C.M. Hadden and D.R. Klimek-McDonald

Michigan Technological University, Houghton, Michigan

E.J. Pineda

Glenn Research Center, Cleveland, Ohio

J.A. King, A.M. Reichanadter, I. Miskioglu, S. Gowtham, and G.M. Odegard

Michigan Technological University, Houghton, Michigan

Mechanical Properties of Graphene Nanoplatelet/

Carbon Fiber/Epoxy Hybrid Composites:

Multiscale Modeling and Experiments

NASA/TM—2015-218731

June 2015
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C.M. Hadden and D.R. Klimek-McDonald

Michigan Technological University, Houghton, Michigan

E.J. Pineda

Glenn Research Center, Cleveland, Ohio

J.A. King, A.M. Reichanadter, I. Miskioglu, S. Gowtham, and G.M. Odegard

Michigan Technological University, Houghton, Michigan

Mechanical Properties of Graphene Nanoplatelet/

Carbon Fiber/Epoxy Hybrid Composites:

Multiscale Modeling and Experiments

NASA/TM—2015-218731

June 2015

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

20th International Conference on Composite Materials

cosponsored by Siemens, LM Wind Power, GOM, Zebicon, Force Technology, et al.

Copenhagen, Denmark, July 19–24, 2015
Acknowledgments

This research was funded by NASA under the Aeronautical Sciences Program (Grant NNX11A072A), the Air Force Offi ce of 

Scientifi c Research under the Low Density Materials Program (Grant FA9550-13-1-0030), the Michigan Space Grant Consortium 

(Grant 2993583), the NSF I/UCRC on Novel High Voltage/Temperature Materials and Structures (Grant IIP-1362040), and the 

Michigan Technological University Summer Undergraduate Research Fellowship Program. The authors thank XG Sciences for 

donating graphene nanoplatelets and Hexcel for donating AS4 carbon fi ber for this work. The authors would also like to thank 

the following undergraduate students for their assistance on this project: Michael T. Best, Courtney A. Castelic, James A. Kenney, 

Kerry L. King, Andrew P. Lewis, Ryan E. McInnis, Mary Kate Mitchell, Ryan J. Patrick, Andrew N. Payton, Travis J. D. Pellosma, 

Alexander E. Powell, Elizabeth J. Skultety, Stephanie L.Tankersley, Peter H. Winegar, and Lucas D. Zoromski. SUPERIOR, a highperformance computing cluster at Michigan Technological University, was used in obtaining results presented in this publication.

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This report is a preprint of a paper intended for presentation at a conference. 

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NASA/TM—2015-218731 1 

Mechanical Properties of Graphene Nanoplatelet/Carbon 

Fiber/Epoxy Hybrid Composites: Multiscale Modeling 

and Experiments 

C.M. Hadden and D.R. Klimek-McDonald 

Michigan Technological University 

Houghton, Michigan 49931 

E.J. Pineda 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

J.A. King, A.M. Reichanadter, I. Miskioglu, S. Gowtham, and G.M. Odegard 

Michigan Technological University 

Houghton, Michigan 49931

Abstract 

Because of the relatively high specific mechanical properties of carbon fiber/epoxy composite 

materials, they are often used as structural components in aerospace applications. Graphene nanoplatelets 

(GNPs) can be added to the epoxy matrix to improve the overall mechanical properties of the composite. 

The resulting GNP/carbon fiber/epoxy hybrid composites have been studied using multiscale modeling to 

determine the influence of GNP volume fraction, epoxy crosslink density, and GNP dispersion on the 

mechanical performance. The hierarchical multiscale modeling approach developed herein includes 

Molecular Dynamics (MD) and micromechanical modeling, and it is validated with experimental testing 

of the same hybrid composite material system. The results indicate that the multiscale modeling approach 

is accurate and provides physical insight into the composite mechanical behavior. Also, the results 

quantify the substantial impact of GNP volume fraction and dispersion on the transverse mechanical 

properties of the hybrid composite while the effect on the axial properties is shown to be insignificant. 

1.0 Introduction 

Carbon/epoxy composites are a prime component of many modern aircraft structures because of their 

exceptional mechanical properties relative to their bulk mass density. The bulk-level mechanical 

properties of these composites depend directly on the mechanical properties and interaction between the 

constituent materials. Traditionally, the constituents have been carbon fibers and epoxy matrix. However, 

the inclusion of graphene nanoplatelets (GNPs) in epoxy has been shown to improve mechanical and 

electrical properties with respect to the un-reinforced epoxy (Refs. 1 to 4), thus showing promise for use 

of GNP-reinforced epoxy as the matrix phase in a fiber composite. The resulting GNP/carbon fiber/epoxy 

hybrid composite could potentially show improvements in mechanical properties with respect to 

traditional carbon fiber/epoxy composites. 

