Modeling the Mechanical Response of a Dual-Phase Steel Based on Individual-Phase Tensile Properties

Round 1

Reviewer 1 Report

I think the reference survey was not enough to write the paper. "Dual phase steel" was invented in Japan in 1970s. After that, many influential papers have been published in Japan  (particularly see Trans. ISIJ and ISIJ Int.), but none of which were referred in this paper. The model employed is too primitive to contribute to this topic. Presumably, it is not easy for the authors to read the above journal (although similar papers can be found in Acta Mater. etc.), and therefore I would like to show two articles (attached) for the progress of your study.

Comments for author File: Comments.zip

Author Response

Dear Reviewer 1:

Please find enclosed the answers to your comments and suggestions.

Best regards

Alberto Monsalve

Author Response File: Author Response.pdf

Reviewer 2 Report

The study introduces a three-dimensional constitutive model based on the law of mixture to predict the mechanical response of dual-phase steels. The law of mixture requires a stress/strain partitioning parameter, q. The authors propose a rate form of such parameter q_prime that is dependent on the accumulated plastic strain. The concept is interesting and novel. However, some major points must be clarified for the study to be beneficial to the scientific community.

- In lines 259-260, it is stated: 

"The model determines strain in each phase considering that only the ferrite phase deforms plastically, while martensite keeps in the elastic region."

In the result section, the stress-strain curves of the martensite and ferrite phases in DP1 and DP2 are not shown. From the sentences in lines 259-260, it is not clear if the YS for martensite is never reached or if the martensite is not allowed to deform plastically. If it is the second case, why is that the case?

- It is not clear in the text which experimental curve has been fitted to calibrate q_prime and which plot is instead showing a comparison of predictions and experimental observations. Is that correct that the tensile tests are used to get q_prime for the two DP steels and then predictions obtained for the bending tests? these aspects need to be clearly stated to avoid confusion.

Author Response

Dear Reviewer 2:

Please find enclosed the answers to your comments and suggestions.

Best regards

Alberto Monsalve

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper addresses an interesting issue; nevertheless it is lacking of accuracy in some points:

• tested steels are distinguished by the C content, which in DP1 is however less than ULC: please clarify;
• it is totally obscure how the finite element model is implemented and on which geometry, and, above all, why it is necessary instead of a numerical calculation by programming;
• it is suggested to show DP1 and DP2 microstructures also, since these are modelled thereafter;
• Table 4 contains an error please fix it;
• YS of martensite should be introduced in Tab. 4;
• Tab. 4 should report the martensite/ferrite ratio also;
• all tensile curves should be shown;
• in the discussion authors cite necking, but it is not clear if the FE model could be able to model it;
• it is not clear the range of validity of the determined q': is it valid for a class of DP steel? Please clarify.

Author Response

Dear Reviewer 3:

Please find enclosed the answers to your comments and suggestions.

Best regards

Alberto Monsalve

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The comments were uploaded.

Comments for author File: Comments.pdf

Author Response

Comments of Reviewer 1

In the introduction, the references were increased but they were not appropriately summarized and therefore the purpose of the present study was not clear. Currently, advanced theoretical computation-methods including the Eshelby-Mori-Tanaka self-consistent model, the secant method coupled with phase field analysis, elastic crystal-plasticity FEM calculation are available. Why did the authors employ such a phenomenological simple model; honestly speaking, I cannot understand the soundness of the model starting from the assumption, “The generalized stress transfer or strain partitioning coefficient q relates stress and strain tensors as ?−??=?(?−??); ??−??=?(??−??)”; I wonder how this assumption corresponds to the strain compatibility condition and stress-equilibrium condition at the interface and constitutive deformation equations of component phases; elastic strains related to stresses and plastic strains are not divided; and so on; hence, I could not follow the calculation procedure.

ANSWER or COMMENT:

Six new references have been included, one of them from a Japanese author (ref10).

The aim of the work has been clarified in the last part of section              1, where it is possible to read:

“…the aim of this work is to explore the possibilities and limitations of this constitutive model in describing the mechanical response of DP steels subjected to different loading conditions.”

About the model.

We agree with the reviewer that more advanced material models, i.e., those based on crystal plasticity using the Taylor or self-consistent assumption, are available. However, the use of such models is a very complex task that involves the definition of the phase interactions, number of active slip planes, crystal hardening response, etc. In addition, they are very computationally demanding in problems with non-homogeneous macroscopic stress and strain patterns (e.g., like those in the bending test). Due to these reasons, the constitutive model we adopt in this work treats the material as a homogenous medium in which its stress and strains are weighted according to the phase volumetric fractions. In this context, although neither the stress equilibrium nor strain compatibility is strictly fulfilled between the two phases, the model was found to reasonably predict the material response of two DP steels both subjected to the tensile and bending tests.

In addition, it should be noted that the use of the proposed constitutive to describe the material response in the bending test is an original aspect of the present work that has not been addressed in the cited literature.

Author Response File: Author Response.pdf

Reviewer 2 Report

The response to the point raised in the first round of revision is satisfactory. 

Author Response

There is no comment.

Reviewer 3 Report

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Author Response

There is no new comment from the referee 3.