Effect of Stress Ratio and Evaluation of Crack Sizes on Very-High-Cycle-Fatigue Crack Propagation Life Prediction of Carburized Cr-Ni Steel
Round 1
Reviewer 1 Report
In generaly good work. However it is not clear about the sufficient effect of stress ratio R on FCG in term of stress intensity range. Usually for long cracks effect of R on FCG is definded mainly by crack clousure (CC). This study considers short cracks, evidently, without CC like the Murakami model, and then no strong effect of R on FCG should be expected (like for long cracks in term of effective stress intersity factor range). This point must be claryfied.
Author Response
Response: Many thanks to Reviewer for your valuable comments. Of the three failure modes that appear in this paper, we consider that except for the interior-failure-with-FGA mode where small crack propagation dominates the full life, only long crack propagation is available for the remaining two failure modes, and for which the role of crack closure in both modes is considered to be significant. As for the interior-failure-with-FGA mode, the maximum tensile stresses as well as the stress-intensity-factor range are different due to different stress ratios, and we believe that this may also have some effect on the rate of small crack expansion, although it may be very limited. In future work, we will conduct further studies on the effect of stress ratio on the rate of small crack propagation. Once again, we would like to express our appreciation for your constructive comments.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The manuscript discussed the life prediction of Cr-Ni steel under HCF/VHCF. The failure behavior was well investigated and the proposed prediction model showed good agreement with the experimental results. I only have a few comments.
1) Page 1, line 30: "107 cycles" ==> "10^7 cycles"
2) Page 2, line 81: "the surface roughness of the specimen reaches 0.32." ==> What parameter was considered? Ra?
3) Page 4, lines 130-131: "the S-N curve presents step or duplex shape at R=0 and 0.3" ==> According to the results in Figure 4, I could not agree with it. It was more like a straight line.
4) Page 6, line 186: About "R_***" in Eq (2) ==> Please explain it here.
5) Page 7, line 218: About "sigma_a" in Eq (4) ==> Please explain it here or on line 128. There was no explanation in the main text.
6) Page 9, line 281: "within factor-of-five lines" ==> In Figure 10, the results were within the lines of a factor of 5 and a factor of 3. Please resolve the conflict.
Author Response
- Page 1, line 30: "107 cycles" ==> "10^7 cycles".
Response: We are very sorry for our incorrect writing. The revised text reads as following on:
For the consideration of economy, efficiency and energy, the parts made of gear steel usually need to bear the loading of more than 107 cycles.
- Page 2, line 81: "the surface roughness of the specimen reaches 0.32." ==> What parameter was considered? Ra?
Response: Thank you for pointing this out. As far as the surface roughness mentioned in the text is indeed Ra, and we have redone the addition in the text as follows:
…, to ensure that the surface roughness (Ra) of the specimen reaches 0.32.
- Page 4, lines 130-131: "the S-N curve presents step or duplex shape at R=0 and 0.3" ==> According to the results in Figure 4, I could not agree with it. It was more like a straight line.
Response: We apologize for causing Reviewer to disagree with our work due to limited experimental data. In fact, for the materials studied in this paper, the slope of the fitted line for interior failure is slightly greater than that for surface failure because of the different failure mechanisms, and the horizontal line region located in the middle of the fitted lines of the two failure modes often exists as a competing region for the two failure modes. This situation is widely mentioned in the cited literature, such as 1,2,3 etc.
- Page 6, line 186: About "R_***" in Eq (2) ==> Please explain it here.
Response: We have added the explanation according to the Reviewer’s suggestion as follows:
where Δσ represents the range of the applied stress, and Rinc, FGA or fisheye represents the radius of inclusions, FGA or fisheye.
- Page 7, line 218: About "sigma_a" in Eq (4) ==> Please explain it here or on line 128. There was no explanation in the main text.
Response: We are very sorry for the negligence of our work. We have added a description here as follows:
where σa is the stress amplitude, and ΔK’ represents the average value of interior long crack propagation threshold and the instability propagation threshold.
- Page 9, line 281: "within factor-of-five lines" ==> In Figure 10, the results were within the lines of a factor of 5 and a factor of 3. Please resolve the conflict.
Response: It is really true as Reviewer suggests, this issue is critical. We have revised the content here, and the details are as follows.
Life prediction results have a good agreement with experimental life, and most of the points fall between the upper factor-of-five lines and lower factor-of-three lines.
