On the Use of Microstructure Characteristics to Predict Metal Matrix Composites’ Macroscopic Mechanical Behavior

Round 1

Reviewer 1 Report

Mechanical properties are an important evaluation index of engineering materials. In this work, the authors hope to predict the mechanical properties of materials (AA7075 alloy reinforced with carbon fibers) by analyzing the microstructure characteristics, such as the content of each phase. The idea is good and the work seems interesting and meaningful, however, there are some things that can be improved:

1.     The statistical surface fraction of each phase is greatly affected by the selection of observation surface. Because the actual processed materials often have uneven microstructure, the authors need to consider how much range of observation surface and what characteristics of observation surface can be selected to ensure the accuracy of prediction results.

2.     Line 120: The authors claim that the results obtained using surface fractions do not differ much from volume fraction described in the literature. In fact, the Mg2Si results obtained 59% differences compared to the literature volume fraction, which is a big difference.

3.     The open-source software 15 DREAM.3D was used to construct 3D ensembles and the Abaqus FEA software was employed for the mechanical testing simulations based on the microstructure characteristics. The question is how the simulation results can be fed back to the actual results of AA7075. What is the corresponding relationship? How is the match? It would be better to conduct some corresponding experimental tests to verify the simulation results.

Author Response

The authors thank the reviewer for his excellent and concise comments, on the basis of which an improved version of the manuscript has been prepared; the revised version addresses all the comments (please see below).

 

Mechanical properties are an important evaluation index of engineering materials. In this work, the authors hope to predict the mechanical properties of materials (AA7075 alloy reinforced with carbon fibers) by analyzing the microstructure characteristics, such as the content of each phase. The idea is good and the work seems interesting and meaningful, however, there are some things that can be improved.

 

The authors thank the reviewer for his positive comment.

 

1. The statistical surface fraction of each phase is greatly affected by the selection of observation surface. Because the actual processed materials often have uneven microstructure, the authors need to consider how much range of observation surface and what characteristics of observation surface can be selected to ensure the accuracy of prediction results.

 

For the purposes of this work, the parameters that needed to be evaluated were the volume fraction and the size distribution function of the two main AA7075 precipitate phases. The former was calculated by equating it with the surface coverage fraction of each phase and the latter by considering that the particles were spherical and by converting the measured area values for each particle (as given by ImageJ) into diameter values. To this end, we considered the SEM image of Figure 1a in our work as representative of the material’s microstructure and compared to literature properties.

 

Therefore, while the reviewer is right to mention that alloys may have uneven microstructure, heavily depending on the heat treatment process, our assumption is supported by the fact that the volume fractions of the precipitates closely match the ones expected from literature, as noted in Table 1. One exception to this is the rather big error regarding the volume fraction of the Mg₂Si phase. However, given that the actual fraction of this phase is very small (~0.3%), they are susceptible to a variability , since the particles of said phase are less in number, which however it is not expected to affect the results of this study.

 

As far as the size distribution is concerned, the extracted particle sizes are also within the expected from literature ranges. More specifically, in [2], the distribution of Al₇Cu₂Fe particles showed that about 82% of them had volume lower than 50 μm³. Almost the same trend was found for the Al₂₃Fe₄Cu phase, which, in our work was not considered as a separate phase. To this effect, we found that about 72% of Al₇Cu₂Fe particles had volume lower than 50 μm³, which is comparable with the literature findings.

 

As the reviewer suggests, it would be safer to use more microscopy images of the same material, in order to get more precise results for the material heterogeneity. However, our analysis showed that the proposed framework is actually able to yield results closely matching. This indirectly shows that the surface included in the SEM image of Figure 1a in our work included all needed characteristics of the microstructure in order to be considered representative. If this was not the case, then a series of such micrographs could be used in order for the observation surfaces to (statistically) include all needed microstructural characteristics.

 

2. Line 120: The authors claim that the results obtained using surface fractions do not differ much from volume fraction described in the literature. In fact, the Mg₂Si results obtained 59% differences compared to the literature volume fraction, which is a big difference.

 

As noted in the previous answer, this error occurs due to the sensitivity of the measurement of the Mg₂Si particles, as a result of the smaller number of available particles in the image, compared to the ones of Al₇Cu₂Fe. This error is non-negligible considering the phase fraction per se, however it is negligible considering the material in its entirety, as the volume fraction of this phase is about 0.3%. For the purposes of this work, this difference was not expected to seriously affect any results. Apart from that, the 59% error shows us that while the methodology followed is correct, in a future work, the measurement of small-scale phases should involve obtaining data from more images, as well as considering improvements in the measuring process. This is now noted in the manuscript, see lines 124-128 p. 3:

 

“A considerable error of 59% can be noticed for the volume fraction of Mg2Si phase, due to the very small number of available particles to be measured, compared to the Al₇Cu₂Fe phase. This error is non-negligible considering the phase fraction per se, however it is negligible considering the material in its entirety, as the volume fraction of this phase is about 0.3%. This difference is not expected to seriously affect the estimated mechanical properties of this study.”

