical Magazine, 86(33-35), 5265-5283.

1. About title: Consider “Determining Radiation Hardening of Steels after Ion Irradiation using Instrumented Indentation” (smoother wording).
2. Line 29. Word “emulating” is better than modeling. Exactly this term was used by Garry Was (References 1 and 2 in your reference list).

4. It is necessary to note that emulation of neutrons by ions is successful not only for metals [1-5], but also for oxides and nitrides. See, for example: Popov, A. I., Lushchik, A., Shablonin, E et al. (2018). Comparison of the F-type center thermal annealing in heavy-ion and neutron irradiated Al2O3 single crystals. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 433, 93-97.
5. Line 31. This sentence in general is not correct “thickness of the irradiated layer usually does not exceed 2 ÷ 3 μm”. In the case of swift heavy ion irradiation, this value  can be up to 10-15 μm for both oxide ceramics and metals: Zdorovets, M. V., Kozlovskiy, et al (2025). Radiation-induced degradation effects of optical properties of MgO ceramics caused by heavy ion irradiation. Optical Materials: X, 26, 100406;  Skuratov, V. A., Uglov, V. V., O’Connell, J., Sohatsky, A. S., Neethling, J. H., & Rogozhkin, S. V. (2013). Radiation stability of the ODS alloys against swift heavy ion impact. Journal of nuclear materials, 442(1-3), 449-457.

1. The paper discusses multiple irradiation species (Ni4+, He+, H+) and blocks up to 60 dpa at 400 °C (irradiation depth ≈ 2.4 μm), but key parameters are not fully specified. Please add: beam energies (per species), fluences and dose partition per block, beam current/current density, rastering strategy, sample temperature control (sensor position and accuracy; gradients across the spot), and dose rate. These are required to reproduce the experiment and to interpret depth profiles (swelling, defect clustering) that may affect pile-ups and contact areas. (See Section 5 and Fig. 9, lines ~428–446 for context.
2. Because your central argument depends on the thin (~2–2.4 μm) non-uniform damage layer and the “soft substrate” effect, please provide calculated depth profiles (e.g., SRIM/TRIM/IM3D). This will help justify the choice of indentation depths (0.2–4.5 μm) and the corresponding interpretation

8. Some equations are inline with punctuation. Please, standardize numbering.
9. You note careful polishing and even EBSD checks for work hardening (lines ~307–313). Please also report quantitative surface roughness (Sa/Sq) at the scale relevant to 0.2–0.6 μm indents and demonstrate that roughness does not confound the shallow-depth hardness rise. A short AFM/optical profilometry summary (unirradiated vs irradiated) would help.
10. Grammar/typos: A few small issues (e.g., “manoscale” → “nanoscale”; “octahedron” → “octagon” for Vickers projection; “dependences” → “dependencies”)—please run a careful proofread. (Lines ~610, ~229, multiple…)
11. Finally, consider adding references of 2023–2025 updates on (i) pile-up-aware hardness extraction, (ii) nanoindentation of ion-irradiated steels with explicit area-function/tip-rounding treatments, and (iii) data-driven or FEM-based contact area corrections. This will strengthen the “state of the art”.

Comments on the Quality of English Language

1. Grammar/typos: A few small issues (e.g., “manoscale” → “nanoscale”; “octahedron” → “octagon” for Vickers projection; “dependences” → “dependencies”)—please run a careful proofread. (Lines ~610, ~229, multiple…)

Author Response

We are grateful to the Reviewer for the comments and remarks. We represent hereafter the detailed answers on all the comments. We tried our best to take into account all comments in the revised paper. We have provided additional clarifications and modifications according to the comments. All the changes in the revised manuscript are highlighted by yellow color.

Comment 1: It is necessary to note that in the world literature, 'Berkovich indenter' is more commonly used instead of 'pyramid'. The Berkovich surname is missing from the reference list. It would be helpful to provide a few general references on this topic. One of the most frequently cited works here is: Chudoba, T., Schwaller, P., Rabe, R., Breguet, J. M., & Michler, J. (2006). Comparison of nanoindentation results obtained with Berkovich and cube-corner indenters. Philosophical Magazine, 86(33-35), 5265-5283.

