Deformation Behavior and Connection Mechanism of EMP Connections in Aluminum Pipe Joints

Round 1

Reviewer 1 Report

As for the part describing the metallographic observations, I recommend to add the method of preparing the specimens for metallographic study (composition of etching solution) and equipment used for structural examination in the section "2. Experimental".

Author Response

Dear Editors and Reviewers,

Thank you for the valuable comments to the manuscript (metals-1940827). According to the comments we received, careful modifications have been made. We hope that the updated manuscript will meet the magazine’s requirements. You will find our point-by-point responses to the reviewers’ comments below.

The modified manuscript has been attached, in which all the modifications are highlighted in blue. Thank you very much.

Reviewer #1:

---Comment 1: As for the part describing the metallographic observations, I recommend to add the method of preparing the specimens for metallographic study (composition of etching solution) and equipment used for structural examination in the section "2. Experimental".

Response to Reviewer Comment No. 1: Thank you for the valuable suggestion. As the reviewer said, we do lack the description of sample preparation method and structural inspection equipment. According to the reviewer's suggestion, we added "2.4 Deformation observation" to the revised manuscript. (On the page 9, line 284-303)

The added contents are as following:

2.4. Deformation observation

In this paper, the laser confocal electron microscope (OLS-3000) produced by Hitachi OLYMPUS was used to observe and measure the contour size of the deformed area of the 6061 pipe fitting after forming.

After the 6061-T4 aluminum alloy pipe fitting is formed, the instrument is used to scan the deformation area of the pipe fitting to obtain the three-dimensional morphology of the pipe fitting, and the contour line can be drawn along the axis direction of the pipe fitting and generate coordinate points. Due to the presence of other interference sources in the test process, the test results will be affected to a certain extent. Based on the test results, noise reduction should be unified to obtain the scanning contour of the deformation area of the pipe fitting. The height of the deformation area of the pipe fitting can be obtained by processing the data coordinates of the contour.

In order to further analyze the local deformation degree of the pipe fitting, the formed pipe fitting was cut along the radial direction, and the section and metallographic structure of the local deformation area were observed by optical microscope. The samples were cut along the radial direction in the deformation zone of the 6061 aluminum alloy pipe fitting. After grinding and polishing with sandpaper, the samples were corroded with corrosion solution (HF:HNO3:H2O=1:3:6) for more than 15s. The metallographic structure of the pipe fitting before and after forming was observed by metallographic microscope.

Author Response File: Author Response.pdf

Reviewer 2 Report

The article submitted for review Deformation behavior and connection mechanism of EMP connections in aluminum pipe joints is interesting from the experimental point of view, and unfortunately very weak in terms of modeling the pipe joining process. 

The language of the article is mostly correct and does not require major linguistic corrections. Authors should correct the descriptions of the drawings, some descriptions are incomplete, some authors use the description a) b) etc but not in the description but in the drawing.

The mathematical model is not described, there is no description of the mathematical model of the material, boundary conditions of the heat exchange equations of friction conditions.

In addition, the authors used a simple flat model which is designed to limit the calculation time, however, the number of elements used in the pipe model is, in my opinion, too small, as shown in Fig. 19, 21, 22 etc. In my opinion, all numerical tests should be repeated with a densified mesh, especially in the zone where deformation occurs. The resulting data cannot be considered representative. Moreover, it is necessary to complete the verification of the mathematical model in relation to the real research. In generally accepted practice, mathematical modeling is the basis for designing the real process. The conclusions are not fully justified in the description.

In addition, the presented data analysis is rudimentary, I suggest limiting the number of presented results and extending their analysis. After the corrections, the article can be significant and make a significant contribution to the knowledge of the EMP pipe joining process.

Author Response

Dear Editors and Reviewers,

Thank you for the valuable comments to the manuscript (metals-1940827). According to the comments we received, careful modifications have been made. We hope that the updated manuscript will meet the magazine’s requirements. You will find our point-by-point responses to the reviewers’ comments below.

