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Investigation on C_{f}/PyC Interfacial Properties of C/C Composites by the Molecular Dynamics Simulation Method

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## Abstract

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_{f}/PyC) interphase in carbon/carbon (C/C) composites manufactured by the chemical vapor phase infiltration (CVI) process was established based on microscopic observation results. By using the MD simulation method, the mechanical properties of the C

_{f}/PyC interphase under tangential shear and a normal tensile load were studied, respectively. Meanwhile, the deformation and failure mechanisms of the interphase were investigated with different sizes of the average length ${\overline{L}}_{a}$ of fiber surface sheets. The empirical formula of the interfacial modulus and strength with the change of ${\overline{L}}_{a}$ was obtained as well. The shear properties of the isotropic pyrolysis carbon (IPyC) matrix were also presented by MD simulation. Finally, the mechanical properties obtained by the MD simulation were substituted into the cohesive force model, and a fiber ejection test of the C/C composite was simulated by the finite element analysis (FEA) method. The simulation results were in good agreement with the experimental ones. The MD simulation results show that the shear performance of the C

_{f}/PyC interphase is relatively higher when ${\overline{L}}_{a}$ is small due to the effects of non-in-plane shear, the barrier between crystals, and long sheet folding. On the other hand, the size of ${\overline{L}}_{a}$ has no obvious influence on the interfacial normal tensile mechanical properties.

## 1. Introduction

_{f}/PyC) interphase in C/C composites manufactured by the CVI process, an MD simulation model of the C

_{f}/PyC interphase was established in this paper. On this basis, the mechanical properties and failure mechanism of the C

_{f}/PyC interphase under tangential shear and a normal tensile load, as well as the strengthening mechanism with different sizes of the average length ${\overline{L}}_{a}$ of fiber surface sheets, were studied. Finally, the interfacial and IPyC matrix properties obtained by the MD simulation were used in the finite element analysis (FEA) of a fiber ejection test on a C/C composite, and the effectiveness of the MD simulation results was verified.

## 2. Materials and Methods

#### 2.1. Microstructure of the C_{f}/PyC Interphase Manufactured by the CVI Process

_{f}/PyC interphase, the MD model used in the simulation must truly reflect the C

_{f}/PyC interphase’s topography. Based on the microscopic observation results in the literature [5,6,16], the microstructural characteristics of the C

_{f}/PyC interphase manufactured by the CVI process are summarized as follows. First, the polyacrylonitrile (PAN) carbon fiber is consistent with the classic skin-core structure [17], and the graphite sheets in the fiber surface have the highest anisotropy and flatness values. Second, the carbon fiber and the pyrolytic carbon nearby are composed of graphite sheets, with no obvious interface. Third, in the pyrolysis carbon matrix far away from the fiber surface, the interphase presents an IPyC structure: there is no obvious lamellar structure or preferred orientation, and the carbon structure shows isotropic characteristics. Fourth, between the fiber surface and the isotropic pyrolytic carbon, there is a thin transition area induced by the fiber surface’s structure. In this area, the distribution of each sheet is discrete, but generally they are approximately along the direction of the fiber surface, showing high anisotropy and flatness. The change in the PyC structure from the fiber surface to the IPyC is asymptotic. Fifth and finally, for high-modulus carbon fiber, which has a larger average size of graphite sheets in the fiber surface (such as T50 carbon fiber), the graphitization degree of the fiber surface is higher, as well as the orientation of graphite sheets in the transition region. Meanwhile, the transition region is thicker (about 15 nm). On the other hand, for high-strength carbon fiber, which has a smaller average size of graphite sheets in the fiber surface (such as T300 carbon fiber), the graphitization degree in the transition region is lower, with smaller graphite sheets. For example, in T300 carbon fiber, the longitudinal length of the graphite sheets in the fiber surface is about 2~4 nm, while the longitudinal length in the transition regions nearby is about 3~5 nm, and the transition region thickness is about 8 nm [18].

#### 2.2. Establishment of the MD Simulation Model

#### 2.2.1. MD Simulation Model for the C_{f}/PyC Interphase

_{f}/PyC interphase region, the PyC deposition in the CVI process was simulated by MD simulation under the following assumptions.

