Failure Rate Model of Materials under Uncertain Constant Amplitude Cyclic Load
Round 1
Reviewer 1 Report
Review of the manuscript under the title “Failure rate model of materials under uncertain constant amplitude cyclic load.”
The failure rate of mechanical components is an essential indicator of their dependability. The failure rate of materials under unknown constant amplitude cyclic loads is investigated in this manuscript. Under a certain number of load cycles, the residual strength of the material follows a specified probability distribution, which meets the random properties of the strength degradation law.
The manuscript needs major revision. Following are some specific issues of the current manuscript:
1. The abstract needs to be revised and avoid the character of the introduction and should focus more on facts related to the study, highlights of materials and methods and results, and the ultimate conclusion of the study. Some concrete outcomes must be mentioned.
2. The introduction overlooks essential milestones in this scientific field, such as the application of Bayesian optimization and artificial intelligence in the fatigue problem.
3. The introduction is not scientifically sound since it is not covering well the diverse aspects of this topic in order to establish how unique the current manuscript is.
4. The introduction overlooks important literature that discusses precisely the same topic, which leads to a loss of coherence with the current state of knowledge.
5. The introduction is too short. This is a result of points 3 and 4. When adequately addressed in the revision, that point will be automatically met.
6. The studied materials are not common, and it is not mentioned how it is manufactured. It is really hard to calibrate it from this point of view with current literature.
7. Please revise this Table 1; data is multiplied twice by 105 and 106, and so on. Please clarify if I understand wrongly.
8. In line number 9: The word “materials” would be replaced by “Ti-6264 alloy”, as the studied material is Titanium only.
9. In line number 26: The sentence needs to be rephrased. The meaning is unclear.
10. In line number 40: The “copula” should start with a capital letter.
11. In line number 103: The quality of the graph can be improved by exporting the graph as a Vector Graphics file format (ex: .svg).
12. In line number 103: The font size of the labels could be larger for readability.
13. In line number 148: Mean and standard deviations are already multiplied by 10^5
14. In line number 266: The conclusion could be organized in a better way: First paragraph without numbering, during the second paragraph in the form of conclusion bullet-points.
15. In general: the quality of the graphs could be improved.
16. The references are not easy to follow since they are not supported by DOI links.
17. Discussion of results is not sufficiently good and leads to unsatisfying conclusions, as it disregards some of the recent literature on precisely the same topic. Including them will make the manuscript fit better among reported results in this community.
Author Response
Expert 1 Opinion Response
Thank you for your comments and suggestions, in particular, the changes to the introduction and many details, which made the paper more readable and coherent, much appreciated.
1. The abstract needs to be revised and avoid the character of the introduction and should focus more on facts related to the study, highlights of materials and methods and results, and the ultimate conclusion of the study. Some concrete outcomes must be mentioned.
The abstract has been completely revised with the addition of the research process, methodology and conclusions. Please check it out.
2. The introduction overlooks essential milestones in this scientific field, such as the application of Bayesian optimization and artificial intelligence in the fatigue problem.
The paper on the combination of machine learning and lapse rate has been added for your review.
3. The introduction is not scientifically sound since it is not covering well the diverse aspects of this topic in order to establish how unique the current manuscript is.
Some relevant literature of this study has been added in the preface, and some irrelevant literature has been removed, so please check.
4. The introduction overlooks important literature that discusses precisely the same topic, which leads to a loss of coherence with the current state of knowledge.
This article has increased the background of the study and the basis of the study, as well as the basis of the P-S-N model, so that the readability and coherence of the article has been enhanced.
5. The introduction is too short. This is a result of points 3 and 4. When adequately addressed in the revision, that point will be automatically met.
The introduction to this article adds a lot of introductions and related literature, so please check.
6. The studied materials are not common, and it is not mentioned how it is manufactured. It is really hard to calibrate it from this point of view with current literature.
The relevant microstructure and material components of Ti-6264 alloy in the section 4 have been added in the text. Experimental verification. There is not much literature on the fatigue of this material, so that only one piece of experimental data was chosen for the experimental verification, but it is enough to verify the model in this paper.
7. Please revise this Table 1; data is multiplied twice by 105 and 106,and so on. Please clarify if I understand wrongly.
105 and 106,are removed from text.
8. In line number 9: The word “materials” would be replaced by “Ti-6264 alloy”, as the studied material is Titanium only.
The text has been revised for your review.
9. In line number 26: The sentence needs to be rephrased. The meaning is unclear.
The text has been revised for your review.
10. In line number 40: The “copula” should start with a capital letter.
The text has been revised for your review.
11. In line number 103: The quality of the graph can be improved by exporting the graph as a Vector Graphics file format (ex: .svg).
The picture has been revised for your review.
12. In line number 103: The font size of the labels could be larger for readability.
The font size of the labels has been revised for your review.
13. In line number 148: Mean and standard deviations are already multiplied by 10^5
The text has been revised for your review.
14. In line number 266: The conclusion could be organized in a better way: First paragraph without numbering, during the second paragraph in the form of conclusion bullet-points.
The conclusion has been rewritten and written in a very hierarchical way based on your comments, so please check it out.
15. In general: the quality of the graphs could be improved.
The text has been revised for your review.
16. The references are not easy to follow since they are not supported by DOI links.
The references are supported by DOI links.
