Strain-Rate Effect on Anisotropic Deformation Characterization and Material Modeling of High-Strength Aluminum Alloy Sheet

Round 1

Reviewer 1 Report

I have some comments:

1) Could you explain why do you choose Johnson-Cook model to evaluate research experiments?

2) Figure 2 and 4 - lack of unit on the axis engeenering strain - please write : (-)

3) Figure 8 - lack of  unit on the axiss (tensile axis angel...0 - please write (degree or "^o")

4) Figure 11 and 12 - lack of magnification value - please complete

5) Figure 11 - what does it mean large dimple - could you describe which dimesion means large (i.e. in micrometeres?)

6) Figure 12/f -  on the image there are visible round inclusions or compounds - could you explain what is their chemical composition?

Author Response

Dear Editor,

Thank you for giving us the chance to revise the manuscript. We have carefully modified the manuscript according to your suggestions and comments. The detailed corrections are listed below point by point, and all the revision is marked in yellow in the revised manuscript.

Comments:

• Could you explain why you choose Johnson-Cook model to evaluate research experiments?

Response:Johnson-Cook model is widely applied to evaluate the influence of strain rate and temperature on the hardening behavior of different metal plates. The prediction accuracy of this model has been validated for AA7075 in literature [18], Mg-7Gd-5Y-1.2Nd-0.5Zr in literature [26] B500A in literature [27] and so on. So here in this study, this traditional Johnson-Cook model was also chosen here to describe the strain rate effect of this 6XXX aluminum alloy material. The corresponding explanation has been added to Section 3.1 in the revised manuscript.

• Figure 2 and 4-lack of unit on the axis engineering strain, please write(-)

Response: All the units for the strain axis of Figure2, 4, 5 and 6 are added.

• Figure 8-lack of unit on the axises (tensile axis angle0-please write (degree or “o”)

Response: The unit for the axis of Figure 8 is added.

• Figure 11 and 12-lack of magnification value- please complete

Response: The magnification value was marked on the figures. Taking Fig11(a) as example, the magnification value was marked in red.

• Figure 11 what does it mean large dimple-could you describe which dimension meas large (i,e, in micrometers)

Response: The dimension of the dimples are relative.In this study, the dimension of the dimples larger than 100um can be regarded as large dimple. In the literature of [9] and [31], the concept of ”larger and deeper dimple” were also mentioned without explaining the concrete dimension information. To keep consistency with other literature, here we also use “larger dimple” instead of “large dimple” in the revised manuscript.

• Figure 12f-on the image there are visible round inclusions or compounds, could you please explain what is their chemical composition?

Response: We also noticed the round components in the SEM images. Sorry we have to be honest we don’t know what it is. The chemical composition should be measured by TEM instead of SEM. However, the fracture section of the samples has changed after such a long time, so it is difficult to measure the accurate components information now. The corresponding information is supplemented in the revised manuscript as follows: ”It should be noted that, some significant round components are observed in Figure 12(f), while they are not obviously seen in other Figures. This may be due to the contamination of the fracture surface in the environment, the corresponding chemical composition would be measured in the future work.”

 In the future, we will work on this issue based on new experimental samples.

Author Response File: Author Response.pdf

Reviewer 2 Report

The submitted paper gives an description about the characterisation of the mechanical behaviour of a 6xxx Al alloys under different conditions of strain rate. The paper has to be changed before being re-considered for the final submission.

Some aspects have to be cleared by the authors.

1. What about the behaviour between QS and 1000 1/s? If the characterisation should provide data for the numerical simulations, what kind of data would be implemented in between?

2. The J-C model is satisfactorily accurate in the hardening region, but after necking the prediction becomes very poor. If such a model has to be used for the numerical simulations, the error that can be committed due to the absence of any softening behaviour after necking would be not negligible.

3. What is the innovative aspect of the research? What has been provided that is not currently available in literature?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

In the paper I found some inaccuracies that should be explained and corrected:

1. line 17 is thorough, should be through

2. line 47, the sentence: Too high forming temperature can reduce the dimensional accuracy and increase the energy consumption. I don’t agree with the statement. Higher temperatures decreasing the energy-force parameters of the process as a result of the lower value of the flow stress.