It has been demonstrated (Refs. 2 to 4) that the effect of GNPs on GNP/polymer composite 

mechanical properties is governed by the amount of GNPs added to the polymer and the dispersion of the 

GNPs within the polymer. It has been also shown through experimentally-validated molecular modeling 

(Ref. 5) that the GNP/epoxy interface contains an interphase region that is on the same size order as GNP 

sheets and can be sensitive to epoxy crosslink density. The interphase region is composed of epoxy 

molecules that have a mass density that is significantly different than that of the bulk. However, it is 

uncertain how the molecular structure of the interphase region and molecular-scale dispersion of GNPs 
NASA/TM—2015-218731 2 

affects the bulk-level elastic properties of GNP/carbon fiber/epoxy hybrid composites. Molecular 

modeling must be used to provide a sufficient amount of physical insight into the effect of the interphase 

molecular structure and the dispersion of GNPs on bulk-level performance of the hybrid composite 

because of the difficulty in experimentally characterizing these factors. 

The objective of this study is to use an experimentally validated multiscale modeling technique to 

determine the molecular structure of the GNP/epoxy interface and understand the influence of the 

interface, GNP dispersion, and GNP volume fraction on the bulk-level elastic properties of a GNP/carbon 

fiber/epoxy hybrid composite. The multiscale modeling approach consists of molecular dynamics (MD) 

and micromechanics modeling. The multiscale model is validated by direct comparison to mechanical 

properties of the hybrid composite determined by mechanical testing of fabricated specimens. The results 

indicate that the multiscale model accurately predicts the bulk-level mechanical properties based on 

molecular-level structure, and GNP dispersion has a tremendous effect on the hybrid composite response. 

2.0 Multiscale Modeling 

MD was used to predict the molecular structure and elastic properties of a representative volume 

element (RVE) containing GNP and the GNP/epoxy interphase region. The corresponding homogenized 

elastic properties, including the influence of the interphase region, were used in subsequent, uncoupled, 

micromechanical analyses to predict the mechanical response of the GNP/epoxy composite as well as the 

GNP/carbon fiber/epoxy hybrid composite. The details of the multiscale modeling are given in this 

section. The modeled epoxy system consisted of the EPON 862 (diglycidyl ether of bisphenol F, DGEBF) 

monomer and the EPIKURE Curing Agent W (diethyltoluenediamine, DETDA). 

2.1 MD Modeling 

MD techniques have been used in several instances to model pure thermoset EPON 862/DETDA 

epoxy systems (Refs. 6 to 9). MD modeling has also been performed on thermoset polymers containing 

carbon nanotubes (Refs. 10 to 17), nanoparticles (Refs. 18 to 20), and in the presence of a surface 

(Refs. 5, 21 to 24). The interfacial region between epoxy and carbon reinforcement (either carbon fiber or 

GNP) has been investigated in many of the aforementioned references. These MD studies, coupled with 

recent backing from experimental imagery (Ref. 5), have revealed the existence of an interfacial region 

near the carbon reinforcement surface in which the local epoxy molecular structure, specifically the mass 

density, differs from that of the bulk. For the GNP-reinforced EPON 862/DETDA system, previous 

research has shown this interfacial region to be approximately 10 Å thick from the graphite surface 

(Ref. 5). Although these studies have given valuable information regarding the physical nature of the 

interfacial region, there has been little effort to implement this information into a bulk-scale model for 

GNP/epoxy composites. 

The MD model of the GNP/epoxy interface was constructed using a multistep approach. First, a 

model of the pure uncrosslinked epoxy system was established. Second, a series of GNP sheets was added 

to the model of the pure epoxy system to establish the GNP/epoxy interface model for different numbers 

of GNP sheets. Finally, the GNP/epoxy MD models were crosslinked to various levels. Each of these 

steps is described in the following subsections. After the systems were constructed, they were exposed to 

applied deformations to predict their mechanical response. The Large Scale Atomic/Molecular Massively 

Parrallel Simulator (LAMMPS) software package (Ref. 25) was used for all of the Molecular 

Minimization (MM) and MD simulations described herein. 

2.1.1 Pure Epoxy MD Model 

The initial uncrosslinked polymer molecular structure was established using a procedure similar to 

that of Bandyopadhyay et al. (Ref. 6), consisting of the EPON 862 monomer and the DETDA hardener 

shown in Figure 1. A stoichiometric mixture of 2 molecules of EPON 862 and 1 molecule of DETDA was 

placed in a MD simulation box with periodic boundary conditions. The initial atomic coordinates file was 
NASA/TM—2015-218731 3 

written in the native LAMMPS format and the Optimized Potential for Liquid Simulations (OPLS) 

United Atom force field developed by Jorgensen and co-workers (Refs. 26 and 27) was used for defining 

the bond, angle, and dihedral parameters. The equilibrium spacing parameter σ of the Lennard-Jones 

potential was taken to be the arithmetic mean of the individual parameters of the respective atom types, 

while the well-depth parameter ε was taken to be the geometric mean of the values for the respective atom 

types. The van der Waals interactions were modeled with an interaction cutoff radius of 10Å. 

This particular force field allows for modeling of CH3, CH2, CH, and alkyl groups as single united 

atoms with their corresponding masses. The described polymer model utilized united atom structures for 

all applicable groups, except for the C and H atoms in the phenyl rings for both monomer and hardener 

molecules along with one CH3 group directly connected to the phenyl ring of the DETDA molecule. 