 

3. The open-source software 15 DREAM.3D was used to construct 3D ensembles and the Abaqus FEA software was employed for the mechanical testing simulations based on the microstructure characteristics. The question is how the simulation results can be fed back to the actual results of AA7075. What is the corresponding relationship? How is the match? It would be better to conduct some corresponding experimental tests to verify the simulation results.

 

Verification of our simulation results with experimental data was also one concern of ours, and the reason why the slopes of our stress-strain curves were compared with longitudinal and transverse rules of mixtures predictions. We wanted to compare them with available experimental results from compression experiments. However, to the best of our knowledge, such data are not currently available in literature apart from micropillar compression tests performed separately on each of the AA7075 phases (matrix and precipitate phases) [1]. But although the alloy has an elastic modulus of 70-80 GPa, the results from [1] indicate an elastic modulus of the matrix phase ( which is >90 at.% Al and  itself has an elastic modulus of 60-70 GPa), of  about 45 GPa! It is noted that such a shortcoming of the micropillar compression tests was dealt in previous research of ours (see [4]) but this was outside of the scope of the present paper.

Thus, the results from micropillar testing of neither the AA7075 alloy nor the MMCs are comparable and only the general trend of the mechanical response can be verified with the literature which is highlighted in lines 245-250.

 

 

1. Singh, S.S.; Guo, E.; Xie, H.; Chawla, N. Mechanical Properties of Intermetallic Inclusions in Al 7075 Alloys by Micropillar Compression. Intermetallics 2015, 62, 69–75, doi:10.1016/j.intermet.2015.03.008.
2. Singh, S.S.; Schwartzstein, C.; Williams, J.J.; Xiao, X.; De Carlo, F.; Chawla, N. 3D Microstructural Characterization and Mechanical Properties of Constituent Particles in Al 7075 Alloys Using X-Ray Synchrotron Tomography and Nanoindentation. J. Alloys Compd. 2014, 602, 163–174, doi:10.1016/j.jallcom.2014.03.010.
3. Wu, J.; Zhang, C.; Meng, Q.; Liu, B.; Sun, Y.; Wen, M.; Ma, S.; He, L. Study on Tensile Properties of Carbon Fiber Reinforced AA7075 Composite at High Temperatures. Mater. Sci. Eng. A 2021, 825, 141931, doi:10.1016/j.msea.2021.141931.
4. Konstantinidis A.A., Michos K. and Aifantis E.C., On the correct interpretation of compression experiments of micropillars produced by a focused ion beam, J. Mechan. Behav. Mater.25, 83-87, 2016. [DOI: 10.1515/jmbm-2016-0009])

Author Response File: Author Response.docx

Reviewer 2 Report

his paper investigates 3D SSRVEs of metal matrix composites. Results indicate that the elastic modulus increases with volume fraction, obeying the rule of mixtures for discontinuous fibrous composites. This manuscript contains some interesting results. However, there are still some questions to be addressed before acceptance. Some comments are listed as follows:

 

1. As the author stated, the microstructure of materials can be obtained by SEM, TEM, EDS and other methods. However, in Figure 1, is it reasonable for the author to use ImageJ software to distinguish material types based on the grayscale of the SEM image? Is it more appropriate to use EDS?

2. In Figures 4 and 5, the materials represented by the different colours should be noted. Also, what does the ruler in the right corner mean? Moreover, it is blurry.

3. In Section 2.3, how do the contact properties between different materials in the finite element model of SSRVEs set?

4. Did the authors consider the comparison of the elastic modulus and yield stress calculated by simulation with the results obtained by experimental tests in the reference? This study would be more meaningful if it could be compared with experiments.

Author Response

The authors thank the reviewer for his excellent and concise comments, on the basis of which an improved version of the manuscript has been prepared; the revised version addresses all the comments (please see below).

Reviewer 2

This paper investigates 3D SSRVEs of metal matrix composites. Results indicate that the elastic modulus increases with volume fraction, obeying the rule of mixtures for discontinuous fibrous composites. This manuscript contains some interesting results. However, there are still some questions to be addressed before acceptance. Some comments are listed as follows:

 

We appreciate the positive comment of the reviewer.

 

1. As the author stated, the microstructure of materials can be obtained by SEM, TEM, EDS and other methods. However, in Figure 1, is it reasonable for the author to use ImageJ software to distinguish material types based on the grayscale of the SEM image? Is it more appropriate to use EDS?

 

Employing the grayscale of a SEM image aimed at extracting data regarding the microstructure of AA7075 alloy, that is, the volume fractions and the size distribution of the precipitate phases. Based on these data, the 3D ensembles mimicking the material’s microstructure were to be constructed. It was shown that starting with SEM imaging, these calculations regarding the precipitate particles are made possible, albeit processing of the images is necessary.

