Transformation of 2D RVE Local Stress and Strain Distributions to 3D Observations in Full Phase Crystal Plasticity Simulations of Dual-Phase Steels
Round 1
Reviewer 1 Report
Strengths and weaknesses
The current content of the paper is a demonstration that the inherent
difference in the local stress and strain fields of a periodic equiaxed and a
periodic columnar grain structure, where the latter is derived from a thin
slice of the former, can be brought closer to agreement by am iterative
"least squares and alternative error" approach. The authors observe a
diminishing improvement with increased iterations of this algorithm.
Moreover, and not surprising, the coefficients are stable when testing
larger and larger systems (since, apparently, the smallest one is already
statistically representative), but differ for different phases in the ferritic–
martensitic microstructure.
The three main issues this reviewer sees with the present manuscript are
(i) it is very poorly written, (ii) much too lengthy, and (iii) fails to address
the actually pressing question of universality of the identified correction
parameters.
Regarding (i), substantial editing and input from an English-native writer
or other professional editing service is strongly recommended. Regarding
(ii) and (iii), a major restructuring is suggested that starts from the
established knowledge (see Fig 11 in [29]) that columnar grain structures
feature a wider distribution and stronger localization of stress and strain
compared to equiaxed structures. After essentially copying the limiting
setup of the columnarity study in [29] and clearly outlining the correction
approach from 2D (fully columnar) to 3D (fully equaxed and decoupled),
the paper should investigate the degree of universality of the (a,b)
parameter series for varying strain levels, volume fractions, and strength differentials. Only with such thorough analysis that provides and discusses the overall usefulness of the correction scheme can the work be considered a publishable contribution.
Summary
In its current state, this is a fairly weak paper that does not warrant
publication as it simply boils down to a (lengthy) statement that two
already similar populations of values can be brought closer to resemblance by an iterative correction scheme, which is in and of itself not very compelling.
The annotated manuscript are attached.
Comments for author File: 
Comments.pdf
Author Response
Response to Reviewer 1
We thank you for taking out time to review this article. All the suggestions and comments were useful in improving the quality of the document. Please note that apart from the suggested changes the article has been significantly improved and all the changes are highlighted yellow in the revised manuscript.
Please see the attached PDF document with a detailed response to your comments and suggestions.
Author Response File: Author Response.pdf
Reviewer 2 Report
The paper appears to offer a method to infer a full 3d stress/strain field from a 2D simulation (crystal plasticity, two dual phase steels.
The leading idea of the paper definitely is worth of investigation and the proposed method and its results - if presented in clear and verifiable manner - would be of significant utility to the community.
Unfortunately, the presentation given in the paper does not meet the - in my view essential - feature of each scientific paper: repeatability of research. The description does not allow for independent verification (=repeating the analysis) of the results. Furthermore, the descriptions provided are vague and , occasionally, incomprehensible. Some (not all) vague or missing or incomprehensible descriptions are listed below:
(1) RVE: various definitions have been used in the literature. Which one has been used in this paper? How does the RVE relate to the periodic boundary conditions used (p6 l 186)?
(2) were the 2D simulations performed in plane strain or plane stress mode?
(3) the statistical conclusions seem to be based on a extremely vaguely defined or perhaps even random combinations or "Least Square Method" (LSM) and "Alternative Error Method" (AEM). Firstly, least square method appears to be a rather widely accepted and known concept; but it is not clear, what is behind the Alternative error method . Further, authors the at various locations in the paper rather to rather random combinations of "LSM", "ASM", "ASM and LSM", "LSM and ASM", ... Finaly, while LSM is mentioned in Section 3, AEM is not....
(4) variable/function f in Section 3 appears to be used in a generic form to denote stresses or strains. The particular choice of presentation, "both stress and strain", "stress-strain" etc might be confusing, as stresses and strains are clearly not linearly correlated and it appears very difficult if not impossible to deduce whether one must use the method in parallel on stresses and strains or 2D stresses appear to be sufficient to predict 3D stresses and strains.
