Determining the Elastic Constants and Thickness of the Interphase in Fiberglass Plastic Composites from Micromechanical and Macromechanical Tests

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, the elastic constant and thickness of the interphase in fiberglass plastic composites are determined through micromechanical and macromechanical tests. Following problems need to be solved:

1.     In this paper, the experiments and  simulations are conducted on the fiberglass plastic composites. But what are the differences from existing researches?

2.     There are too many keywords, it is recommended to delete those unrelated to the main work of this paper.

3.     Except for the device for micromechanical testing, the macromechanical testing devices should be  supplemented.

4.     In the tension test of a single fiber, there is a lack of comparison of multiple sets of data, and the experimental results are not convincing. Moreover, the fiber diameters are varying in Figure 1, so how did the authors consider the influence of fiber diameter on the tension?

5.     The computational model was used to compute the interphase parameters in Table 2, but how to ensure the accuracy of the results? Did the authors validate it through experiments?

6.     Some references are not closely related to the main work of this paper, and it is recommended to delete them.

7.     There are some grammatical errors in this paper, such as “single glass fibers” in Line 12.

Author Response

We would like to sincerely thank you for accepting the revisions made to our manuscript. Your constructive feedback was invaluable in improving the clarity and quality of our work, and we deeply appreciate the time and effort you dedicated to this process.

Comment 1.     In this paper, the experiments and  simulations are conducted on the fiberglass plastic composites. But what are the differences from existing researches?

Response.

As noted in the review of the article, the mechanical properties of the interphase are calculated. The accuracy of the calculations depends on which experimental data will be incorporated into the model. The article describes the experimental and computational method proposed by us for determining the parameters of the interphase. The main difference between our research and other studies is the complexity of our approach. This paper not only demonstrates how to calculate the mechanical characteristics of interphase, but also provides methods for experimentally determining the mechanical properties of both the fiber and the matrix at the microscopic level, as well as measuring the thickness of the interphase. Specifically, it addresses the challenge of experimentally determining the Poisson's ratio of glass fibers through micromechanical testing. The issue of accurately determining the thickness of the interphase using atomic force microscopy has been successfully addressed. Unlike other investigations, we have managed to overcome the adverse impact of the disparity in height between the fiber and the matrix on the measured parameters of the interphase thickness. To accomplish this, we proposed creating a thin section at a 30-degree angle using an ion beam technique. The use of an integrated approach allowed us to draw a rather important conclusion that the thickness of the interphase can be calculated with acceptable accuracy, but this is a rather laborious and lengthy process.

Using the method described in this paper for determining the thickness and mechanical properties of the interphase, we are completing work aimed at studying the influence of polymerization conditions (pressure and temperature) on the parameters of the interphase and its effect on the mechanical properties of the composite at the macro level. In our opinion, the experimental and computational method described in this work for determining the parameters of the interphase is quite easy to use, which allows conducting relevant studies fairly quickly.

Comment 2.     There are too many keywords, it is recommended to delete those unrelated to the main work of this paper.

Response.

We have reduced the number of keywords.

Comment 3.     Except for the device for micromechanical testing, the macromechanical testing devices should be  supplemented.

Response.

In the process of conducting micromechanical tests, only one standard installation is used. Below is a description of its application, and the text dedicated to its use has been highlighted in the article using a special marker.

«The tensile tests on a macrolevel were performed in an Instron 8801 servo-hydraulic experimental testing machine. Deformations were measured directly on the specimen in two directions by means of an Instron AVE noncontact video extensometer, which ensured the absence of additional external influences on the specimen surface».

Comment 4.     In the tension test of a single fiber, there is a lack of comparison of multiple sets of data, and the experimental results are not convincing. Moreover, the fiber diameters are varying in Figure 1, so how did the authors consider the influence of fiber diameter on the tension?

Response.