The modified manuscript has been attached, in which all the modifications are highlighted in blue. Thank you very much.

Reviewer #2:

The article submitted for review Deformation behavior and connection mechanism of EMP connections in aluminum pipe joints is interesting from the experimental point of view, and unfortunately very weak in terms of modeling the pipe joining process. The language of the article is mostly correct and does not require major linguistic corrections.

---Comment 1: Authors should correct the descriptions of the drawings, some descriptions are incomplete, some authors use the description a) b) etc but not in the description but in the drawing.

Response to Reviewer Comment No. 1: Thank you for the valuable suggestion. As the reviewer said, our description of some drawings is not complete, so we provide supplementary instructions for these drawings. For Fig. 9, the drawing method of Fig. 9a) and b) is supplemented. For Fig. 16, add a supplementary description to the drawing. ( On the page 10, line 321-325；On the page 14, line 435-436)

The added contents are as following:

The scanning position was selected in the deformation zone of the tube with a discharge voltage of 7 kV and a gap of 1 mm. 6 scanning lines were selected along the circumferential direction to obtain the 3D morphology shown in Fig. 8, with the X direction in the axial direction, the Y direction in the circumferential direction, and the Z direction in the radial direction. The green area is the raised area, i.e., the deformation zone where the tube was embedded in the groove after forming. The profile was drawn as shown in Fig. 9. As shown in Fig. 9a), draw the lower limit of the contour coordinate of the pipe fitting deformation area under 6kV discharge voltage to the same horizontal line, take the mean value of the high coordinate area and the low coordinate point area of the curve in the figure, and put the low coordinate point to 0, and further obtain the approximate contour as shown in Fig. 9b). Within the margin of error caused by roughness, the height of the deformed area was more consistent, indicating a more uniform forming in the circumferential direction.

Under the same discharge voltage, the forming effect under different initial clearance is shown in Fig. 16, with an increase of the initial gap between the tube and the tube, as shown in Fig. 16c), the area where the tube was deformed and embedded in the groove of the tube kept getting larger to the bottom of the trench.

---Comment 2: The mathematical model is not described, there is no description of the mathematical model of the material, boundary conditions of the heat exchange equations of friction conditions.

Response to Reviewer Comment No. 2: Thank you for the correction and valuable suggestion. As the reviewer said, our description of the finite element model is not sufficient. According to the reviewer's suggestions, we rewrote "2.3 Finite Element Model" and further supplemented the finite element model, finite element solver and friction conditions. (On the page 6, line 189-204; On the page7-8, line 219-241)

The added contents are as following:

In the numerical simulation of this paper, in order to improve the computational efficiency, the 2D axisymmetric model is adopted. The 3D model is consistent with the 2D axisymmetric model in the geometric dimension, and the main difference is the difference of the torus Angle.

In LS-DYNA, for the 3D model, the EM_Solver developed by LS-DYNA adopts the finite element and boundary element algorithm, which can automatically couple multiple physical fields such as electromagnetic field, temperature field and force field in 3D space without dividing the air grid, and obtain the physical quantity information of the complete model. The computational efficiency of the solver is low, but the modeling is simple, and it is suitable for most numerical simulation of electromagnetic forming. For 2D-axially symmetric models, the 2D axi-symmetric EM_solver developed by LS-DYNA is able to solve the electromagnetic field equation in a two-dimensional plane, and then expand the two-dimensional electromagnetic field, Lorentz force, and Joule heat into 3D elements by rotating around the axis. This allows the 2D electromagnetic field to be coupled with the 3D force field and temperature field, thus greatly reducing the computational time and keeping the 3D functionality of LS-DYNA available [15]. The solver is only suitable for the model with good axial symmetry, and the electromagnetic bulging process of pipe fittings has good axial symmetry, so it is appropriate to use the solver.

