Effect of Process Parameters and Definition of Favorable Conditions in Multi-Material Extrusion of Bimetallic AZ31B–Ti6Al4V Billets

Round 1

Reviewer 1 Report

I think it is better to clarify in the article the following moments:

1. Why was the problem considered as 3D case (section 2.2)? Geometry is axisymmetric.
2. Why was the Coulomb friction model used? I think that for for extrusion process the shear model is more suitable. Also it should be explained why the sleeve-core contact is separable.
3. As stated in the article (line 142) Cockroft-Latham criterion is "typically used in cold metal forming". However, authors used it for modelling of hot extrusion.
4. Why so important parameter of extrusion process as extrusion ration wasn't considered? See Fig. 7.
5. From what point of view authors have chosen the level's values of variables during DOE (Table 5)?
6. Tables 6-11 - please, add units of variables. Table 12 - units of force. Table 13, 15 - remove units for variables, add unit for force.
7. Line 279-280: please, explain how does the billet's volume influence on the force? I think that in this case force increases because increases the area of side face, i.e. friction forces on this surface!
8. Line 286: please, clarify hardening behaviour of AZ31B alloy. It is not typical. I haven't found articles proving this.
9. Fig. 11, 13-14 - please, add "effective" to the stress.
10. Line 327-328: if 30 degree angle is optimal (force is minimum), than in both directions from this point the force will increase.
11. Line 339-340: In what part of core is damage factor measured? Why is damage considered only in core (not in sleeve)?
12. Table 16, line 372: during simulation the friction was changed on all contact surfaces. How is it possible to state that exactly "the friction at the core-sleeve interface" is the most influential?
13. Please, add figure giving schematic of extrusion process with all parameters.  

Author Response

REVISION LETTER

November 09, 2020

Editor and reviewers, Applied Sciences

Dear Reviewer,

We think the comments are very constructive and provide an improvement to the quality of paper. We would like to thank the you for your comments and suggestions. The changes have been incorporated to the manuscript in blue color.

We hope that the paper is finally accepted to be published in the "Special Issue of the Manufacturing Engineering Society 2020 (SIMES-2020)" of the journal Applied Sciences.

Sincerely yours,

Daniel Fernández, Alvaro Rodríguez-Prieto and Ana María Camacho

Department of Manufacturing Engineering

UNED

• Why was the problem considered as 3D case (section 2.2)? Geometry is axisymmetric

Thank you very much for the constructive comment. Although the problem is axisymmetric and it could be solved as 2D case, the 3D simulation has been chosen to keep using this model in future studies where the incorporation of microstructure variation, modeling of the interface bonding, thermal expansion among other factors will be considered. Nevertheless, taking advantage of the axial symmetry of the problem, we have modeled only a quarter of the process in order to reduce the computation time and other computational resources such as storage needs.

We have included the following text:

In: 2.2 Finite Element Modeling

…………….

”Taking advantage of the axial symmetry of the problem, only a quarter of the process has been modeled in order to reduce the computation time and other computational resources such as storage needs”.

• Why was the Coulomb friction model used? I think that for for extrusion process the shear model is more suitable. Also it should be explained why the sleeve-core contact is separable.

Thank you very much for your comment. We completely agree that the shear friction model is commonly used in metal forming operations. But along with shear friction model, Coulomb friction model is also a classical friction model used in the analysis of bulk metal forming processes as stated by Zhang and Ou (2016), and as it can be seen in many works in the scientific literature and in reference books in metal forming analysis such as Rowe (1977). In fact, in the specific field of multi-material components, some examples of previous works considering Coulomb friction model in forming of bimetallic components are the one of Plancak et al. (2012) and Essa et al. (2012).

According to Rowe (1977) and Leu (2009), the upper limit of Coulomb friction coefficient is 0.577 for Von- Mises criterion and 0.5 for Tresca criterion; and the values of μ in our work are less than these limit values, so validity of the Coulomb friction model is guaranteed.

