Finite Element Analysis-Based Assessment of Damage Parameters for Ultra-Low-Cycle Fatigue Behavior of Structural Steels

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

What needs to be improved in the manuscript is added as an annex.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

The overall English expression of the manuscript is smooth, with fewer grammatical errors, which can effectively convey the research content.

Author Response

Dear Reviewer 1,

First of all, the authors would like to thank you for your comments that helped to improve this manuscript. Your guidelines were extremely helpful. Thank you. In the revised manuscript, content modifications made in line with your comments are highlighted in yellow. You may consider the manuscript to be technically correct now. Specific responses to your comments are as follows.

Comments 1 of Reviewer 1: “The description of the experimental method in the last two paragraphs of the introduction of the manuscript is mostly placed in the “Experimentation” section, and the last part of the introduction should be simplified.”

Response to Comments 1 of Reviewer 1: The last paragraph of the introduction was modified and moved to Section 2. This modified paragraph was inserted where there were sentences with the same details. Sentences of Section 2 with the same content are removed. Consequently, the introduction ended with the following sentence: “Finally, available experimental data were used for calibration purposes and this research provided results applicable in practice.” Therefore, the introduction is shortened and simplified, and there is no more repetition of the same information in successive sections of the paper. In addition, a careful review of the penultimate paragraph of the introduction revealed that it contained only a minimum of information relating to the available experimental data. For this reason, there was no need for any extensive modification of this paragraph. Regardless, this paragraph was simply divided into two smaller paragraphs.

Comments 2 of Reviewer 1: “The format of “0.2%/s” in the “These specimens were tested at a constant strain rate of 0.2%/s for a loading protocol with constant strain amplitudes of ±5% and ±7%.” Should be 10^-3s^-1 or 0.002s^-1.”

Response to Comments 2 of Reviewer 1: According to this comment, the unit "p.u./s" is used instead of the unit "%/s" throughout the revised manuscript.

Comments 3 of Reviewer 1: “In the part “Experimental Testing”, the strain amplitudes of species in the “These specimens were tested at a constant strain rate of 0.2%/s for a loading protocol with constant strain amplitudes of ±5% and ±7%.” is “±5% and ±7%”. Why in the sentence “According to [30], these loading cycles were performed at a constant strain rate of 0.2%/s and at constant strain amplitudes ranging from ±0.5% and ±4%.” is “±0.5% and ±4%”?”

Response to Comments 3 of Reviewer 1: The first sentence refers to the experimental results from Reference [26], while the second one refers to some mechanical and kinematic properties of S355 structural steel obtained experimentally and provided in Reference [30]. The experimental results from Reference [26] were obtained using “an ultimate tensile strength (UTS) load frame”, and the mechanical and kinematic properties from Reference [30] were obtained using “a universal tension, compression and torsion fatigue testing machine (MTS 880)”. Therefore, the experimental data used in this study were generated with two different testing machines in two different laboratories. These details were already provided in Section 2.2 together with the given sentences.

Comments 4 of Reviewer 1: “The picture in Figure 7 should be clearer.”

Response to Comments 4 of Reviewer 1:  The first version of Figure 7 represents a screenshot of a geometric model generated in the SIMULIA Abaqus 6.11 software. This software does not allow for the direct export of geometric models of this kind to another document or file. In this regard, the authors have attempted to improve the quality of Figure 7 and a slightly clearer version of this illustration is now included in the revised manuscript.

Comments 5 of Reviewer 1: “Equation 1 lacks an explanation for “a”.”

Response to Comments 5 of Reviewer 1: After Equation (1), the missing parameter definitions are now added. Specifically, for the stress and the backstress.

Comments 6 of Reviewer 1: “The format of Figure 3 is suggested to be uniform, such as picture size and font color.”

Response to Comments 6 of Reviewer 1: The formats of Figures 3a and 3b are now uniform, that is, the size of these figures and the font color in them are unified as requested.

Comments 7 of Reviewer 1: “Specify the constraints on the grip end of the specimen (e.g. fully fixed or allow sliding friction)”

Response to Comments 7 of Reviewer 1: The response to this comment is as follows: “The left grip of the specimen was fully fixed along its entire circumference, while the right one could move freely under the effect of the applied displacement amplitude. Specifically, the right grip was movable, and its nodes were tied to a reference point on the specimen axis. The reference point belongs to the end surface of the right grip.” These three sentences were added to Section 4 in the paragraph where the term “displacement amplitude” is mentioned for the first time.

Comments 8 of Reviewer 1: “The number of meshing points in Figure 7 suggests that relevant literature should be supplemented.”

