Molecular Dynamics for the Prediction

of the Interfacial Shear Stress and

Interface Dielectric Properties of

Carbon Fiber Epoxy Composites

RAJNI CHAHAL, ASHFAQ ADNAN, KENNETH REIFSNIDER,

RASSEL RAIHAN, YUAN TING WU, VAMSEE VADLAMUDI

and MUTHU RAM PRABHU ELENCHEZHIAN

Proceedings of the American Society for Composites—Thirty-third Technical Conference

ABSTRACT

The thermoset epoxy resin Diglycidyl ether of Bisphenol F (EPON 862),

crosslinked with the Diethylene Toluene Diamine (DETDA) hardening agent, are

utilized as the polymer matrix component in many graphite (carbon fiber)

composites. Since it is difficult to experimentally characterize the interfacial region,

computational molecular modeling is a necessary tool for understanding the

influence of the interfacial molecular structure on bulk-level material properties. The purpose of this research is to evaluate and compare the interfacial shear stress

and dipole moment for the pristine carbon fiber composite and the one with the moisture

content at the interface. Molecular models are established for Carbon fiber reinforced

EPON 862-DETDA polymer with and without the moisture content at the interface.

Interatomic interactions are defined by Reactive Force Field (ReaxFF). Material

characteristics such as polymer mass-density and dipole moment are investigated near the

polymer/fiber interface. It is determined that a region exists near the carbon fiber surface in

which the polymer mass density and dipole moment are different than that of the bulk

values. It can further be seen that material having larger values of dipole moment in

interface region have comparatively lesser values of interfacial shear stress.

_____________

1Rajni Chahal, PhD Student, Department of Mechanical & Aerospace Engineering, The University of Texas at Arlington, TX- 76019, U.S.A. 2Ashfaq Adnan, Associate Professor, The University of Texas at Arlington, TX- 76019, U.S.A. 2Kenneth Reifsnider, Director of the Institute for Predictive Performance Methodologies at University of Texas at Arlington Research Institute, TX – 76118, U.S.A. 2Rassel Raihan, Research Engineer at University of Texas at Arlington Research Institute, TX – 76118, U.S.A. 3Yuan Ting Wu Post-Doctoral Student, Department of Mechanical & Aerospace Engineering, The University of Texas at Arlington, TX- 76019, U.S.A. 4Vamsee Vadlamudi, PhD Candidate, Department of Mechanical & Aerospace Engineering, The University of Texas at Arlington, TX- 76019, U.S.A. 4Muthu Ram Prabhu Elenchezhian, PhD Student, Department of Mechanical & Aerospace

Engineering, The University of Texas at Arlington, TX- 76019, U.S.A.

INTRODUCTION

Composites are heterogeneous material systems which are generally made up of

multiple phases (i.e., fiber, defects, matrix, and voids in structural composites)

which have different conductivities. Since, they are substantially light in weight and

deliver other desirable properties, i.e., corrosion and wear resistance, as compared

to metals, ceramics or other materials, they are being used in a variety of different

sectors, especially the aerospace industry. Thermoset epoxy/carbon fiber composites have long been one of the primary

material choices for modern aerospace applications. These materials exhibit an

excellent strength to weight ratio and can be easily manufactured to have specific

performance characteristics.

The aerospace industry certification approach follows a strict fail-safe

philosophy which sometimes restricts the use of many technological breakthroughs.

Reifsnider et al. [1] showed the evidence that dielectric properties can extract

material state information and can be utilized to predict the performance of these

complex material systems. In the current research, it is aimed to observe and

establish similar relation on molecular level. Dielectric investigation of material can get information at different level, i.e.,

polarization mechanisms such as ionic (molecular), dipolar (orientational), electronic,

interfacial (Maxwell–Wagner–Sillars) polarization and hopping charge polarization [2].

The following Figure 1 shows the different types of polarization and their effect on the

dielectric response and its corresponding effective frequency range.

Figure 1. Dielectric response of material constituents at

broad band frequency ranges.

Figure 2. Through thickness measurement of dielectric response for off-

axis loading of woven glass epoxy coupons.