D.-W. Zhang and H. Ou: 2016. Relationship between friction parameters in a Coulomb–Tresca friction model for bulk metal forming, Tribology International, Vol. 95, 13-18.

D.-K. Leu: 2009. A simple dry friction model for metal forming process, Journal of Materials Processing Technology, Vol. 209, 2361–2368.

G.W. Rowe: 1977, Principles of Industrial Metalworking Processes, Edward Arnold Publishers, London.

2012. Plancak, I. Kacmarcik, D. Vilotic, M. Krsulja: 2012. Compression of bimetallic components–analytical and experimental investigation, Annals of Faculty Engineering Hunedoara–International Journal of Engineering, X-2 (2012) 157-160.

2012. Essa, I. Kacmarcik, P. Hartley, M. Plancak, D. Vitolic: 2012. Upsetting of bi-metallic ring billets, J. Mater. Process. Tech. 212 (2012) 817-824.

We have included the following text:

In: 2.2 Finite Element Modeling

…………….

”…that, along with the shear friction model, is one of the classical friction models in metal forming analysis [20]”.

On the other hand, the sleeve-core contact is separable because we would like to use this FE model in the future to analyse the influence of different interface conditions, to study their influence on the extrusion process. Anyway, in this work it has been considered that the ring and core have been assembled with an interference fit.

Finally, we have corrected one misprint found in the text: the friction considered in this analysis is the friction between the sleeve -container / die interface.

• As stated in the article (line 142) Cockroft-Latham criterion is "typically used in cold metal forming". However, authors used it for modelling of hot extrusion

C-L can be used independently of the working temperature. The literature does not mention a temperature condition, but it is true that many authors use it in cold forming; however, there are many other studies that also use this damage criterion considering warm and hot forming conditions (see the list of references below, as some examples). Anyway, the reason to use this criterion is its simplicity and generalized used as very little material data is required for calculations. In addition, this criterion is the one used in Deform by default.

Huang, X., Wang, B., Zhou, J., Ji, H., Mu, Y., Li, J., 2017. Comparative study of warm and hot cross-wedge rolling: numerical simulation and experimental trial. Int. J. Adv. Manuf. Technol. 92, 3541–3551. https://doi.org/10.1007/s00170-017-0399-6.

Silva, M.L.N., Pires, G.H., Button, S.T., 2011. Damage evolution during cross wedge rolling of steel DIN 38MnSiVS5. Procedia Eng. 10, 752–757. https://doi.org/10.1016/j.proeng.2011.04.125.

Guo-zheng Quan, Gui-chang Luo, An Mao, Jian-ting Liang, and Dong-sen Wu: 2014. Evaluation of Varying Ductile Fracture Criteria for 42CrMo Steelby Compressions at Different Temperatures and Strain Rates, The Scientific World Journal, http://dx.doi.org/10.1155/2014/579328.

We take into account this comment to modify this sentence in the paper in order to define it more precisely.

In: 2.2 Finite Element Modeling

…………….

“…typically used for predicting damage in metal forming operations [23], due to its simplicity and the accessibility of material data required for its calculation.”.

• Why so important parameter of extrusion process as extrusion ration wasn't considered? See Fig. 7.

Because the values range was very small in comparison with the rest which appears in figure 7 and it was directly dependent on the extrusion semi-angle, when the initial diameter of the billet is constant. Also, because more than six parameters would increase the number of simulation when Taguchi’s method is applied, we chose temperature instead extrusion ratio taking into account the values range.

We will incorporate this parameter in future studies.

• From what point of view authors have chosen the level's values of variables during DOE (Table 5)?

The values tried to reproduce a wide range of values that can be used in extrusion practices and to take into account enough variation in order to detect clear trends. A lot of simulations were performed and in some of them the solver did not converged when you combine some values of the variables or the simulation took a lot of time. However, we humbly think that the ranges used gave us enough results to explain the observed behaviour and to establish general trends in this kind of processes.

• Tables 6-11 - please, add units of variables. Table 12 - units of force. Table 13, 15 - remove units for variables, add unit for force

Tables updated

• Line 279-280: please, explain how does the billet's volume influence on the force? I think that in this case force increases because increases the area of side face, i.e. friction forces on this surface!