Response to Comments 8 of Reviewer 1: Since all geometric models were created in SIMULIA Abaqus 6.11 software, it is sufficient to use Reference [22] regarding the finite element meshes and Figure 7. This reference provides the relevant details on meshes used. Based on Reference [22], the following answer is given: “According to [22], finite elements of type C3D8R were used for the discretization of each S355 specimen. The number of finite elements was 4032, and they were connected to a total of 504 nodes.” This answer was added to Section 4 in the paragraph describing Figure 7.

Comments 9 of Reviewer 1: “The overall English expression of the manuscript is smooth, with fewer grammatical errors, which can effectively convey the research content.”

Response to Comments 9 of Reviewer 1: In connection with this comment, a number of grammatical errors were identified and removed from the content.

 

Sincerely Yours,

 

Prof. Dr. Dardan Klimenta

On behalf of all the authors.

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper, the ULCF behavior of S355 and S690 steel specimens was studied based on finite element analysis. The damage parameters in the ULCF of structural steels were also studied. The content is interesting.

Due to the limited knowledge of the reviewer, the content of the paper is difficult to understand. Please add at least a detailed explanation (including figures) of the Kliman model and Chaboche–Lemaitre (C–L). Equations (7) and (9) contain an explanation of the damage parameters (hysteresis loop area), but a more detailed explanation (including diagrams) is needed. I think an explanation is needed regarding the specific element division diagram of the test piece in FEA and the calculation time, etc.

Please also consider the following points.

(1) Lines 109-116 and 120-127:

The description of the experimental data is duplicated. I think it would be better to delete one of them.

(2) The values ​​of the damage parameters are shown in Table 2. Compare these values ​​with values ​​obtained from other studies and discuss their physical meaning and validity.

(3) Figures 3 and 4:

Please indicate the representative number of cycles (5, 10, 15, 20) in the figures. Also, why is the total strain not constant in the simulation? The conditions are different from the experiment.

(4) Please add a discussion on N0 in equation (7). Also, please discuss the effect of the total strain amplitude on N0 and compare and discuss the results with the experimental results.

(5) Figures 4 and 5:

Is the relationship between D and N linear? Also, show the effect of total strain on the D-N relationship and compare it with the experimental results.

(6) Please add the relationship between the total strain range and fatigue life Nf. Please compare it with the experimental trends of ULCF and low cycle fatigue, and discuss it so that the characteristics of ULCF can be understood.

Author Response

Dear Reviewer 2,

First of all, the authors would like to thank you for your comments that helped to improve this manuscript. Your guidelines were extremely helpful. Thank you. In the revised manuscript, content modifications made in line with your comments are highlighted in green. You may consider the manuscript to be technically correct now. Specific responses to your comments are as follows.

General comments of Reviewer 2: “In this paper, the ULCF behavior of S355 and S690 steel specimens was studied based on finite element analysis. The damage parameters in the ULCF of structural steels were also studied. The content is interesting.

Due to the limited knowledge of the reviewer, the content of the paper is difficult to understand. Please add at least a detailed explanation (including figures) of the Kliman model and Chaboche–Lemaitre (C–L). Equations (7) and (9) contain an explanation of the damage parameters (hysteresis loop area), but a more detailed explanation (including diagrams) is needed. I think an explanation is needed regarding the specific element division diagram of the test piece in FEA and the calculation time, etc.

Please also consider the following points.”

Response to the general comments of Reviewer 2: First of all, the authors are grateful for the recognition of the significance of this study and thank Reviewer 3 for the suggestion to expand the content. However, the Kliman’s model for the hysteresis energy of cyclic loading and the non-linear Chaboche–Lemaitre (C–L) combined isotropic–kinematic hardening model cannot be given on this occasion because their presentation would significantly expand and overload the content of this paper. The source references where these models are described in detail are duly cited throughout the content and interested readers can easily find them via the DOI identifier. For instance, a description of the Kliman’s model can be found in References [36] and [37], while a description of the non-linear Chaboche–Lemaitre model can be found in References [22] and [24]. The same applies to Equations (7) and (9). Explanations regarding these two equations can be found in Reference [23]. The finite element meshes were generated automatically in the SIMULIA Abaqus 6.11 software and more details on how they were generated can be found in the online source [22]. In accordance with these general comments, the revised content now includes data on the type of finite elements, their total number and the total number of nodes connecting them, as well as the computation time. Specifically, details about the finite elements used and computation time are given by the following sentences: “According to [22], finite elements of type C3D8R were used for the discretization of each S355 specimen.”, “The number of finite elements was 4032, and they were connected to a total of 504 nodes.”, and “Each FEA-based simulation lasted about 8 hours.”, which are inserted in the table of contents.

