Study on Properties Prediction and Braiding Optimization of Axial Braided Carbon/Carbon Composite

Round 1

Reviewer 1 Report

Authors of the paper

Study on properties prediction and microstructure optimization of axial braided Carbon/Carbon composite

presented new finding in a well-researched area, by using the results of previous research and combining them into a complex prediction method. The literature review gave a good overview of the state of the art in the field. The modelling results show good agreement with the experimental data.

Some further points to check in main text:

L25

According to Zhang2019, the reinforcing phase is carbon fiber Toray T70 und the matrix material is TDE-85 epoxy. Turner2016 has also use Gurit Prime 20LV epoxy as matrix. These literatures are not relevant to carbon-carbon composite.

L44

The paper of Zhang Weihong is number 17 in the Reference list. Reference number 12 and 20 are the same one.

FIG 3 appeared also in the Paper of Gao2012 (https://doi.org/10.4028/www.scientific.net/AMM.161.30). Is this the own work of the authors or taken from others? Please clarify.

Reviewer encourage the authors to check the draft and improve for the final version.

Author Response

Dear Professor:

We feel great thanks for your professional review work on our article. We have studied the comments carefully and have made correction which we hope meet with reviewers’ approval. The detailed corrections are listed below.

1. According to Zhang2019, the reinforcing phase is carbon fiber Toray T70 und the matrix material is TDE-85 epoxy. Turner2016 has also use Gurit Prime 20LV epoxy as matrix. These literatures are not relevant to carbon-carbon composite.

Reply: Accept. At that time, we referred to the research ideas of Zhang2019 and Turner2016. The above two references have been updated as references on C/C.

2. The paper of Zhang Weihong is number 17 in the Reference list. Reference number 12 and 20 are the same one.

Reply: Accept. The number of the paper of Zhang Weihong has been updated in the Manuscript. Literature 20 was updated.

3. FIG 3 appeared also in the Paper of Gao2012 (https://doi.org/10.4028/www.scientific.net/AMM.161.30). Is this the own work of the authors or taken from others? Please clarify.

Reply: Accept. Gao Bo and I are members of the same research group. The mathematical model used for performance prediction is the same model. For this figure 3 is the same.

4. Reviewer encourage the authors to check the draft and improve for the final version.

Reply: Accept. We will carefully examine and improve the manuscript to avoid errors in writing and formatting.

I greatly appreciate both your help and that of the referees concerning improvement to this paper. I hope that the revised manuscript is now suitable for publication.

If you have any questions, please don't hesitate to contact me.

Best regards,

Chunguang WANG

Reviewer 2 Report

This paper utilizes homogenization and finite element methods to study the macroscopic properties of axial braided C/C composites. The manuscript is suggested for publication after addressing the following comments:

• please mention the name of FE software.

• why are the porosity percentage different on the x-axes of Fig. 5a and b?

• what do you mean by “preliminary test statistics” on page 5 line 143? have you performed an actual experiment? or these values are coming directly from fig. 5 a and b?

• a big missing item is a section on the experimental details. experimental data have been mentioned at various sections but no details are given! Please provide more details. For example how many tests were performed? what was the error on the data? what was the standard deviation? explain the test rig and testing method, ...
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• on page 6, line 167, several error values are reported that are all higher than 10%. Why do you suggest that these values show that the calculation method of the reinforcement phase is reliable?! what are the sources of these errors? how could those be reduced? what were the errors for matrix and interface, in section 3.2.1?

• why are there "early-stage" experimental results in table 2? does this mean that your work isn’t complete yet and these data might change?!

Author Response

Dear Professor:

We feel great thanks for your professional review work on our article. We have studied the comments carefully and have made correction which we hope meet with reviewers’ approval. The detailed corrections are listed below.

1. Please mention the name of FE software.

Reply: Accept. The finite element simulation calculation in this paper is based on ABAQUS software, which has been added in line 48.

2. why are the porosity percentage different on the x-axes of Fig. 5a and b?

Reply: FIG. 5a shows the porosity of the matrix and FIG. 5b shows the porosity of the interface. According to the test, their porosity range is very different, so they cannot use the same x-coordinate.

3. what do you mean by “preliminary test statistics” on page 5 line 143? have you performed an actual experiment? or these values are coming directly from fig. 5 a and b?

Reply: Accept. In this paper, the porosity of matrix and interface has been obtained by a large number of experiments. Some of the results can be referred to in reference 2.

4. a big missing item is a section on the experimental details. experimental data have been mentioned at various sections but no details are given! Please provide more details. For example how many tests were performed? what was the error on the data? what was the standard deviation? explain the test rig and testing method, ...

Reply: Accept. We have added a chapter to the manuscript to introduce the mesoscopic and macroscopic mechanical experiments that have been carried out. The experimental and statistical results of stiffness characteristics of fiber rod and axial braided C/C composites were presented, as shown in Line 99 to 120.

5. on page 6, line 167, several error values are reported that are all higher than 10%. Why do you suggest that these values show that the calculation method of the reinforcement phase is reliable?! what are the sources of these errors? how could those be reduced? what were the errors for matrix and interface, in section 3.2.1? why are there "early-stage" experimental results in table 2? does this mean that your work isn’t complete yet and these data might change?!

