Analysis of Nonuniform Deformation in Aluminum Wires Under Varying Torsional Loads Using EBSD Measurement and Multiscale Crystal Plasticity

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Comments on the manuscript ‘Sensitivity Investigation of Aluminium Wire under Different Torsional Loading Using EBSD and Multi-Scale Crystal Plasticity’ (Ref: metals-3403704)

In this work, the authors use crystal plasticity simulation to study the evolution of plastic strain and texture in a pure aluminium sample which has been subjected to shear stress loading through torsion test. The tests have been conducted at different loading rates; the change in texture has been evaluated through EBSD measurements and these data have been correlated to factors such as Schmid factor and Taylor factor respectively. The same exercise has been carried out for different loading rates and different extents of total shear strain in the outer fibre of the sample. Though the results, especially the data on EBSD measurements, are interesting, the methods and results are not presented clearly in the manuscript. Moreover, the details of method of calibration of parameters of crystal plasticity model, the validation of the results of CPFE simulation with experimental data etc. are not presented. There are lot of ambiguity regarding effect of loading rate on mechanical property. At some places, it is written that by increasing strain rate, the strength decreases, whereas exactly opposite has been stated at other places. Hence, the manuscript needs thorough and careful revision in order to present and interpret the results consistently without any ambiguity. The reviewer has the following detailed comments.

1. Instead of using strain and strain rates, the authors have used rotation and rpm respectively, which is not the correct way to relate the measure of prior material deformation (i.e., work hardening) at a point to the change in the corresponding mechanical properties. The manuscript needs substantial revision and clear presentation of the results. In addition, all the properties should be related to strain and strain rates respectively, which is the standard way to present microstructure-property correlations.

2. The mundane details of CPFE as presented in Section 2.2 and other well-known concepts should be avoided. This shall make the manuscript more readable.

3. The abstract needs to be modified to bring clarity to the objective and conclusions from this work. The novelty of the work is not imminent from the abstract and the content of the paper. The abstract needs to be shortened and only few important conclusions need to be included along with the aim and objective of the work. Detailed description or mentioning of the name of software are not required.

4. The first sentence (in the abstract) is very general and it is not needed here. Moreover, you are not developing a new crystal plasticity model in this work, rather the standard hardening type model has been used in the simulation, which is very standard in literature.

5. Don’t use acronyms like ‘DAMASK’, ‘CPFE’, ‘CPFEM’ in the abstract without defining them first. Moreover, these are not necessary and may be avoided.

6. Line-7 of abstract: The word ‘microstructure evolution’ should be replaced with more specific details such as change in texture or hardness etc. Use ‘EBSD measurement’ in place of ‘EBSD test’. What are A, B, C, A1*, A2* components? These nomenclature for crystal orientations should not be used in the abstract.

7. Keywords: The keyword ‘microstructure and texture evolution’ is very general and it is not very specific to this paper. Use some more appropriate keywords. Moreover, this paper doesn’t involve multiscale modelling as you can apply simple torsion loading in the CPFE model. Use of von Mises theory and crystal plasticity models can’t be used simultaneously as the former uses stress-strain data as input whereas stress-strain curve is an output for CPFE simulation. I will provide more details to this comment later. However, I want to mention here that use of keyword ‘multi-scale modelling’ is not relevant for this work and should be avoided.

8. You have shown contour band of Taylor’s factor in Fig. 12. However, you mentioned that ‘it changed between 2.65 and 3.04 when the strain reached from 0.5 to 2.5 revolutions’. The Taylor factor has a distribution for each location. Hence, are these values ‘2.65’ and ‘3.05’ average of the distribution? Please clarify and rectify the sentence.

9. You have mentioned that grain size is 55 micron. However, there is a distribution for grain size. Mention the statistical parameter here. Please clarify and rectify the sentence accordingly.

10. Last line of abstract: Please check the sentence “yield stress increase s as the strain rate decreases”. Is it correct? Does the material show negative strain rate sensitivity? This is usually not the case for Aluminium and its alloys as reported in literature. Moreover, the opposite is written in the conclusions for grain size of 150 microns. Please elaborate and clarify.