Comment 1 of Reviewer 2: “Lines 109-116 and 120-127: The description of the experimental data is duplicated. I think it would be better to delete one of them.”

Response to Comment 1 of Reviewer 2: The last paragraph of the introduction was modified and moved to Section 2. This modified paragraph was inserted where there were sentences with the same details. Sentences of Section 2 with the same content were deleted. Consequently, the introduction ended with the following sentence: “Finally, available experimental data were used for calibration purposes and this research provided results applicable in practice.” Therefore, the introduction is shortened and simplified, and there is no more repetition of the same information in successive sections of the paper. Moreover, this is also a part of the response given to Comment 1 of Reviewer 1.

Comment 2 of Reviewer 2: “The values ​​of the damage parameters are shown in Table 2. Compare these values ​​with values ​​obtained from other studies and discuss their physical meaning and validity.”

Response to Comment 2 of Reviewer 2: The parameter values ​​from Table 2 were obtained by applying empirical researches and calibration based on available experimental data, existing literature and a large number of FEA-based simulations in SIMULIA Abaqus 6.11 software for different S355 steel specimens at total strain amplitudes of ±0.05 p.u. and ±0.07 p.u. This was also stated at the beginning of Section 4. In particular, the parameters ​​from Table 2 were obtained for material types and test conditions identical to those from Reference [26], and to the best of the authors' knowledge, there are no other results of such or similar studies in the available literature. This is the main reason why the obtained damage initiation and evolution parameters could not be compared with some other damage parameters. For instance, Reference [5] provides certain values of the damage initiation and evolution parameters, but these parameters were generated for 9Cr alloy steel exposed simultaneously to thermal and mechanical loadings. Logically, the values ​​of such damage parameters cannot be compared with the values ​​of the corresponding damage parameters from Table 2, and so on.

Comment 3 of Reviewer 2: “Figures 3 and 4: Please indicate the representative number of cycles (5, 10, 15, 20) in the figures. Also, why is the total strain not constant in the simulation? The conditions are different from the experiment.”

Response to Comment 3 of Reviewer 2: The number of cycles to failure in the caption of Figure 3 was incorrect. The caption of Figure 3 is now as follows: “Figure 3. Stress-strain curves of the first S355 specimen generated for a total strain amplitude of ±0.05 p.u. and: (a) 10 cycles to failure – experimental result taken from [26]; (b) 20 cycles to failure – simulated result.” Accordingly, the representative numbers of cycles to failure are now correctly indicated. This was an authors' oversight that occurred during the writing process. Specifically, the number of half-cycles to failure appears in the experimental results from Reference [26], while the number of cycles to failure has been used in this paper. Therefore, 20 half-cycles to failure from Reference [26] are actually equal to 10 cycles to failure, and so on. In connection with this, in Reference [26], three identical specimens were tested under the same conditions and the number of cycles to failure was 20, 9.5 and 10 for them. To avoid confusion, the simulated result from Figure 3b corresponds to the experimental result obtained for the first specimen from this series, and Figure 3a shows the experimental result that corresponds to the third specimen from the same series. Therefore, none of the three tests provided the same number of cycles to failure. Similarly, it was not possible to faithfully reproduce the test conditions from the laboratory in SIMULIA Abaqus 6.11. Moreover, from the damage diagram in Figure 4a, it can be seen that a smaller number of cycles to failure corresponds to linear material degradation. By default, the requirement for direct cyclic analysis is to achieve a stabilized hysteretic response, but, under ULCF conditions, achieving a stabilized state is difficult due to the small number of cycles to failure. According to Figure 1, 6 or 7 cycles are required to achieve a stabilized hysteretic response, which can be seen (in Figure 3b) as a gradual increase in deformation up to the specified value. Figure 3b shows the result of the simulation where failure occurred after 20 cycles out of the specified 30 cycles. The specified number of cycles to failure is greater than the actual one, but the simulated result remained within the limit values ​​from the corresponding experiment. According to Figure 4a, the loading time of 120 s corresponds with the specified 30 loading cycles, considering that, according to Figure 4b, one single cycle lasts 4 s. The increase in deformation relative to the specified value occurs in cycles and final failure is the result of overall disintegration of the model. For this reason, the total strain amplitude in the simulations could not be constant. This issue has now been addressed by revisions within discussion of Figure 3, as well as throughout the content. In this regard, the following paragraph was added to Section 4: “In fact, according to [26], the first S355 specimen belonged to a series of three identical specimens (labeled with “L3C51”, “L3C52” and “L3C53”) that were tested under the same conditions and the number of cycles to failure for them was 20, 9.5 and 10. To avoid confusion, the simulated result from Figure 3b corresponds to the experimental result obtained for the first (“L3C51”) specimen from this series. While Figure 3a shows the experimental result that corresponds to the third (“L3C53”) specimen from the same series. None of the three tests resulted in the same number of cycles to failure. Accordingly, a reproduction of the conditions from the given tests in SIMULIA Abaqus 6.11 could have resulted in any number of cycles to failure in the range of 9 to 20. However, it turned out that the simulation gave 20 cycles to failure. Therefore, the experimental result in Figure 3a was chosen from three available results with the intention of showing that a FEA-based simulation does not have to generate a number of cycles to failure that is identical to that from the corresponding experiment.”