17. Discussion of results is not sufficiently good and leads to unsatisfying conclusions, as it disregards some of the recent literature on precisely the same topic. Including them will make the manuscript fit better among reported results in this community.
The paper has added the latest relevant research in the introduction, before and after the connection is better.Conclusion has been modified as required, please check it out.
Reviewer 2 Report
General Evaluation
The current paper attempts a statistical study of fatigue failure of a Ti-alloy. The topic of the study is interesting and renders potential applications in statistical reliability of aerospace components. In addition, the subject is within the Journal scope and the language/grammar seems quite sufficient. However, the novelty aspects of the research are recommended to be explicitly referred in the Introduction. Suggestions for further improvement are also followed, in order to be considered for publication in Metals.
Scientific / Technical Comments
11. There are numerous symbols in the paper; a nomenclature (list of symbols) section is suggested to increase the readership of the manuscript.
22. The material (Ti-alloy) under study needs to further described, in terms of chemical composition, microstructure and mechanical properties.
33. Experimental details are not provided, concerning the fatigue experiments. Only a reference is given which seems that it doesn’t correspond to a Conference paper [21].
44. Table 1 shows a high variability in fatigue life results with respect to the stress. Also indicate in the Table the type of the stress (alternating, mean?). Please check and advise.
55. The eq. [1] differs from the expression of the usual Basquin equation. Please comment.
66. Please comment the specific statistical law followed, compared to the established ones in the literature, e.g. Weibull distribution function.
77. The influence of material parameters variation is not clearly shown on the statistical curves plotted in Figure 5. How the material parameters decrease? Please check this trend in the curves of Figure 5. Also specify the material parameters that are referred (m, C?).
88. Additional References including recent citations are recommended if they are available.
Minor Issues (mostly editorial type comments)
99. Please check the two last rows in Table 2. They seem identical (P = 0.90).
110. Please leave one space gap between the numerical part and the unit; e.g. 40 MPa (instead of 40MPa).
111. The language/grammar is sufficient. However, a final proofreading is necessary to eliminate minor spelling errors.
Author Response
Expert 2 Opinion Response
Thank you for your comments and suggestions, especially for the conclusion and the many small details that make the paper more readable and coherent, much appreciated.
- There are numerous symbols in the paper; a nomenclature (list of symbols) section is suggested to increase the readership of the manuscript.
Nomenclature has been added to the text for your review
- The material (Ti-alloy) under study needs to further described, in terms of chemical composition, microstructure and mechanical properties.
The relevant microstructure and material components of Ti-6264 alloy in the section 4 have been added in the text.
- Experimental details are not provided, concerning the fatigue experiments. Only a reference is given which seems that it doesn’t correspond to a Conference paper [21].
The fatigue test loading conditions and data are taken from reference [13, 26]. The experimental data is feasible and reliable, please check.
- Table 1 shows a high variability in fatigue life results with respect to the stress. Also indicate in the Table the type of the stress (alternating, mean?). Please check and advise.
It is Cyclic alternating stress, from fatigue experimental data.
- The eq. [1] differs from the expression of the usual Basquin equation. Please comment.
This equation comes from equation 6 in literature 19, which has the same basic form, so please check it. The original literature is ----Basquin OH. the exponential law of endurance tests. proc ASTM 1919;10:625-30. DOI: 10.1007/BF01893477.
- Please comment the specific statistical law followed, compared to the established ones in the literature, e.g. Weibull distribution function.
Based on the theory of interference analysis and Weibull distribution in the field of reliability engineering, an interference model of cyclic stress-loss rate is established. The Fatigue life distribution in the paper are based on this.
- The influence of material parameters variation is not clearly shown on the statistical curves plotted in Figure 5. How the material parameters decrease? Please check this trend in the curves of Figure 5. Also specify the material parameters that are referred (m, C?).
Figure 6 shows fatigue life distributions of Ti-6246 at different survival probabilities are quite different. Combined with the P-S-N parameters of Ti-6246 alloy in Table 2, the mean of fatigue life decreases when the material parameters decrease. Similarly, the standard deviation of fatigue life decrease with the decreasing of material parameters. This phenomenon indicates that Ti-6246 alloy property parameters m and C have an important influence on the probability distribution pattern of the fatigue rate.
- Additional References including recent citations are recommended if they are available.
Relevant research literature has been added for your review.
Minor Issues (mostly editorial type comments)
- Please check the two last rows in Table 2. They seem identical (P = 0.90).
Duplicate P = 0.90 have been removed, please check.
- Please leave one space gap between the numerical part and the unit; e.g. 40 MPa (instead of 40MPa).
The text has been revised for your review.
- The language/grammar is sufficient. However, a final proofreading is necessary to eliminate minor spelling errors.
The full text has been revised and is available for your review.
Round 2
Reviewer 2 Report
Thank you for the revisions. Apart from the responses to the review comments and manuscript amendments, please check the following issues:
1. The studied Ti-6246 alloy has to be clearly addressed concerning its chemical composition (nominal contents could be sufficient or standard alloy designation).
2. The hardness/mechanical properties range of the studied Ti-alloy seems that are not addressed.
3. The microstructure is taken from a previous reference [26]. The corresponding Figure 3 has to be original and unpublished, unless prior permission has been granted. Also, the description of phases is standard using Greek alphabet characters; α (= alpha) and β (= beta).
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