Using Broadband Dielectric Spectroscopy (BbDS), Raihan et al. studied the

dielectric response of woven cross ply glass reinforced epoxy composite measured

through the thickness of the coupons and those results were compared with all other

variables. [3] An example of those data is shown in Figure 2, along with a general

interpretation of the relationship of the micro-details with the dielectric

measurements. The changes in dielectric response are not monotonic; they show

unique changes in magnitude and direction depending on the changes in the

mechanisms of damage. It was observed over a wide range of composite materials

and applied conditions (mechanical, thermal, electrical, chemical) that the through

thickness dielectric response is directly and uniquely related to the internal

microstructure and changes in local morphology Nandini et al. studied the dielectric responses of degraded and non-degraded

composite prepreg materials. The partial crosslinking was observed which showed

the result of decrease in the dielectric parameters. [4] Also, from the static tensile

test it was proved that the mechanical strength was lesser for the degraded sample

and the dielectric relaxation strength was higher as shown in Figure 3. Dielectric

relaxation Strength (DRS) is the difference of the real part of the dielectric property

between lower and high frequency.

Figure 3. Dielectric Response vs. Mechanical Strength of

degraded and non-degraded composites.

Polar molecules are contained inside of heterogeneous materials and may have

interfaces with different electrical properties. In the presence of an applied electric

field it will polarize the material by orienting the dipole moments of polar

molecules and charge accumulation at the interfaces of dissimilar materials. Molecular Dynamics is a computational tool for understanding the interfacial

behavior of heterogeneous materials such as CFRP composites. Chunyu Li et al. [5]

used COMPASS force-field to observe the interface of crosslinked epoxy in the

presence of carbon fiber and calculated it’s mechanical. Hadden [6] used OPLS

United Atom force-field developed by Jorgensen and co-workers to study the

tensile and shear properties of Carbon Fiber reinforced epoxy composites.

Whereas traditional force fields are unable to model chemical reactions because

of the requirement of breaking and forming bonds (a force field's functional form

depends on having all bonds defined explicitly), Reax Force Field (ReaxFF)

eschews explicit bonds in favor of bond orders, which allows for continuous bond

formation/breaking. In the ReaxFF, the potential energy is defined as a function of

bond order with energy penalties for nonequilibrium configurations. The ReaxFF

was initially developed to model bond dissociation and formation in carbon-based

materials [7]. Odegard et al. [8] proved ReaxFF to be working for bulk epoxy

system using parameters obtained by Liu et al. [9].

An important part of ReaxFF is the charge equilibration procedure. Charge

equilibration (QEq) procedure [10] approximates the partial charges on atoms by

minimizing the electrostatic energy of the system. Charge equilibration is

mathematically formulated as the solution of a large sparse linear system of

equations. This solve needs to be performed accurately at each time-step because it

significantly impacts forces and total energy of the system. Since partial charges on

atoms are fixed in conventional MD, this is not a consideration for conventional

methods. Chakrabarty et al. [11] studied the piezoelectric properties of carbon

nanotube polymer nanocomposites using Dreiding Force Field. In this paper, we have used ReaxFF force-field to study the interfacial and

dielectric properties of Carbon Fiber/EPON 862-DETDA nanocomposite system.

Molecular dynamics study is performed to evaluate interfacial shear stress (ISS) and

dipole moment for carbon fiber composites. Mechanical and electrical properties,

such as interfacial shear strength and dipole moment have been calculated and

compared for both pristine carbon fiber composite systems and systems having

moisture content at their interfaces.

MOLECULAR STRUCTURE OF CARBON FIBER/EPOXY

SYSTEM Carbon Fiber

At the molecular level carbon fibers consist of stacked layers of graphene. This

is a two-dimensional layer with carbon-carbon sp2 hybridized covalent bonds that

result in outstanding mechanical properties [15].

Figure 4. Predicted internal structure for carbon fibers, surface atom structures, and

aromatic carbon ring structure. Image courtesy of NASA Report 4084 © L.T.

Drzal [15].

For the creation of the graphite surface, a program was written to create sheets of

carbon based on the aromatic pattern for which graphite surfaces are well known. The

simulated graphite surface was constructed from 3 sheets of stacked graphene, each

sheet containing 448 carbon atoms for a total of 1344 atoms. The graphene sheets were

oriented along the x-y plane, with periodic boundary conditions in the x and y-

direction, and had an interlayer spacing of 3.35Å. The graphite structures were relaxed

using a series of MM and MD simulations in LAMMPS [16]. While equilibrating the

graphite, the z-direction box coordinate was chosen to implement interlayer spacing for

periodic boundary conditions. Thus, the top surface was influenced by the bottom

surface and visa-versa, representing many layers of bulk graphite. Initial graphite

structures are shown in Figure 4 as visualized in Ovito [17].