Comment 4 of Reviewer 2: “Please add a discussion on N0 in equation (7). Also, please discuss the effect of the total strain amplitude on N0 and compare and discuss the results with the experimental results.”

Response to Comment 4 of Reviewer 2: In response to this comment, the following text was added after Equation (7):  “where  is the accumulated inelastic hysteresis strain energy per stabilized cycle.  and  are the damage initiation parameters for the type of material used, which will be calibrated using appropriate experimental data. According to [35], a linear relationship between the accumulated inelastic hysteresis strain energy and damage initiation per each cycle can be obtained by taking the logarithms of both sides of Equation (7). Moreover, according to some relevant standards, there are criteria for damage initiation and final failure based on the plastic strain amplitude  obtained experimentally [35]. For specimens exposed to ULCF loadings in laboratories, the plastic strain amplitudes usually are equal to or greater than 0.025 p.u., which means that the specimens can be damaged even in the first cycle.” For this response, the following reference was used: 35. Song, W.; Liu, X.; Xu, J.; Fan, Y.; Shi, D.; Yang, F.; Xia, X.; Berto, F.; Wan, D. Low-cycle fatigue life prediction of 10CrNi3MoV steel and undermatched welds by damage mechanics approach. Front. Mater. 2021, 8, 641145. https://doi.org/10.3389/fmats.2021.641145. This resulted in the change of ordinal numbers of some references within the content.

Comment 5 of Reviewer 2: “Figures 4 and 5: Is the relationship between D and N linear? Also, show the effect of total strain on the D-N relationship and compare it with the experimental results.”

Response to Comment 5 of Reviewer 2: Figure 4 corresponds with the simulated hysteretic response from Figure 3b that was obtained for the first S355 specimen at a total strain amplitude of ±0.05 p.u., while Figure 5 shows the stress-strain curves of the second S355 specimen generated for a total strain amplitude of ±0.07 p.u. Therefore, Figures 4 and 5 are not mutually comparable. In this regard, the correlations between Figures 4 and 3b, as well as between Figures 6 and 5b, have already been described in Section 4. In addition, the dependence of the damage on the number of cycles to failure from Figure 6a is linear. This information is provided in Section 4 within the paragraph describing Figure 6.

Comment 6 of Reviewer 2: “Please add the relationship between the total strain range and fatigue life Nf. Please compare it with the experimental trends of ULCF and low cycle fatigue, and discuss it so that the characteristics of ULCF can be understood.”

Response to Comment 6 of Reviewer 2: To the best of the authors' knowledge, a formula or expression that directly correlates the total strain amplitude and the total number of cycles to failure does not exist. For this purpose, procedures such as the one proposed and described in the present paper can be used. The revised content provides comparisons of simulated and experimental results, explains specific trends of the results, and discusses the results to a greater or lesser extent.

 

Sincerely Yours,                                                                  

 

Prof. Dr. Dardan Klimenta

On behalf of all the authors. 

Reviewer 3 Report

Comments and Suggestions for Authors

Employing a direct cyclic algorithm via SIMULIA Abaqus 6.11 FEA software and utilizing previously reported experimental results, the present study calibrated the damage parameters associated with ultra-low cycle fatigue (relevant for severe seismic events) of structural steels.  

The following points should be addressed during revision. 

A1. Figs. 3, 5 and others– It is not clear why the simulated total strain amplitude is much higher than that used for calibration purposes (experimental from literature). Clearly explain the deviation scientifically. 

A2. “In the numerical analysis, the initiation of damage and the rate of damage/crack evolution in the specimen were not defined, but a continuum damage model for ULCF of the material. ….” – Why?

A3. Page 14: “The experimental result corresponds with 23 cycles to failure, and the numerical result corresponds with 12 cycles to failure.” – Why? Explain.

 

B1. The results and discussion section are monotonous. Some examples of experimental and simulation results (& figures) from Ref. [26] should be dropped (say, Figs. 11 and 12 and related text).