11. Fig. 1: This (i.e., linear variation of shear stress with distance from centre) is very standard and can be found in standard textbooks. Please remove this figure.

12. The method referencing literature is not correct. For example, ‘Wang and et al.” (page-2, line-60) should be replaced with ‘Wang et al.’. Similar mistakes (Mao and et al., line-77, page-2), Lu and et al. etc. are repeated at many places. Please correct.

13. Second paragraph, Page-3: This presents the details of previous work (Ref. 24) of the authors’. As it is another literature, so much details are not required. Hence, 2nd and 3rd paragraphs of page-3 should be shortened.

14. Line 115, Page-3: Please refer to the sentence “An analysis of the high and low-grain boundaries was conducted using a Python algorithm designed for this purpose”. What the importance of ‘Python algorithm’ here? Python scripting is just another way to program and hence, these mundane details are not required here. On the other hand, the novelty of the literature [24] vis-à-vis this work should only be mentioned.

15. Line 135, Page-3: Please refer to the sentence “To investigate the mechanical properties of samples, hardness and shear yield stress were evaluated”. Mechanical properties refer to Yield strength, UTS, ductility, strain rate sensitivity etc. If you are evaluating only shear yield stress and hardness, these do not refer to the complete list of mechanical properties. Please revise the sentence accordingly.

16. Table-1: This Table is not necessary as it mentions holding time, heating rate and annealing temperature for annealed sample. What is its relevance for as-received sample here? Please remove and mention the annealing parameters in the text.

17. Mention 55 and 150 microns as average grain size of the relevant distribution for the samples as grain size has always a distribution. Please show a histogram for the same (i.e., before and after annealing heat treatment).

18. Table-2: Don’t use twist speed and revolution. Refer to torsional loading with ‘radians’ and ‘radians per second’. Similarly refer to ‘mean grain size’ instead of ‘grain size’. It may be noted that ‘strain’ is not same as revolution and ‘rpm’ is not same as strain rate though these are related through specimen dimension and polar moment of inertia. Instead, use terms like rotation (in radians) and rate of rotation respectively to describe the loading.

19. Shear strain and shear stress are not uniform in the specimen. They vary linearly with distance from centre. Hence, mentioning a constant strain or strain rate for the torsion test is not proper and it should be avoided. It is suggested extent of rotation and rate of rotation may be used to describe the test, however, for discussion of results, the localized shear stress and strain values should be mentioned as you know the location of measurement of hardness and orientation distribution after the tests.

20. There is no need to mention ‘SANTAM’ machine. It may be noted that commercial information should not be used in a scientific paper.

21. Fig. 2: This figure is not clear. Why tow orientations are shown. Just the right figure is sufficient. Moreover, spacing of hardness measurement locations are missing. Please provide relevant details.

22. Section 2.1.3. Shear strain is evaluated at 400 micron from border. However, hardness measurements are carried out at 300 microns from the outer surface. Are these consistent. Moreover, one can calculate the shear strain very easily at any distance from centre using standard expressions. Hence, use actual data instead of approximating the same.

23. Page 5: “TESCAN Mira3 was used with an EBSD Hikari camera (EDAX-Ametek) and the software APEX V2.5.1. OIM Analysis software v.8.6” Are these commercial details required here? These may be removed.

24. Fig. 3 is not necessary. These can be found in elementary textbooks. In fact, whole section 2.2 should be shortened. Only mention the flow and hardening rules of CPFE models very briefly and refer the reader to the relevant literature for the details.

25. Last paragraph of Page-6 and page-7 in whole: It may be noted that you want to use crystal plasticity model for some portion of the specimen as it is not possible to model the whole specimen with CPFEM. However, you have mentioned that you are using multi-scale model. This is not appropriate as J2 or von Mises plasticity used stress-strain data as input, whereas CPFE doesn’t need such data and stress-strain curve is an output.