Thank very much because your comment has helped us to clarify this concept in the paper. Of course, you are right, and the increase of the force is due to the increase of the contact area (not the volume) of the billet with the container, that generates an increase of the energy component due to friction.

We have modified the text as follows.

In: 3.2.2. Billet height:

“… as the height increases, the contact area of the billet with the container increases too; as a consequence, this causes an increase of the energy component due to friction and, therefore, of the total force required”

• Line 286: please, clarify hardening behaviour of AZ31B alloy. It is not typical. I haven't found articles proving this.

This was a mistake applying the exponential model developed by Wen-Juan et al. in the article “Flow stress characteristics of AZ31B magnesium alloy sheet at elevated temperatures”. International Journal of Applied Physics and Mathematics 2012, Vol. 2, No. 2, 83 – 88. Table 4 has been updated.

Simulations have been performed again and the results are very similar. The following explanation has been added:

In: 3.2.3. Ram speed

“This effect can be explained because as the ram speed increases the temperature increases due to the friction in the container/billet interface. This increase of temperature reduces the stress necessary to deform the billet and thus the extrusion force is lower and remains practically constant at the highest speed.”

• 11, 13-14 - please, add "effective" to the stress

Done

• Line 327-328: if 30 degree angle is optimal (force is minimum), than in both directions from this point the force will increase.

Thank you for the comment because, as you mentioned, it was not correctly explained. We have changed the paragraph as follows:

In: 3.2.6. Die semi-angle

“Die semi-angle is the most relevant factor to obtain a small extrusion force. The conclusion that can be obtained from the graph in Figure 10f is that there is an optimal value where the extrusion force is minimal; this value has been set at 30°. From this optimal value, the extrusion force increases as the extrusion semi-angle increases or decreases and allows identifying a situation of minimum energy.”.

• Line 339-340: In what part of core is damage factor measured? Why is damage considered only in core (not in sleeve)?

The damage is calculated in the whole core. Deform solves the equation:

(see document attached)

measuring the σ_max and the equivalent plastic strain in each step. The value computed and used for comparison is the maximum damage in the whole core.

The damage in the core is mentioned because there is a pattern in most of the cases (shown in figure 15) and one of the main defects in extrusion processes (the chevron crack defect) is located along the extrudate axis, being the finite element simulation very useful to predict the appearance of this internal defect and to establish favorable forming conditions to avoid it. Damage reaches a peak at the beginning of the simulation and afterwards it descends quickly until a value which remains stationary during the process due to the permanent regime achieved in the process.

• Table 16, line 372: during simulation the friction was changed on all contact surfaces. How is it possible to state that exactly "the friction at the core-sleeve interface" is the most influential?

Thank you very much for your useful comment. It is a mistake, table 16 has been updated and the text below modified as follows:

In: 3.4. Summary of most influential parameters

“....The most influential parameters considering both criteria (minimum values of forces and damage) are the die semi-angle and friction at the sleeve-container /die interface, so special attention should be paid to obtain favourable interface contact conditions;......”.

• Please, add figure giving schematic of extrusion process with all parameters

In: 2.1. Materials and Geometrical Dimensions

Figure 2 has been added

      Figure 2. Extrusion process schema (see document attached)

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper presents an interesting study of the extrusion process to manufacture bimetallic cylinders combining a magnesium alloy core (AZ31B) and a titanium alloy sleeve (Ti6Al4V), with help numerical simulation. 

1. It is not clear what type of extrusion is used: direct or reverse
2. What type of test is used for the flow stress determination
3. In figures 10, 11, 14 is better to specify the temperature (even this is constant)
4. An image of the deformed part as it results from simulations will be interesting to show.
5. A more deeply discussion about damage will be useful, including some charts (see ref. 25)
6. In Johnson law what is the extrusion ratio?
7. Notations from figure 7 are not find in the text (H/D and D/d)   
8. The conclusions are clear and are in accordance with the simulation work

Some editing aspects have to be implemented:

line 173 - "where" with small caps

line 340 - finish the proposition with a point

line 361 - the text is not aligned

Author Response

REVISION LETTER

November 09, 2020

Editor and reviewers, Applied Sciences

Dear Reviewer,

We think the comments are very constructive and provide an improvement to the quality of paper. We would like to thank the you for your comments and suggestions. The changes have been incorporated to the manuscript in blue color.

