Ratcheting Evaluation of SS304 Samples Undergoing Peak-Valley Loading Reversals with Hold Time Periods at Room Temperature Through the Incorporation of the Static Recovery Term

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript investigates the ratcheting behavior of SS304 stainless steel under peak–valley loading conditions with hold times, by incorporating a static recovery term into the Ahmadzadeh–Varvani (A–V) kinematic hardening model and the Lee–Zavrel (L–Z) isotropic hardening model. Although the topic has certain engineering relevance, the current manuscript exhibits significant shortcomings in terms of originality, methodological rigor, and validation depth.

1. In the last sentence of the first paragraph of the Introduction, the authors state that "The ratcheting response of a material is strongly influenced by factors including the material's microstructural characteristics, applied stress levels and rates, dwell time periods, and loading patterns." However, the paper does not provide the metallographic structure of SS304 stainless steel, and therefore does not consider the influence of microstructural characteristics.
2. The Introduction section of the manuscript provides a detailed review of the research status of the ratcheting phenomenon, particularly offering a critical assessment of existing mechanical models. Nevertheless, it does not clearly identify the novelty, significance, or the key issues to be addressed by the present study.
3. The manuscript evaluates the ratcheting response of 304 stainless steel samples under uniaxial asymmetric loading cycles at room temperature using the combined A-V kinematic hardening framework and L-Z isotropic hardening framework. With regard to the experimental data, what is the number of experimental repetitions? Were the results consistent across repeated tests? In cases where inconsistencies occurred, what criteria were used for data inclusion or exclusion?
4. Furthermore, the number of tested variables is somewhat limited, or the amount of experimental data for different values of the same variable is insufficient. As a result, the obtained findings are questionable.

Author Response

Comment 1: In the last sentence of the first paragraph of the Introduction, the authors state that "The ratcheting response of a material is strongly influenced by factors including the material's microstructural characteristics, applied stress levels and rates, dwell time periods, and loading patterns." However, the paper does not provide the metallographic structure of SS304 stainless steel and therefore does not consider the influence of microstructural characteristics.

Response 1: The authors would like to extend their thanks to the reviewer for the valuable comment. The microstructure of the material influences the ratcheting response of the material; however, it is not the primary scope of the current manuscript. Therefore, the authors only briefly mentioned that the material is an austenitic chromium-nickel alloy used for its formability and corrosion resistance in the material testing section to give readers a brief overview of its microstructure before continuing with the investigation of the static recovery condition.

Comment 2: The Introduction section of the manuscript provides a detailed review of the research status of the ratcheting phenomenon, particularly offering a critical assessment of existing mechanical models. Nevertheless, it does not clearly identify the novelty, significance, or the key issues to be addressed by the present study.

Response 2: Thanks for the reviewer’s comment. The authors would like to highlight the last paragraph in the introduction section, where the static recovery terms (SRT) in the A-V kinematic and L-Z isotropic hardening rules are outlined. The inclusion of the SRT in (i) the kinematic hardening rule, and (ii) the combined kinematic-isotropic hardening framework is the outlook of the present research, as addressed in the last paragraph of the introduction section.

Comment 3: The manuscript evaluates the ratcheting response of 304 stainless steel samples under uniaxial asymmetric loading cycles at room temperature using the combined A-V kinematic hardening framework and L-Z isotropic hardening framework. With regard to the experimental data, what is the number of experimental repetitions? Were the results consistent across repeated tests? In cases where inconsistencies occurred, what criteria were used for data inclusion or exclusion?

Response 3: The authors would like to express their thanks for the comment. The reference [34], where the data have been taken, presents no statistical data. The ratcheting data were found consistent in trend and discussion. The authors plan to perform more research investigations in future to study such consistency.

Comment 4: Furthermore, the number of tested variables is somewhat limited, or the amount of experimental data for different values of the same variable is insufficient. As a result, the obtained findings are questionable.

Response 4: The authors appreciate the valuable comment made by the reviewer. The authors’ intention is to further extend the present research and study different variables involved in the ratcheting of materials at various loading spectra, and elaborate on a more consistent and reliable assessment in the next phase of this research.