 

C1. The conclusions part may be divided into ‘conclusions’ and ‘limitations and future work’.

 

D1. It is true that the authors have adequately cited and referred to the source of experimental results taken from the literature. Even then, section ‘2. Experimentation’ is unjustified for the present article since the current research is only limited to ‘simulation’.

Furthermore, this part and the last paragraph of the Introduction section (and similar statements elsewhere) are nothing but unnecessary repetition.

It is suggested that ‘2. Experimentation’ should be dropped entirely. A small section may be added at the end of the Introduction section, which will very briefly highlight the experimental details that were utilized for calibration in the present simulation work.

 

E1. Rewrite it indirectly – “Due to ultra-low cycle fatigue (ULCF), steel structures subjected to earthquakes 15 or extreme cyclic loadings can undergo extensive damages leading to fractures.”

E2. Instate of writing what was studied in Refs. XX or YY only, some findings of these reports should also be highlighted, which was not the case at present in the Introduction. 

 

Comments on the Quality of English Language

Polishing of English is needed.

Author Response

Dear Reviewer 3,

First of all, the authors would like to thank you for your comments that helped to improve this manuscript. Your guidelines were extremely helpful. Thank you. In the revised manuscript, content modifications made in line with your comments are highlighted in turquoise. You may consider the manuscript to be technically correct now. Specific responses to your comments are as follows.

General comments of Reviewer 3: “Employing a direct cyclic algorithm via SIMULIA Abaqus 6.11 FEA software and utilizing previously reported experimental results, the present study calibrated the damage parameters associated with ultra-low cycle fatigue (relevant for severe seismic events) of structural steels.  

The following points should be addressed during revision.”

Response to the general comments of Reviewer 3: The authors are grateful for the recognition of the contributions presented in this study and once again thank Reviewer 3 for the comments.

Comment 1 of Reviewer 3: “A1. Figs. 3, 5 and others– It is not clear why the simulated total strain amplitude is much higher than that used for calibration purposes (experimental from literature). Clearly explain the deviation scientifically.”

Response to Comment 1 of Reviewer 3: In the simulations of the initial loading cycles, the total strain amplitude was less than or approximately equal to ±0.05 p.u. (Figures 3b and 9b) because the material under consideration was deformed to a lesser extent. With the simulation of each subsequent loading cycle, the material was more and more deformed, and the total strain amplitude gradually exceeded the value of ±0.05 p.u. This phenomenon was originally illustrated in Figure 2. Moreover, the same occurred when the total strain amplitude was ±0.07 p.u. (Figures 5b and 11b), regardless of the material from which the tested specimen was made. Each FEA-based simulation lasted about 8 hours. Therefore, the main reason for the deviation of the simulated hysteresis loops from the experimental ones were the conditions specified in the model. These conditions directly affected the establishment of stabilized states during the simulations of the ULCF behaviors of the considered specimens. Specifically, in these simulations the number of cycles to failure was low, and the model itself tended to reach a stabilized hysteretic response after 6 or 7 cycles. At lower total strain amplitudes, this negative phenomenon was not particularly pronounced. This can be seen from the plots in Figure 13 which were generated for a total strain amplitude of ±0.0074 p.u. This response refers to the results from Figures 3b, 5b, 9b and 11b, and is inserted within the discussion of Figure 13 in Section 4.

Comment 2 of Reviewer 3: “A2. “In the numerical analysis, the initiation of damage and the rate of damage/crack evolution in the specimen were not defined, but a continuum damage model for ULCF of the material. ….” – Why?”

Response to Comment 2 of Reviewer 3: In the direct cyclic analysis, it is not possible to model the crack initiation and the rate of crack growth/evolution in materials. For this kind of analysis, SIMULIA Abaqus 6.11 uses a method based on a J-integral method and a Paris Law type relationship. The advantages of defining a continuum damage model for ULCF of any material are the simplicity of modeling and the possibility of applying it to real structural elements, as well as good agreement of simulated fractures using this model with the corresponding experimental data. The disadvantages of the model based on the crack initiation and the rate of crack growth are the requirements regarding a large number of assumed parameters ​​and applications limited to scientific purposes only. In addition, the sentence mentioned in this comment is modified in the following way: “In the numerical analysis, the initiation of damage and the rate of damage/crack evolution in the specimen material were not defined, but a continuum damage model for ULCF of the material was applied (in SIMULIA Abaqus 6.11).”

Comment 3 of Reviewer 3: “A3. Page 14: “The experimental result corresponds with 23 cycles to failure, and the numerical result corresponds with 12 cycles to failure.” – Why? Explain.”

