A Cyclic Plasticity Model with Martensite Transformation for S30408 and Its Finite Element Implementation
Round 1
Reviewer 1 Report
Thank you for this interesting work.
Introduction: on page 3, line 23, you mention Sito as author of [24], please check spelling
Uniaxial experiments: on page 4 you provide a table for the mechanical properties of S30408. Please indicate for which temperature this data are valid. If the tension curve exhibits a plateau at 580 MPa, up to 8% strain, and assuming this plateau is due to the formation of martensite, please give a comment on the further strain hardening mechanism of the material since σb reaches 1324 MPa ! The same Table 1: please give a reference if you used data from another work and provide an explanation for the σ0 parameter because you are using it later in the paper, you can also omit the explanation later
Uniaxial ratcheting experiments: on page 5, Fig.3, please indicate for each subgraph in Fig.3, the number of cycles. This will give an idea about the amount of ratcheting strain accumulated per cycle. On page 6, line 8, you write cycle times, do you mean cycle number ?
Improve quality of Fig.4, one curve is not visible.
Presentation of the constitutive models: The authors should give a bit more explanations about the parameters used in the equations, specially the significance of dp in equations 4 -8, for instance. All calculated parameters shown in Table 3 should be found in the models (χ=0?)
The constitutive model with martensite transformation: again in equation 17 the significance of parameters , Q, R an p should be explained ! Please cite also an adequate reference.
On point 7 , page 10, you state that the martensite content presents a rapid increase at the begining and then is stable. Where from do you know it? Can you give a reference? How big is the saturation value? or you should better present the results of Fig. 9b there
Determination of constitutive model parameters:
Where from equation 19, give a reference and explain the parameters used?
At the bottom of page 11, determined by trail at present , do you mean trial?
Change the caption of the x-axis in Fig.9 a,b to Cumulative plastic strain
Use two colors to differentiate the lines ωm =1 and 3 in Fig.9 c
Regarding the parameters C and Q, you fit them using Fig.9a, showing only 8% of cumulative strain. Which loading condition have you used to generate Fig.9 a ? Indicate them! Did you determine the martensite content in the same experiment? Did you observe some isotropic softening at a cumulative strain of 30%?
Give the unit of Q in Table 3, page 12. This table should be Table 4!
Model prediction results:
It seems you missed the y axis label in Fig.13, page 14! You should also improve the choice of the symbols and line settings to make the diagram more readable, line 290/215 is invisible!
In Fig.20, please change the legend , experiment and simulation (instead of martensite)
Conclusions:
On page 21, first conclusion. I think you could improve the text: because of the consideration that the deformation induced martensite influences both the isotropic and the kinematic hardening
Second conclusion: has higher prediction ability... do you mean gives a good prediction for the martensite content ?
There is a spelling error on the word semitrailor, you write semitraior at two locations on page 21
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The Ohno-Wang II model was extended to take into account the effect of martensitic transformation in a metastable austenitic stainless steel S30408. It was assumed that martensitic transformation affects both isotropic and kinematic hardening. The extended model was used to accurately simulate uniaxial ratchetting experiments of the material that were performed at a cryogenic temperature 110K. The extended model was implicitly implemented in ANSYS via a user subroutine, and was used to analyze uniaxial ratchetting of round bar specimens. A combined tension-torsion multiaxial ratchetting test was also analyzed to show a good agreement with the experiment. This paper has new contents, and is of quite interest. The paper is, therefore, recommended for publication provided that the paper is revised based on the following comments.
- It was assumed martensitic transformation affects not only isotropic but also kinematic hardening. It is recommended to describe why kinematic hardening is affected by martensitic transformation. This description helps the readers understand the paper.
- Four material parameters, h, b, Q, and ωm, were introduced for the effect of martensitic transformation in kinematic and isotropic hardening equations (Eqs. (16)-(18)). They were determined by fitting the experimental data shown Fig. 9(a)-(c), but no explanation is found for h. It is requested how h was determined.
- The Ohno-Wang II model was extended to take into account the effect of martensitic transformation. The simulated data of uniaxial ratchetting obtained with the Ohno-Wang II model and the extended model are shown in Fig. 7 and Fig. 12, respectively. Comparing the simulated data in these figures suggests that the effect of martensitic transformation is not large. The readers then may ask why it is necessary to consider the effect of martensitic transformation. It is requested to describe it.
- A combined tension-torsion multiaxial ratchetting test was performed (Figs. 5 and 6). Which shape of specimens was used, solid bar or thin-walled tubular specimens?
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
The manuscript is well written and presented. The experimental testing of the ratcheting phenomenon under cryogenic temperature seems to be new and interesting. The idea to introduce martensite transformation into the evolution laws of kinematic and isotropic hardening is physically consistent. However, before recommending the paper for publication in the Applied Sciences journal, Reviewer requests the Authors to answer/comment specific questions and make revisions accordingly. The reviewer questions are written and numbered directly in the attached copy of the manuscript.