26. Moreover, local and global equilibrium procedure requires stress update in a linear problem which is carried out differently using classical plasticity and CPFE models. If you want to use nodal deformation as input to the CPFE calculation, this is very simple in this problem as you have to provide a rotation to the CPFEM model. Hence, multi-scaling is not required here. Moreover, it is erroneous as both the schemes are inconsistent. Please check this aspect and revise Section 2, Fig. 5 and Fig. 6 accordingly. This is a major drawback of the description, which needs to be revised. You can still relate all your CPFE results with EBSD measurements without invoking this complexity.

27. Fig. 6 is not clear and it is also not relevant here. Please refer to my previous comment.

28. Section 3.1: Please include grain size distribution information for both samples before presenting the grain size.

29. Fig. 7: Please show scale in Fig. 7(a) and (b). The EBSD data is for a small portion of sample. The scale in EBSD data is also not legible. Please improve this figure.

30. Please include a discussion regarding the difference in pole figures of as-received and annealed samples.

31. Fig. 8: Is it experimental data? If yes, please show the strain rate used in the test. Are these shear stress and shear strain? Please mention the same here? What about tensile stress-strain data? Is this data similar to those available in literature? There are lot of data for pure aluminium in literature. Please refer and compare.

32. Page-10, line-1: What is meaning of ‘ultimate strength’ in torsion test? Ultimate tensile strength is evaluated from tensile tests and this word is not relevant here.

33. Fig. 9: This result is very ambiguous and it is not correctly presented. S0.5 and R0.5 represent extent of loading and loading rates respectively. For a given rate, all tests represents same data except the statistical scatter. However, it has been presented as effect of strain and loading rates respectively, which is not correct. Moreover, what is the meaning of ‘as-received data’ here? It must have been tested at a given rate. Please clarify and mention the loading rate. Similar is the case of Fig. 9(b). What you are presenting here is the statistical scatter for a given rate only. Different extents of rotation is not a loading effect.

34. Fig. 10: Hardness tests have been conducted at different locations. Hence, there is a scatter in data. Please show the same instead of using just one data for each sample in Fig. 10.

35. Please change the notation of ‘revolution’ and ‘rpm’ throughout the discussion in Section 3 and other sections as mentioned earlier. Map the strain and strain rate of the location and correlate with change in measured data.

36. Section 3.3.1: The results of pole figures from CPFE simulations are presented directly here. However, I don’t find any discussion regarding parameters of CPFE model for the material as used in the simulation. How are they calibrated? How do they compare with experimental data? These are crucial details and these must be included in the revised paper.

37. One of the major drawbacks of the paper is the lack of drawing of the specimen and loading conditions. Fig. 4 is a simplified model. The actual specimen should have a gauge and shoulder region (for holding during the test). What is the gauge length to diameter ratio of the specimen here? If the wire is too thin, there may be localized buckling of the wire, which shall affect the results significantly. These details should be included in the discussion.

38. How do you model the boundary conditions in the FE simulation? Are you applying shear strain or stress? Are you using fixed boundary conditions at one end? If so, what about the stress concentration region near the fixity boundary condition? Please show distribution of shear stress and strain in the specimen as obtained from simulation.

39. Have you carried out mesh convergence analysis? What kind of elements and sizes are used here? Do they provide converged results?

40. Fig. 11: There are many sub-figures. Please use nomenclature (a), (b) etc. to denote the sub-figures.

41. Second and 4th row of Fig. 11: The experimental and CPFE pole figures so not match at all. What is the reason for the same? Does it mean the CPFE parameters are not correct to describe the material deformation as observed experimentally? Please elaborate and include some discussions for the same.

42. What is relevance of Table -3? You are just mentioning the orientations for which you compare with experiment. It doesn’t convey much meaning here and may be removed.
Line-398, Page-13: Please check the sentence “It is observed that A, B, C, A1*, A2* components have the highest frequency among the mentioned tests. I don’t find any results regarding frequency of these parameters here. Please clarify and elaborate.

43. Fig. 12: Once you present pole figures in Fig, 11, what is the relevance of inverse pole figures, except just another form of presentation?