Thus, the use of united atoms reduced the modeled 2:1 structure from 117 to 83 atoms. The location of 

each united atom is shown in Figure 1, with 31 total atoms in the molecule of EPON 862 and 21 in the 

molecule of DETDA. 

The 2:1 molecular model was subjected to four MM minimizations and three 100 ps MD simulations. 

MM simulations utilized the conjugate gradient stopping criterion, and MD simulations were performed 

using the NVT (constant volume and temperature) ensemble at 300 K. This process minimized internal 

forces and thus reduced internal residual stresses that were created from the initial construction of bonds, 

bond angles, and bond dihedrals. 

2.1.2 Epoxy/GNP Model 

After the structure stabilized to a relatively low energy value, the initial 2:1 stoichiometric structure 

was replicated, and the replicated models were randomly rotated and then translated along the three 

Cartesian axes and combined into a much larger structure with an EPON 862:DETDA ratio of 250:125, 

containing 10,375 total united atoms. Therefore, the resulting system consisted of 250 randomly oriented 

clusters of the small 2:1 ratio cluster stacked loosely together in a manner much like that of a simple cubic 

crystal structure. 

This larger polymer model was mirrored about a graphene structure positioned in the x-y plane central 

to the z-axis (Fig. 2). As a result, each system contains a 500:250 ratio of EPON 862:DETDA totaling 

20,750 polymer atoms. The centralized graphene structures varied in thickness from 1 atomic layer to 

4 layers thick, each layer containing 4200 carbon atoms. The largest system, comprised of a 4-layer 

graphene sheet, contained 37,550 total atoms and the initial box size was 101×104×210 Å. All models 

employed 3-D periodic boundary conditions. The initial box size produced a polymer density 

approximately equal to half of a fully cured solid EPON 862 epoxy (~0.5 g/cc in all four systems). 

In order to achieve the desired polymer density of 1.17 g/cc, the four separate models were subjected 

to twelve cycles of deformation along the z-axis (Fig. 2). Each cycle included a MM followed by a 100 ps 

MD NVT simulation in which the z coordinate was reduced in equal amounts from both the positive and 

negative z-coordinate boundaries using the LAMMPS fix/deform tool. A Nose/Hoover thermostat and 

barostat was implemented for temperature and pressure control, respectively (Ref. 28). The amount of 

deformation decreased with each cycle as the models became closer to the desired density. This was done 
NASA/TM—2015-218731 4 

to avoid large energy increases to the system by packing the molecules together too quickly. This entire 

densification process was performed over a total of 1.2 ns for each of the four systems. The final 

z-coordinate boundary enabled for polymer atoms to extend ~13 Å from the graphene surface, to ensure 

that the interfacial region was fully captured and to show a minimal influence from the bulk polymer 

characteristics during deformation. The fully equilibrated, noncrosslinked, structures for all four systems 

are shown in Figure 3. 

2.1.3 Crosslinking Procedure 

The equilibrated models were crosslinked based on the root mean square (RMS) distance between the 

CH2 groups of the EPON 862 and the N atoms of DETDA molecules using the same procedure described 

previously (Ref. 5). A total of 16 molecular systems were established, each having a unique crosslink 

density (65, 70, 75, and 80 percent) and number of graphene layers (1-4). The crosslink density was 

defined as the ratio of the total number of crosslinks that were formed to the maximum number of 

crosslinks that could be formed. It is important to note that for industrial grade epoxies, a broad range of 

crosslink densities of 60 to 95 percent is typically observed in experiments (Refs. 29 to 33). Therefore, the 

simulated crosslink densities were chosen to span part of this range. It was observed that crosslinking 

above 80 percent resulted in molecular structures with unnaturally high internal stresses. 

After crosslinking to the desired density, each structure was allowed to equilibrate using a series of 

three MM minimizations and two MD NVT simulations of 2 ns each. A 1 ns NPT (constant pressure and 

temperature) simulation followed to minimize internal stresses. The density of formed crosslink atoms 

(C-N and O-H) as a function of the z-axis is shown in Figure 4, where the origin of the z-axis lies in the 

center of the graphene structures and the mass density is calculated for all values of x and y. The figure 

contains data for 80 percent crosslinked structures only, and shows good dispersion of crosslinks 

throughout the polymer structure with unique profiles for each crosslink density. Crosslink density 

profiles for 65, 70, and 75 percent crosslinked structures were similar. 