_{f}/PyC interphase model, as shown in Figure 1d. The changes in system temperature and total energy over time during the entire annealing process are shown in Figure 2a,b, respectively. At the end of the relaxation, the temperature and total energy of the system tended to be stable at a relatively low level, which indicated that a relatively stable MD simulation configuration of the C

_{f}/PyC interphase was obtained.

_{f}/PyC interphase. After the model was generated, the average length ${\overline{L}}_{a}$ of graphite sheets in the carbon fiber surface region was recalculated statistically:

_{ai}is the length of sheet i.

_{f}/PyC interfacial mechanical properties, multiple MD models were established with different ${\overline{L}}_{a}$, as shown in Figure 3. In particular, due to the randomness of the established model, the calculated results of mechanical properties also have a certain dispersion, especially with small ${\overline{L}}_{a}$. In order to eliminate the influence of this randomness on the final calculation results, multiple C

_{f}/PyC interphase MD simulation models with the same ${\overline{L}}_{a}$ were generated when needed.

#### 2.2.2. MD Simulation Model for the IPyC Matrix

^{3}. The AIREBO potential function [19] was still used with a cut-off distance of 13.6 angstrom. Using the NVT ensemble and periodic boundary conditions, the model temperature was rapidly raised from 300 K to 4500 K (above the melting point), with a time step of 1 fs. The temperature increment was set to 500 K (except the last one, which was set to 200 K), and it was run for 1 ps at each intermediate temperature. A relaxation of 200 ps was conducted at 4500 K to destroy the carbon ring structure of graphite and to obtain the discrete C atoms. After this, the temperature was slowly reduced to 300 K, with a temperature increment of 100 K (1 ps at each intermediate temperature). A second relaxation of 200 ps was conducted at 300 K to form the final IPyC matrix model, as shown in Figure 4. Due to the periodic boundary conditions and the control of the box size, the density of the model had no change during the simulation.

^{2}and sp

^{3}exist. This is consistent with the structural characteristics of the IPyC model built by Thomas et al. [20].

## 3. Results

#### 3.1. MD Simulation Results of the C_{f}/PyC Interphase under Normal Tensile Conditions

#### 3.1.1. Interfacial Normal Tensile Property with Different ${\overline{L}}_{a}$

_{f}/PyC interphase established in Section 2.2.1, the normal (z direction) tensile properties with different ${\overline{L}}_{a}$ were calculated at room temperature (300 K). In each calculation, graphite sheets within 1.5 nanometers from the top and bottom of the simulation box were defined as the top and bottom boundaries, respectively (including those sheets that were partially within the range). The bottom boundary atoms were fixed by setting the velocity equal to 0. Meanwhile, the velocity of the top boundary atoms was set to V in the Z direction and equal to 0 in the other two directions. V was calculated as follows:

_{Z-load}is the Z directional length of the simulation box except for boundary regions. With a time step of 1 fs, the tensile strain increased 0.001 every 1000 steps. The volume-average virial stress of all atoms, except those in boundary regions, was calculated every 1000 steps to form the stress–strain relationship. The typical normal tensile stress–strain curves are shown in Figure 5b,c, respectively.

_{f}/PyC interphase with different ${\overline{L}}_{a}$ are plotted as shown in Figure 6a,b. The progressive line (the dotted line) in Figure 6 is the calculation result when ${\overline{L}}_{a}=\infty $.

_{f}/PyC interfacial normal tensile mechanical properties.

#### 3.1.2. Failure Mechanism of the C_{f}/PyC Interphase under a Normal Tensile Load

_{f}/PyC interphase under a normal tensile load. For a small (e.g., 3 nm) and a large (e.g., 10 nm) ${\overline{L}}_{a}$ value, the failure modes of the C

_{f}/PyC interphase under a normal tensile load are shown in Figure 7 and Figure 8, respectively.