 

EDS elemental mapping is used to display the spatial distribution of elements within the various phases of the sample and, as a result, evaluate the atomic fraction of each element. For the AA7075 alloy, the material under study, EDS has been used to assess the atomic ratio of each element in every phase of the alloy [1], however using only EDS spectral data to draw results about the microstructure is not enough. Using SEM-EDS data however gives a better understanding of the material’s microstructure. Such data were extracted by [2]. The said figures are shown below:

 

Figure 1: A pristine surface of AA7075-T651 prior to exposure to the electrolyte, namely: (a) 5 kV InLens backscattered image of the microstructure, (b) 25 kV energy dispersive spectroscopy (SEM-EDS) compositional dot map for atomic compositions of the inclusions and the matrix and (c) IPF map of the examined area [2]

 

All in all, it can be seen that the contrast SEM image (Fig. 1a) shows better color contrast. At best, the data collected by SEM and EDS should be used complementarily. SEM imaging shows better the individual particles in terms of size, color and shape (thus the segmentation was operated on a SEM image) and EDS shows what the chemical composition of these particles is.

 

2. In Figures 4 and 5, the materials represented by the different colours should be noted. Also, what does the ruler in the right corner mean? Moreover, it is blurry.

 

We thank the Reviewer for highlighting this. The ruler in each right corner signified the different phases and was given by Paraview, however it did not really serve a use. The materials noted with different colors have been labelled, as asked, and the ruler has been removed.

 

3. In Section 2.3, how do the contact properties between different materials in the finite element model of SSRVEs set?

 

For the Abaqus FEA simulations, the default settings for the contact properties were chosen, which account for no friction and no thermal interactions between the phases. For the purposes of this work, which signifies the first step towards developing a computational framework for simulating the mechanical behavior of heterogeneous materials, the incorporation of data regarding the frictional interactions between the phases (that is the interactions between the precipitates with the matrix phase and between the carbon fibers and the matrix phase) was not taken into account as to the best of our knowledge there are sufficient data for a possible slip between different phases. This is now clarified in lines 202-204 p. 6 in the manuscript as follows:

 

“Regarding contact properties between the phases, the default contact property model was selected, which assumes zero friction and no thermal interactions.”

 

At this stage of the study, it is considered to be out of the scope to include friction interactions. However, in a future work, we plan to evaluate the incorporation of data regarding friction and thermal interactions, based on experimental data.

 

4. Did the authors consider the comparison of the elastic modulus and yield stress calculated by simulation with the results obtained by experimental tests in the reference? This study would be more meaningful if it could be compared with experiments.

 

Verification of our simulation results with experimental data was also one concern of ours, and the reason why the slopes of our stress-strain curves were compared with longitudinal and transverse rules of mixtures predictions. We wanted to compare them with available experimental results from compression experiments. However, to the best of our knowledge, such data are not currently available in literature apart from micropillar compression tests performed separately on each of the AA7075 phases (matrix and precipitate phases) [1]. But although the alloy has an elastic modulus of 70-80 GPa, the results from [1] indicate an elastic modulus of the matrix phase ( which is >90 at.% Al and  itself has an elastic modulus of 60-70 GPa), of  about 45 GPa! It is noted that such a shortcoming of the micropillar compression tests was dealt in previous research of ours (see [5]) but this was outside of the scope of the present paper.

Thus, the results from micropillar testing of neither the AA7075 alloy nor the MMCs are comparable and only the general trend of the mechanical response can be verified with the literature which is highlighted in lines 245-250.

 

 

1. Singh, S.S.; Schwartzstein, C.; Williams, J.J.; Xiao, X.; De Carlo, F.; Chawla, N. 3D Microstructural Characterization and Mechanical Properties of Constituent Particles in Al 7075 Alloys Using X-Ray Synchrotron Tomography and Nanoindentation. J. Alloys Compd. 2014, 602, 163–174, doi:10.1016/j.jallcom.2014.03.010.
2. Torbati-Sarraf, H.; Stannard, T.J.; La Plante, E.C.; Sant, G.N.; Chawla, N. Direct Observations of Microstructure-Resolved Corrosion Initiation in AA7075-T651 at the Nanoscale Using Vertical Scanning Interferometry (VSI). Mater. Charact. 2020, 161, 110166, doi:10.1016/j.matchar.2020.110166.
3. Singh, S.S.; Guo, E.; Xie, H.; Chawla, N. Mechanical Properties of Intermetallic Inclusions in Al 7075 Alloys by Micropillar Compression. Intermetallics 2015, 62, 69–75, doi:10.1016/j.intermet.2015.03.008.
4. Wu, J.; Zhang, C.; Meng, Q.; Liu, B.; Sun, Y.; Wen, M.; Ma, S.; He, L. Study on Tensile Properties of Carbon Fiber Reinforced AA7075 Composite at High Temperatures. Mater. Sci. Eng. A 2021, 825, 141931, doi:10.1016/j.msea.2021.141931.
5. Konstantinidis A.A., Michos K. and Aifantis E.C., On the correct interpretation of compression experiments of micropillars produced by a focused ion beam, J. Mechan. Behav. Mater.25, 83-87, 2016. [DOI: 10.1515/jmbm-2016-0009])

 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The draft can be accepted.

Author Response

A thorough English proofreading was performed and changes are highlighted in the attached text.

Author Response File: Author Response.pdf

Reviewer 2 Report

After the author's revision, the quality of the manuscript has been greatly improved. However, there are still some minor problems such as language.

Author Response

A thorough English proofreading was performed and changes are highlighted in the attached text.

Author Response File: Author Response.pdf