 
NASA/TM—2015-218731 5 

 
NASA/TM—2015-218731 6 

Shown in Figures 5 to 8 is the overall mass density of the 16 models along the z-axis, which were 

calculated the same way as with Figure 4. These curves follow a similar trend to that demonstrated by 

Hadden et al. (Ref. 5). There are large peaks at the locations corresponding to the graphene sheets. These 

peaks are not perfectly symmetrical because the equilibrium configuration of the graphene sheets includes 

a considerable amount of waviness (Fig. 3). Immediately adjacent to these peaks are smaller peak values 

of density of epoxy near the graphene surface, followed by diminishing oscillations along the z-axis. At 

about ~10 Å from the outer graphene surfaces the density is steady near the bulk density level of 

1.17 g/cc, thus the interphase region is ~10 Å thick. 
NASA/TM—2015-218731 7 
NASA/TM—2015-218731 8 

2.1.4 Mechanical Deformation 

The 16 molecular models were subjected to MD-simulated uniaxial mechanical deformations to 

predict their elastic mechanical responses. The models were deformed with uniaxial 5 percent strains in 

tension and compression along the x-, y-, and z-axes over a period of 1 ns. Poisson contractions were 

allowed in the transverse directions for the direct calculation of Young’s modulus and Poisson’s ratio. 

Additionally, shear deformations of 5 percent were performed separately along the x-y, y-z, and x-z planes 

over the period of 1 ns for each model. Representative stress versus strain curves for the tensile 

deformation along the x-axis and shear in the x-y plane are shown for the 80 percent crosslinked models in 

Figure 9. The corresponding stress-strain behavior for the other crosslink densities and deformation 

modes showed similar trends. The values of Young’s modulus in the three orthogonal directions (Ex, Ey, 

Ez), the shear modulus in the x-y plane (Gxy), and the Poisson’s ratios for all 16 systems are given in 

Table 1. The shear modulus values in the y-z and x-z planes are not included in Table 1 because they were 

nearly zero-valued based on the dominance of the van der Waals bonds between the graphene sheets and 

polymer and the periodic boundary conditions. As expected, the values of Ez are much lower than those of 

Ex and Ey because the dominance of van der Waals forces in that direction and because the graphene is 

alined in the x-y plane. The volume fraction of the graphene (vGNP) for each of the 16 MD models is also 

given in Table 1. 

From Figure 9 it is clear that there was a linear-elastic response of the models up to tensile and shear 

strains of 5 percent. From Table 1 it can be seen that Ex and Ey are nearly identical in each model, as is 

expected given the material symmetry (Fig. 3). Ez was much lower in magnitude than Ex and Ey because the 

graphene sheets were oriented in the x-y plane. The overall magnitude of Ex, Ey, and Gxy increase 

substantially with the number of graphene layers, which corresponds to the increase of vGNP. The values of 

Poisson’s ratio do not appear to be strongly dependent on the number of graphene layers in the model. There 

appears to be no significant influence of the epoxy crosslink density on the elastic properties of the interface. 
NASA/TM—2015-218731 9 

TABLE 1.—PREDICTED ELASTIC PROPERTIES FROM MD SIMULATIONS (MODULUS GIVEN IN GPa) 

Epoxy 

crosslink 

density, 

percent 

vGNP Ex Ey Ez Gxy vxy vyx vxz vyz vzx vzy

65 1 layer—0.111 94.0 94.2 2.397 0.242 0.132 0.148 0.636 0.590 0.018 0.004 

65 2 layers—0.187 177.4 175.7 2.846 0.433 0.153 0.152 0.615 0.584 0.012 0.071 

65 3 layers—0.271 240.5 238.1 2.855 0.580 0.155 0.150 0.490 0.479 0.002 0.033 

65 4 layers—0.330 294.4 291.9 3.218 0.705 0.153 0.153 0.489 0.501 0.007 0.073 

70 1 layer—0.111 93.3 93.0 2.590 0.290 0.142 0.146 0.491 0.500 0.042 0.083 

70 2 layers—0.187 170.4 170.7 3.008 0.424 0.146 0.159 0.468 0.462 0.042 0.007 

70 3 layers—0.271 240.0 236.8 2.815 0.483 0.153 0.151 0.500 0.490 0.010 0.023 

70 4 layers—0.330 294.5 295.3 3.294 0.542 0.153 0.155 0.507 0.454 0.011 0.035 

75 1 layer—0.111 91.9 93.8 2.684 0.234 0.144 0.157 0.516 0.564 0.095 0.049 

75 2 layers—0.187 174.8 175.2 2.768 0.429 0.154 0.163 0.550 0.516 0.017 0.018 

75 3 layers—0.271 238.6 238.1 3.034 0.579 0.154 0.151 0.514 0.493 0.020 0.004 

75 4 layers—0.330 293.5 293.4 3.244 0.713 0.163 0.154 0.483 0.535 0.007 0.010 

80 1 layer—0.111 93.4 94.8 2.432 0.243 0.130 0.158 0.460 0.471 0.109 0.025 

80 2 layers—0.187 174.6 172.5 2.731 0.424 0.168 0.153 0.437 0.524 0.056 0.015 

80 3 layers—0.271 239.4 238.3 3.005 0.582 0.152 0.151 0.440 0.446 0.010 0.034 

80 4 layers—0.330 293.1 295.5 3.251 0.725 0.159 0.156 0.455 0.452 0.011 0.009 

2.2 Micromechanics 

Once the mechanical response of the molecular models shown in Figure 3 was determined, then the 

elastic properties shown in Table 1 were used as input to the next higher length-scale (continuum) 

analysis. Figure 10 shows the modeling strategy for using the molecular-scale elastic properties for 

ultimately predicting the elastic properties of the GNP/carbon fiber/epoxy hybrid composite. 