Reviewer 2 Report

Comments and Suggestions for Authors

This is a good paper on refining a constitutive model for predicting room-temperature ratcheting in austenitic chromium-nickel steel under cyclic loading with intermediate holding times. In the Introduction section, the authors clearly demonstrated the evolution of models for predicting the ratcheting effect and justified the purpose of the study. The mathematical part is described consistently and clearly. The experiment is well thought out. The authors demonstrated that including the static recovery term in the model significantly improves its accuracy, both in the kinematic and isotropic approaches. I have few questions about the paper.

How was the backstresses determined?

It appears that A-V fits the data better than A-V + L-Z in Figure 9.

What explains the discrepancy between the experiment and the model for the 10th cycle in Figure 8b?

Why do the authors write the strain rate as "%/sec" instead of the usual "1/sec"?

“Stainless steel 304 alloy” or “SS304 alloy” is an inappropriate expression. From here on, write “AISI 304 stainless steel” or “AISI 304 steel”.

Reference [12] appears before reference [11].

Author Response

Comment 1: How was the backstresses determined?

Response 1: The backstress increments were determined through use of the A-V kinematic hardening model (Eqs 10-11) as the loading magnitude exceeded the yield point (with the plastic strain increments). Backstress increments represent the shift of the center of the yield surface in the deviatoric stress space during plastic loading. These increments were calculated as load cycles were applied.

Comment 2: It appears that A-V fits the data better than A-V + L-Z in Figure 9.

Response 2: The authors would like to thank this valuable comment. The A-V hardening rule predicted ratcheting of steel samples tested at various hold time loading conditions (See figures 9 and 10) with a closer agreement with experimental data as compared with those predicted by the combined isotropic-kinematic framework. These figures intend to address the contribution of the SRT function, as coupled with the isotropic description. This trend is different in Figure 12(a) as the combined hardening framework, coupled with the SRT, resulted in a better prediction in the absence of dwell time in compression events. The authors keep working on different cases to further elaborate on such responses in upcoming research steps.

Comment 3: What explains the discrepancy between the experiment and the model for the 10th cycle in Figure 8b?

Response 3: The predicted hysteresis loops in Figure 8 by means of the A-V kinematic hardening model in the absence of the static recovery function in the framework. In Figure 8(b), the absence of SRT in the A-V model shows a slight underprediction of the predicted 10^th and 40^th hysteresis loops as compared with measured data obtained for loading with peak-valley hold times. This has been clarified in the manuscript.

Comment 4: Why do the authors write the strain rate as "%/sec" instead of the usual "1/sec"?

Response 4: The authors employed %/sec as the strain term was expressed by percentage (%) throughout the manuscript. To keep the units consistent, the strain rate is presented as %/sec.

Comment 5: “Stainless steel 304 alloy” or “SS304 alloy” is an inappropriate expression. From here on, write “AISI 304 stainless steel” or “AISI 304 steel”.

Response 5: The authors thank the comment made by the reviewer. This notation has been used earlier by several researchers in the literature. The authors will take note of this and implement the suggestions in any future works.

Comment 6: Reference [12] appears before reference [11].

Response 6: The correction has been implemented as recommended by the reviewer.

Reviewer 3 Report

Comments and Suggestions for Authors

1. Figure 8 shows the predicted hysteresis loops vs. the measured loops tested at 78 ± 234MPa with different conditions. Why the comparison analyses were inconsistant? For example, one is 100th cycle and the other is only 40th cycle.
2. What is the motivation for the material (i.e., 304 stainless steel) selection? If other metals, e.g., aluminium alloys or high strength steel, are also suitable for the proposed model ?
3. The section 2.1 elastic and plastic strain components is general knowledge. I suggest to shorten or remove this part. 
4. The strain rate effect should play a considerable role on the proposal work. However, the obtained results has few works on this effect. Please give a supplement or explanation.
5. If the elastic behaviour and yield function can make some effects on the ratcheting evaluation? 
6. The conclusions should be reorganized for the main findings with some quantitative results, especially for the comparison analyses between the proposal ratcheting evaluation method and the other method with single model.