Figure 5. Carbon Fiber.

After equilibration, Graphite density is 2.2 g/cc, while the reported density =

2.09– 2.23 g/cm³.

Epoxy

The modeled epoxy system was composed of 64 EPON 862 (Diglycidyl ether of

Bisphenol F) crosslinked with 32 DETDA (Diethylene Toluene Diamine) molecules [18]. Figure 4 shows the molecular structure of EPON 862 monomer & DETDA

before crosslinking. During the crosslink process, each amine group in DETDA can

react with two epoxide groups in EPON 862. Therefore, a molar ratio of 2:1 of

EPON 862 to DETDA molecules is necessary for a stoichiometric mixture.

Figure 6. Molecular Structures of EPON 862 and DETDA monomers.

64 EPON-862 & 32 DETDA molecules are put in a larger box and is minimized

and equilibrated using ReaxFF with the parameterizations of Liu et al. [9]. The initial

density of the system was 0.3 g/cc. The model was further allowed to shrink under NPT

ensemble for nearly 150 ps at 300 K, using 0.1 fs of timestep. After this step, the final

density of epoxy system was 1.12 g/cc. To release the residual stresses in the system,

equilibration is performed in NVT ensemble for 50 ps at the same timestep. Average

residual stress after this step is close to zero. Figure 7 shows typical molecular structure

of equilibrated and crosslinked EPON-DETDA molecules.

Figure 7. Molecular structure of equilibrated and densified Epoxy with ReaxFF. Coloring scheme: CPK.

CARBON FIBER/EPOXY SYSTEM:

Without Water Content

The nano-scale material system in this study is composed of Carbon fiber and

EPON 862-DETDA matrix. Specifically, a Carbon fiber is embedded in polymer

matrix. Previously equilibrated and compressed small epoxy blocks are put above and

below the Carbon fiber. The size of Carbon fiber was previously chosen such that its

length and width was approximately equal to the size of two epoxy blocks put together

in x and y direction. Therefore, final model is having 8 epoxy blocks each above and

below the fiber. This model contains 8784 atoms including 1344-C-atom Carbon fiber,

128 EPON 862 & 64 DETDA molecules. The dimensions of the system are ~ 3.5 x 3.5

x 8 nm. Average density of the system is ~ 1.18 g/cc after equilibration.

Figure 8. Molecular model of Carbon fiber inside epoxy matrix. Coloring scheme: CPK.

In the molecular dynamics, the entire material system is represented with the

ReaxFF potential. The system is replicated across periodic boundaries in each of the

3-dimensions, thereby making Carbon fiber & polymer chains infinitely long.

Before equilibration, a minimization is performed to find configuration that will

hopefully be in local potential energy minimum, and the new atom positions to be

computed. This model is further equilibrated in NVT ensemble for 70 ps at a

timestep of 0.1 fs. Figure 8 shows the final CF/epoxy model after minimization and

equilibration, which is ready for pull-out simulations.

With Water Content

Epoxy has been believed to absorb moisture from the atmosphere by diffusion

[14, 19, 20]. The absorbed moisture eventually finds its way to the interface and is

available for hydration of the interface. In this study, 10 water molecules (0.531% w/w) are included at both the interface

regions of Carbon fiber and epoxy. The final model contains 8844 atoms including

1344-C-atom Carbon fiber, 128 EPON 862 & 64 DETDA molecules. The dimensions

of the system are ~ 3.5 x 3.5 x 8 nm. Average density of the system is ~ 1.181 g/cc.

Figure 9. Molecular model of Carbon fiber inside contaminated epoxy matrix. Coloring scheme: CPK.

This model is further minimized and equilibrated for 100 ps at a timestep of 0.1 fs. Figure 9 shows the final CNT/epoxy model after minimization and equilibration.