The generalized method of cells (GMC) micromechanics theory was used to provide the continuumlevel predictions (Refs. 34 to 36). With this method, a repeating unit cell (RUC) representing the periodic 

material microstructure is devised. This RUC may contain as many constituent phases as is necessary to 

represent the composite material accurately. The RUC is discretized into a number of subcells, each of 

which is occupied by a single phase of the composite. Continuity of displacement and traction is enforced 

at each of the subcell interfaces, along with periodic boundary conditions, in an average (or integral) 

sense, to arrive at a strain concentration matrix. Once the strain concentration matrix is obtained, the local 

subcell stresses and strains, and the homogenized RUC stiffness tensor, can be readily obtained. The 

semi-analytical procedure is extremely computationally efficient and provides solutions on the order of 

seconds, or less. 

GMC is implemented with the MAC/GMC software package, developed by the NASA Glenn 

Research Center (Ref. 37). The MAC/GMC software was utilized to perform two levels of micromechanical analysis. First, the effective properties of MD unit cells (Fig. 3) were determined. These effective 

properties were then used in a GMC RUC, which contained additional subcells of pure epoxy to arrive at 

the desired GNP volume fractions. The homogenized properties of the GNP/epoxy RUC were integrated 

over all possible orientations in 3-D space to simulate a random distribution of the GNPs in the epoxy 

matrix. Second, the corresponding properties of the randomly distributed GNP/epoxy composites were 

used in a subsequent MAC/GMC analysis to simulate a GNP/carbon fiber/epoxy hybrid composite. The 

details of these analyses are described in the following subsections. 

2.2.1 GNP/Epoxy Composite 

As shown on the left side of Figure 10, the GNP/epoxy was initially modeled as a GMC RUC 

containing the effective properties of a single MD unit cell embedded in a pure epoxy matrix. It is important 

to note that the MD simulations were not directly integrated into the MAC/GMC simulations. Figure 10 

shows the MD simulation cell in the GMC RUC for conceptual clarity. The properties of the subcell 
NASA/TM—2015-218731 10 

representing the MD unit were taken from Table 1, and the Young’s modulus of the EPON 862/DETDA 

was 2.72 GPa (Ref. 3). Since the Gxz and Gyz values were nearly zero, they were given a nominal value of 

1 MPa for all systems in the MAC/GMC analysis. Also, for simplicity, the values of Ex and Ey were given 

the same value as input in the MAC/GMC analysis for each system. The values of Ex and Ey that were input 

were the average values of the two quantities for each system (Table 1). 

The MD models contained four different numbers of graphene sheets (1-4), each with a different 

volume fraction of GNP (vGNP from Table 1). Thus, to obtain a specific value of GNP volume fraction for 

the GNP/epoxy composite in the MAC/GMC analysis, the volume of the subcell using the GNP/epoxy 

properties from the MD models had to be adjusted relative to the volume of the pure epoxy subcells in the 

RUC. Specifically, the overall GNP volume fraction in the composite (FGNP) is simply the product of the 

volume fraction of the GNP/epoxy subcell (FMD) in the MAC/GMC analysis and the volume fraction of 

GNP in the MD model (vGNP from Table 1). That is, 

F Fv GNP MD GNP  (1)

Therefore, the elastic properties of the GNP/epoxy composite could be easily determined for any volume 

fraction of GNP without requiring new MD simulations. This approach allowed for an efficient process to 

predict the influence of GNP volume fraction on overall elastic properties, as detailed below. 

GNP/epoxy composites typically are processed with a random distribution of GNPs within the 

surrounding epoxy (Fig. 10, center). To obtain the effective properties of a GNP/epoxy composite 

containing a random distribution of GNPs, the homogenized properties of the RUC (Fig. 10, left) were 

integrated over all possible orientations in 3-D space (Ref. 38). The corresponding elastic properties were 

thus isotropic and dependent on the GNP volume fraction and number of adjacent graphene layers 

together. Thus, perfect dispersion was simulated for the case of a single graphene layer, with 

incrementally worsening of dispersion conditions with increasing numbers of simulated layers (2-, 3-, and 

4-layers). The elastic properties predicted from these simulations were used as input into the next level of 

MAC/GMC analysis containing the nanoenhanced epoxy matrix and carbon fibers. 
NASA/TM—2015-218731 11 

2.2.2 GNP/Carbon Fiber/Epoxy Hybrid Composite 

The MAC/GMC software was used to predict the elastic properties of the GNP/carbon fiber/epoxy 

hybrid composite shown on the right side of Figure 10. The fiber architecture was chosen as a 26 by 26 

circular array shown in Figure 11. This figure shows the representative unit cell (RUC) used for 

composite data calculations. The outer portion (green) represents the GNP-doped epoxy, the properties of 

which were obtained a priori (see Section 2.2.1). The blue subcells in the center of the RUC represent the 

circular carbon fiber. Input parameters for the carbon fiber were chosen to accurately represent the fibers 

used in the experiments described below (Ref. 39), and are given in Table 2. 