_{f}/PyC interphase under a normal tensile load when the value of ${\overline{L}}_{a}$ is large. The failure process is similar to that when ${\overline{L}}_{a}$ is smaller. The structural damage still begins with the deflection of some graphite sheets, resulting in the expansion of the original micro-voids (as marked with the dotted line in Figure 8 when $\epsilon =5.2\%$). Finally, the entire structure fails (as marked with the dotted line in Figure 8 when $\epsilon =16.8\%$).

_{f}/PyC interphase under a normal tensile load, as shown in Figure 9. It is also the main reason for the sharp declines in both the tensile modulus and strength compared with the perfect graphite structure. Since the failure mechanism and process do not change significantly with different ${\overline{L}}_{a}$, the ${\overline{L}}_{a}$ value has no obvious influence on the normal tensile mechanical properties of the C

_{f}/PyC interphase.

#### 3.2. MD Simulation Results of the C_{f}/PyC Interphase under Tangential Shear

#### 3.2.1. Interfacial Tangential Shear Property with Different ${\overline{L}}_{a}$

_{f}/PyC interphase and perfect hexagonal graphite under tangential shear was similar to that under a normal tensile load, except that the velocity V setting for top boundary atoms was in the X direction. Typical tangential shear stress–strain curves are shown in Figure 10. The tangential shear modulus and strength of the interphase with different values of ${\overline{L}}_{a}$ are drawn in Figure 11a,b, respectively. The calculated shear modulus and strength of perfect hexagonal graphite were 0.431 GPa and 0.013 GPa, respectively. The horizontal asymptotic line (the dotted line) in Figure 11 is the calculation result when ${\overline{L}}_{a}=\infty $.

_{f}/PyC interphase decreases obviously. To be specific, when ${\overline{L}}_{a}\ge 10\text{}\mathrm{nm}$, the shear stress–strain curves reach the ultimate strength under small strain, and then enter an approximately constant amplitude oscillation stage, which is similar to the response of perfect hexagonal graphite. As shown in Figure 11, the interfacial shear modulus and shear strength have obvious regularity with the change in ${\overline{L}}_{a}$. After fitting the calculated data points, it was found that the variation law of interfacial shear modulus G

_{S}with the average length of fiber surface sheets ${\overline{L}}_{a}$ approximately satisfies the power function:

_{S}with the average length of fiber surface sheets ${\overline{L}}_{a}$ approximately satisfies the exponential relation:

#### 3.2.2. Failure Mechanism of the C_{f}/PyC Interphase under Tangential Shear

_{f}/PyC interphase, failure behaviors are compared between ${\overline{L}}_{a}$ being small (taking 3 nm as an example) and large (taking 10 nm as an example), as shown in Figure 12 and Figure 13, respectively.

_{f}/PyC interphase is the relative slip between the large graphite sheets in the fiber surface region, while the PyC region has a small amount of deformation. In this way, the tangential shear properties of the entire C

_{f}/PyC interphase mainly depend on the sliding behavior between the large graphite sheets in the fiber surface, which is similar to the deformation mode of perfect graphite crystal. Therefore, the interfacial shear properties with a larger ${\overline{L}}_{a}$ are lower.

_{f}/PyC interphase are greatly improved due to the effects of non-in-plane shear behavior, the barrier between crystals, and the long sheet folding. As the value of ${\overline{L}}_{a}$ increases, the interfacial shear modulus and strength decrease. When ${\overline{L}}_{a}$ increases to a certain extent, the main shear failure mechanism of the C

_{f}/PyC interphase changes to the relative slip between large crystal sheets in the fiber surface region. At this time, the interfacial shear modulus and strength are low, and no longer change significantly with the increase in ${\overline{L}}_{a}$.

#### 3.3. MD Simulation Results of the IPyC Matrix under Tangential Shear

^{2}and sp

^{3}exist in the IPyC matrix, the shear properties of IPyC are much higher than those of perfect hexagonal graphite (which will slide between graphite sheets under in-plane shear). The calculated shear modulus G

_{IPyC}= 9.8 GPa, and the shear strength S

_{IPyC}= 105 MPa.