Response 1: We have changed term “Berkovich pyramid” on “Berkovich indentor” through the whole text. We have added the reference proposed by you. (See Line 682)

 

Comment 2: About title: Consider “Determining Radiation Hardening of Steels after Ion Irradiation using Instrumented Indentation” (smoother wording)

Response 2: The paper, first of all, is devoted to the methodology of determination of microhardness which is more adequate for specimen after ion irradiation. The purpose of this paper wasn’t the determination of irradiation of hardening of the steel. Irradiation hardening determination in this paper is considered as an example of the proposed methodology. That’s why we believe the title of this paper presented by us is more adequate.

 

Comment 3: Line 29. Word “emulating” is better than modeling. Exactly this term was used by Garry Was (References 1 and 2 in your reference list)

Response 3: The text has been corrected according this comment.

 

Comment 4: It is necessary to note that emulation of neutrons by ions is successful not only for metals [1-5], but also for oxides and nitrides. See, for example: Popov, A. I., Lushchik, A., Shablonin, E et al. (2018). Comparison of the F-type center thermal annealing in heavy-ion and neutron irradiated Al2O3 single crystals. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 433, 93-97.

Response 4: Certainly, there is a lot of types of materials that can be investigated using ion irradiation. Besides oxides (ceramics) and nitrides the ion irradiation is widely used for investigation of polymers, semiconductors and other materials. In Introduction we pay attention on the ion irradiation as a method for emulation of neutron irradiation and on the features of ion irradiation regardless of the material type.

Moreover, the article is dedicated to methodical features of microhardness investigation of steels. Mention of other types of materials in Introduction can confuse the readers. That’s why we believe that inclusion of different types of materials in Introduction is not necessary.

 

Comment 5: Line 31. This sentence in general is not correct “thickness of the irradiated layer usually does not exceed 2 ÷ 3 μm”. In the case of swift heavy ion irradiation, this value  can be up to 10-15 μm for both oxide ceramics and metals: Zdorovets, M. V., Kozlovskiy, et al (2025). Radiation-induced degradation effects of optical properties of MgO ceramics caused by heavy ion irradiation. Optical Materials: X, 26, 100406;  Skuratov, V. A., Uglov, V. V., O’Connell, J., Sohatsky, A. S., Neethling, J. H., & Rogozhkin, S. V. (2013). Radiation stability of the ODS alloys against swift heavy ion impact. Journal of nuclear materials, 442(1-3), 449-457.

Response 5: We have added information about beam energy for irradiated layer with thickness of 2 ÷ 3 μm.

 

Comment 6: The paper discusses multiple irradiation species (Ni4+, He+, H+) and blocks up to 60 dpa at 400 °C (irradiation depth ≈ 2.4 μm), but key parameters are not fully specified. Please add: beam energies (per species), fluences and dose partition per block, beam current/current density, rastering strategy, sample temperature control (sensor position and accuracy; gradients across the spot), and dose rate. These are required to reproduce the experiment and to interpret depth profiles (swelling, defect clustering) that may affect pile-ups and contact areas. (See Section 5 and Fig. 9, lines ~428–446 for context.

Response 6: We have extended the description of irradiation parameters (See page 9).

 

Comment 7: Because your central argument depends on the thin (~2–2.4 μm) non-uniform damage layer and the “soft substrate” effect, please provide calculated depth profiles (e.g., SRIM/ TRIM/ IM3D). This will help justify the choice of indentation depths (0.2–4.5 μm) and the corresponding interpretation

Response 7: We have added the figure with damage dose and injected ion profiles (See Fig. 5)

 

Comment 8: Some equations are inline with punctuation. Please, standardize numbering.