Figure 12 shows the predicted axial modulus of the hybrid composite as a function of GNP volume 

fraction for a carbon fiber volume fraction of 58 percent. From this figure it is clear that the case of 

perfect dispersion (1 GNP layer) results in a tensile modulus that increases at a faster rate (with respect to 

GNP volume fraction) than the 2-, 3-, and 4-layer scenarios. Thus, increasing levels of dispersion result in 

more efficient load transfer between epoxy and GNPs. However, examination of the vertical scale in 

Figure 12 reveals that increasing volume fractions of GNP do not result in substantial increases of axial 

modulus, even for the case of perfect GNP dispersion. This is because the carbon fibers dominate the 

reinforcing effect in the axial direction, which overshadows the contribution from the GNPs. 

Figure 13 shows the predicted transverse modulus of the unidirectional hybrid composite as a 

function of GNP volume fraction for a fiber volume fraction of 58 percent. Similar to the results for the 

axial modulus (Fig. 12), the data shows the greatest reinforcing effect for the case of perfect GNP 

dispersion. Contrary to the results for axial modulus, the inclusion of GNPs in the hybrid composite 

shows a significant increase in the transverse modulus, even in the cases of 2-, 3-, and 4-layer GNPs. This 

result makes sense given that carbon fibers typically have a low transverse stiffness and limited influence 

on the transverse modulus of unidirectional composites. 

TABLE 2.—MECHANICAL PROPERTIES FOR AS4 CARBON FIBERS 

Property Value 

Axial modulus 231 GPa 

Transverse modulus 9.6 GPa 

Shear modulus 112 GPa 

Poisson’s ratio 0.3 

Fiber volume fraction 58 percent 
NASA/TM—2015-218731 12 
NASA/TM—2015-218731 13 

3.0 Experimental Fabrication and Testing 

The multiscale modeling approach discussed in Section 2.0 was validated experimentally with the 

fabrication and mechanical testing of the GNP/carbon fiber/epoxy hybrid composite. The details of the 

experimental portion of this work are detailed in this section. 

3.1 Materials 

The epoxy material system used in this study is the same as that modeled (EPON 862/DETDA). The 

viscosity of EPON 862 and EPIKURE Curing Agent W at 25 C is ~35 P and ~200 cP, respectively. 

EPON 862 is a low viscosity, liquid epoxy resin manufactured from epichlorohydrin and Bisphenol-F 

(Refs. 40 and 41). This epoxy system is available from Momentive Specialty Chemicals, Inc. The GNP 

system was xGnP-C-300, available from XG Sciences. It has a 2 m average platelet diameter and a 

thickness of 2 nm. xGnP-C-300 has a density of ~2.0 g/ml and a surface area of 300 m2

/g (Ref. 42). 

Photomicrographs of xGnP are shown elsewhere (Refs. 42 to 46). The continuous carbon fiber used in 

this study was HexTow AS4-GP/3K (1.00 percent)(5000). HexTow AS4 carbon fiber is a continuous 

PAN-based fiber with a high strength and high strain, manufactured by Hexcel. The fiber was surface 

treated and sized (1 wt% sizing). The density of the AS4 carbon fiber is 1.79 g/mL and the modulus is 

231 GPa (Ref. 39). 

The concentrations (shown in wt% and the corresponding vol%) for composites tested in this study 

are shown in Table 3. It is important to note that increasing filler amount typically increases composite 

melt viscosity and, at some point, becomes difficult to fabricate into a composite part. Thus, a maximum 

of 3 wt% GNP was used. Table 3 also shows tensile properties determined by macroscopic methods. The 

results shown in Table 3 for the neat epoxy and GNP/epoxy composites have been previously reported 

(Refs. 3 to 47). 

TABLE 3.—EXPERIMENTALLY-OBTAINED 

PROPERTIES FOR GNP/CARBON FIBER/ 

EPOXY SYSTEMS 

Material 

system 

Filler, 

wt% 

Filler, 

vol% 

Axial 

modulus, 

GPa 

Neat epoxy 0 0.0 2.720.04 

n = 6 

GNP/epoxy 1 0.60 2.800.04 

n = 7 

GNP/epoxy 2 1.21 2.880.07 

n = 8 

GNP/epoxy 3 1.82 2.930.09 

n = 8 

Carbon 

fiber/epoxy 

67 57.6 134.39.27 

n = 6 

GNP/carbon 

fiber/epoxy 

GNP-0 

CF-67 

GNP-0 

CF-58 

134.299.27 

n = 6 

GNP/carbon 

fiber/epoxy 

GNP-1 

CF-67 

GNP-0.8 

CF-58 

137.59.33 

n = 15 

GNP/carbon 

fiber/epoxy 

GNP-2 

CF-67 

GNP-1.6 

CF-58 

137.06.53 

n = 15 

GNP/carbon 

fiber/epoxy 

GNP-3 

CF-67 

GNP-2.3 

CF-58 

137.19.75 

n = 11 

 
NASA/TM—2015-218731 14 

3.2 Test Specimen Fabrication 

To fabricate the neat epoxy, 100 g of EPON 862 was added to 26.4 g of EPIKURE Curing Agent W 

at 23 °C and mixed by hand for 3 min. The mixture was degassed inside an oven at 90 °C and 29 in. Hg 

vacuum for 30 min and then poured into rectangular molds. The molds were heated in an oven to 121 °C 

over 30 min, held at 121 °C for 2 h, heated to 177 °C over 30 min, held for another 2 h at 177 °C, and 

finally cooled to ambient temperature (Refs. 40, 48, and 49). 

