A New Approach to Estimate the Fatigue Limit of Steels Based on Conventional and Cyclic Indentation Testing

Round 1

Reviewer 1 Report

The development of new methods for using minimally invasive methods (such as indentation) to assess the cyclic durability of materials is an important scientific and practical task, so this article is very relevant. At the same time, there are a few recommendations for its improvement:

1. I propose to supplement the introduction with an analysis of a recent article by Professor Chausov et al.: https://www.mdpi.com/2075-4701/11/10/1625. In it, he uses physical premises that are ideologically very close to this approach and investigations on RUMUL TESTRONIC machine too.
2. Professor Chausov's method also takes into account the scutter of hardness data and is based on the use of statistically significant (15 or more) indentation data. How to take into account the scutter of indentation's data in your method?
3. It is known that indentation is a very sensitive method to changes in microstructure

(loo for example: https://link.springer.com/article/10.1007/s11003-008-9077-z, perhaps in this article it is worth writing for which group of steels the authors recommend their approaches. This will limit the proposed method, and will describe the zone of its physical and mechanical correctness.

4. The conclusions of the article should be specified. It is necessary to show what the authors have proposed that is new, in comparison with the well-known studies of other authors, and what this gives for science and practice.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This manuscript studies the relationship of fatigue limit and Vickers hardness HV of steels under cyclic hardening, which is interesting and useful. However, the following matters should be noticed.

1.     In this study, it refers to “cyclic hardening potential”, what does “potential” mean?

2.     With respect to fatigue limit assessment, more recent progress should be strengthened, like defect tolerant fatigue assessment in Int J Fatigue 160 (2022) 106884, also Beretta and Murakami et al. work and safe and reliable design in Int J Fatigue 142 (2021) 105912;

3.     In figure 2, the axis corresponding to depth amplitude does not have any number and units.

4.     In this study, “cyclic hardening exponent” is a critical parameter. Does it mean cyclic strain hardening exponent  in Ramberg–Osgood curve? Or are they related?

5.     On page 9, it writes “In summary, the values of σw given in Table 3 are mainly related to the mechanical properties of the material volume”. However, there are not any information about material volume.

6.     In the Discussion, there is an analysis with respect to relative errors. Nevertheless, the fatigue limit in the study is fitted by the data, not predicted directly just like the 1.6HV. Thus, the reviewer thinks that the comparison is meaningless.

7.     Scatter is always a problem in fatigue, can this idea be applied to predict fatigue limit dispersion by using the probabilistic method.

8.     The final section can be modified to “Conclusions and prospects”.

Author Response

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Reviewer 3 Report

This is a paper on the estimation of the fatigue limit of steels from indentation tests. The work carried out is very good, as well as the methodology used and the presentation and analysis of the results. As they explain, it is about the correlation with the axial fatigue limit corresponding to specimens with mirror polished surface finishing and no residual stresses or microstructural defects that would modify the value of the limit.

I have no objection to the article that would prevent its publication in its present form.

Author Response

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Reviewer 4 Report

Many thanks to the authors for this research. Also, the presented results are very valuable and their interpretation, which is one of the strength points of this manuscript, shows that the authors are experts in this field. This article has many strengths points. For example, the material section is written in great detail, and any other scientist can repeat it step by step and make similar laboratory samples. In addition, the reason for skipping some test results is well stated. Also showing the staircase method visually is another strength of this article. However, I believe that authors should pay attention to the following points and provide revised manuscript:

1- it is strongly suggested the final version of the manuscript should be reviewed by a Native Englishman. 

2- please check the frequency value on page 4 and line 154, for low cycle fatigue test.

3- related to conclusion section, the authors checked the new proposed formula to obtain fatigue limit in terms of hardness and cyclic hardening exponent compared to experimental data and reported in Figure 8. I agree with the authors to use this technique, but they should notice that the obtained results using formula should be checked with experimental data that do not use to extract formula by Regression. So, it is necessary to show which experimental data do not used and so, this part of discussion should be rewritten. 

Author Response

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Round 2

Reviewer 1 Report

Accept.

Reviewer 2 Report

The work has been well refined, it can be accepted as it is. 

Reviewer 4 Report

The authors have tried to provide the revised manuscript based on the reviewer's comment and response all comments one bye one. So, I believed that the quality of the present manuscript is better than previous one and it can be published in the present form.