There are three main parts in this process: coil, tube and sleeve. In order to constrain the ring direction of the tube sleeve, the sleeve ring part is added, which is consistent with the actual forming. Considering that the tube, sleeve and coil all belong to axisymmetric pattern and are placed symmetrically with the axis, this direct electromagnetic expansion connection has good axial symmetry.

Firstly, the finite element model of the coil and tube was established in LS-Prepost software. The model was 1/64 of the whole, the outer diameter of the tube was 49.2mm, the wall thickness was 0.9mm, and the length was 33.8mm. The coil was made of red copper, the cross section was 3mm×7mm, the number of turns was 5, and each turn of the coil was a separate part. All components adopt single point integration element, and finally form the finite element model as shown in Fig. 7. The element grid setting of the finite element model is shown in Table 3.

Temperature has little influence on the forming effect during the process of electromagnetic bulging of pipe fittings, so only electromagnetic field and force field are considered in the simulation. The mechanical property parameters of each component are set as shown in Table 4. In the numerical simulation, the coil and the sleeve ring are set as rigid bodies. In this model, only the tube and the sleeve are in contact, and the contact is set as double-sided contact. The static friction coefficient is 0.15, and the dynamic friction coefficient is 0.1.

Figure 6. Finite element model of magnetic pulse forming of pipe joint.

Table 4. Element mesh setting in finite element model.

Table 5. Finite element model mechanical properties’ parameter settings.

---Comment 3: In addition, the authors used a simple flat model which is designed to limit the calculation time, however, the number of elements used in the pipe model is, in my opinion, too small, as shown in Fig. 19, 21, 22 etc. In my opinion, all numerical tests should be repeated with a densified mesh, especially in the zone where deformation occurs. The resulting data cannot be considered representative. Moreover, it is necessary to complete the verification of the mathematical model in relation to the real research. In generally accepted practice, mathematical modeling is the basis for designing the real process. The conclusions are not fully justified in the description.

Response to Reviewer Comment No. 3: Thank you for the valuable suggestion. First of all, the model used in this paper is a 2D axisymmetric model, and its comparison with the 3D model is shown in the following figure, which is not a simple plane model. Considering the symmetry of the whole model, the finite element model adopted in this paper is 1/64 of the whole circle in order to save calculation cost. At the same time, we supplemented the introduction of the 2D axisymmetric model and its solver, and verified the reliability of the 2D axisymmetric model. The final error was less than 10%, so we believed that the simulation results were representative. In addition, it is time-consuming and costly to repeat all the numerical simulation experiments using the overall 3D model.(On the page 6-7, line 193-218)

1. a) 3D model b) 2D axisymmetric model

Figure . Difference between 3D model and 2D axisymmetric model

The added contents are as following:

In LS-DYNA, for the 3D model, the EM_Solver developed by LS-DYNA adopts the finite element and boundary element algorithm. The computational efficiency of the solver is low, but the modeling is simple, and it is suitable for most numerical simulation of electromagnetic forming. For 2D-axially symmetric models, the 2D axi-symmetric EM_solver developed by LS-DYNA is able to solve the electromagnetic field equation in a two-dimensional plane, and then expand the two-dimensional electromagnetic field, Lorentz force, and Joule heat into 3D elements by rotating around the axis. This allows the 2D electromagnetic field to be coupled with the 3D force field and temperature field, thus greatly reducing the computational time and keeping the 3D functionality of LS-DYNA available [15]. The solver is only suitable for the model with good axial symmetry, and the electromagnetic bulging process of pipe fittings has good axial symmetry, so it is appropriate to use the solver.

In order to verify the reliability of the numerical model, a 3D model and a 3D axisymmetric model of 6061-T4 aluminum alloy pipe fitting were established. The free bulging test and numerical simulation were carried out under the discharge voltage of 4kV, as shown in Fig. 5. The results of the test, 3D model and 2D axisymmetric model are basically consistent. The length of the forming zone L and the maximum outside diameter D of the pipe fitting are measured and compared with the simulation results, as shown in Table 3. It can be found that the error between the length of the forming zone L and the maximum outside diameter D of the pipe fitting and the test results is less than 10% in both the 3D model and the 2D axially symmetric model, which indicates that the numerical simulation results are reliable.

a)Test results ; b) 3D model simulation results; c) 2D axisymmetric model simulation results

Figure 5. Comparison between experimental and numerical simulation results

Table 3. Element mesh setting in finite element model.

