A Physical-Based Plane Stress Constitutive Model for High Strength AA7075 under Hot Forming Conditions

Round 1

Reviewer 1 Report

This paper deals with a dislocation mechanics-based constitutive model to predict both the flows stress curves and the concurrent evolved microstructures of high strength aluminium alloy AA7075  under a direct heating forming condition proposed by the authors in a previous work [19, 20]. Electron Back Scattering Diffraction technique was used to visualize the high temperature and strain rate induced geometrical necessary dislocation (GND) distributions in 7075 aluminium alloy to capture the statistical nature of GNDs and grain sizes in hot deformation. The model was further extended to plane stress states to provide a direct estimation of the hardening of 2 mm thickness alloy sheet in metal forming conditions.

 

Overall, the authors limit their work to the application of only one damage model proposed by the same authors. The paper deals with an interesting subject, but improvements are necessary.

 

Detailed comments:

1. In Eq. (5) for the hardening stress, the temperature effect is introduced in the coefficient a(T) but as given in Eq. (6) a is function not only temperature but also the strain or strain rate. What means and what is the form of the function s(.,.) in Eq.(6). The rate form of Eq.(5) is given in Eq.(7) with material constant B as a temperature dependent. Please clarified theses equations
2. In Eq.(9) a critical dislocation density, ?̅_?, beyond which recrystallization occurs, is introduced as a function of strain rate. What strain rate it is: total or plastic strain rate?
3. (14) is obtained by substituting Eq. (2) into Eq. (13). Where is the paremeter A_e in Eq.(14)?
4. In Table 2, the equation of damage rate is cut on right side.
5. In Table 4 with the determined 51 material constants of proposed model include _?30(-), _?40(-), _?1(-), _?2(-). Where these parameters are in the described model?
6. The definitions for the damage parameter w in the uniaxial and bi-axial test must be added.
7. In Conclusions last sentence: ”Compared with the traditional phenomenal models, the physically-based model in this work show advantages in describing the microstructure evolutions.”. The reviewer is not convinced by this statement. Here, the authors used model with so many constants (Table 4) which should be identified with experimental tests. Using proposed material model in prediction of metal forming processes of metal alloys is not lack of difficulty and the authors should minimised the number of material constants. The authors should see this comment as a suggestion for additional studies and, in the paper; they should add some comments addressing these ideas.

In conclusion, the paper is not recommended for publication in its present form and needs major revision.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors,

I would like to congratulate you for your work presented in manuscript titled "A physical-based plane stress constitutive model for high strength AA7075 under hot forming conditions". I've found the manuscript well written and useful for readers. The followings are my questions and suggestions to improve the manuscript:

1. Have you measured the time spent before quenching samples after removing them from Gleeble 3800 grips? Were the time spent constant for all samples? If so, please address it in the manuscript because it can affect the EBSD micro-structure shown.
2. Please rearrange Tables 2, 3 and 4 as they are confusing to read through, if needed, use only one column or two column with the first being the parameters and second being the values.
3. Please address in the manuscript if the parameters shown in Table 4 have any physical meaning. For example, K0 or k0 although in MPa, have very small values. What is the range of these parameters considering the physical boundaries?
4. How did you calculate parameters reported in Tables 4, 5 and 6 (i.e. regression? optimization? randomized?). Please explain or mention the method used.
5. The difference between predicted and experimental values of stress is significant in some cases shown. For example at temperatures of 350oC and strain rates of 0.1/s, the difference is about 35%. In case of 350oc and 5/s strain rate, the predicted values, especially around the yielding is significantly higher than experimental values. This makes the use of presented constitutive equation limited to higher temperature. I think the manuscript would improved significantly if you could add a figure or table summarizing the accuracy of the model at different temperature and stain rates (i.e. MSE or R-squared for each case).

 

Please check the the manuscript thoroughly again to ensure it meets journal's requirements.

Sincerely

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Dear authors, here are some comments:

1. Page 2, line 90 - what was the width of the sheet? What is "T6 condition"? Could you, please, explain?
2. Page 4, Equation 1 labelling - one of the brackets is redundant (on the left).
3. Page 5, line 154, is space needed between "necking" and "[22]"?
4. Page 5, line 168, is space needed between "С₂" and "are"?
5. Page 5, line 181: which equation is meant in this line?
6. Figure 6, Figure 7, Figure 8, Figure 9: "...solid symbols represent experimental results and solid lines represent numerical fittings.." - it is fine. But at some places on the figures arrows confuse a bit. It is not clear, whether they are pointed at the line or at the solid symbol. Is it possible to redesign?
7. Numerical values characterizing accuracy of the model are strongly desirable. Third paragraph of the Conclusions states that model results agree well with experiments. Could you, please, characterize it numerically?

 

 

 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

All the necessary corrections were made, in my view.