Response to Comment 3 of Reviewer 3: Obviously, this comment refers to Figure 9a. It is true that the sentence describing Figure 9 read: “The experimental result corresponds with 23 cycles to failure, and the numerical result corresponds with 12 cycles to failure.” However, this was an authors' oversight that occurred during the writing process. Specifically, the number of half-cycles to failure appears in the experimental results from Reference [26], while the number of cycles to failure has been used in this paper. Therefore, 23 half-cycles to failure from Reference [26] are equal to 11.5 cycles to failure, which is approximately equal to 12 cycles to failure obtained in the corresponding FEA-based simulation. The given sentence now reads: “The experimental result corresponds with 11.5 cycles to failure, and the numerical result corresponds with 12 cycles to failure.” This issue has now been addressed by revisions throughout the content.

Comment 4 of Reviewer 3: “B1. The results and discussion section are monotonous. Some examples of experimental and simulation results (& figures) from Ref. [26] should be dropped (say, Figs. 11 and 12 and related text).”

Response to Comment 4 of Reviewer 3: It is true that some parts of Section 4 entitled "Results and Discussion" are monotonous, but these parts are very important because they include available experimental data that were used for calibration of the damage parameters. Unfortunately, there are not many linguistic options for presenting and describing the data generated by conducting a series of the same experiments, so monotony of content is inevitable in these parts. In the same way, the exclusion of some experimental data from Reference [26] and the associated simulated results and illustrations cannot be done because it would reduce the generality of the calibrated damage parameters. Specifically, this study used the minimum amount of experimental data necessary for generalizing the results and conclusions, namely experimental data obtained for two types of structural steels and two values ​​of the total strain amplitude.

Comment 5 of Reviewer 3: “C1. The conclusions part may be divided into ‘conclusions’ and ‘limitations and future work’.”

Response to Comment 5 of Reviewer 3: It is uncommon for the concluding section to be divided into subsections, so this was not done on this occasion. However, the conclusion is divided into paragraphs so that it is clear what are the conclusions (first three paragraphs), limitations (penultimate paragraph), and future research (last paragraph).  In this regard, in the penultimate paragraph, the term "shortcomings" was replaced with the term "limitations". Also, in accordance with Comment 8 of Reviewer 4, the last paragraph providing future researches now reads: “Future research will focus on typical application scenarios for structural steels of the types S355 and S690 in seismic structures, calibration of material damage parameters for other types of structural steels, and a comparative analysis of results obtained using the direct cyclic algorithm and other applicable models. In addition, the implementation of some FEA-based models that would include the reality, that is, the nonlinearity of material damage growth, could also be considered.”

Comment 6 of Reviewer 3: “D1. It is true that the authors have adequately cited and referred to the source of experimental results taken from the literature. Even then, section ‘2. Experimentation’ is unjustified for the present article since the current research is only limited to ‘simulation’.

Furthermore, this part and the last paragraph of the Introduction section (and similar statements elsewhere) are nothing but unnecessary repetition.

It is suggested that ‘2. Experimentation’ should be dropped entirely. A small section may be added at the end of the Introduction section, which will very briefly highlight the experimental details that were utilized for calibration in the present simulation work.”

Response to Comment 6 of Reviewer 3: According to the first part of this comment, the title of Section 2 which read "2. Experimentation" was replaced by the following title "2. Experimental Background". In addition, in accordance with the second part of this comment, the following modifications were made: The last paragraph of the introduction was modified and moved to Section 2. This modified paragraph was inserted where there were sentences with the same details. Sentences of Section 2 with the same content were deleted. Consequently, the introduction ended with the following sentence: “Finally, available experimental data were used for calibration purposes and this research provided results applicable in practice.” Therefore, the introduction is simplified, and there is no more repetition of the same information in successive sections of the paper. Moreover, this is also a part of the response given to Comment 1 of Reviewer 1, as well as the response given to Comment 1 of Reviewer 2. Finally, in connection with the third part of this comment, Section 2 was not deleted, but the last paragraph of the introduction was removed, and in this way a compromise was made between this suggestion and the corresponding comments of Reviewers 1 and 2. The authors sincerely hope that this response is acceptable.

Comment 7 of Reviewer 3: “E1. Rewrite it indirectly – “Due to ultra-low cycle fatigue (ULCF), steel structures subjected to earthquakes 15 or extreme cyclic loadings can undergo extensive damages leading to fractures.””

Response to Comment 7 of Reviewer 3: The given sentence was rewritten in the following way: “Steel structures subjected to earthquakes or extreme cyclic loadings may undergo extensive damages and fractures due to ultra-low cycle fatigue (ULCF).”