---Comment 4: In addition, the presented data analysis is rudimentary, I suggest limiting the number of presented results and extending their analysis. After the corrections, the article can be significant and make a significant contribution to the knowledge of the EMP pipe joining process.

Response to Reviewer Comment No. 4: Thank you for the correction and valuable suggestion. According to the reviewer's suggestion, the part about the width and depth of the groove in "3.1.2. Effect of tube sleeve groove dimensions" was deleted. This part of research belongs to the extension of forming process, and the deletion will have no influence on the overall structure logic of this paper. Meanwhile, we extended "3.2 The deformation behavior analysis".(On the page 14-15, line 443-451; On the page 15-16, line 457-467)

The added contents are as following:

In the case of only focus on 6061 fitting local deformation, natural big initial gap and voltage can cause more severe local deformation, but from the perspective of the forming effect of actual pipe joint, on the one hand, pipe - set of initial gap will make the pipe - set of preset clearance is difficult, even pipe fittings had happened in the preset clearance deformation strengthening. On the other hand, it can be found from the numerical simulation results that the groove edge of the sleeve is crushed under the condition of excessive clearance and voltage. Therefore, when the embedding rate of pipe joint is more than 85%, a smaller gap should be selected to avoid the phenomenon of groove edge collapsing.

The groove embedment rate was measured under the conditions of different pipe-tube sleeve initial gaps. As shown in Fig. 18, the embedment rate was 88.7% under the condition of a 1 mm initial gap, which reached the requirement of 85%. When the gap reached 1.5 mm and 2 mm, the groove embedment rate was close to 100%, but the groove edge "slumped". Therefore, in the variable gap electromagnetic bulging process scheme, the initial gap and discharge voltage should be selected to be as small as possible while ensuring the groove embedding rate, so as to avoid the phenomenon of serious deformation of the sleeve’s groove edge. From the point of view of the forming effect under a discharge voltage of 6 kV, it is appropriate to select the initial gap between the pipe and casing of 1 mm. At this time, the forming process of the pipe joint is shown in Fig. 19.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper shows an interesting note but needs significant improvements. Please follow the comments carefully.

1.         Add some quantitative results to the abstract.

2.        Add more detail to the conclusion.

3.        Add more discussion about figure 7 “Finite element model of …”.

4.        Provide a thorough discussion of reported results in Table 4 “Finite element model mechanical properties’ parameter settings”. The presented discussion can not clarify the happening phenomena. Provide more fundamental information.

5.        Add more results to your conclusion.

6.        Al has different usage in various industries, especially in additive manufacturing. Read and add the following four papers on this application to highlight the contribution of your paper.

·          Additive manufacturing on the façade: functional use of direct metal laser sintering hatch distance process parameters in building envelope

·          A review of Industry 4.0 and additive manufacturing synergy

·          Effect of direct aging and annealing on the microstructure and mechanical properties of AlSi10Mg fabricated by selective laser melting

·          Additive manufacturing of Ti-Al functionally graded material by laser based directed energy deposition

Author Response

Dear Editors and Reviewers,

Thank you for the valuable comments to the manuscript (metals-1940827). According to the comments we received, careful modifications have been made. We hope that the updated manuscript will meet the magazine’s requirements. You will find our point-by-point responses to the reviewers’ comments below.

The modified manuscript has been attached, in which all the modifications are highlighted in blue. Thank you very much.

Reviewer #3:

The paper shows an interesting note but needs significant improvements. Please follow the comments carefully.

---Comment 1: Add some quantitative results to the abstract .

