Multiscale methods for graphene based nanocomposites

Nanocomposites for Aerospace Applications Symposium, NSQI, Bristol, 12/02/2013

www.bris.ac.uk/composites

Acknowledgements

Nanocomposites for Aerospace, KTN

S. Adhikari, Y. Chandra, R. Chowdhury, J. Sienz, C. Remillat, L. Boldrin, E. Saavedra-

Flores, M. R. Friswell

Royal Society of London, European Project FP7-NMP-2009- LARGE-3 M-

RECT, A4B and WEFO through the WCC and ASTUTE projects

Content

Nanocomposites for Aerospace, KTN

Rationale

The hybrid atomistic-FE multiscale approach

Examples

Epoxy/graphene nanocomposite models

Developments and conclusions

Rationale

Nanocomposites for Aerospace, KTN

DGEBA/33DDS with (a) a parallel MLG, and (b) a normal MLG, after 400 ps NPT equilibration

(Li et al., 2012. Comp. Part A, 43(8), 1293)

• MD simulations using Dreiding and COMPASS force models • Composite with DGEBA/33DDS and MLG • 69,120 atoms à large CPU times involved in parallel processor machine

Rationale

Nanocomposites for Aerospace, KTN

• MD and DFT tools are used mainly by the physics and chemistry community à engineers tend to use CAE/FEA tools

• MD and DFT methods are very computational expensive for large systems, accurate in predicting mechanical and electronic properties

• Continuum mechanics models (like FEA) are used to design composites

Can we bridge between MD/DFT and continuum mechanics?

Hybrid atomistic – FE in sp2 CC bonds

Nanocomposites for Aerospace, KTN

• Atomic bonds are represented by beam elements

• Beam properties are obtained by energy balance

Utotal =Ur +Uθ +Uτ

Ur =12kr Δr( )2 Uθ =

12kθ Δθ( )2 Uτ =

12kτ Δφ( )2

Uaxial =12Kaxial (ΔL)

2 =EA2L(ΔL)2

Utorsion =12Ktorsion (Δβ)

2 =GJ2L(Δβ)

Ubending =12Kbending (2α)

2 =EI2L4+Φ1+Φ

(2α)2

(Li C, Chou TW, 2003. Int. J. Solid Struct. 40(10), 2487-2499) (Scarpa, F. and Adhikari, S., Journal of Physics D: Applied Physics, 41 (2008) 085306)

Hybrid atomistic – FE in sp2 CC bonds

Nanocomposites for Aerospace, KTN

(Scarpa, F. and Adhikari, S., Journal of Physics D: Applied Physics, 41 (2008) 085306)

The structural mechanics approach

Nanocomposites for Aerospace, KTN

The equivalent mechanical properties of the CC-bond beams are input in a FE model representing a 3D structural frame

[ ]{ } { }fuK = [K] à stiffness matrix {u} à nodal displacement vector {f} à nodal force vector

(Li C, Chou TW, 2003. Int. J. Solid Struct. 40(10), 2487-2499)

The graphene nanostructure is then represented as a truss

assembly either in graphitic or corrugated shape

Examples – buckling of carbon nanotubes

Nanocomposites for Aerospace, KTN

(a) Molecular dynamics

(b) Hyperplastic atomistic FE (Ogden strain energy density function )

Comparison of buckling mechanisms in a (5,5) SWCNT with 5.0 nm length. (Flores, E. I. S., Adhikari, S., Friswell, M. I. and Scarpa, F.,

"Hyperelastic axial buckling of single wall carbon nanotubes", Physica E: Low-dimensional Systems and Nanostructures, 44[2] (2011), pp. 525-529)

Examples – graphene

Nanocomposites for Aerospace, KTN

Circular SLGS (R = 9: 5 nm) under central loading. Distribution of equivalent membrane stresses. 8878 atoms

Deformation of rectangular SLGS (15.1 x 13.03 nm2) under central loading. ~ 7890 atoms

Scarpa, F., Adhikari, S., Gil, A. J. and Remillat, C., "The bending of single layer graphene sheets: Lattice versus continuum approach", Nanotechnology, 21[12] (2010), pp. 125702:1-9.

