Effect of Anisotropic Yield Functions on Prediction of Critical Process Window and Deformation Behavior for Hydrodynamic Deep Drawing of Aluminum Alloys
Round 1
Reviewer 1 Report
The paper "Effect of Anisotropic Yield Functions on Prediction of Critical Process Window and Deformation Behavior for Hydrodynamic Deep Drawing of Aluminum Alloys" describes the theoretical analysis and finite element model of the deep drawing of aluminum sheets. The models developed by the authors show high accuracy and can be applied for industrial applications. However, the paper is needed to be improved accordingly following comments:
1. The term "Hydrodynamic" is hard may be used in the title and other parts of the paper. It may mislead the reader, that the deformation proceeds directly under the pressure of the liquid. However, the authors just used a hydraulic pump system to move the punch. It is better to use the term "hydromechanical" instead of the "Hydrodynamic".
2. The deformation rate during the tensile test should be included to the experimental description.
3. How authors include to the constructed model strain rate? It has a significant influence on the accuracy of the model, because of non-uniform deformation during punching.
4. It may be adiabatic heating during the real punching process. The temperature increasing also should be included in the constructed model.
Author Response
Dear Editors and Reviewers:
Thank you for your letter and for the reviewer’s comments concerning our manuscript entitled “Effect of Anisotropic Yield Functions on Prediction of Critical Process Window and Deformation Behavior for Hydrodynamic Deep Drawing of Aluminum Alloys” (ID: metals-755175). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:
Responds to the reviewer’s comments:
- Comment: The term "Hydrodynamic" is hard may be used in the title and other parts of the paper. It may mislead the reader, that the deformation proceeds directly under the pressure of the liquid. However, the authors just used a hydraulic pump system to move the punch. It is better to use the term "hydromechanical" instead of the "Hydrodynamic".
Response: Thank you very much for your comment. Hydrodynamic deep drawing is a process that uses liquid as force transmittion medium instead of conventional rigid die, and makes the blank fit the punch under the pressure of liquid. In our research, the hydraulic system of the forming equipment we applied can not only provide the power of blank holder force and forming force for the blank holder and the punch, but also provide the hydraulic pressure for the liquid chamber in the HDD process. As the punch moves down, the medium produces pressure on all sides, pressing the sheet being formed onto the punch in the HDD process, as shown in Figure S1 (Figure 2 in manuscript). Frictional force generated between the punch and the sheet transmits part of the drawing force onto the cup wall; meanwhile, the liquid leaks from the gap between the sheet and the die. This means that the force passed across the bottom of the drawn part reduces, and the area of the workpiece under the maximum stress changes from the bottom of the workpiece towards the drawing radius. Moreover, the workpiece bulged backward under the effect of pre-bulging pressure before the punch contacts the blank, which is a valid approach to avoid the origination of the wrinkle on the unsupported region. We apologize for the misunderstanding caused by the incomplete introduction of the concept and experimental test. We have supplemented the introduction of hydrodynamic deep drawing principles and the applied forming equipment in the manuscript.
Figure S1. Comparision of CDD process and HDD process.
- Comment: The deformation rate during the tensile test should be included to the experimental description.
Response: Thanks for your comment. We have supplymented the deformation rate information in the uniaxial tension test in Line 298. We conducted the uniaxial tensile tests of 2024-O and 5754-O aluminum alloys with the strain rate of 10-3 s-1. We also complemented the forming rate with 15mm/min in the HHD process of aluminum alloy in Line 316.
- Comment: How authors include to the constructed model strain rate? It has a significant influence on the accuracy of the model, because of non-uniform deformation during punching.
Response: Thank you very much for your question. Strain rate has a significant effect on the plastic behavior of metals, which is manifested in the flow stress increases with increasing strain rate of most metallic materials. Therefore, based on the results of finite element simulation, we performed strain rate analysis of the feature points in different regions of the workpiece during the HDD process of 2024-O and 5754-O aluminum alloys with the forming rate of 15min/min. According to the analysis results, it is found that the strain rate of each feature point changes with the forming process, and the strain rate of diverse feature points changes differently. Based on the results of finite element analysis, the strain rate of the feature points of the main deformation region during the study of HDD process of 2024-O and 5754-O ranges from 8.7 × 10-4 s-1 to 5.5 × 10-3 s-1 and 8.2 × 10-4 s-1 to 6.1 × 10-3 s-1, respectively. Considering the sensitivity of the flow stress to the strain rate, we added the uniaxial tension tests of two aluminum alloys with the strain rate of 7.0 × 10-4 s-1, 3.0 × 10-3 s-1, and 6.0 × 10-3 s-1. The results of the tenson tests under various strain rates are shown in Table S1. It can be found that the flow stress of two aluminum alloys in the range of 7.0 × 10-4 s-1 to 6.0 × 10-3 s-1 with room temperature hardly varis with the change of strain rate, that is, the strain rate sensitivity indexs of 2024-O and 5754-O aluminum alloys are very low. Many scholars have also found that the test results of aluminum alloys at room temperature show that the strain rate sensitivity is not obvious, but when the strain rate exceeds 1000 s-1, they found that the strain rate sensitivity becomes obvious. Considering the real-time adjustment of the liquid chamber pressure with the displacement of the punch during the HDD process, the forming rate could not be too high, and the strain rate of the workpiece would be between 10-2 s-1 and 10-4 s-1. Therefore, the HDD process can be regarded as a quasi-static deformation process. Above all, in this article, the effect of strain rate on the yield behavior of aluminum alloys and the deformation of materials during the HDD process can be ignored. However, for processes such as high-temperature HDD forming and high-speed forming, the influence of the strain rate on the forming results must be considered.