44. Please show distribution of Taylor and Schmid factors in addition to the contour maps. Contour maps don’t provide information regarding statistical distribution across the grains in the microstructure.

45. Fig. 14: Taylor factor has been plotted as function of different parameters. Is it the mean value or the maximum value of Taylor factor, especially as it has a distribution? Please clarify.

46. Line 470, Page-16: Please check the sentence “it is observed that with an increase in revolution and grain size, the TF also rises, leading to greater complexity in deformation mechanisms, including the activation of slip systems”. This is very ambiguous. What is meant by “complexity in deformation mechanisms”. Please elaborate.

47. Higher Taylor factor rises with rotation. This means more hardening. But, hardening usually decreases with increase in grain size. However, your observation is exactly reverse here. Please clarify. You may plot experimental data for the two grain sizes for the same rate of loading and discuss of hardening increases or decreases with grain size.

48. Table 4: Why are Schmid factors zero for certain orientations? If it is zero, plastic deformation cannot occur. Please check.

49. Page-17: Instead of referring T2, T4 etc. in the text, please refer strain and strain rate at the material point. This shall make the discussion more relevant and meaningful.

50. Fig. 15: Mention strain and stain rate instead of revolution and rpm. Why is the distribution of Schmid factor exponentially decaying type? Usually, it follows Gaussian. Please check literature and consistency of your data.

51. Fig. 16: Schmid factor has been plotted as function of different parameters. Is it the mean value or the maximum value of Schmid factor, especially as it has a distribution? Please clarify.

52. Conclusions: The first paragraph of a repetitions of earlier texts and it should be avoidd. Please shorten the conclusion section. Please provide only relevant conclusions in brief and in a bulleted manner. Instead of using ’revolution’ and ‘rpm’, please use material point strain and strain rate as mentioned earlier.

53. There are many research literature regarding experimental and CPFE simulation of pure aluminium and aluminium alloys. These have not been included in the literature review section and the references section. The references section should be modified accordingly. Literature regarding other materials such as magnesium alloy and copper (Example, Ref. 10, 11, 12, 14 etc.) are not required and these must be removed. Please modify this section accordingly in order to make it more relevant.

54. Title: The title is not appropriate as it doesn’t reflect the content of the work. This should be modified. The suggested title is ‘Correlation of microstructure of aluminium with cumulative strain and strain rate at a material point as obtained from FE analysis’.

55. There are many grammatical and spelling mistakes in the manuscript and these must be corrected. For example: “Inverse” is written as ‘invers”. Check the correctness of the sentence “This occurs due to the increased significantly in dislocation density”.

56. The novelty aspect of the work should be mentioned in the abstract and the introduction section.

Comments on the Quality of English Language

There are many grammatical and spelling mistakes in the manuscript and these must be corrected. For example: “Inverse” is written as ‘invers”. Check the correctness of the sentence “This occurs due to the increased significantly in dislocation density”.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript introduces the author's research on the microstructural evolution of pure aluminum wires under torsional loading using electron backscatter diffraction testing and multi-scale crystal plastic finite element simulation. The study also analyzes the effects of initial grain size, loading strain rate, and loading strain on the microstructural evolution of the aluminum wire material. The results and conclusions obtained by the author are of reference value.

However, the manuscript also has some shortcomings that need further improvement by the author:

1.        Figure 1, which illustrates the stress distribution, appears to be incorrect. The stress distribution depicted in Figure 1 is only characteristic of materials in a linear elastic state, whereas the text emphasizes the plastic deformation process.

2.        The measurement of the Taylor factor is related to the stress state set up, and different stress states will yield different results. The authors need to introduce or explain the stress state selected during the EBSD testing process.

3.        It is necessary to clarify how the strain on the horizontal axis and the stress on the vertical axis of Figure 8 are defined—whether they are defined based on shear components or equivalent definitions? Without explanation, readers may misinterpret the data.