To produce the GNP/epoxy composites, the appropriate amount of GNP was added to EPIKURE 

Curing Agent W and mixed using a 2 in. diameter disperser blade in a Ross high shear mixer 

HSM-100 LSK-I at 3500 rpm for 150 min. The mixture was then placed in a Branson Bath Sonicator 

CPX2800H operating at 40 kHz for 60 min at 23 °C. The appropriate amount of EPON 862 was added to 

the GNP/Curing Agent W mixture and stirred with the Ross mixer at 1000 rpm for 3 min at 23 °C. The 

mixture was degassed inside an oven at 90 °C and 29 in. Hg vacuum for 30 min and then poured into 

rectangular-molds. The same curing cycle was used as described for the neat epoxy. For the neat epoxy 

and the GNP/epoxy systems, the fabricated samples were rectangular bars (165 mm long by 19 mm wide 

by 3.3 mm thick). 

To fabricate the continuous unidirectional carbon fiber/epoxy composites, 100 g of EPON 862 was 

added to 26.4 g of EPIKURE Curing Agent W at 23 °C and mixed by hand for 3 min. The appropriate 

amount of epoxy was added to the carbon fiber tow via a winding process to produce a unidirectional 

composite containing 67 wt% carbon fiber and 33 wt% epoxy. The uncured epoxy/carbon fiber was cut into 

sheets (248 by 248 mm) and placed in a picture frame mold (254 mm by 254 in.). To fabricate the 

unidirectional composite plate, five plies were placed with the carbon fiber in the 0° direction. A Wabash 

Compression Molding Machine Vantage Series Model V75H-18-CLX was used. Initially, the composite 

plate was heated to 121 °C and held at a constant pressure of 30 psi for 2 hr. The press was then ramped up 

to 177 °C and held at a constant pressure of 1000 psi for 2 hr. Cooling water was used to cool the press until 

the platen temperature was 30 °C, then the composite plate (1.7 mm thick) was removed. 

To fabricate the GNP/carbon fiber/epoxy hybrid composites, the appropriate amount of GNP was 

added to 26.4 g EPIKURE Curing Agent W and mixed using a 2 in. diameter disperser blade in a Ross 

high shear mixer HSM-100 LSK-I at 3500 rpm for 150 min. Next the mixture was placed in a Branson 

Sonicator CPX2800H operating at 40 kHz for 60 min at 23 °C. The appropriate amount of epoxy 

(100 g EPON 862 added to 26.4 g of EPIKURE Curing Agent W) was added to the GNP/Curing 

Agent W mixture and stirred with the Ross mixer at 1000 rpm for 3 min at 23 °C. The appropriate amount 

of GNP/epoxy were added to the carbon fiber tow using a winding process to produce a unidirectional 

carbon fiber composite containing the following compositions: 

 1 wt% GNP/67 wt% carbon fiber/32 wt% epoxy 

 2 wt% GNP/67 wt% carbon fiber/31 wt% epoxy 

 3 wt% GNP/67 wt% carbon fiber/30 wt% epoxy 

The uncured GNP/carbon fiber/epoxy composite was cut into sheets and cured as described for the neat epoxy. 

3.3 Field Emission Electron Microscope Imaging 

To image the GNP in the epoxy sample at a relatively high magnification, samples were prepared for 

field emission electron microscopy (FESEM). Thin strips, approximately 2 mm thick by 2 mm wide by 

10 mm long were cut so that the transverse tensile fracture surface would be viewed. The samples were 

sputtered with platinum (2 nm thickness) using an Anatech Ltd. Hummer 6.2 Sputtering System. A 

Hitachi S-4700 FE-SEM at 2.0 kV accelerating voltage was used to view the composites. Figure 14 

shows the transverse tensile fracture surface of a 2 wt% GNP/68 wt% carbon fiber/30 wt% epoxy 

composite. This figure clearly shows the GNP on top of a carbon fiber. 
NASA/TM—2015-218731 15 

3.4 Tensile Testing 

For the neat epoxy and GNP/epoxy composites, a Tensilkut Engineering router was used. The tensile 

properties (at ambient conditions, 16.5 cm long, 3.3 mm thick ASTM Type I sample geometry) were 

determined using ASTM D638 at a crosshead rate of 1 mm/min for reinforced plastics (Ref. 50). An 

Instru-Met Sintech screw driven mechanical testing machine was used. The tensile modulus was 

calculated from the initial linear portion of the stress-strain curve. For each formulation, at least 6 samples 

were tested. Prior to testing, the samples were conditioned at 23 °C and 50 percent relative humidity for 

2 days, which is a standard ambient condition. 