Author Response File: Author Response.pdf
Reviewer 3 Report
Title: Effect of stress ratio and evaluation of crack sizes on fatigue crack propagation life prediction of carburized Cr-Ni steel
Reviewer Comments
This work investigates the very high cyclic fatigue behavior and the effect of the stress ratio of carburized Cr-Ni steel. The manuscript content is interesting and addresses today's industrial problems, therefore, the review would suggest it for publication after responding to the following comments and modifying the manuscript accordingly.
1. It is important to have “very high cyclic fatigue” in the title to distinguish it from normal or low-cyclic fatigue works
2. The abstract must be reconstructed to have a structured form that addresses the manuscript content briefly, including 1) Introduction, 2) Objective, 3) Method, 4) Result, and 5) Conclusion, by using SHORT SENTENCES.
3. Add “very high cyclic fatigue” in the keyword
4. The introduction is short and should cover a critical review of the works that have been done in the field. I suggest the authors start this section by providing a review of other critical cases and applications to fatigue and review https://doi.org/10.3390/met10121581 , https://doi.org/10.1016/j.msea.2022.143357 , https://doi.org/10.1016/j.ijfatigue.2021.106703
5. The lack of science in the previous study must be highlighted strongly and it should be strongly brought as the reasoning that motivates you to do this study. Please provide such information in the introduction section
6. The scope and objectives of the study should be highlighted in the last paragraph of the introduction
7. Section 2.1 should include the standard test with the reference
8. Could you please add a flowchart of the research process in subsection 2.3?
9. Could we consider the content of sections 3 and 4 under a separate section as “results and discussion”
10. How do you physically determine/distinguish the interior and surface failure (does it affect the structure response), presented in the test result provided in figure 4? Please explain in the text
11. Types of failures are normally classified in the standard test method, does such classification is provided in the case of this study, if so please mention it in the text and accordingly explain figure 5.
12. Could you combine figures 6-8 into one figure with three sections?
13. The caption of figures 3, 5, and 9 should be modified with the detail of the plots
14. The title of section 4.2.1 is not suitable
15. The title of Table 1 should be modified
16. The percentage error of the predicted result compared to the experiment should be provided in the text (figures 10 and 11)
17. Line 303: the main FINDINGS
18. Please provide future research as a continuation of this work for the lack of science that is not addressed, at the end of the conclusion.
Author Response
Thank you for your comments, please see the attachment for details.
- It is important to have “very high cyclic fatigue” in the title to distinguish it from normal or low-cyclic fatigue works.
Response: Thanks for Reviewer’s good suggestion, this issue is critical. We have revised the title and the details are as follows:
Effect of stress ratio and evaluation of crack sizes on very-high-cycle-fatigue crack propagation life prediction of carburized Cr-Ni steel
- The abstract must be reconstructed to have a structured form that addresses the manuscript content briefly, including 1) Introduction, 2) Objective, 3) Method, 4) Result, and 5) Conclusion, by using SHORT SENTENCES.
Response: We have re-written the abstract according to the Reviewer’s suggestion as follows:
Carburized Cr-Ni steel is widely used in the manufacture of components in many fields due to excellent performance, of which the service life has been a concern. In order to investigate the high-cycle fatigue and very-high-cycle fatigue properties of carburized Cr-Ni gear steel, axial loading fatigue tests were performed by QBG-100 with stress ratios of -1, 0 and 0.3. The Generalized Pareto distribution is used to evaluate the inclusion size of carburized Cr-Ni gear steel. Based on the stress ratio and the evaluated crack size, a new fatigue life prediction model for carburized Cr-Ni gear steels was constructed. The results show that the S-N characteristics of carburized Cr-Ni gear steel represent the continuously descending tendency. Based on long crack propagation threshold and the instability propagation threshold of carburized Cr-Ni gear steel, the sizes of FGA, fisheye and SSA can be evaluated, respectively. And the maximum size of surface and interior inclusion of carburized Cr-Ni gear steel are 17.50 μm and 6.46 μm with cumulative probability of 99.9%. By validating the new established model, the prediction result is acceptable according to the good consistency between the predicted life and the experimental life.
- Add “very high cyclic fatigue” in the keyword.
Response: We have added “very high cycle fatigue” in the keyword according to the Reviewer’s suggestion as follows:
Keywords: Very high cycle fatigue; Cr-Ni gear steel; Stress ratio; Generalized Pareto distribution; Crack propagation; Fatigue life prediction
- The introduction is short and should cover a critical review of the works that have been done in the field. I suggest the authors start this section by providing a review of other critical cases and applications to fatigue and review https://doi.org/10.3390/met10121581, https://doi.org/10.1016/j.msea.2022.143357, https://doi.org/10.1016/j.ijfatigue.2021.106703
Response: Thanks to the Reviewer’s suggestion and recommended papers. These papers are very good and very helpful to our paper and we have already cited them as references [20], [29] and [30] in our paper.