4.        There seems to be an error in Figure 9a regarding T3-G55-S5-R2.5; R2.5 should be R0.5.

5.        The relevant parameters in the material model, including elastic constants and crystal plasticity model parameters, are not introduced or explained in the text and should be supplemented.

6.        In the calculations, Abaqus/Explicit and Abaqus/Standard modules were used successively. The author should explain the differences between these two algorithms and how they are connected to ensure the rationality of the results.

7.        The text does not provide a detailed introduction to the finite element polycrystal model (RVE), including the selection of elements, the number of grains, and the size of the RVE, all of which need to be supplemented.

8.        The introduction of the results in Figure 11 seems to require an explanation of the initial state of the actual measurement and simulation, the experimental process, and the settings of the simulation conditions. Otherwise, it will be difficult for readers to understand why such results were obtained.

9.        The definition of the material's yield strength mentioned in the text also needs to be clarified.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

The authors investigated the microstructural evolution in pure aluminium wire under torsional loading using EBSD test and multi-scale CP Finite Element simulation.

Unfortunately, there are so many unclear points, especially, on modelling. Additionally, I could say the manuscript is not reader-friendly. Therefore, I do not recommend this version for the publication to Metals.

The following comments are useful.

1. The descriptions from line #226 to #243 and from #267 to #281 are quite unclear. For instance, J2 plasticity model is basically not CP-based. I do not understand what kind of yield function the authors chose? The yield function can be obtained after the formulation by FE-square? What kind of yield function is assumed here. What is the hardening model for the macromodel. Huge volume on this part should be modified and restructured.

2. DAMASK is based on the spectral method and it has an interface to ABAQUS used in the paper. This means the simulation can be performed without FE-square process and there is nothing new on the modelling.

3. I do not find why two sub-models with different length scale are necessary for this kind of modelling. Which model, sub-model1 or 2 should be RVE? Probably, the sub-model2 to global can be achieved by a use of ABAQUS and DAMASK through the interface. In this case, there is nothing new.

4. How to realize to connect the global and sub-model1. In this case periodic boundary condition should not be imposed.

5. The authors referred Ref. 62 for FE-square formulation. However, the reference is targeting the machine learning(ML). ML is currently including to the work?

6. The authors referred Refs. 34 to 37 as references for the multi-scale modeling. The most of them dealt with D-FE-square. However, there is no D-FE-square formulation in this manuscript.

7. Related to the above, Ref. 35 is related to a multi-scale model but not FE-square.

8. Refs. 55 and 56 are the same.

9. I think there are so many points to be clarified. I strongly recommend the careful revisions to the authors. If the understandings are different from mine, it is possible to reject the next version.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

In the reviewed manuscript, computational crystal plasticity (CP) models have been developed to analyze the deformation responses of materials at the microstructural level under macroscopic loading conditions. As stated in the paper, the challenge of linking microstructural evolution with macroscopic loading can be effectively addressed using the multiscale (FE2) CPFE approach. The study presented in the manuscript analyzed the microstructural evolution in pure aluminum wire subjected to torsional loading, employing electron backscatter diffraction (EBSD) studies and multiscale crystal plasticity finite element method (CPFEM) simulations.

The scientific article focuses on the influence of initial grain size, strain rate, and strain values on microstructural evolution and mechanical properties at room temperature. As shown in the study, the heterogeneous initial texture of the sample in its original state was determined using EBSD analysis and incorporated into the CP code, DAMASK, for conducting multiscale CPFEM simulations. The microstructural evolution derived from pole figures indicated that components A, B, B, C, A1*, and A2* were the most frequently observed during the torsion tests.

Furthermore, the authors also noted that quantitative analysis of the obtained texture using the Taylor factor (TF) revealed that the TF value varied from 2.65 to 3.04 as the strain increased from 0.5 to 2.5 revolutions. As demonstrated in the reviewed scientific article, increasing the number of revolutions from 0.5 to 2.5 caused an 11% increase in hardness near the outer surface of specimens with a grain size of 55 µm. The results obtained by the authors showed that the change in strain rate affects the yield strength of the specimens—yield strength increases as strain rate decreases.