#### 3.4. Verification of MD Simulation Results

^{3}. C/C composites were processed into experimental pieces with a thickness of 84 μm. The test was carried out on the nano indentation tester using a diamond pressure head. The head radius was 0.3 times that of the fiber. The bottom of the test specimen was held by an aluminum base.

#### 3.4.1. Establishment of the FEA Model

_{f}/PyC interphase satisfied the bilinear constitutive relation, the contact element containing the cohesive force model and the Traction–Separation bilinear constitutive were used to characterize the mechanical properties of the interphase [23]. It can be obtained from [18,24] that the average length of graphite sheets in the surface of T300 carbon fiber is 2~4 nm. The median value ${\overline{L}}_{a}$ = 3 nm was taken in formulas (3) and (4) to calculate the shear modulus (G

_{S}) and the shear strength (S

_{S}) of the C

_{f}/PyC interphase, respectively. The normal tensile modulus (K

_{T}) and strength (S

_{T}) were set according to the mean value of the calculated results in Section 3.1.1, and are listed in Table 1. Based on the calculated results in Section 3.3, the properties of the IPyC matrix used in the FEA are also listed in Table 1. The properties of T300 carbon fiber were obtained from [25], and are listed in Table 2. The maximum stress criterion was used as the failure criterion for both the interphase and the matrix, while fiber failure and aluminum base failure were not considered.

#### 3.4.2. FEA Results of the Fiber Ejection Test Simulation

## 4. Conclusions

_{f}/PyC interphase. On this basis, the mechanical properties and failure mechanism of the C

_{f}/PyC interphase under tangential shear and a normal tensile load were studied with different sizes of ${\overline{L}}_{a}$, while the influence of ${\overline{L}}_{a}$ on the interfacial mechanical properties and failure mechanism was obtained. The shear properties of the IPyC matrix were also presented by MD simulation. Based on the MD simulation results, the fiber ejection test of C/C composites at a micron scale was simulated by the FEA method, and the correctness of the MD simulation results was verified. Through the research in this paper, the following conclusions were obtained:

_{f}/PyC interphase is mainly caused by the rotation of these deflected graphite sheets, which results in the expansion of the original micro-voids and leads to the interruption of force transmission paths. ${\overline{L}}_{a}$ has no obvious influence on the C

_{f}/PyC interfacial normal tensile mechanical properties (initial modulus and ultimate strength).

_{f}/PyC interphase is relatively high. As ${\overline{L}}_{a}$ increases, the shear failure mode gradually turns into the relative slip between the large sheets in the fiber surface, and the shear performance of the interphase decreases and converges to the value when ${\overline{L}}_{a}=\infty $. The variation law of interfacial shear modulus G

_{S}with ${\overline{L}}_{a}$ approximately satisfies the power function, while the variation law of interfacial shear strength S

_{S}with ${\overline{L}}_{a}$ approximately satisfies the exponential relation.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Establishment of the molecular dynamics (MD) model of the C

_{f}/PyC interphase. (

**a**) initial perfect hexagonal graphite structure; (

**b**) deformed using the cosine function; (

**c**) after cutting; (

**d**) final structure.

**Figure 2.**The change in system temperature and total energy with time during annealing: (

**a**) system temperature; (

**b**) system total energy.

**Figure 5.**Typical normal tensile stress–strain curves: (

**a**) perfect hexagonal graphite; (

**b**) the C

_{f}/PyC interphase with ${\overline{L}}_{a}$ equal to 2–6 nm; (

**c**) the C

_{f}/PyC interphase with ${\overline{L}}_{a}$ equal to 8 nm-∞.

**Figure 6.**The normal tensile mechanical properties of the C

_{f}/PyC interphase with different sizes of ${\overline{L}}_{a}$: (

**a**) Modulus; (

**b**) Strength.

**Figure 7.**Typical failure modes of the C

_{f}/PyC interphase under a normal tensile load when ${\overline{L}}_{a}=3\text{}\mathrm{nm}$.

**Figure 8.**Typical failure modes of the C

_{f}/PyC interphase under a normal tensile load when ${\overline{L}}_{a}=10\text{}\mathrm{nm}$.