Reply:

Question 1: In general, the prediction accuracy of the enhanced phase is very low, and the error between the prediction result and the test result can be controlled at about 10%, indicating that the prediction accuracy has been very reliable. And we did a lot of testing and statistical analysis to get to this conclusion.

Question 2: The cause of the error has been analyzed in the manuscript, as shown in Line 193 to 195. The error itself is irreducible.

Question 3: Since the performance of the matrix and interface is difficult to be directly tested, this paper adopts the numerical prediction method to obtain the performance of the matrix and interface. Therefore, there is no error between the numerical calculation results and the test results.

Question 4: We have added a chapter to the manuscript to introduce the mesoscopic and macroscopic mechanical experiments that have been carried out, as shown in Line 99 to 120.

I greatly appreciate both your help and that of the referees concerning improvement to this paper. I hope that the revised manuscript is now suitable for publication.

If you have any questions, please don't hesitate to contact me.

Best regards,

Chunguang WANG

Reviewer 3 Report

This work reports a very classical homogenization procedure for the computation of Young's modulus and CTE of a C/C composite.

I don't think that in its current form, this paper meet the required standard to be published. It primarily lacks in clarity regarding the details of the methods used, and the way results are reported are also somewhat confusing, or at least not consistent between the different parts of the article, which makes it hard to appreciate the favorable comparison with the experimental results.

Major comments

It is not clear to what particular homogenization method the authors are referring. Indeed, they have listed references mainly dealing with analytical methods (using iso-strain or iso-stress conditions [17]), but they seem to employ FEM to compute the homogenized properties. They would need to make this point much clearer.

Also, why use a different method for the calculation of the CTE than the one used for the stiffness prediction? This is confusing if no other comments are given with respect to this particular choice.

Regarding the energy-based method, terms in Eq.2 needs to be defined, as well as the derivation of the expression of alpha's as they are not given in the corresponding references [16,17].

Sec. 2.3 : homogenization doesn't formally require periodic boundary conditions. Any BC that meet the Hill’s lemma could be used; periodic BC are just a particular case, as well as kinetic or static uniform, or mixed BC.

Sec. 4.2 : if the authors have indeed used FE calculations with periodic BC, why the RVE for matrix and interphase (Fig. 4) are not periodic? It would be more appropriate to refer to interphase rather than interface as the authors have considered a non-zero thickness. Also, the thickness of the interphase is not reported, neither its effect on the apparent properties.

Fig. 5, the term "porosity of voids" is improper: it is either "porosity" or "void volume fraction"...

Fig.5a show a very limited effect of the matrix porosity, at least in the reported porosity range. Is it really necessary to take into account the porosity in the matrix phase, as the "pure" matrix has a reported Young's modulus of 12 GPa vs. 11.5 GPa with porosity?

It is unclear if the reported value of the CTE of the matrix (-1.3e-6/K) is for "pure" matrix or matrix with porosity. It is a bit disappointing to sell the effort to incorporate porosity in the prediction of the matrix stiffness, but not for the CTE.

Sec 5.3: I am confused by the inconsistency between the values of E and alpha reported in Fig. 7 and the ones in Tab. 5 and 6... According to Fig. 7, the reported values of alpha_x=-0.5e-6/K, alpha_z=0.145e-6/K seem to correspond to an inter-rod distance of 3.2 mm. The corresponding predicted values of E and alpha for this distance do not match with the ones reported in Tab. 5 and 6. The distances that match the values of alpha_z=0.15e-6/K and alpha_x=0.145e-6/K are closer to resp. 3.15mm and 3.05mm, for which 45 < Ez < 46 GPa and 38 < Ex < 39 GPa, which are not consistent with the values reported in Tab. 5. This is at least confusing, if not dubious.

Minor remarks

English could be improved. There are misspellings and hard to understand sentences.

The Greek letter mu (µ) is generally used for the shear modulus, not for the Poisson's ratio, for which the Greek letter nu is preferred. Tension would be more appropriate than stretch when referring to mechanical tests.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The authors did respond to the questions/remarks I've raised in my first review.

The most problematic point concerning the inconstitency between the values reported in Tab.5/6 and in Fig.7 have been addressed. It is still regrettable that the authors didn't check their data more carefully before submitiing their paper.

Concerning remark #1, the response is not completely what I anticipated. I was simply expecting that they clearly indicate how they have used FEM to solve the asymptotic homogenization problem, rather than giving full details on the derivation the equation, or that they add some more relevant references to the literature on FE-based homogenization that is numerous.

Concerning remark #2, my point was to understand why they didn't use energy-based method for stiffness prediction, if it's more convenient why not using it in all cases, or why they didn't use FEM to evaluate the homogenized CTE? This requires only on extra simulation when the stiffness has already been evaluated this way, see e.g. "J. Wippler, S. Fünfschilling, F. Fritzen, T. Böhlke, and M. J. Hoffmann. Homogenization of the thermoelastic properties of silicon nitride. Acta Materialia, 59(15):6029–6038, 2011"

There are still some misspellings (e.g. l.382 microcosmic vs microscopic?)

Despite the modifications, I still find the paper a bit confusing and below the standard required for a publication. My initial recommendation was to not accept the paper, my overall feeling remains unfavourable. Yet, I'll let the editor do what he thinks to be the best for the journal based on the other peer-reviews.

Author Response

The attachment are my rebuttal to reviewer 3. I hope it can meet the editor's request. Many thanks.

Author Response File: Author Response.pdf