3. line 83, the sentence: Finite element analysis is a vital tool in various industries to accurately predict the elastic-plastic deformation behavior of the metal plates. Only plates?

4. line 87, is Jenab et al [13], after al add dot

5. line 105, is 5A06 aluminum? probably should be 5006

6. Table 1, is Actural? Where from are the min. and max. values of chemical cmposition?

7. line 159, is (as shown in Fig 1(a). There is no the second bracket

8. line 175, r value should be compared with other aluminium alloys

9. line 185, the sentence: As shown in Fig 1(b), the SHTB system consists of the incident bar, transmitter bar and stretching bar. In fig. 1b we can’t see it. Authors should add into the figure

10. Table 2, is Mpa

11. Fig. 6, the model is only compatible up to a certain range of deformation, add some comments

12. Fig. 7a, is strain rat, should be strain rate

13. all manuscript is Barlat and Lian’s 1989, the year is not necessary

14. Eqs. 8 and 9, what does sigxx, sigyy, sigxy mean? Are they components of stress tensor?

15. line 308, m1=8, what is the basis of the value?

16. line 310, is Table 1, should be Table 2

17. line 315, m=8, what is the basis of the value?

18. In Eq. (9), there is no m parameter, should be m2

19. All manuscript, is microcosmic, should be microscopic

20. line 383, is 10 um, should be 10 mm

21. line 384, check unit, is mm, should be mm

Author Response

Dear Editor,

Thank you for giving us the chance to revise the manuscript. We have carefully modified the manuscript according to your suggestions and comments. The detailed corrections are listed below point by point, and all the revision is marked in yellow in the revised manuscript.

Comments:

• Line 17 is thorough, should be through.

Response: ”thorough understanding ” here means “complete understanding”, If changing it to “through understanding”, the meaning of the sentence is not correct.

• Line47, the sentence: too high forming temperature can reduce the dimensional accuracy and increase the energy consumption. I don’t agree with the statement. Higher temperatures decreasing the energy-force parameters of the process as a result of the lower value of the flow stress.

Response: We agree with you that higher temperatures decrease the force parameters of the process as a result of the lower value of the flow stress. However, if applying higher heating temperature during the forming process, the heating equipment should be added, thus the production energy consumption is increased, to finally increase the overall manufacturing cost. In addition, too higher temperature can cause oxide scale on the metal surface and increase the subsequent surface treatment process. To avoid misunderstanding, the corresponding description is modified in the revised manuscript.

• Line83, the sentence: Finite element analysis is a vital tool in various industries to accurately predict the elastic-plastic deformation behavior of the metal plates. Only plates?

Response: Finite element analysis is widely applied in many industries for various plates, tubes and blocks, and so on. However, the focus of this study is 6xxx aluminum alloy plate, so here we only refer to the application of finite element analysis in metal plates.

• Line87, is Jenab et al[13], after al add dot.

Response: a dot has been added after Jenab et al.

• Line 105, is 5A06 aluminum? Probably should be 5006.

Response: In the literature of [19], the name of the materials used by the authors is 5A06 and 5A02 as shown in the following picture,so we can not change it to 5006 here in this manuscript.

• Table 1, is Actual? Where from are the min. And max. Values of chemical composition?

Response: “Actural” should be changed as “Actual”.

By defining the Max. value and Min. Value, Table 1 shows the appropriate range of each chemical composition of the 6xxx aluminum alloy. The actual value and the standard values are all obtained from the manufacturer of this aluminum alloy sheet.

• Line159, is (as shown in Fig1(a). there is no the second bracket.

Response: The second bracket has been added.

• Line 175, r value should be compared with other aluminium alloys.

Response: r value of this 6xxx aluminum alloy is compared with other aluminum alloys (AA5XXX and AA6011) and the corresponding literature is added before Fig 2 in the revised manuscript.

• Line 185, the sentence: As shown in Fig1(b), the SHTB system consists of the incident bar, transmitter bar ans stretching bar, In Fig 1(b) we can’t see it. Authors should add into the figure.

Response: The three bars have been marked in Fig1(b) in the revised manuscript.

• Table 2, is Mpa.

Response: The unit has been revised as “MPa”.