Comment 8 of Reviewer 3: “E2. Instate of writing what was studied in Refs. XX or YY only, some findings of these reports should also be highlighted, which was not the case at present in the Introduction.”

Response to Comment 8 of Reviewer 3: In the introduction, the literature review was modified in accordance with this comment. In particular, the most important findings or conclusions from some of the references reviewed were included in the introduction.

Comment 9 of Reviewer 3: “Polishing of English is needed.”

Response to Comment 9 of Reviewer 3: In connection with this comment, the authors have carefully revised the text and removed a number of existing grammatical errors.

 

Sincerely Yours,                                                                  

 

Prof. Dr. Dardan Klimenta

On behalf of all the authors.

Reviewer 4 Report

Comments and Suggestions for Authors

- The abstract does not explain the difference between the innovation of the research and the existing research. Clearly list the main innovations of the research.

- Literature citations focus on reviews before 2023, but the latest studies in recent two years are not fully discussed.

- The objective of the study is vague, and it is not clear why S355/S690 steel was chosen and its engineering significance. The typical application scenarios of the two types of steel in seismic structures are suggested to add, and the practical value of parameter calibration need to be emphasized.

-Add parameter definitions and engineering explanations of values in the manuscript.

-The physical meaning of the symbols in the formula is not clear.
-No explanation was given as to why the model was chosen over other models, and comparative analysis was lacking.

-The calibration process does not mention statistical methods and lacks confidence verification.

-Key findings were not summarized in the conclusion, and future work was presented in general terms.

-Some sentences are long and concise.

Author Response

Dear Reviewer 4,

First of all, the authors would like to thank you for your comments that helped to improve this manuscript. Your guidelines were extremely helpful. Thank you. In the revised manuscript, content modifications made in line with your comments are highlighted in pink. You may consider the manuscript to be technically correct now. Specific responses to your comments are as follows.

Comment 1 of Reviewer 4: “The abstract does not explain the difference between the innovation of the research and the existing research. Clearly list the main innovations of the research.”

Response to Comment 1 of Reviewer 4: In the abstract, the main innovation of this study has already been provided in the following sentence: "Although assessments of the damage initiation and evolution parameters have been carried out for some steels exposed to low cycle fatigue, so far these parameters for structural steels exposed to ULCF have neither been sufficiently studied nor quantified. " Therefore, the main innovation of this study is: Analysis and quantification of the damage initiation and evolution parameters for some structural steels exposed to ultra-low cycle fatigue (ULCF). At the same time, in the given sentence the main innovation was contrasted with the existing researches. In addition, there are four scientific and/or engineering contributions and they are highlighted at the end of the introduction. These contributions could not be included in the abstract due to the existing limitation on the number of words.

Comment 2 of Reviewer 4: “Literature citations focus on reviews before 2023, but the latest studies in recent two years are not fully discussed.”

Response to Comment 2 of Reviewer 4: In the literature review, the period up to 2023 is covered by the review papers [6] and [7]. References [6] and [7] review a number of literature sources published in 2023. References published in 2023 are References [8-10] and they are all mentioned in the introduction. After the references from 2023, references published in 2024 and 2025 were also included in the review. The authors re-checked the literature review and found that all references representing the relevant state-of-the-art were included.

Comment 3 of Reviewer 4: “The objective of the study is vague, and it is not clear why S355/S690 steel was chosen and its engineering significance. The typical application scenarios of the two types of steel in seismic structures are suggested to add, and the practical value of parameter calibration need to be emphasized.”

Response to Comment 3 of Reviewer 4: The finite element analyses of S355 and S690 steels were carried out because these materials belong to two different groups of structural steels. S355 steel belongs to the group of ordinary structural steels, it is a structural steel of increased strength, applicable in the construction of bridges, buildings, etc. The use of non-alloy structural steels is the most common. S690 steel belongs to the group of high-strength steels (i.e., the group of structural steels with improved yield strength), which are increasingly used for modern constructions of tall buildings and bridges with larger spans and/or loadings. The steels with improved yield strength are all steels that are quenched which means the complete elimination of oxygen from their composition. Ordinary S355 steel was chosen because it is often used in the design of new structures, as well as actual-state analyses of existing structures. High-strength S690 steel was chosen because of its mechanical properties and application in high-rise building and structures, but also because, compared to ordinary steels, it has low fracture toughness without a pronounced plasticity level. In structures, low fracture toughness represents a danger due to exceeding the yield stress of the material without any clear limit, as well as the possibility of fracture of the material without warning under the effect of deformation. The practical significance of the considered damage initiation and evolution parameters is related precisely to the modeling of real structural elements, such as beam-to-column connections and truss structures, as demonstrated in Figures 8a and 8b using finite elements of different types. Typical application scenarios for these two types of steel in seismic structures are not given on this occasion because their analysis would significantly expand the content of the paper. Also, these typical application scenarios are listed at the end of the conclusion as one of future research. In connection with this comment, the following sentences: “S355 steel was chosen because it belongs to the group of ordinary structural steels whose usage is the most common.”, “While S690 steel was chosen because it belongs to the group of structural steels with improved yield strength whose applications in the construction industry are extensive.”, and “The practical significance of the damage parameters is related precisely to the modeling of real structural elements such as beam-to-column connections and truss structures.” were inserted in the appropriate places in the introduction.