As part of this research, we conducted a series of ten fiber stretching tests in order to determine their average modulus of elasticity. This was done because the averaged mechanical properties of the fibers were used as input parameters for a mesomechanical model. The purpose of this study was to determine the average thickness of the interphase and the average modulus of elasticity and Poisson's ratio of this zone. Within the scope of this research, we limited our analysis to applying a distribution law to determine the fiber diameter and orientation. Our goal was not to develop a distribution law for mechanical properties of the fibers. To address this issue, a larger number of experiments would be needed, and we plan to conduct further research on both the elastic modulus of the fiber and Poisson's ratio in the future. To calculate the elastic modulus and ultimate strength of the fiber, we utilized the measured diameter of each individual fiber. In this article, we presented the technique for measuring fiber diameter -  “In order to determine the diameter of each fiber under test, the free end of the fiber was cut off, which was not in the grips of the tensile device. Then each fiber was filled with epoxy resin separately from the others. Prior to this process, the fiber was arranged such that it passed through the resin in a direction perpendicular to the future cross-sectional plane. Subsequently, the thin section was made in the transverse direction of the fiber. The diameter of the fiber was then measured using an optical microscope.”

Initially, we intended to measure the fiber diameter directly on our stretching device using the Veeco WYKO NT1100 optical profilometer. However, since the fiber is optically transparent, the profilometer data turned out to be underestimated in terms of fiber diameter. As a result, we had to resort to the technique of determining the diameter of the fiber under test, which was described in our article.

Comment 5.     The computational model was used to compute the interphase parameters in Table 2, but how to ensure the accuracy of the results? Did the authors validate it through experiments?

Response.

We determined the average thickness of the interphase experimentally using dynamic force microscopy. We verified the calculated mechanical properties of the interphase based on a comparison of the elastic coefficients of the simulated (problem statement in 3.4) and experimentally performed tensing of cross-reinforced fiberglass (Section 4.3). Since the mechanical properties of the structural elements of the monolayer (exception of the interphase) were determined experimentally, the results of comparing the simulated and experimentally measured elastic coefficients indicate that the calculation of the elastic properties of the interphase was performed with sufficient accuracy. To date, we do not know a more reliable method for verifying the mechanical properties of the interphase, since its size is extremely small. This is confirmed by the data presented in Figure 12, which shows an attempt to determine the mechanical properties of the interphase using indentation. The results were influenced by the neighboring environment of the interphase (fiber and matrix).

Comment 6.     Some references are not closely related to the main work of this paper, and it is recommended to delete them.

Response.

We reviewed the list of references again and removed some of the papers.

Comment 7.     There are some grammatical errors in this paper, such as “single glass fibers” in Line 12.

Response.

We have removed the grammatical errors that you pointed out.

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper the elastic properties of the interphase in fiberglass plastic composites are calculated form the results of micromechanical tests (elastic modulus in x and y directions and Poisson´s ratio xy) and micromechanical tests (elastic modulus and Poisson´s ratio of the fiberglass and the matrix).

The paper is reasonably well written and organized although point 4 Results and Discussion is difficult to follow. My suggestion is to include intermediate points 4.1, 4.2 and so on.

I would like to know if the idea of using the mixtures rule to the three phases (fiber, matrix and interphases) to derive the elastic properties of the interphase is new or it has been previously used. In the latter case, which are the original contributions of the authors to this approach.

I think that some intermediate steps to derive equations (6) and (7) can be useful to the reader.

The mixtures rule for determining elastic properties in composites are based in some hypothesis on stress and strains, that is, assuming constant strain along the longitudinal direction of the fiber or constant stress along the transverse direction, the authors can derive equations (6) and (7). But I cannot see how equation (8) is obtained. Please, provide some explanation.

Is not there a contradiction between the hypothesis of constant stress in the transverse direction and the stress distribution of figure 14?

The calculations of the elastic constants of Table 1 are explained for the fiber, but not for tha matrix. I imagine that the Poisson`s ratio is obtained from reference 54. Is this correct?

When the initial set of values are determined, how the thickness is computed from the volume fraction in problem 2? Can be the volume fraction derived from the known thickness of the interphase in problem 1?