Response to Reviewer Comment No. 1: Thank you for the valuable suggestion. We have added quantitative results for the lowest voltage at which the trench embedding rate reaches more than 85% under different gap conditions to the existing abstract. ( On the page 1, line 19-23)

The added contents are as following:

Abstract: The joint is a key component of the aviation piping system, with severe performance requirements and better requirements for the connection technology. With a focus on the manufacturing demand of AA6061 aerospace pipe joints, as well as the characteristics of high-rate EMP forming technology, this paper investigates the deformation behavior of the EMP forming on AA6061 aerospace pipe joints, the influence of process parameters and groove characteristics (i.e., groove rounding, groove width, groove depth, and groove width-depth ratio) on the deformation behavior, and the deformation mechanism of the tube wall on the deformation mechanism of the tube wall to tube sleeve groove filling. The results show that under the conditions of this paper, with an increase of the initial tube-sleeve gap and discharge voltage, the degree of local deformation of the AA6061 tube wall and the trench embedding rate increase. Keeping the width and depth of the grooves as 1.14mm and 0.23mm, the embedding rate of the grooves is less than 85% under the clearance conditions of 0.11mm and 0.5mm, while the lowest voltage for the embedding rate of the grooves to reach more than 85% under the clearance conditions of 1mm, 1.5mm and 2mm is 7kV, 6kV and 5kV respectively. The metallographic organization of the deformation area shows that the tube is deformed by the intense shear at the edge of the groove of the tube sleeve, thereby showing streamlined organization characteristics and deformation characteristics. The electromagnetic pulse forming process of AA6061 tube is mainly divided into two stages: free bulging and local deformation; the inertia of high-rate deformation causes the groove filling to exhibit volume deformation characteristics in the local deformation stage. With an increase of the tube-sleeve gap, the more significant the effect of the groove filling is.

---Comment 2: Add more detail to the conclusion.

Response to Reviewer Comment No. 2: Thank you for the valuable suggestion. According to the reviewer's suggestion, we have added the relevant details of finite element simulation in the conclusion. ( On the page 21, line 591-592)

The added contents are as following:

In this study, 2D axisymmetric model is used for finite element simulation, which greatly saves the computational cost. According to the results of finite element simulation, the embedding rate is 88.7% under the condition of 1mm initial clearance, which has reached the requirement of 85%. When the clearance reaches 1.5mm and 2mm, the groove embedding rate is close to 100%, but the groove edge "collapse" occurs. Therefore, in the process of electromagnetic bulging with variable gap, small initial gap and discharge voltage should be chosen as far as possible to avoid the serious deformation of the tube groove edge under the condition of ensuring the groove embedding rate. According to the forming effect under 6kV discharge voltage, it is appropriate to choose 1mm initial gap between tube and sleeve.

---Comment 3: Add more discussion about figure 7 “Finite element model of …”.

Response to Reviewer Comment No. 3: Thank you for the correction and valuable suggestion.We added the introduction to the finite element model, including the components of the model, basic dimensions and mesh division. ( On the page 8, line 223-244)

The added contents are as following:

There are three main parts in this process: coil, tube and sleeve. In order to constrain the ring direction of the tube sleeve, the sleeve ring part is added, which is consistent with the actual forming. Considering that the tube, sleeve and coil all belong to axisymmetric pattern and are placed symmetrically with the axis, this direct electromagnetic expansion connection has good axial symmetry.

Firstly, the finite element model of the coil and tube was established in LS-Prepost software. The model was 1/64 of the whole, the outer diameter of the tube was 49.2mm, the wall thickness was 0.9mm, and the length was 33.8mm. The coil was made of red copper, the cross section was 3mm×7mm, the number of turns was 5, and each turn of the coil was a separate part. All components adopt single point integration element, and finally form the finite element model as shown in Fig. 6. The element grid setting of the finite element model is shown in Table 4.