**Figure 10.**Typical tangential shear stress–strain curves: (

**a**) the C

_{f}/PyC interphase with different sizes of ${\overline{L}}_{a}$; (

**b**) perfect hexagonal graphite.

**Figure 11.**The tangential shear mechanical properties of the C

_{f}/PyC interphase with different sizes of ${\overline{L}}_{a}$: (

**a**) Modulus; (

**b**) Strength.

**Figure 12.**Typical failure modes of the C

_{f}/PyC interphase under a tangential shear load when ${\overline{L}}_{a}=3\text{}\mathrm{nm}$.

**Figure 13.**Typical failure modes of the C

_{f}/PyC interphase under a tangential shear load when ${\overline{L}}_{a}=10\text{}\mathrm{nm}$.

**Figure 14.**The main mechanism of the C

_{f}/PyC interphase to improve the shear mechanical properties when ${\overline{L}}_{a}$ is smaller: (

**a**) non-in-plane shear behavior; (

**b**) the barrier between crystals; (

**c**) long sheet folding.

**Figure 15.**The tangential shear stress–strain curve of the isotropic pyrolysis carbon (IPyC) matrix.

**Figure 16.**The simulation model of the fiber ejection test on the carbon/carbon (C/C) composite: (

**a**) geometric model; (

**b**) finite element model.

**Figure 17.**A comparison between the simulation and experimental results of the C/C composite fiber ejection test: (

**a**) the load–displacement curves; (

**b**) the deformation of the ejected fiber in the simulation.

**Table 1.**The mechanical properties of the C

_{f}/PyC interphase (${\overline{L}}_{a}$ = 3 nm) and the IPyC matrix.

C_{f}/PyC Interphase | K_{T}/GPa | G_{S}/GPa | S_{T}/GPa | S_{S}/GPa | ||
---|---|---|---|---|---|---|

4.94 | 0.67 | 0.55 | 0.2 | |||

IPyC matrix | G/GPa | ν | S/MPa | |||

9.8 | 0.23 [26] | 105 |

**Table 2.**The elastic properties of the T300 carbon fiber and aluminum base [25].

T300 Fiber | E_{11}/GPa | E_{22} = E_{33}/GPa | G_{12} = G_{13}/GPa | G_{23}/GPa | ${\mathit{\nu}}_{12}={\mathit{\nu}}_{13}$ | ${\mathit{\nu}}_{23}$ |
---|---|---|---|---|---|---|

220 | 22 | 4.8 | 7.7 | 0.12 | 0.42 | |

aluminum base | G/GPa | ν | ||||

70 | 0.33 |

**Table 3.**A comparison of the experimental and simulated results of fiber ejection on the C/C composite.

$\mathit{t}/\mathsf{\mu}\mathbf{m}$ | P/mN | IFSS/MPa | |
---|---|---|---|

Experiment [21] | 84 | 97 ± 7 | 53 ± 4 |

simulation | 84 | 111.7 | 60.5 |

Error (%) | - | 7%–23% | 7%–23% |

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## Share and Cite

**MDPI and ACS Style**

Zhou, Y.; Ye, T.; Ma, L.; Lu, Z.; Yang, Z.; Liu, S.
Investigation on C_{f}/PyC Interfacial Properties of C/C Composites by the Molecular Dynamics Simulation Method. *Materials* **2019**, *12*, 679.
https://doi.org/10.3390/ma12040679

**AMA Style**

Zhou Y, Ye T, Ma L, Lu Z, Yang Z, Liu S.
Investigation on C_{f}/PyC Interfacial Properties of C/C Composites by the Molecular Dynamics Simulation Method. *Materials*. 2019; 12(4):679.
https://doi.org/10.3390/ma12040679

**Chicago/Turabian Style**

Zhou, Yuan, Tianyuan Ye, Long Ma, Zixing Lu, Zhenyu Yang, and Shouwen Liu.
2019. "Investigation on C_{f}/PyC Interfacial Properties of C/C Composites by the Molecular Dynamics Simulation Method" *Materials* 12, no. 4: 679.
https://doi.org/10.3390/ma12040679