RESULTS AND COMPARISONS

Interfacial Shear Stress Calculation

PULLOUT SIMULATIONS OF PRISTINE & CONTAMINATED CARBON

FIBER REINFORCED COMPOSITE

The simulation cell with periodic boundary condition in y-z plane as shown in

Figure 8(a) is composed of a fragment of Carbon fiber totally embedded inside

EPON-DETDA matrix. To capture the complete pull-out of Carbon fiber from

epoxy matrix, periodic condition has been removed in the pullout-direction (i.e. x

direction). Size of simulation cell in pullout-direction of Carbon fiber is chosen to

be slightly larger than the Carbon fiber length. This prevents Carbon fiber from

going out of the simulation cell after it has been completely pulled out of epoxy

matrix. Box dimensions are 8 x 3.5 x 8 nm.

Figure 10. Snapshots from the MD Simulation of Carbon Fiber Pullout from Pristine CFRP.

The pull-out simulations of Carbon fiber from epoxy matrix are carried out by

applying a constant velocity of 0.01 Å/fs to approximately 3 Å layer of carbon atoms at

the pullout side of Carbon fiber. Nearly 3 Å right and left part of epoxy matrix is held

fixed during the pullout. The simulation is run for ~ 40,000 MD time steps of 0.1 fs.

Figure 11. Snapshots from the MD Simulation of Carbon Fiber Pullout from Contaminated CFRP.

Interfacial Shear Stress Calculation

In the carbon fiber reinforced composites, the bonding strength between the

Carbon fiber and epoxy resin can be evaluated by interfacial bonding energy. The

nature of interfacial bonding energy primarily comes from the electrostatic and van

der Waals forces in the molecular system. The initial and final total energy of the pullout simulation for pristine CFRP and

contaminated CFRP are listed in Table I. The potential energy of both the CFRP system

increased as the Carbon fiber was pulled out of the epoxy. In the pullout simulation, the

entire Carbon fiber and epoxy resin were not held fixed. The potential energy of the Carbon

fiber and epoxy resin increased due to the changes of their configurations during the

pullout. The deformation of the Carbon fiber and epoxy resin during the pullout has

influence on the pullout energy [21]. After the pullout, the difference in final and

initial potential energies was noted for both the cases. Gou et al. [21] defined the pullout energy as:

(1)

In the same reference, Gou et al. defined the relation between pullout energy

and interfacial shear strength for the case when fiber has circular cross-section. This

can be modified to relate pullout energy and interfacial shear strength for

rectangular fiber cross-section:

2

(2)

(3)

Where:

L = Length of the Carbon Fiber in pullout-

direction b = Width of the Carbon Fiber

TABLE I. EFFECT OF MOISTURE CONTENT ON ISS VALUE OF CFRP.

Model EInitial

Interfacial Shear

EFinal EPullout Stress, ISS

(kcal/mol) (kcal/mol) (kcal/mol) (Mpa)

CFRP 1118328.3 1119250.5 922.2 188

(Pristine) CFRP

(Moisture Content = 1124884.9 1125453.6 568.7 116

0.53 % w/w)

From equation (1) & (2), the interfacial shear strength between the carbon fiber

and epoxy was calculated to be about 188 MPa & 116 MPa for pristine &

contaminated CFRP, respectively.

Dipole Moment Calculation

In the electrically heterogeneous material, dispersion occurs in the bulk properties

from the charging of the interfaces within the material. This phenomenon does not arise

from dielectric relaxation in the bulk phases of the material, but it is a consequence of

the boundary conditions on the field at the interfaces between phases. The dielectric behavior is associated with the non-uniform distribution of free

electronic charges across the interface between the dissimilar dielectric materials

under the influence of electric field. Carbon fiber and epoxy have their own free

charge carries concentration and associated charge carries mobility. To achieve

current continuity through materials 1 and 2 there will have to be a charge carrier

concentration discontinuity across the interface. This interfacial charge build-up or

polarization, as function of frequency gives rise to the dielectric dispersion

exhibited by inhomogeneous system [22].

In physics, the electric dipole moment is a measure of the separation of positive

and negative electrical charges within a system, that is, a measure of the system's

overall polarity [23].

Figure 12 shows pristine and contaminated CFRP under the influence of

Positive electric field of magnitude 0.2 eV.