For the carbon fiber/epoxy and GNP/carbon fiber/epoxy composites, tensile bars were cut to 12.7 mm 

wide and a length of 203 mm. Tabbing material (fiberglass/epoxy) was attached to the ends of each 

sample. The tensile properties were determined using ASTM D3039 at a crosshead rate of 2 mm/min for 

fiber reinforced plastics (Ref. 51). The same mechanical testing machine and conditioning was used as 

described in the previous paragraph. 

Table 3 shows the tensile results (mean, standard deviation, and number of samples tested) for the 

neat epoxy, GNP/epoxy composites, carbon fiber/epoxy, and GNP/carbon fiber/epoxy composites. From 

the data it is clear that adding 1 to 3 wt% GNP to carbon fiber/epoxy composites did not cause the axial 

modulus to change significantly. This result is expected due to the large amount and high axial modulus 

of the carbon fiber. 

4.0 Discussion 

This section will discuss the combined computational/experimental results. First, the combined 

results for the GNP/epoxy materials will be covered, followed by the results for the GNP/carbon 

fiber/epoxy hybrid composite. 

 
NASA/TM—2015-218731 16 

4.1 GNP/Epoxy Composite 

Figure 15 shows the combined computational/experimental results for the elastic modulus of 

GNP/epoxy system for 1-4 layers of graphene. There are three important observations from this Figure. 

First, it is clear that increases in GNP volume fraction have a significant effect on the elastic modulus in 

the case of perfect dispersion. For lower levels of dispersion, the influence of GNP on the elastic modulus 

is greatly diminished. Second, the figure shows excellent agreement between the experimental data and 

the 4-layer GNP/epoxy model, suggesting that the computational model is valid and that the experimental 

specimens have, on average, at least 4 GNP layers adhered together. This observation reveals that the 

multiscale model is a powerful tool that can be used to assess the dispersion quality in GNP-reinforced 

polymers. Finally, the data in Figure 15 also indicate that the epoxy crosslink density (shown only for the 

1-layer system for clarity) has a minimal effect on the elastic modulus of the GNP/epoxy composite for 

the crosslink density range considered. 

4.2 GNP/Carbon Fiber/Epoxy Hybrid Composite 

Figure 16 shows the experimentally determined and computationally predicted axial modulus of the 

GNP/carbon fiber/epoxy composite as a function of GNP volume fraction. This figure shows the same 

computational data shown in Figure 12 with the experimental data given in Table 3. There are several 

important points of discussion concerning this figure. First, the agreement between the models and 

experiment validates the multiscale modeling method. However, there are some discrepancies between 

the predictions and the experimental data for the carbon fiber/GNP/epoxy systems. This could indicate 

some error in the properties used for the carbon fiber in the models, or variation in the volume fraction of 

the carbon fiber. Second, the predicted increase in axial modulus is insignificant relative to the 

experimental scatter associated with the experiments (error bars for the experimental data points indicates 

standard deviation from replicate tests). Third, the data indicate that the influence of GNPs on the hybrid 

composite axial modulus is minimal, regardless of the GNP volume fraction. Since the carbon fiber 

dominates the stiffness in the axial direction, it is not practical to use nanoenhanced epoxy to improve the 
NASA/TM—2015-218731 17 

axial stiffness. However, doping the epoxy matrix of a carbon fiber/epoxy system with GNP can provide 

significant transverse and shear reinforcement and improve the performance of the structure in the event 

that it encounters unexpected loads. Moreover, the use of GNP may allow for the minimization of the 

transverse and shear reinforcing plies in the structural design, reducing the overall weight of the structure. 

Finally, the epoxy crosslink density (for the crosslink density range considered herein) has a negligible 

influence on the axial modulus. 

5.0 Conclusions 

In this study a hierarchical multiscale modeling method has been developed and experimentally 

validated to predict the elastic properties of GNP/epoxy composites and GNP/carbon fiber/epoxy hybrid 

composites. The multiscale modeling method incorporates MD simulation on the molecular level and 

micromechanical simulation on the microscopic level. Fabrication and testing of specimens of the 

modeled materials were used to validate the model and to provide insight into the capabilities of the 

modeling method. 

There are four major conclusions from this research. First, the developed multiscale modeling method 

is accurate and can provide physical insight into the mechanical behavior of GNP-reinforced composites. 

This includes the potential to use the method to quantify GNP dispersion via correlation of simulation and 

test data. Second, the GNP volume fraction in the hybrid composite can have a strong influence the 

composite transverse tensile and shear properties. Third, GNP dispersion quality has a strong effect on the 

transverse tensile and shear properties of the composite. Fourth, GNP volume fraction and dispersion has 

a minimal influence on the hybrid composite axial properties where the carbon fiber is the primary 

reinforcement agent. Therefore, GNP-doping in carbon fiber/epoxy composites is most valuable in cases 

where composite parts are designed to transmit significant loads in the direction transverse to the fiber 

alignment or protect the structure against unforeseen loading scenarios. 
NASA/TM—2015-218731 18 

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