Examples – graphene

Nanocomposites for Aerospace, KTN

Scarpa, F., Adhikari, S., Gil, A. J. and Remillat, C., "The bending of single layer graphene sheets: Lattice versus continuum approach", Nanotechnology, 21[12] (2010), pp. 125702:1-9.

0 0.5 1 1.5 2 2.5 30

5

10

15

20

25

30

35

w/d

FR2 /Y/d3

Lattice R = 2.5 nmContinuum R = 2.5 nmLattice R = 5.0 nmContinuum R = 5.0 nmLattice R = 9.5 nmContinuum R = 9.5 nmEq. (17)

0 0.5 1 1.5 20

5

10

15

20

25

30

35

w/d

F a

b/Y/

d3

Lattice a = 3.88 nmContinuum a = 3.88 nmLattice a = 5.0 nmContinuum a = 5.0 nmLattice a = 15.1 nmContinuum a = 15.1 nmEq. (18)

circular SLGS rectangular SLGS

Examples – bilayer graphene

Nanocomposites for Aerospace, KTN

Scarpa, F., Adhikari, S. and Chowdhury, R., "The transverse elasticity of bilayer graphene", Physics Letters A, 374[19-20] (2010), pp. 2053-2057.

• Equivalent to structural “sandwich” beams • C-C bonds in graphene layers represented with classical equivalent beam models • “Core” represented by Lennard-Jones potential interactions:

Ef =0.5 TPa (I.W. Frank, D.M. Tanenbaum, A.M. van der Zande, P.L. McEuen, J. Vac. Sci. Technol. B 25 (2007) 2558)

Epoxy/SLGS nanocomposite

Nanocomposites for Aerospace, KTN

Chandra, Y., Chowdhury, R., Scarpa, F., Adhikari, S. and Seinz, J., "Multiscale modeling on dynamic behaviour of graphene based composites", Materials Science and Engineering B, in press.

Polymer Matrix

van der Waals interaction

Graphene sheet

0 5 10 15 200

50

100

150

200

250

t1 (G

Hz)

Length (nm)

ArmchairïGRP2ZigzagïGRP4

Epoxy/SLGS nanocomposite

Nanocomposites for Aerospace, KTN

Continuous SLGS reinforcement Short SLGS reinforcement

• RVE representing 0.05 wt % of SLGS with epoxy matrix • Epoxy represented by 3D elements with 6 DOFs and Ramberg Osgood approximation (E = 2 GPa) • SLGS with 1318 beam elements max • LJ interactions by 21,612 nonlinear spring elements • Short and long (continuous) SLGS inclusions • Full nonlinear loading with activation/deactivation of LJ springs based on cut-off distance • Coded in ABAQUS 6.10 • Models with different orientations in space

Epoxy/SLGS nanocomposite

Nanocomposites for Aerospace, KTN

Direction || to loading

Direction 45o to loading

Epoxy/SLGS nanocomposite

Nanocomposites for Aerospace, KTN

Model compares well with single/few layer graphene-epoxy composites existing in open literature in terms of stiffness and strength enhancement

(Chandra Y., Scarpa F. , Chowdhury R. Adhikari S., Sienz J. Multiscale hybrid atomistic-FE approach for the nonlinear tensile behaviour of graphene nanocomposites. Comp. A 46 (2013), 147)

Developments and conclusions

Nanocomposites for Aerospace, KTN

(Adhikari S., E. Saavedra-Flores, Scarpa F. Chowdhury R., Friswell M. I., 2013. J. Royal Soc. Interface. Submitted)

Significant potential for multiphysics

modelling using FEA and bridging length

scales

Possibility of coding in any commercial FEA code à can be used by stress engineers and designers

Large possibilities of multiphysics loading and material properties – from embedding viscoelasticity, thermal and piezoelectric environment to crack propagation simulation

Can be extended to non CC bonds and represent other chemical groups (Example: DNA modelling)

Nanocomposites for Aerospace, KTN

Thanks for your kind attention

Any question?