Table S1. Material characteristic coefficients obtained from tension tests with various strain rates.
|
Materials |
Strain rate |
(MPa) |
(MPa) |
(MPa) |
K |
n |
|
2024-O |
7.0×10-4 s-1 |
79.37 |
75.95 |
77.66 |
289.51 |
0.183 |
|
1.0×10-3 s-1 |
79.51 |
75.98 |
77.71 |
289.34 |
0.183 |
|
|
3.0×10-3 s-1 |
79.61 |
75.99 |
77.79 |
288.40 |
0.183 |
|
|
6.0×10-3 s-1 |
79.67 |
76.11 |
77.98 |
288.34 |
0.182 |
|
|
5754-O |
7.0×10-4 s-1 |
108.54 |
108.51 |
113.11 |
403.34 |
0.254 |
|
1.0×10-3 s-1 |
108.67 |
108.68 |
113.39 |
403.24 |
0.254 |
|
|
3.0×10-3 s-1 |
108.74 |
180.81 |
113.48 |
403.22 |
0.253 |
|
|
6.0×10-3 s-1 |
108.90 |
108.88 |
113.62 |
403.13 |
0.253 |
- Comment: It may be adiabatic heating during the real punching process. The temperature increasing also should be included in the constructed model.
Response: Thanks you very much for your question. Deformation temperature has a crucial effect on the flow behavior of aluminum alloy sheets and the flow stress decreases with increasing temperature in most metallic materials. When the sheet is plastically deformed, most of the plastic work is transformed into thermal energy. Many scholars have studied the energy conversion rate of plastic work to thermal energy (η coefficient). Among them, Meyer et al.[1] found that, ignoring the heat loss, when the strain rate is considered to be greater than 100 s-1, and the value of η is 0.95, and when the strain rate is less than 10 s-1, the η coefficient is lower, and the η value is about 0 at a lower strain rate (10-3 s-1) through simulation and experimental research. Moreover, the following two processes can be considered as adiabatic processes: the process that surrounds the system with a good thermal insulation material or the process that proceeds faster and the system has no time to exchange heat with the outside environment. During the HDD process of aluminum alloy, the sheet material is in contact with the liquid, and at the same time, it is in close contact with the punch under the action of liquid pressure. Therefore, the heat generated by the plastic deformation of the material will be transferred to the liquid and the mold, and it does not have a good insulating material surrounding conditions. On the other hand, the HDD process of aluminum alloy sheet is similar to the quasi-static deformation process. Its forming velocity is slower and the forming time is longer (with minutes level). The heat generated by the plastic deformation of the sheet during the forming process can be exchanged with the liquid or the mold. Therefore, we think that perhaps the HDD process of aluminum alloy sheet does not belong to the adiabatic heating process in the strict sense, so our study did not involve the influence of temperature on the yield behavior of aluminum alloy and the deformation of the material during the HDD process. However, your presious question provides us with a good idea. We may carry out research on the heat transfer during the sheet metal HDD process and the research on the warm hydrodynamic deep drawing of the aluminum alloy sheet in the subsequent work.
[1] Meyer, L.W.; Herzig, N.; Halle, T.; Hahn, F.; Krueger, L.; Staudhammer, K.P. A basic approach for strain rate dependent energy conversion including heat transfer effects: An experimental and numerical study. Journal of Materials Processing Technology, 2007, 182, 319-326.
We have done our best to improve the manuscript and many changes have been made in the new version of the manuscript. These changes, however, would not affect the content and framework of the paper. Here we do not list all the changes but highlighted in red in the revised manuscript. We appreciate editor and reviewers for giving valuable comments and this opportunity to improve the quality of the manuscript. Wish you all the best!
Sincerely yours,
Chu Wang
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper presents extensive introduction, calculations and experimental part. The Authors performed extensive experimental measurements on two commercial grades and providing their grades is not sufficient. The Authors should determine and list in a table the specific chemical composition of both alloys.
Author Response
Dear Editors and Reviewers:
Thank you for your letter and for the reviewer’s comments concerning our manuscript entitled “Effect of Anisotropic Yield Functions on Prediction of Critical Process Window and Deformation Behavior for Hydrodynamic Deep Drawing of Aluminum Alloys” (ID: metals-755175). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:
Responds to the reviewer’s comments:
- Comment: The Authors should determine and list in a table the specific chemical composition of both alloys.
Response: Thanks for your comment. We have supplymented the specific chemical compositon of both alloys in Table 1.
We have done our best to improve the manuscript and many changes have been made in the new version of the manuscript. These changes, however, would not affect the content and framework of the paper. Here we do not list all the changes but highlighted in red in the revised manuscript. We appreciate editor and reviewers for giving valuable comments and this opportunity to improve the quality of the manuscript. Wish you all the best!
Sincerely yours,
Chu Wang
Round 2
Reviewer 1 Report
The authors have improved the paper by additional information about HDD process, and have answered on other comments. The paper may be accepted in present state.