Especial attention should be given to Section 3.3, where the Authors should differentiate their own contribution from what was done by others and is used in the manuscript, and to Section 4.2, where some inconsistency of how the new parameters are incorporated into a numerical scheme seems to be present. Also it is not clear which method of solving the nonlinear equation for Δp was used (Newton-Raphson or successive substitution).
Comments for author File: Comments.pdf
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 4 Report
The current manuscript intends to examine mainly uniaxial ratcheting response of of S30408 austenitic stainless steel at cryogenic temperatures. Based on the Ohno -Wang II model, a new cyclic plastic constitutive model with martensitic transformation is proposed to relates the content of deformation induced by martensite content through terms in isotropic and kinematic hardening rules. Results of experimental data, predicted and simulated curves were compared and discussed. The manuscript holds fundamental equations of plasticity and constitutive models. Authors require to justify how martensitic structure of SS30408 steel alloy at cryogenic temperatures fundamentally undergo progressive plastic strain over asymmetric loading cycles.
Following are a number of comments to be addressed by authors, before the manuscript get accepted for publication in the journal.
- The title of the manuscript is long. Make it shorter and to the point.
- In the abbreviation LNG should be specified as “Liquefied Natural Gas (LNG)” when it first appears in the abstract.
- Authors need to provide equivalent of SS30408 Chinese designation to AISI?
- Page 3, the 2ndline: Change "but the prediction effect of multiaxial ratcheting strain was not still very well." to "but multiaxial ratcheting prediction is yet to successfully accomplish."
- Page 3, end of 4thline: Include a reference for recent modification as " A comparative study in descriptions of coupled kinematic hardening rules and ratcheting assessment over asymmetric stress cycles, Fatigue & Fracture of Engineering Materials & Structures, Vol 40, Issue 6, pp. 882-893 (2017).
- In the 2ndparagraph of page 3: Rephrase this statement "the prediction effect of the experiment, ".
- Page 3, under the 4thparagraph: “ constitutive models….[30-32]: Add a new reference:
Local ratcheting assessment of steel samples undergoing various step and block loading conditions
Theoretical and Applied Fracture Mechanics, Volume 107, pp. 2020, 102533
- For materialistic structure of steel alloy, one may assume relative brittle nature of materials . How do authors describe cyclic plastic progress over loading cycles for this alloy in the presence of cryogenic temperatures.
- In figure 2: Provide temperature and rate of loading inside of figure box.
- Below equation (10), Change “Where” to “where”.
- Figure 7: Authors are to check ratcheting in Y-axis of figure 7 (part e). The magnitude of ratcheting has increased significantly. Is it an error in graphical presentation?
- Change “back stress” to “backstress” over entire manuscript.
- Just a line above figure 9, revise “omega-m”.
- Below figure 11: Prediction based on what models? Authors need to clarify it in figures 12 and 13. In these figures, authors need to change simulation to prediction and specify kinematic hardening models used.
- Authors have related the influence of Martensitic content to isotropic hardening rule through equations 24-26 as well as second term of O-W hardening rule. Authors may elaborate how martensitic content are related to these terms based on physical phenomenon one expect to evidence over progressive plastic deformation.
- Algorithm described in figure 14 needs to explained and presented in a better format.
- Data of multiaxial ratcheting in this manuscript are very few. It is better that manuscript fully focus on uniaxial ratcheting. and remove few multiaxial ratcheting given in text and figure 20 as is very incomplete.
- Shorten the conclusion in length. Highlight main outcomes of the present study.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Thank you for your corrections and improvement of figures.
just some language and grammatical corrections:
page 3/27, second paragraph line17: but multiaxial ratcheting prediction is yet be successfully demonstrated
page 4/27, last paragraph, a few articles have been omitted :
Under cryogenic temperatures, a plastic plateau occurs due to the formation of martensite and secondary hardening can be observed after the plastic plateau
page 5/27, added sentence:
It is shown that the strain accumulated in the direction of the mean stress (no comma!) and the accumulating rate decrease (plural) continuously ...
On page 9/27, please adapt
“where μi is the ratcheting parameter, η is a parameter affecting ratchet deformation, η∞1 ,η∞2 ,η1 ,η2 are material constants, dp is magnitude of the plastic strain increment tensor, χ is the multiaxial parameter. The uniaxial ratcheting studied in this study is χ=0. “
You should also introduce the parameter ω!
On page 12/27, last paragraph elasto-palstic should be elasto-plastic
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
The paper has been revised by taking into account the comments, and is recommended for publication in the journal.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
The Authors answered reviewer's comments satisfactorily, except for one question: which method was used to solve the nonlinear equation for Δp, Newton-Raphson or successive substitution? In the beginning of section 4, it is said "The local Newton-Raphson (N-R) iteration is realized by the radial return method, and the trial strain increment is determined by the consistent tangent matrix". However, Fig. 12 shows a successive substitution method. The two methods are principally different. Which one is used? Or both of them are used? Moreover, in the scheme of Fig. 12, new Qn+1 has been appeared with no definition before.
Author Response
Please see the attchment.
Author Response File: Author Response.pdf
Reviewer 4 Report
No more comments.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
