Supplementary Materials

Shock Engineering the Additive Manufactured graphene-metal nanocomposite with high

density nanotwins and dislocations for ultra-stable mechanical properties

Dong Lin1, Maithilee Motlag1, Mojib Saei1, Shengyu Jin1, Raheleh Mohammad Rahimi3,

David Bahr3, Gary J. Cheng1,2,3,*

1 School of Industrial Engineering, Purdue University, West Lafayette, Indiana, USA-47907.

2 School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA-47907.

3 School of Materials Engineering, Purdue University, West Lafayette, Indiana, USA-47907.

MD simulation of crack propagation process in the iron-graphene nanocomposite

The simulations were performed by molecular dynamics simulation package LAMMPS 1 and OVITO 8 was used to visualize the results. Non-equilibrium molecular dynamics (NEMD) simulations were conducted to simulate the crack propagation process in the iron-graphene nanocomposite and to study the effect of graphene and the interface of twinned boundaries of iron on the crack propagation. Finnis-Sinclair embedded atom method (EAM/FS) was used to model the atomic behavior of iron 4. The inter particle interactions between Carbon and Iron atoms were defined using Lennard -Jones potentials obtained from the Lorentz-Berthelot mixing rule and adaptive intermolecular reactive empirical bond order (AIREBO) potential 2 was employed for Carbon-Carbon interaction.

Periodic boundary conditions were imposed along thickness (Z direction) of the specimen. The system was equilibrated using energy minimization at 300 K via Nose-Hoover thermostat. A pre-crack with approximate 10 % of the length of the specimen was created by deleting two atomic layers of atoms. Each specimen was approximately 360 ×230 × 30 Å. Deformation controlled simulations were carried out by applying strain rate of 0.01 ps-1 in Y direction. Strain increment was applied to the nanostructure after every time step (0.1 fs).

Effects of shock strengthened graphene/metal interface on crack propagation

Molecular dynamics modeling was conducted to understand the effects of the hybrid

microstructure, consisting of graphene/metal interface reinforced with nanotwining, on the crack

propagation behavior (see supplementary materials for details of the MD simulation). A pre-

crack with approximate 10 % of the length of the specimen was created. Graphene/metal

interface with and without nanotwining was generated in two computation cells respectively.

Deformation controlled simulations were carried out by applying strain rate of 0.01 ps-1 in Y

direction. Fig. S1A illustrates the evolution of crack tip with time for both the configurations.

As the crack propagates, graphene did not break in either of graphene/metal composite

nanostructures, however, impede the crack from propagate through the structure. In the case of

graphene/metal without nanotwining, the shear stress at graphene-iron interface was higher than

the interfacial shear strength between graphene and iron which caused the sliding of graphene

and crack propagation through the graphene/metal interface. While in the case of

graphene/metal with nanotwining, hierarchical twin bands were generated with high density of

dislocation emissions from the twin boundaries with advent of crack propagations. The kink

bands were formed in the graphene/metal with nanotwining (See Fig. S1B), which provide

additional strengthening mechanism and increased ductility in the graphene/metal

nanocomposite. The stress/strain curves during the deformation of the cells were plotted in Fig.

S1C. There is strong work hardening in the metal/graphene with nanotwining due to the

interaction of cracks and nanotwining, while there is no work hardening in the metal/graphene

without nanotwining and necking occurs at small amount of strain. The dips and the fluctuations

in stress strain curve of nanotwining strengthened graphene/metal structure indicates the

interaction of crack with the twin boundaries, while there were no fluctuations for the case of

metal/graphene without nanotwining. This nanotwining strengthened graphene/metal interface

significantly reduced the crack propagation rate (Fig. S1D). For the nanotwin strengthened

graphene/metal interfacial structure, the crack growth rate decreased and several marked plateaus

observed in the crack growth curve, as the crack interacts with the nanotwins.

Figure S1 │ (A) Evolution of crack tip in nano-twinned configuration. B) Observation of secondary twins in Twinned-Iron-Graphene Nanocomposite from MD simulation. (C) The stress strain relationship during the deformation of the cells in fig S1A. (D) Crack propagation rate of the graphene/Iron structure with and without nanotwins.

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4. Mendelev MI, Han S, Srolovitz DJ, Ackland GJ, Sun DY, Asta M. Development of new interatomic potentials appropriate for crystalline and liquid iron. Philosophical Magazine 83, 3977-3994 (2003).