Lines 373-376 are confusing

I suggest indicating the thickness of the interphase for problem 1 in Table 2.

The scope of figure 11 is to show the difficulties of obtaining the properties of the interphase by micro indentation. Is this correct?

As indicated above, I think that point 4 should include subpoints, to make easy the reading.

 

Author Response

We would like to sincerely thank you for accepting the revisions made to our manuscript. Your constructive feedback was invaluable in improving the clarity and quality of our work, and we deeply appreciate the time and effort you dedicated to this process.

 

Comment 1. The paper is reasonably well written and organized although point 4 Results and Discussion is difficult to follow. My suggestion is to include intermediate points 4.1, 4.2 and so on.

Response.

Thank you for your suggestion to improve the structure of the article's presentation. We have divided the fourth section into several sections.

Comment 2. I would like to know if the idea of using the mixtures rule to the three phases (fiber, matrix and interphases) to derive the elastic properties of the interphase is new or it has been previously used. In the latter case, which are the original contributions of the authors to this approach.

Response.

The application of the mixture rule to determine the elastic characteristics of the interphase is not novel, provided that the volume fraction of this region is known. If the volume fraction of the interphase is not known, then we have not found any studies aimed at calculating the mechanical properties and thickness of this zone based on the mixture rule. This is probably due to the fact that the application of this hypothesis results in a rather low accuracy of the results. We have demonstrated this in our current work, and there is also information about the low accuracy of calculations using the mixture rule in [E.Egorikhina, S. V. Bogovalov, I. V. Tronin, Phys. Procedia 72 (2015) 66–72. DOI: 10.1016/j.phpro.2015.09.021]. We use this hypothesis only to determine the initial values of the interphase parameters when solving the optimization problem. We determined the parameters of the interphase using a mesomechanical model.

Comment 3. I think that some intermediate steps to derive equations (6) and (7) can be useful to the reader.

Response.

Thank you for the recommendation to improve the presentation of the article. We have looked at our intermediate steps for deriving formulas (6) and (7). Writing formulas in these steps is quite cumbersome, but not complicated, since they simply represent the simplest mathematical operations. Therefore, we decided not to clutter the article with this cumbersome conclusion.

The reader can easily verify the accuracy of formulas (6) and (7) by substituting some values for fiber, matrix, and composite into them. Then, they can insert the resulting values of the elastic modulus of the interphase and the volume fraction into equalities (2), (4), and (5). If the equalities hold after substitution, formulas (6) and (7) are correct. This is how we checked the correctness of the output of formulas (6) and (7).

Comment 4. The mixtures rule for determining elastic properties in composites are based in some hypothesis on stress and strains, that is, assuming constant strain along the longitudinal direction of the fiber or constant stress along the transverse direction, the authors can derive equations (6) and (7). But I cannot see how equation (8) is obtained. Please, provide some explanation.

Response.

Thank you for your attention at this juncture. Formula (8) is derived from the mixture rule and the boundary conditions for stress on the free surfaces of a sample when it is subjected to stretching along the fiber laying direction. A comprehensive derivation of the equation for the relationship between a monolayer's Poisson's ratio and the Poisson's coefficients of both a fiber and a matrix is presented in section 2 of the freely available article [E. Egorikhina, S. V. Bogovalov, I. V. Tronin, Phys. Procedia 72 (2015) 66–72 DOI: 10.1016/j.phpro.2015.09.021]. As a similar derivation regarding equality (8) was reached in that publication, we have refrained from reiterating it here to avoid redundancy. Instead, we have provided a reference to [E. Egorikhina, S. V. Bogovalov, I. V. Tronin, Phys. Procedia 72 (2015) 66–72 DOI: 10.1016/j.phpro.2015.09.021], where a detailed derivation similar to equality (8) can be found.

Comment 5. Is not there a contradiction between the hypothesis of constant stress in the transverse direction and the stress distribution of figure 14?