(a) (b) Figure 12. (a) Pristine CFRP Under Positive Electric Field, (b)

Contaminated CFRP Under Positive Electric Field.

After the application of electric field, compute dipole/chunk command has been

used to calculate the dipole moment for the specified chunk thickness along z-direction.

This compute calculates the x, y, z coordinates of the dipole vector and the total dipole

moment for each chunk, which includes all effects due to atoms passing through periodic

boundaries. For chunks with a net charge the resulting dipole is made position independent

by subtracting the position vector of the center of mass or geometric center times the net

charge from the computed dipole vector. Figure 13 & 14 show the variation of average total

dipole moment calculated over a slice (in x-y plane) of thickness = 0.5

Å for the pristine & contaminated composite system, respectively.

Figure 13. Average Dipole Moment of Pristine CFRP along simulation box Z-axis.

Figure 14. Average Dipole Moment of Contaminated CFRP

along simulation box Z-axis.

Further, to calculate average interfacial dipole moment, dipole moment values

have been averaged for the interface regions in Figure 13 & 14. The calculated values for the average interfacial dipole moment are reported in

Table II below.

TABLE II. EFFECT OF DIRECTION OF ELECTRIC FIELD (EZ = ± 0.2 V/Å) ON

AVERAGE DIPOLE MOMENT OF PRISTINE AND CONTAMINATED CFRP.

Average Dipole Moment Average Dipole Moment

Model (charge*Å) (charge*Å)

Ez = 0.2 V/ Å Ez = -0.2 V/ Å

CFRP 5.99 6.07

(Pristine)

CFRP 10.8 10.9 (Moisture Content = 0.531 % (80.3 % increase) (79.6 % increase)

w/w)

Table II shows that percentage increase in the average values for dipole moment

for pristine CFRP and the moisture absorbed CFRP also seems to be independent of

the direction of electric field (Ez = ± 0.2 V/Å). It is nearly 80 % in both the cases.

TABLE III. COMPARISON OF ISS AND AVERAGE DIPOLE MOMENT FOR

PRISTINE AND CONTAMINATED CFRP.

ISS Average Dipole Moment

Model (MPa) (charge*Å)

@Ez = 0.2 V/ Å

CFRP 188 5.99

(Pristine)

CFRP 116 10.8 (Moisture Content = 0.531 % (38.30 % decrease) (80.3 % increase)

w/w)

We know that Polarization Density is directly proportional to Dipole Moment.

Thus, Dipole Moment, hence polarization, increases if there are external impurities

(here water) are present at the interface.

CONCLUSIONS

Reactive force field is used to evaluate the mechanical (Interfacial Shear Stress)

and electrical (Dipole Moment) properties of Pristine and Contaminated carbon

fiber reinforced epoxy composite. As calculated from pullout simulations, the ISS

value for Pristine CFRP is found to be 188 MPa, while the ISS value is lowered to

116 MPa when 0.531 % w/w moisture content was present in the system. Further,

average dipole moment is evaluated at the interface region of Pristine and

Contaminated CFRP is 5.99 charge x Å and 10.8 charge x Å, respectively.

It can be observed that for pristine composite system, value of dipole moment is

lower than that for composite with water content at the interfaces, while it has better

Interfacial Shear Stress than latter. It seems to be consistent with the experimental

results obtained by Reifsnider et al. [1]. Therefore, lesser the value for interfacial

dipole moment, hence interfacial polarization, better are the mechanical properties

(interfacial shear stress) of the composite material. As predicted by Tan et al. [11] in certain cases, the effect of Efield could not be

completely observed due to the charge equilibration (QEq) [10, 12] method used in

the simulations. With the further development of this method, such as the

polarizable charge equilibration method (PQEq), the polarization can be better

described to reveal more details of the effects of Efields in molecular simulations.

REFERNCES

1. Reifsnider, K. L., Fazzino, P., Majumdar, P. K., & Xing, L. 2009. “Material state changes

as a basis for prognosis in aeronautical structures,” Aeronautical Journal, 113(1150), 789-

798 (Silver Award, 2010, Royal Aeronautical Society). 2. Kremer F., Schoenhals A., Broadband Dielectric Spectroscopy, in Springer-Verlag, 2002.