Temperature has little influence on the forming effect during the process of electromagnetic bulging of pipe fittings, so only electromagnetic field and force field are considered in the simulation. The mechanical property parameters of each component are set as shown in Table 5. In the numerical simulation, the coil and the sleeve ring are set as rigid bodies. In this model, only the tube and the sleeve are in contact, and the contact is set as double-sided contact. The static friction coefficient is 0.15, and the dynamic friction coefficient is 0.1.

Figure 6. Finite element model of magnetic pulse forming of pipe joint.

Table 4. Element mesh setting in finite element model.

Table 5. Finite element model mechanical properties’ parameter settings.

---Comment 4: Provide a thorough discussion of reported results in Table 4 “Finite element model mechanical properties’ parameter settings”. The presented discussion can not clarify the happening phenomena. Provide more fundamental information.

Response to Reviewer Comment No. 4: Thank you for your correction and valuable advice. We provide more basic information on finite element parameter Settings, including material mechanical model, electromagnetic property Settings, current loop Settings, and constraints. (On the page 8, line 241-253; On the page 9, line 278-282)

The added contents are as following:

In the electromagnetic field, the circuit adopts RLC series resonance circuit parameter input, Rsys, Lsys, Csys as the circuit input parameters, namely, the system inductance, capacitance and resistance. In the numerical simulation of this paper, the EMF50kJ/18kV electromagnetic forming equipment of the Key Laboratory of Metal Hot Working of Harbin Institute of Technology is adopted. The oscilloscope and Roche coil are used to measure the current under 3kV discharge voltage, as shown in Fig. . According to the RLC parameters fitted by the measured current curve, the Rsys, Lsys and Csys of the electromagnetic forming system were 14.86mΩ, 0.675µH and 304µF, respectively. By inputting circuit parameters such as Rsys, Lsys and Csys in the circuit Settings and presetting the initial charging voltage, the discharge process with the same voltage can be simulated in the real situation.

Figure 7. Finite element model of magnetic pulse forming of pipe joint.

Since the model is axisymmetric, constraints are set in the direction of the pipe and sleeve rings. Since the actual length of the pipe fitting is much longer than the sleeve, full constraints are set on the two end faces of the pipe fitting. The coil and the sleeve ring basically do not deform or move during actual forming, and the coil and the sleeve ring are also set with full rigid body constraints.

---Comment 5: Add more results to your conclusion.

Response to Reviewer Comment No. 5: Thank you for the valuable suggestion. In the conclusion, we add the adverse effects of excessive initial clearance between tube and sleeve and the results related to the selection of optimal initial clearance. (On the page 21, line 591-601)

The added contents are as following:

In this study, 2D axisymmetric model is used for finite element simulation, which greatly saves the computational cost.According to the results of finite element simulation, the embedding rate is 88.7% under the condition of 1mm initial clearance, which has reached the requirement of 85%. When the clearance reaches 1.5mm and 2mm, the groove embedding rate is close to 100%, but the groove edge "collapse" occurs. Therefore, in the process of electromagnetic bulging with variable gap, small initial gap and discharge voltage should be chosen as far as possible to avoid the serious deformation of the tube groove edge under the condition of ensuring the groove embedding rate. According to the forming effect under 6kV discharge voltage, it is appropriate to choose 1mm initial gap between tube and sleeve.

---Comment 6:  Al has different usage in various industries, especially in additive manufacturing. Read and add the following four papers on this application to highlight the contribution of your paper.

• Additive manufacturing on the façade: functional use of direct metal laser sintering hatch distance process parameters in building envelope
• A review of Industry 4.0 and additive manufacturing synergy
• Effect of direct aging and annealing on the microstructure and mechanical properties of AlSi10Mg fabricated by selective laser melting
• Additive manufacturing of Ti-Al functionally graded material by laser based directed energy deposition

Response to Reviewer Comment No. 6: Thank you for the valuable suggestion. After careful reading, we believe that all the papers you provided belong to the field of additive manufacturing, which does not quite match the research field of this paper. Therefore, for the time being, we only quote one article in the section "1. Introduction". (On the page 2, line 90-92)