- The lack of science in the previous study must be highlighted strongly and it should be strongly brought as the reasoning that motivates you to do this study. Please provide such information in the introduction section.
Response: Thanks to the Reviewer’s suggestion, we have revised it and the details are shown in question 6.
- The scope and objectives of the study should be highlighted in the last paragraph of the introduction.
Response: Thanks to the Reviewer’s suggestion. We have re-written the introduction and the details are as follows:
Gear steels are widely used for the manufacturing of core parts in the fields of automobile industry, military weapons, engineering machinery and aerospace due to their excellent mechanical properties and fatigue resistance in combination with the good hardenability [1,2]. With the rapid development of technology in various countries, the safety and stability of mechanical equipment are put forward higher requirements in service life. For the consideration of economy, efficiency and energy, the parts made of gear steel usually need to bear the loading of more than 107 cycles [3]. However, the-low/high-cycle-fatigue (LCF/HCF) theory and analysis methods cannot be applicable for the fatigue life prediction of mechanical products or components manufactured by gear steels in very-high-cycle-fatigue (VHCF) region [4-6]. Therefore, in order to ensure the long-term safety and stability of mechanical parts, it is necessary to further investigate the fatigue behavior and relevant fatigue life evaluation methods of gear steel in VHCF region.
In order to improve the mechanical property of gear steel, carburizing [7,8], nitriding [9] or shot peening [10] are usually used to strengthen the steel surface. Nonetheless, a small number of studies have indicated that the surface strengthening cannot obviously improve the interior fatigue performance of gear steel. With the increase of fatigue life and the decreasing of stress amplitude, the fatigue crack source of gear steel gradually transitions from surface to interior, and the interior non-metallic inclusion produced by metallurgy become the main crack source of gear steel [11-15]. The damage mechanism of VHCF is very different from that of LCF/HCF [16-18], which has aroused the interest of many scholars. Some studies show that the fisheye formed by crack propagation is the typical feature of interior failure and can often be observed on fracture surfaces. Sometimes a rough area appears around the inclusion, which is called the fine granular area (FGA) by Sakai [19]. The formation of FGA is thought to be the result of grain refinement based on stress concentration at the inclusions, which is different from grain boundary fracture mechanism based on grain boundary intrusion and grain boundary extrusion [20]. It has been confirmed by many scholars that the formation of FGA consumes more than 90% of the fatigue life of the gear steels [21,22]. Therefore, FGA plays an important role for life prediction in VHCF regime.
With the higher demand for the long-term effectiveness of components, the fatigue performance of VHCF regime for gear steels has attracted the attention of domestic and foreign scholars, and some fatigue strength or life prediction models have been pro-posed. Based on the dislocation theory, Tanaka and Mura [23,24] established a fatigue crack initiation model considering defects and microstructure characteristics. Based on the Basquin equation, Liu et al. [25] proposed a model including Vickers hardness and inclusion size to predict the fatigue life of high-strength steel in ultra-high cycle system. Hou et al. [26] constructed a fatigue life prediction model considering the average stress and stress ratio based on Kachanov's damage law [27]. Based on the cumulative damage method, Deng et al. [28] proposed a fatigue life prediction model of Inclusion-FGA-Fisheye failure under different stress ratios. Benedetti et al. [29] established a new multi-axial fatigue criterion based on the theory of critical distances and defect sensitivity, which in turn led to a more accurate prediction of the multiaxial plain and notch fatigue strength of thick-walled ductile iron with multi-axial flat and tangent. Surprisingly, although the effect of different factors (such as inclusion size, FGA size, fisheye size, stress amplitude, etc.) on the fatigue performance of gear steel has been studied, more models invariably neglect the utility of the stress intensity factor in the fatigue failure process, and thus fail to characterize the stress field strength near the elastic crack tip under external forces. In addition, numerical software, such as ANSYS and ABAQUS, which have achieved excellent performance in the field of physical field analysis of structures or fluids, have been widely used in fatigue life prediction one after another. Mazlan et al. [30] achieved life prediction with good agreement with the test results at room temperature and high temperature by importing the tensile strength, ultimate strength, modulus of elasticity and life cycle of aluminum as valid parameters into ANSYS Workbench. However, the life prediction of alloy steels based on numerical simulations is still strongly limited considering the stochastic nature of crack feature sizes such as inclusions and the complexity of failure mechanisms. In conclusion, few studies have clearly established a fatigue life assessment method involving both crack characteristic sizes and stress in-tensity factor threshold.