• 6 the model is only compatible up to a certain range of deformation, add some comments.

Response: According to Figure 6, Johnson-Cook model can well describe the plastic deformation behavior of this aluminum alloy at quasi-static condition and at higher strain regions for high strain rate condition. However, it somewhat underestimates the yielding stress at the initial tensile stage for the cases with high strain rate, especially for the case with strain rate of 3000 s^-1. The difference may be caused by the inevitable experimental error induced by vibration. Since the theoretical prediction at initial yielding region is 6% less than the experimental data. So it can be concluded that Johnson-Cook model can be regarded as an appropriate hardening model to describe the plastic deformation behavior of this 6XXX aluminum alloy sheet at all strain rates. The above comments and analysis can be found in the paragraph before Figure 6 in the revised manuscript.

• Fig7a is strain rat, should be strain rate.

Response: The mistake has been modified according to your kind suggestion.

• All manuscript is Barlat and Lian’s 1989, the year is not necessary.

Response: Professor Barlat has proposed many yield functions. The most widely applied one is generally called “Barlat and Lian’s 1989”yield function, this concept is widely cited in many literature and even some finite element software.  For consistency with other literature, “Barlat and Lian’s 1989” is also used here.

• 8 and 9, what does sigxx, sigyy, sigxy mean? Are they components of stress tensor?

Response: Yes,  , and  are the components of stress tensor. To make it clearer, the corresponding explanation has been added to the revised manuscript.

• Line308, m1=8, what is the basis of the value?

Response: is a material parameter associated with the crystal structure of the sheet metal. For BCC and FCC metals, the values of  equal to 6 and 8 respectively. This is explained very well in many literature of Professor Barlat. For the experimental aluminum alloy sheet, the value of  is 8.  The explanation has been added to the revised manuscript.

• Line310, is Table 1, should be Table 2.

Response: The mistake has been modified according to your kind suggestion.

• Line 315, m2=8, what is the basis of the value?

Response: As the same as,  is also the material parameter associated with the crystal structure of the sheet metal. For aluminum alloy, the value of  equals to 8. This is explained very well in many literature of Professor Barlat. The explanation has been added to the revised manuscript.

• In Eq.9, there is no m parameter, should be m2.

Response: The mistake has been modified according to your kind suggestion.

• Line383, is 10um，should be 10mm

Response: We carefully observed the SEM sample and re-measured the dimension of the dimples, the unit should be um instead of mm, so the unit and the value in the two paragraph are all modified, please check the revised manuscript.

• Line384, check unit, is mm, should be mm.

Response: The unit for this paragraph is all changed as um. Because the dimension of the biggest dimple shown in Figure 11 is 150um.

Author Response File: Author Response.pdf

Reviewer 4 Report

Characterization of anisotropic behavior of 6XXX series aluminum alloy during quasi-stationary and high-strain rate tests was performed. Stress-strain hardening model and two yielding functions were used to describe the hardening and yielding behaviors of the alloy. Finally, SEM fractographic analysis was performed, showing a change of a ductile fracture in quasi-static deformation to partially ductile and shear fracture at high strain rates.

The manuscript shows the predictive power of FE simulations. Several details should be cleared:

Specify in more detail the initial state of the sheet used in the study

242 define experimental scatter

290 provide information about experimental scatters

Formal errors:

94 Explain abbrev. FLC

153 actural --> actual

258-259 remove redundant part of the sentence

etc.

The introduction, especially the first part, is too general and not too concise

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The comments highlighted by the Reviewer have been satisfactorily addressed. As a minor comment, it would be of great impact if the authors could provide also the comparison between the experimental and the predicted yield stresses and r-values also for the higher investigated strain rates (basically, as done for the quasi static conditions). The paper has only minor revision to be applied, according to what stated above, and then it can be considered suitable for the final publication. 

Author Response

Dear reviewer,

According to your suggestion, the comparison between the experimental and the predicted yield stresses and r-values  under the three high strain rate conditions are listed in the revised manuscript as shown in the new Fig 10, the corresponding explanation are also added just before Figure 10, please check the content marked in yellow.  In addition, the sequence of the following figures has also been modified accordingly.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper is ready for publication

Author Response

Thank you for your approval.