Determining the Drawing Force in a Wire Drawing Process Considering an Arbitrary Hardening Law

Round 1

Reviewer 1 Report

The work is theoretical in nature. The research (calculations) is based on known material models for example von Misses criterion. Authors did not make any original contribution to the paper. It is not clear what is original and what is already developed. The paper has very low application potential. It can be assumed that this potential is equal to zero. The work has scientific value but only in the sense of mathematical description of physical phenomena. It does not solve the problem of materials in terms of technology and application and certainly not in terms of engineering. It is a purely scientific manuscript without experimental verification. Both theoretical and experimental studies should relate to specific process parameters. The material is also important. Only then you can verify if the results are close to reality. Such theoretical analyses can be verified, for example, by FEM simulations.  The authors did not present specific examples on which they performed the analysis. What material is used to analyze the problem, what geometric and velocity parameters and what lubricant. The work can be successfully published in theoretical journals. The authors claim that an engineering approach was used. The approach used is purely scientific and has nothing to do with engineering.  The authors claim to have used an engineering approach in presenting the effects of process parameters on dimensionless drawing force. The engineering approach does not include dimensionless drawing force. The drawing force in engineering has units from the Si system. 

 

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Hi

Well written paper - i like that you include many details in the deriviation of equations.

It could be nice to have some comparison with other methods, E.g. FEM - and also a comparison with published results with other upper bound methods who include experiemental results

Author Response

Response.

1. The conclusion section compares our result with that reported in [16], where the upper bound theorem was applied for drawing through a die with a small angle.
2. We have added Section 7. This new section compares upper bound and FE solutions and emphasizes the advantages of our solution.

Reviewer 3 Report

The results in chapter 6 are compared only with the solution provided in [16]. It would be very helpfull to compare with experimental data (eather original or from other authors).  

It is not clear the range of use of the obtained solution: materials, lubricants, temperature range, draving velocity, etc. 

It is interesting which advantage in the accuracy of calculation give the presented solution, also the drawing equipment is selected for some range of maximal force. 

Author Response

1. The results in chapter 6 are compared only with the solution provided in [16]. It would be very helpfull to compare with experimental data (eather original or from other authors).  

Response. The difficulty with comparing the solution and experimental data from the literature is that the sources usually do not provide all the necessary information for finding the corresponding theoretical solution. We have added Section 7, in which the general comparison of upper bound and finite element solutions is provided.

2. It is not clear the range of use of the obtained solution: materials, lubricants, temperature range, draving velocity, etc. 

Response. All the theoretical solutions, including finite element solutions, operate with models rather than materials, lubricants, etc. We adopt the general model widely used in commercial finite element packages. This model is rate-independent (i.e., the drawing speed is immaterial). It is usually accepted that the model is valid at room temperature. This issue is outside the scope of our paper. It is not particularly related to drawing or upper bound solutions. The short answer to your comment is that the range of applicability of the solution is restricted to the range of applicability of the material and friction models. The numerical example is for AISI-316 stainless steel. We have clarified it in the revised manuscript.

3. It is interesting which advantage in the accuracy of calculation give the presented solution, also the drawing equipment is selected for some range of maximal force.

Response. Figure 5 shows no advantage for rigid perfectly plastic material and small die angles. The paper emphasizes this feature of the solution. The advantage is revealed when one applies the solution strain hardening materials. The present solution is much more accurate because the realistic stress-strain curve is considered.

Reviewer 4 Report

In this work, the authors investigated the wire drawing process from a primarily analytic aspect.
Based on the upper bound theorem, they considered a wire drawing process through a conical die.
An approximate solution for the drawing force was elaborated under the assumption of an arbitrary hardening law.
In particular, since the upper bound theorem does not apply to the stationary flow in strain hardening materials, an engineering approach is adopted where the original material model was replaced with a non-homogeneous perfectly plastic model.
Subsequently, the kinematically admissible velocity field was derived from an exact semi-analytical solution for the flow through an infinite channel.
The solution regarding the homogeneous perfectly plastic material was then compared with available ones.
It is argued that the general solution is valid for any die angle.
Also, since the material model is pressure-independent, the solution can be straightforwardly adopted for calculating the force in extrusion.

The manuscript is well-written and brings us a better understanding of the wire drawing associated with the application of the upper bound theorem.
In particular, the solution can be reduced to several ordinary integrals that facilitate numerical calculations, which also brings some practical advantages.
Moreover, the kinematically admissible velocity field was taken from the exact solution for material flow through an infinite channel.
Through numerical calculations, the effect of process parameters on the dimensionless drawing force, obtained by assuming the specific hardening law, agrees with physical expectations.
The solution also largely coincides with the existing ones in the literature, which were developed for small die angles.
Therefore, the obtained results are more general.

For the reasons above, I recommend the paper be published on Processes.

Author Response

This reviewer has not made critical comments.

Reviewer 5 Report

This manuscript does an excellent job. I believe the importance of this paper stems from the applicability of the approach on a field that has only recently boomed. The article is well written, treats an actual problem. and the authors have collected a unique dataset using cutting  edge methodology. The paper is generally well structured. However, in my opinion the  paper has some shortcomings in regards to some data analyses and coments. I also missed a background, but I enjoyed what clearly has the potential to be published. 

Author Response

Response. We have added Section 7 to summarize our findings.

Round 2

Reviewer 1 Report

Dear Autors

The reviewer still maintains his position. The work is very theoretical. The journal deals with the research of materials as existing materials. Such work may be published in journals on mathematical models, equations, applied mathematics, etc. The work has no practical application. Such theoretical analyzes for equations and models can be found in many scientific books. I believe that the scientific value of the work is high but not new and with no chance for practical application. This is not an engineering approach.