The aim of this study is to predict the very-high-cycle-fatigue life of carburized alloy steels under uniaxial loading at multiple stress ratios. The QBG-100 high frequency fatigue test machine with a frequency of about 95 Hz was used to conduct VHCF test on carburized gear steel at R = -1, 0 and 0.3. After the test, the crack characteristics of the gear steel were studied according to the experimental results. The inclusion size was evaluated based on the Generalized Pareto (GP) distribution, and the FGA size, fisheye size and SSA size were evaluated by the stress intensity factor threshold. Based on stress ratio and evaluation of crack sizes, a life prediction model of carburized Cr-Ni gear steel in VHCF regime was established.
- Section 2.1 should include the standard test with the reference
Response: We have added reference to this section as Reviewer suggested, as follows:
In order to minimize the influence of surface scratch left by machining on fatigue test, the middle arc part of each specimen was sequentially polished along the axis of the specimen with the sandpapers of 360-2400#, to ensure that the surface roughness (Ra) of the specimen reaches 0.32 [31].
- Could you please add a flowchart of the research process in subsection 2.3?
Response:
Thanks to the Reviewer’s suggestions, we have sorted out the experimental process and the added flow chart is shown in the manuscript:
- Could we consider the content of sections 3 and 4 under a separate section as “results and discussion”.
Response: Thanks to the Reviewer’s suggestion, we have revised it.
- The title of section 4.2.1 is not suitable.
Response: As suggested by the Reviewer, we have merged sections 3 and 4 in the text. As a result, sections 4.1, 4.2 and 4.3 have been replaced by sections 3.4, 3.5 and 3.6, respectively. In addition, in response to suggestion (14), we have deleted the three-level headings 4.2.1 and 4.2.2, and unified them with the second-level headings 3.5.
- How do you physically determine/distinguish the interior and surface failure (does it affect the structure response), presented in the test result provided in figure 4? Please explain in the text.
Response: It is really significant as Reviewer suggested that how to go about distinguishing these two failure modes in figure 4. In fact, we determined the interior and surface failure modes based on the location of crack initiation observed by scanning electron microscopy. We apologize for the ambiguity in this section due to the oversight of our work. We have complemented the partial description in section 3.1, as follows:
The failure modes of carburized Cr-Ni gear steel can be roughly divided into interior failure and surface failure according to the crack initiation location observed by SEM.
- Types of failures are normally classified in the standard test method, does such classification is provided in the case of this study, if so please mention it in the text and accordingly explain figure 5.
Response: As mentioned by the Reviewer, we have specified three failure types according to the crack initiation location and failure fracture morphology in section 3.2, namely surface failure, interior failure with FGA and interior failure without FGA. And following Reviewer’s suggestion, we have explained them in the appropriate positions.
- Could you combine figures 6-8 into one figure with three sections?
Response: We have made correction in the text according to the Reviewer’s suggestion.
- The caption of figures 3, 5, and 9 should be modified with the detail of the plots.
Response: We have made changes in the text in response to the Reviewer’s suggestions, as detailed below:
Figure 3. The relationship between the Vickers hardness (HV) and the distance from the surface depth.
Figure 6. Observation of typical fracture surfaces: (a)-(b) interior failure without FGA, (c)-(d) interior failure with FGA, and (e)-(f) surface failure.
Figure 8. GP distribution of inclusion size: (a) interior inclusion size, and (b) surface inclusion size.
- The title of Table 1 should be modified.
Response: We have considered and rewritten the title of Table 1 as suggested by the Reviewer, as follows:
Table 1. Best-fit value for identified parameters (C, m and α) in equation (15)
- The percentage error of the predicted result compared to the experiment should be provided in the text (figures 10 and 11).
Response: First of all, we thank the Reviewer’s for your suggestion. We introduced in Figures 9-10 (i.e., original Figures 10-11) in either the triplet factor line or the quintuplet factor line. As can be seen, almost all points in Figure 10 lie within the factor of three, so the fit is much better than in Figure 9, which lies within the factor of five. That is, factor line is equivalent to the percentage band.
- Line 303: the main FINDINGS.
Response: We have made changes here based on the Reviewer's suggests, as follows:
The main findings of this paper are as follows:…
- Please provide future research as a continuation of this work for the lack of science that is not addressed, at the end of the conclusion.