(5) units in some figs and tabs are missing: Fig 2, Fig 5, Fig 6, Tab 5 (yes, mean and st dev of Normal distribution also have physical units). Not all are listed...
(6) axes labels in some figs appear confusing: Fig 3 (and some others): Different stress, Repaired Stress; different strain, repaired strain. What are definitions? Fig 6 (and similar) Density=>Probability Density? Fig 9 Avg. Error stress => needs a definition (spatial average of the entire stress field?). Not all are listed....
(7) the term Probability Distribution Function in section 4.1.4 appears to hide the Normal or Gaussian distribution (eq 19). The authors do not bother to support this choice. Further, the figs (6, 11...) appear to depict the a rather strange combination of Normal and Standard Normal distributions (means appear to be normalized, the st devs appear to be non-normalized). This comes as (unexplained!!) surprise: even if there would be a utility in such approach, the authors definitely did not bother to elaborate/explain it.
(8) Based on values of R2, the performance of iterations 2 and 4 is practically equivalent = one might attempt to conclude that 2 iterations are sufficient. Alternative view could be what happens with in iterations above 4, in particular in even numbered iterations above 4. Elaboration of why exactly the 4 iterations are considered the best choice, also compared to iterations above 4
Author Response
Response to Reviewer 2
We thank you for taking out time to review this article. All the suggestions and comments were useful in improving the quality of the document. Please note that apart from the suggested changes the article has been significantly improved and all the changes are highlighted yellow in the revised manuscript.
Please see the attached PDF document with a detailed response to your comments and suggestions.
Author Response File: Author Response.pdf
Reviewer 3 Report
This manuscript proposed an innovative approach to transform the stress and strain distribution from a 2D RVE model of a DP steel to that of a 3D RVE model. The revised stress/strain distribution from the 2D RVE model well agreed with that of the 3D model, and statistical analysis of the results also supported this. Overall speaking, the scientific gap is well stated, and the proposed approach can partially fill it up. I would recommend publishing if the authors can address the below concerns/comments:
- The writing needs to be improved. While the idea and work in this paper is great, the writing needs significant improvements. The major writing issues are strange wording and lengthy descriptions.
Strange wording: There are a lot of strange wording that needs to be revised. A few examples are (the authors should check the entire manuscript and revise):
Line 68: a quantitative behavior.
Line 161-163: the surface distribution for 2D and 3D have been simulated by … and Ferrite (F) as well as Martensite (M) separately display for better visualization.
Figure 1: Convergent analysis (usually should be “convergence analysis”)
Line 182 and many other lines: the letters denoting a tensor is bolded in the equation, but not in the text.
x and y in equation 3 and 4 were not defined in the text.
Line 236: “Where the different error of m-2 revised …”. You cannot start a statement with “Where”.
Stress-strain: when trying to say “stress or strain”, “stress/strain” should be used instead of “stress-strain” - the latter is very confusing.
Different stress: For what the authors want to express, stress difference (or something similar) should be a better option. (Also applies to different strain)
Equation 7: the equation for a_1 should be simplified, unless there are special reasons to not to do so
Lengthy description: the authors described a lot of details on how to move from iteration 0 to iteration 1, and then to iteration 2, etc. Since these are standard iteration operations, the relevant descriptions can be shortened to make the manuscript concise and focus on the most important aspects. One such example is the second paragraph of section 4.1.2.
- What out-of-plane stress state did the authors assume for the 2D RVE model? Plane strain? Plane stress? It should be clarified.
- What was the convergence criterion the authors used for the iteration process? Since this is critical to the proposed approach, the authors should clearly describe it.
- The authors picked 25% global strain for analysis, what about other global strain levels, will the parameter values be different? If the parameter values are global strain dependent, how can this be addressed?
Author Response
Response to Reviewer 3
We thank you for taking out time to review this article. All the suggestions and comments were useful in improving the quality of the document. Please note that apart from the suggested changes the article has been significantly improved and all the changes are highlighted yellow in the revised manuscript.
Please see the attached PDF document with a detailed response to your comments and suggestions.
Author Response File: Author Response.pdf