The added contents are as following:

In addition to the two above forming techniques, there are other pipe joint forming techniques that correspond to the forming needs of aerospace pipe joints. Henriksen et al. [8] proposed a method for joining pipes and grooved sleeves by expanding a rigid die with bumps. Przybylski et al. [9] proposed a method for forming lightweight pipe joints by rolling from the outer diameter and noted that joints with trapezoidal grooves have a higher pull-off strength compared to circular grooves. Cai D et al. [10] proposed a method for electro-hydraulic joining of aluminum alloy tubes and stainless-steel pipe sleeves and found that the joint performance improved with increasing discharge voltage and slot width. At the same time, additive manufacturing (AM) plays an important role in process 4.0 due to its flexibility, and may be able to produce joint joints, but there are few relevant studies[11].

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

As the autors write in respond "the model used in this paper is a 2D axisymmetric model, and its comparison with the 3D model is shown in the following figure, which is not a simple plane model" And here there is a certain inaccuracy - this model is not a 3D model, but only a flat representation of a 3D model with an assumed axis of rotation. The authors hide behind a long computational time, which does not seem true (a 3D model of a similar process on a related computational program with a densified mesh is counted about 20 hours using a circular segment of 5 degrees and with the number of elements over 200,000). As can be seen in Figures 20, 21, 23 the assumed mesh density is not sufficient, or rather the obtained results of theoretical research are not accurate). if the authors believe otherwise, please compare the obtained shapes of the connection zone from theoretical and experimental studies. I think that the refinement of the mesh in the connection zone where such intense deformation occurs is necessary. 

Author Response

Dear Reviewer:

Thank you for your valuable comments on the manuscript (metals-1940827). Based on the comments we've received, revisions have been made. We hope that the updated manuscript will meet your requirements. Attached you will find our point-by-point responses to reviewer comments, with all revisions highlighted in blue. Thanks.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper is ready to go.

Author Response

Thank you very much

Round 3

Reviewer 2 Report

I still believe that in the deformation zone, mesh refinement is required, which is ideally presented in Fig. 15, where the resulting deformation of a single element causes its detachment along its entire length, a comparison of the superimposed shapes obtained in experimental and numerical data (in any CAD program) would bring more than descriptive data are presented in Fig. 15. Therefore, it is necessary to supplement the article with such a figure.The remaining amendments improve the scientific quality of the article, but I still consider the problem of convergence of the numerical solution for the adopted mesh parameters as debatable.

Author Response

Dear Editors and Reviewers,

Thank you for the valuable comments to the manuscript (metals-1940827). According to the comments we received, careful modifications have been made. We hope that the updated manuscript will meet the magazine’s requirements. You will find our point-by-point responses to the reviewers’ comments below.

The modified manuscript has been attached, in which all the modifications are highlighted in blue. Thank you very much.

Reviewer #2:

I still believe that in the deformation zone, mesh refinement is required, which is ideally presented in Fig. 15, where the resulting deformation of a single element causes its detachment along its entire length, a comparison of the superimposed shapes obtained in experimental and numerical data (in any CAD program) would bring more than descriptive data are presented in Fig. 15. Therefore, it is necessary to supplement the article with such a figure. The remaining amendments improve the scientific quality of the article, but I still consider the problem of convergence of the numerical solution for the adopted mesh parameters as debatable.

Response to Reviewer: Thank you for your correction and valuable suggestion. According to the comments of reviewer, we compared the actual experiment and the finite element simulation, obtained the superposition diagram of the two shapes, and annotated and analyzed the data in the diagram. In the figure, the dimensions of each part of the deformation area are clearly marked, and the shape comparison is further carried out. According to the comparison results, it can be shown that the finite element results have credibility. We fully agree with the reviewer's "convergence problem of the numerical solution of the adopted grid parameters". In the future research, we will further deepen the research in related fields. Thank you again for your valuable suggestion. (On the page 17-18, line 490-509)

Author Response File: Author Response.pdf