Response 8: The text has been corrected

 

Comment 9: You note careful polishing and even EBSD checks for work hardening (lines ~307–313). Please also report quantitative surface roughness (Sa/Sq) at the scale relevant to 0.2–0.6 μm indents and demonstrate that roughness does not confound the shallow-depth hardness rise. A short AFM/optical profilometry summary (unirradiated vs irradiated) would help

Response 9: As the height of pile-ups for Berkovich indentor differs from Vickers indentor it may be concluded that roughness does not affect the shallow-depth hardness.

 

Comment 10: Grammar/typos: A few small issues (e.g., “manoscale” → “nanoscale”; “octahedron” → “octagon” for Vickers projection; “dependences” → “dependencies”)—please run a careful proofread. (Lines ~610, ~229, multiple…)

Response 10: The text has been corrected

Comment 11: Finally, consider adding references of 2023–2025 updates on (i) pile-up-aware hardness extraction, (ii) nanoindentation of ion-irradiated steels with explicit area-function/tip-rounding treatments, and (iii) data-driven or FEM-based contact area corrections. This will strengthen the “state of the art”.

Response 11: We have added some recent references.

Reviewer 4 Report

Comments and Suggestions for Authors

 

The paper is generally suitable for publication, but some details need to be clarified.

1. Does the term “pyramid” sound too informal or like jargon? Using “indenter” would be better, as it’s the proper, academic term and more suitable for publication.
2. How is radiation hardening related to the defects formed in a material? Please provide a detailed description of their structure and evolution with fluence.
3. Unfortunately, key experimental parameters are not fully specified. Please provide details on beam energies for each ion type, fluences, and temperatures. Otherwise, comparison with other studies and reproduction of the results will not be possible.
4. Please provide calculated damage depth profiles.
5. Finally, please provide data from a comparative analysis of the surface condition before and after irradiation. Indicate the time elapsed between irradiation and the measurements, and include a detailed experimental protocol.

Author Response

We are grateful to the Reviewer for the comments and remarks. We represent hereafter the detailed answers on all the comments. We tried our best to take into account all comments in the revised paper. We have provided additional clarifications and modifications according to the comments. All the changes in the revised manuscript are highlighted by yellow color.

 

Comment 1: Does the term “pyramid” sound too informal or like jargon? Using “indenter” would be better, as it’s the proper, academic term and more suitable for publication.

Response 1: The text has been corrected according to this comment

 

Comment 2: How is radiation hardening related to the defects formed in a material? Please provide a detailed description of their structure and evolution with fluence.

Response 2: Purpose of this paper is not analysis of the effect of irradiation-induced microstructure on radiation hardening but the development of methodology for determination of microhardness which is more adequate for specimen after ion irradiation. Radiation hardening determination in this paper is considered as an example of the proposed methodology.

 

Comment 3: Unfortunately, key experimental parameters are not fully specified. Please provide details on beam energies for each ion type, fluences, and temperatures. Otherwise, comparison with other studies and reproduction of the results will not be possible.

Response 3: We have extended the description of irradiation parameters (See page 9).

 

Comment 4: Please provide calculated damage depth profiles.

Response 4: We have added the figure with damage dose and injected ion profiles (See Fig. 5)

 

Comment 5: Finally, please provide data from a comparative analysis of the surface condition before and after irradiation. Indicate the time elapsed between irradiation and the measurements, and include a detailed experimental protocol.

Response 5: The surfaces of the specimens were carefully prepared by mechanical polishing and subsequent electropolishing. The surface condition before irradiation was controlled by scanning electron microscopy and electron backscatter diffraction by visualizing the so-called Kikuchi lines.

After ion irradiation the surface condition was controlled to avoid oxidation or radiation induced phase precipitation on the surface. Such investigation was performed with transmission electronic microscopy by cutting microsample normal to surface. Oxidation layer thickness was less than 50 nanometers.

The time elapsed between irradiation and the measurements was about 3-4 months. We believe that such period didn’t affect the results because the specimens were stored in special boxes that excludes a possibility of surface oxidation.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have successfully revised their manuscript, and I recommend it for publication

Reviewer 4 Report

Comments and Suggestions for Authors

After successful revision, this paper can be accepted