Author Response

Comment 1: Figure 8 shows the predicted hysteresis loops vs. the measured loops tested at 78 ± 234MPa with different conditions. Why the comparison analyses were inconsistant? For example, one is 100th cycle and the other is only 40th cycle.

Response 1: The authors would like to extend their thanks for this valuable question. This is based on the availability of the experimental data reported in reference [34]. The no-hold tests conducted in this reference showed the experimental loops up to the 100^th cycle, whereas the hold condition only showed up to the 40^th cycle.

Comment 2: What is the motivation for the material (i.e., 304 stainless steel) selection? If other metals, e.g., aluminium alloys or high strength steel, are also suitable for the proposed model ?

Response 2: The importance of 304 stainless steel in ratcheting assessment of materials in the presence of dwell-time loading conditions are attributed to the time-dependency (rate dependency) of stainless steel. SS304 alloy is a broadly used material in industry for its great time-dependent characteristics, including corrosion resistance, and rate dependency of materials. These characteristics in stainless steels make them great candidates to investigate.

Comment 3: The section 2.1 elastic and plastic strain components is general knowledge. I suggest to shorten or remove this part.

Response 3: The authors thank the reviewer for this comment. The authors agree that these components are basic; they are essential parts of equations, and the authors wish to keep them in the manuscript.

Comment 4: The strain rate effect should play a considerable role on the proposal work. However, the obtained results has few works on this effect. Please give a supplement or explanation.

Response 4: The authors thank the comment made by the reviewer. A reference has been added and highlighted for the strain rate effect on the material, and this effect is given in Figure 2.

Comment 5: If the elastic behaviour and yield function can make some effects on the ratcheting evaluation?

Response 5: Thanks for the valuable comment/ question. The elastic response and yield function are essential to determine the yield surface as the onset of yielding in constitutive cyclic plasticity models. Section 2 in the manuscript addresses and describes the elements of cyclic plasticity modeling and their functions to assess backstress increments over loading cycles and to evaluate the ratcheting response.

Comment 6: The conclusions should be reorganized for the main findings with some quantitative results, especially for the comparison analyses between the proposal ratcheting evaluation method and the other method with a single model.

Response 6: This comment has been addressed as suggested by the reviewer.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The experimental data used by the authors for fitting are taken from a reference, and the issue of insufficient sample size in this manuscript is merely deferred to future research. This inevitably casts doubt on the scientific validity and credibility of the paper. It is recommended that the authors obtain the original experimental data from the cited reference or conduct experimental validation.

Author Response

Comment 1: The experimental data used by the authors for fitting are taken from a reference, and the issue of insufficient sample size in this manuscript is merely deferred to future research. This inevitably casts doubt on the scientific validity and credibility of the paper. It is recommended that the authors obtain the original experimental data from the cited reference or conduct experimental validation.

Response 1: The authors would like to thank the reviewer for this valuable comment. The objective of the present study is to analyze and assess the ratcheting results reported in reference [34] through the proposed analytical model. Test data at ambient temperature are the results of ratcheting in steel samples tested at a given cyclic stress level of 78 +/- 234 MPa, as demonstrated in Figure 4, to enable consistent evaluation of different loading spectra with and without hold time periods. The additional dataset falls outside the scope of the current work. The experimental results presented in reference [34] were considered sufficient to calibrate and assess ratcheting in the presence and absence of peak-valley hold time events at a constant applied cyclic stress level. While the authors acknowledge that a broader experimental dataset could further strengthen future investigations, the main focus of the present manuscript is to keep the framework of the assessment reflecting the influence of the hold-time period on the ratcheting level when the SRT is implemented.

Reviewer 3 Report

Comments and Suggestions for Authors

The revised manuscript and comments' replies can be accepted now.

Author Response

Comment 1: The revised manuscript and comments' replies can be accepted now.

Response 1: The authors would like to extend their thanks to the reviewer for the positive review of the manuscript.