Comment 4 of Reviewer 4: “Add parameter definitions and engineering explanations of values in the manuscript.”

Response to Comment 4 of Reviewer 4: Definitions and physical meanings of all parameters used are given in the content, and more information about these parameters can be found in the references cited. Specifically, each definition is supported by a citation to the appropriate literature source.

Comment 5 of Reviewer 4: “The physical meaning of the symbols in the formula is not clear.”

Response to Comment 5 of Reviewer 4: An additional check of the formulas used revealed that the physical meaning was not provided for only two parameters in Equation (1). This issue has now been addressed. This was also requested by Reviewer 1 in Comment 5.

Comment 6 of Reviewer 4: “No explanation was given as to why the model was chosen over other models, and comparative analysis was lacking.”

Response to Comment 6 of Reviewer 4: The presented direct cyclic algorithm was chosen because of its applicability in practical calculations of engineering structures and because it provides the possibility of specifying the number of loading cycles and enables monitoring of material damage by individual loading cycles. In this paper, the emphasis is placed on defining the damage parameters based on data obtained by testing specimens made from specific materials, i.e., structural steels of the types S355 and S690. This was done because there is a lack of data for the structural steels considered. In connection with this, the following has already been stated in the introduction: “According to [22,23], the direct cyclic algorithm combines a Fourier series approximation with a time integration scheme (for the non-linear UCLF behavior of the specimens) to obtain the stabilized hysteretic responses iteratively using modified Newton method. In particular, the direct cyclic algorithm was used to determine the number of cycles to the initiation of damage and the rate of damage after each individual loading cycle. Compared to other standardized models that provide total damage over the fatigue life of a material, the application of the direct cyclic algorithm to the ULCF behavior of the specimens represents an advantage, and also another contribution of this research.” Another applicable model for material damage analysis would be one that deals with crack initiation and growth, the so-called “XFEM model”, which cannot be easily used for calculations of real structures because it is based on a local solution of the problem. Furthermore, there are a number of other models that can be applied to analyze this problem. Certainly, a comparative presentation of the results obtained using the mentioned models is desirable, but it would significantly expand the content of this paper. Accordingly, this detail is added at the end of the conclusion as a potential topic for future research.

Comment 7 of Reviewer 4: “The calibration process does not mention statistical methods and lacks confidence verification.”

Response to Comment 7 of Reviewer 4: Statistical methods were not used for the calibration of the damage initiation and evolution parameters, so there was no need to verify confidence. In connection with the calibration process, the following has already been provided in the first paragraph of Section 4: “Based on available experimental data, existing literature and a large number of simulations performed in SIMULIA Abaqus 6.11 [22], the values ​​of the damage initiation and evolution parameters for different S355 steel specimens at total strain amplitudes of ±0.05 p.u. and ±0.07 p.u. were empirically treated and calibrated.”

Comment 8 of Reviewer 4: “Key findings were not summarized in the conclusion, and future work was presented in general terms.”

Response to Comment 8 of Reviewer 4: An additional check of the conclusion revealed that the key findings together with possible future researches were already provided. It is also true that future research directions are given in general form. In this regard, the part of the conclusion where future researches are listed is modified as follows: “Future research will focus on typical application scenarios for structural steels of the types S355 and S690 in seismic structures, calibration of material damage parameters for other types of structural steels, and a comparative analysis of results obtained using the direct cyclic algorithm and other applicable models. In addition, the implementation of some FEA-based models that would include the reality, that is, the nonlinearity of material damage evolution, could also be considered.”

Comment 9 of Reviewer 4: “Some sentences are long and concise.”

Response to Comment 9 of Reviewer 4: Extremely long and non-concise sentences were logically shortened or divided into clearer sentences.

 

Sincerely Yours,                                                                  

 

Prof. Dr. Dardan Klimenta

On behalf of all the authors.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The revisions are acceptable.