The reviewed article is well-written and deserves to be shared with the public; however, certain revisions and improvements are needed before final publication:

1. Abstract: It is too long—please shorten it and avoid presenting results or descriptions of research methods. The abstract should entice readers to explore the article and indicate its scope in a maximum of 5–6 sentences. 

2. Introduction: The introduction is adequate; the authors conducted a thorough literature review and included an illustration. However, it is recommended to improve the quality of the graphic by converting it to a vector format. 

3. Terminology: In scientific writing, the term "work" should not be used. Preferred alternatives include "manuscript," "article," "paper," "study," or "scientific article." Please revise accordingly. Similarly, the term "sample" should not be used when referring to laboratory test materials. Instead, follow ISO, BS, and ASTM standards and use "specimen." Update the manuscript accordingly. 

4. Units: Physical units in figures and tables should be enclosed in square brackets, with a space after the symbol to which the unit refers. Avoid parentheses for units. Some graphs and illustrations lack physical units; please address this. 

5. Figure 5: The block diagram in Figure 5 should be larger and clearer. Consider preparing it in vector format to improve its legibility. 

6. Finite Element Model Description: Enhance the description of the finite element method (FEM) model by including the final number of finite elements used in the modeling, the number of nodes, the type of finite elements applied, the number of nodes per finite element, and information on the numerical integration points within the finite element. Provide details about the Jacobian points, the locations where quantities were estimated (nodes or integration points), and the type of finite element formulation utilized. The manuscript currently lacks this information. 

7. Mesh Convergence: Address the convergence of the FEM model. Explain how convergence was evaluated and justify the chosen meshing approach. Include information on the actual structure's division into finite elements and mesh refinement. 

8. Figures and Graphs: All figures should be prepared in vector format to improve quality. Graphs should ideally be created in professional mathematical software, such as GRAPHER, rather than MS Excel, to enhance their aesthetic and "engineering" appeal. 

9. Nomenclature: Include a full list of abbreviations, symbols, and notations used in the manuscript, preferably at the end. 

10. Conclusions: The conclusions should be more developed, indicating potential future research directions and discussing how the obtained results can be applied to solve real-world engineering problems. 

Overall Assessment: The manuscript is promising but requires careful revisions. I suggest a major revision. Please incorporate the recommended changes and resubmit the manuscript for review.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed all the comments of the reviewer and have revised the manuscript accordingly. The revised version of the manuscript may be accepted for publication.

Author Response

Dear reviewer. Thanks for accepting our version of the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

The author has responded to the reviewer's questions and made corresponding modifications. The reviewer believes that the manuscript may have been published.

Author Response

Dear Reviewer, thanks for your recommendation.

Reviewer 3 Report

Comments and Suggestions for Authors

In total, I do not find where the authors modified the manuscript based on my comments. As a reader, this paper is not so kind.

In addition, according to the answers from the authors, the FE-square is not used but the authors has paragraphs on it with the related equation. On the modelling, there is nothing new. 

Thus, I could achieve my conclusion the paper should be rejected.

 

Author Response

Dear Reviewer. Thank you very much for your comments. Please send our answer in the attachment and the revised manuscript

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The author has addressed almost all of my previous comments in the resubmitted version of the paper.

As a result, the paper has become more valuable and readable, likely to capture the interest of readers.

Additionally, they supplemented the paper with some information.

Overall, the paper is engaging, and I have no further substantive comments to make.

I recommend the paper for publication.

Author Response

Dear Reviewer, thank you very much for your recommendation.

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you very much for the authors' polite responses.

However, I do not totally understand why the submodel1 can be a unit cell for FE-square. There is no periodicity of the model. Once again, I would like to require to the authors to explain them well on the text. Is it common periodicity is not guaranteed? 

Additionally, my understanding is still insufficient as well why the authors should perform the simulation at the three levels, explicit, FE-square with the J2 plasticity and FE-square aided by DAMASK. The results at just only one level was shown. 

 

Author Response

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