We hope that the paper is finally accepted to be published in the "Special Issue of the Manufacturing Engineering Society 2020 (SIMES-2020)" of the journal Applied Sciences.

Sincerely yours,

Daniel Fernández, Alvaro Rodríguez-Prieto and Ana María Camacho

Department of Manufacturing Engineering

UNED

• It is not clear what type of extrusion is used: direct or reverse

Thanks for the comment. You are right, it is not clear, therefore a new figure with a schema of the process has been included.

In: 2.1. Materials and Geometrical Dimensions

Figure 2 has been added

Figure 2. Extrusion process schema (see document attached)

• What type of test is used for the flow stress determination

The flow curves used for Ti6Al4V are from DEFORM library.

For the AZ31B magnesium alloy it was used the exponential model defined by Wen-Juan et al. in the article “Flow stress characteristics of AZ31B magnesium alloy sheet at elevated temperatures”. International Journal of Applied Physics and Mathematics 2012, Vol. 2, No. 2, 83 – 88.  The flow stress data can be consulted in table 4 of the section 2.2. Finite Element Modeling.

• In figures 10, 11, 14 is better to specify the temperature (even this is constant)

A note with the temperature value has been added to the caption of the figures.

• An image of the deformed part as it results from simulations will be interesting to show

Thanks for the comment. A new figure and the following text have been added.

In: 3.4. Summary of most influential parameters

“As an example of the simulations preformed, Figure 16 shows the effective stress and temperature distribution respectively in the FE model, in different stages of the simulation.”

Figure 16. Contour diagrams. (a) Effective stress distribution during co-extrusion process; (b) Temperature distribution during co-extrusion process (see document attached)

• A more deeply discussion about damage will be useful, including some charts (see ref. 25)

The damage is calculated in the whole core. Deform solves the equation:

(see document attached)

measuring the σ_max and the equivalent plastic strain in each step. The value computed and used for comparison is the maximum damage in the whole core.

The following comments have been added:

In: 2.2. Finite Element Modeling

“...typically used for predicting damage in metal forming operations [23], due to its simplicity and the accessibility of material data required for its calculation”

[23] Stebunox, S.; Vlasov, A.; Biba, N. Prediction of the fracture in cold forging with modified Cockcroft – Latham criterion. Procedia Manufacturing. 2018.

In: 3.3. Other factors related to the quality of the extrudate: Damage factor

“...at the core (where inner defects such as chevron cracks can appear in extrusion under specific forming conditions)”

We will incorporate in future studies a comparative among different damage models such as Freudenthal or Oyane, to conclude which ones models better the likelihood of ductile fracture during multi-material forming.

• In Johnson law what is the extrusion ratio?

The extrusion ratio is calculated by this expression:

r_x= A0/A, where A0 is the initial area, and A is the final area.

In order to clarify it, the following paragraphs have been modified:

In: 2.3. Finite Element Model Validation

“…where rx is the extrusion ratio (A0/A)”

“Three simulations have been performed to validate the model. In all the simulations the cylinder had 12 mm of external diameter and 20 mm of height and the final external diameter was 9 mm, therefore the extrusion ratio (rx) is 1.77.”......

• Notations from figure 7 are not find in the text (H/D and D/d)   

The following paragraph has been added:

In: 2.4. Design of experiments (DOE)

.............

“H₀ is the initial height of the billet, D₀ is the initial external diameter of the sleeve and d₀ is the initial diameter of the core.”....

• The conclusions are clear and are in accordance with the simulation work

Thank you very much

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

All my comments were taken into account and comprehensive comments were given. Thanks!