3. Raihan, R., Adkins, J. M., Baker, J., Rabbi, F., & Reifsnider, K. "Relationship of dielectric

property change to composite material state degradation." Composites Science and

Technology 105 (2014): 160-165.

4. Nandini, A., Shute, N., Elenchezhian, M.R.P., Vadlamudi, V., Raihan, R., Reifsnider, K.,

“Dielectric property investigation of degraded pre-preg and performance prediction of the

final composite part” Proceedings of SAMPE 2018, Long Beach CA May 21-24 2018.

5. Li, C., et al. 2012. “Atomistic simulations on multilayer graphene reinforced epoxy

composites,” Composites Part A: Applied Science and Manufacturing. 43(8): p. 1293-1300. 6. Hadden, C. 2015. "Molecular Modeling of Epon 862-Detda / Carbon Composites,"

Dissertation, Michigan Technological University. 7. van Duin, A.C.T., Dasgupta, S., Lorant, F., and Goddard, W.A. 2001. “ReaxFF: A reactive force

field for hydrocarbons,” Journal of Physical Chemistry A, 105(41): 9396-9409.

8. Odegard, G.M., Jensen, B.D. 2014. “Predicting mechanical response of crosslinked epoxy

using ReaxFF,” Chemical Physics Letters, Volume 591, Pages 175-178. 9. Liu, L.C., Liu, Y., Zybin, S.V., Sun, H., and Goddard, W. A. 2011. “ReaxFF-/g: Correction of

the ReaxFF Reactive Force Field for London Dispersion, with Applications to the Equations of

State for Energetic Materials,” Journal of Physical Chemistry A. 115(40): 11016-11022. 10. Rappé, A. K. & Goddard, W. A. 1991. “Charge Equilibration for Molecular Dynamics

Simulations,” J. Phys. Chem. 95, 3358–3363. 11. Tan, S., Xia, T., Shi, Y., Pfaendtner, J., Zhao, S., & He, Y. 2017. “Enhancing the Oxidation

of Toluene with External Electric Fields: a Reactive Molecular Dynamics Study,”

www.nature.com/scientificreports. 12. Aktulga, H. M., Fogarty, J. C., Pandit, S. A. & Grama, A. Y. 2012. “Parallel reactive molecular

dynamics: Numerical methods and algorithmic techniques,” Parallel Comput. 38, 245–259.

13. Chakrabarty, A. 2008. “Carbon Nanotube Polymer Nanocomposites for Electromechanical

System Applications,” Doctoral dissertation, Texas A&M University. 14. Frankland, S.J.V. & Hinkley, J.A. 2008. “Molecular Dynamics Simulations of Adhesion at

Epoxy Interfaces,” NASA Technical Report. 15. Drzal, L. T., Bascom, W. D. 1987. “The surface properties of carbon fibers and their

adhesion to organic polymers,” Report/Patent Number: NASA-CR-4084, NAS 1.26:4084. 16. Plimpton, S. 1995. “Fast Parallel Algorithms for Short-Range Molecular Dynamics,” J

Comp Phys, 117, 1-19.

17. Stukowski, A. 2010. “Modelling Simul. Mater. Sci. Eng.,” 18, 015012.

18. Komuves, F., Kelkar, D. A., Mohan, R., and Kelkar, A. V. 2011. "Prediction of Mechanical

Properties of EPON 862 (DGEBF) cross-linked with Curing Agent W (DETDA) and

SWCNT using MD Simulations," in 52nd AIAA/ASME/ASCE/AHS/ASC Structures,

Structural Dynamics and Materials Conference, Denver. 19. El-Sa'ad, L., Darby, M. I. & Yates, B. 1990. “Moisture absorption by epoxy resins: the

reverse thermal effect,” Journal of Material Science 25, 3577-3582. 20. De'Nève, B. & Shanahan, M.E.R. 1993. “Water absorption by an epoxy resin and its effect on

the mechanical properties and infrared spectra,” Polymer, Volume 34, Issue 24, Pages 175-178.

21. Gou, J., Minaie, B., Wang, B., Liang Z., and Zhang, C. 2005. "Computational and

experimental study of interfacial bonding of single-walled nanotube reinforced

composites," Computational Materials Science, vol. 31, pp. 225-236.

22. Raju, G.G. 2003. “Dielectrics in Electric Field,” New York: Marcel Dekker.