Response: We have added future research at the end of the conclusion with the following details:
Current research has focused on the very-high cycle-fatigue performance of carburized alloys at room temperature. The specific effect of stress ratio on small cracks is still more controversial, and further elucidation of the failure mechanism in this direction is essential. In addition, metal fatigue under high temperature effects exhibits very different failure modes and fracture mechanisms compared to room temperature. In view of the fact that a wide range of parts are subjected to high temperature conditions, it is necessary to make an in-depth study in this field in conjunction with engineering practice.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
The manuscript is revised well, I just need the authors to do the following minor corrections:
1. the author must specify the Scope of the study and also the Objective in the short form at the end of the introduction. I suggest you use the word SCOPE and OBJECTIVES when addressing this issue too. In the scope, you need to specify the limitation of study to what materials, and conditions, while in the objective, you address the main point to be solved.
2. in my previous comment "Section 2.1 should include the standard test with the reference", I request you to add the reference of the STANDARD Test method which you follow to prepare the specimen and perform the test, such as ASTM standards
3. regarding my previous comment "11) How do you physically determine/distinguish the interior and surface failure (does it affect the structure response), presented in the test result provided in figure 4? Please explain in the text.". Please elaborate it further in the manuscript text.
Author Response
Dear Editor and Reviewers:
On behalf of my co-authors, we are very grateful to the Editor and Reviewers for acknowledging our previous revisions and giving us the opportunity to further improve our manuscript. In response to the issues that emerged from the revised version, we once again provide a thoughtful reflection on our work. We thoroughly checked the manuscript for grammatical and spelling errors and rectified them in the text using the "track changes" function, as detailed in the manuscript. Most of all, we have made careful and deliberate revisions in accordance with the suggestions made by the Reviewers, as described in the following response.
- The author must specify the Scope of the study and also the Objective in the short form at the end of the introduction. I suggest you use the word SCOPE and OBJECTIVES when addressing this issue too. In the scope, you need to specify the limitation of study to what materials, and conditions, while in the objective, you address the main point to be solved.
Response: Thanks to the Reviewer for the specific suggestions here to address our shortcomings. For the last part of the introduction, we have redone the additions with the following details.
The scope of this study here concerns the fatigue failure analysis of carburized Cr-Ni steels due to crack propagation in the VHCF regime and prediction of the VHCF life of carburized alloy steels under uniaxial loading at multiple stress ratios. The QBG-100 high frequency fatigue test machine with a frequency of about 95 Hz was used to con-duct VHCF test on carburized gear steel at R = -1, 0 and 0.3. After the test, the crack characteristics of the gear steel were studied according to the experimental results. The inclusion size was evaluated based on the Generalized Pareto (GP) distribution, and the FGA size, fisheye size and SSA size were evaluated by the stress intensity factor threshold. Based on stress ratio and evaluation of crack sizes, a life prediction model of carburized Cr-Ni gear steel in VHCF regime was established. With the objective of im-proving the accuracy of fatigue failure analysis and life prediction of carburized Cr-Ni steels in actual engineering practice, the theoretical framework proposed based on the VHCF regime is of great value and serves as an effective reference for fatigue reliability studies.
- In my previous comment "Section 2.1 should include the standard test with the reference", I request you to add the reference of the STANDARD Test method which you follow to prepare the specimen and perform the test, such as ASTM standards.
Response: We are sorry for the trouble we caused you due to our misunderstanding, and as a correction, we have re-referenced the ASTM standard here. The corresponding sections are as follows:
In this paper, all fatigue tests were performed in accordance with the Chinese national standard GB/T3075. The chosen material is Cr-Ni gear steel with nominal chemical composition of 3.65Ni, 1.65Cr, 0.60Mn, 0.37Si, 0.16C, 0.035S, 0.035P and other Fe.
- Regarding my previous comment "11) How do you physically determine/distinguish the interior and surface failure (does it affect the structure response), presented in the test result provided in figure 4? Please explain in the text.". Please elaborate it further in the manuscript text.
Response: According to the Reviewer's suggestion, we have made a detailed explanation here, as follows:
Furthermore, the method of fatigue test is based on the principle of electromagnetic resonance. For both surface and interior failure, the operating frequency of specimen is almost the same during the test. As a result, the structural response of different failure modes is the same. Then, the early crack characteristic size is very limited, while the fracture is very rapid when the crack extends to a certain extent, regardless of the failure mode. This also means that the influence of the failure mode and the failure process on the structural response is negligible. In this paper, based on the crack direction and inclusion’s location observed by SEM, it can be roughly divided into surface failure and interior failure, as shown in Figure 6(a) and 6(e).
We appreciate for Editor and Reviewers’ warm work earnestly, and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions.