Response.

Indeed, there exists a discrepancy between the postulate of stress invariance and the actual distribution of stress at the microscopic level. The inappropriateness of this assumption is one of the factors contributing to the substantial divergence between the experimentally obtained mechanical properties of composite materials and those calculated theoretically. We resort to this hypothesis solely for the purpose of establishing the initial values for interfacial zone parameters in the process of solving an optimization problem, where we determine these parameters using a mesomechanical model.

Comment 6. The calculations of the elastic constants of Table 1 are explained for the fiber, but not for the matrix. I imagine that the Poisson`s ratio is obtained from reference 54. Is this correct?

Response.

Any reference value leads to inaccuracies in calculations when modeling a specific material. The value of the Poisson's ratio of 0.33 for the matrix was taken as the average value of the spread of this parameter for the matrix material, which is in the range of 0.31 -0.35, which, as can be seen, is quite small.  Determining the Poisson's ratio based on microindentation data is a non-trivial task. In order for us to determine the Poisson's ratio based on microindentation, we need two indenters of a different shape. We do not have different indenters for microindentation, but we plan to purchase a flat diamond indenter, which will allow us to calculate the Poisson's ratio of the matrix as a result of solving a mechanical problem.

Comment 7. When the initial set of values are determined, how the thickness is computed from the volume fraction in problem 2?

Response.

There are two possible solutions to this problem.  The first variant is derivate the formula. It can be derived by looking at Figure 4. Since we know the average diameter of the fiber and its volume fraction, we can calculate the volume of the matrix per conventional unit of fiber length. Knowing the volume of the matrix, the average diameter of the fiber, the volume fraction of the fiber and the interphase, it can write an equation to calculate the average thickness of the interphase.

The second variant of calculating the thickness of the interphase involves employing solid-state model, as depicted in Figures 4 and 6 of the article. To do this, a program (such as SolidWorks) builds a representative volume of a composite monolayer. Fibers with an average diameter are placed in it, while the volume fraction of the fibers should be equal to the volume fraction of the fibers determined experimentally. Then an interphase is added to the fiber surface. Further, by adjusting the thickness of the interphase h in the program, it is necessary to ensure that the volume fraction of the interphase equals the volume fraction determined by formula (7). The volume fraction of the interphase can be calculated at its current thickness, since the software allows us to know the volume of any object added to the solid-state model. Knowing the volume of any object, it can easily calculate the volume fraction that this object occupies. We used the second variant to solve the problem, since  a solid-state monolayer model  can be easily built using software.

Comment 8. Can be the volume fraction derived from the known thickness of the interphase in problem 1?

Response.

The volume fraction of the interphase in the solid-state model (Figure 6 in the article) can be determined through the program in which this model was built, since the software allows you to know the volume of any object added to the solid-state model. Knowing the volume of any object, you can easily calculate the volume fraction that this object occupies.

The volume fraction of the interfacial zone in the solid-state model (Figure 6 in the article) can be determined using the program in which the model was created, as the software allows users to know the volume of any added object. By knowing the volume of an object, the volume fraction it occupies can be easily calculated.

Comment 9. Lines 373-376 are confusing

Response.

We have removed these sentences from the article text.

Comment 10. I suggest indicating the thickness of the interphase for problem 1 in Table 2.

Response.

We have added this value to the table.

Comment 11. The scope of figure 11 is to show the difficulties of obtaining the properties of the interphase by micro indentation. Is this correct?

Response.

Yes. In addition, we wanted to show the overall pattern of fiber distribution within the matrix, considering the interphase region.

Comment 12. As indicated above, I think that point 4 should include subpoints, to make easy the reading.

Response.

We have divided the fourth section into several sections.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have replied and conducted corrections according to the review comments.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have answered in detail my questions. Some of these responses have been incorporated in the manuscript, but not all of them. I think that these explanations help the reader to understand the research presented in this paper. I strongly suggest the authors to take into consideration extend a little bit the paper including such explanations.