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Molecular Dynamics Simulations of Dynamic Friction and Mixing at Rapidly Moving Material Interfaces. Nicholas Epiphaniou, Dimitris Drikakis & Marco Kalweit Fluid Mechanics & Computational Science (FMCS) Group, Aerospace Sciences Department Cranfield University & Graham Ball
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Molecular Dynamics Simulations of Dynamic Friction and Mixing at Rapidly Moving Material Interfaces Nicholas Epiphaniou, Dimitris Drikakis & Marco Kalweit Fluid Mechanics & Computational Science (FMCS) Group, Aerospace Sciences Department Cranfield University & Graham Ball AWE, Aldermaston
Project’s Objectives Objective: • To investigate dynamic friction at material interfaces • To investigate the connection between velocity weakening and structural transformation of nano-crystalline materials. • To develop hybrid MD-Continuum approaches in order to investigate the time-dependent behaviour of the sliding interfaces. Outline of presentation: • Molecular dynamics techniques. • Dynamic friction simulations. • Results for temperature variation and diffusion across the interface. • Conclusions and future work.
Molecular Dynamics Method • Based on Born-Oppenheimer approximation which is the basis for removing the electrons from the model and make effective interatomic potential energies as given functions of the relative positions of the atoms. • Simulation of thermal vibration of atoms is a classical way for solving the equation of motion. • Atomic momenta, atomic positions, atomic trajectories. • The most important parameter is the interatomic potential which determines the accuracy of the simulation. Widely used potentials are EAM & Lennard Jones methods. • Time scale and size also play a vital role for realistic simulations. Large systems may involve up to millions of atoms.
Schematic Representation of Simulation Cell Forces are acting on the reservoirsReservoirs are thermostatted at 298K, and contained the same atoms as the bulk. PBC used in x and z direction.The system is brought to equilibriumFn is 5.1GPaFt is an average force acting in such that atoms experience the same force at each time step. The atoms’ velocities remain constant Cu block Ag block
LANL and Cranfield’s (FMCS) MD models LANL: • Sliding of Cu (010) on Ag(010) in the <100> direction • Molecular system of 2.8M atoms • 3D Embedded Atom Method (EAM) potentials • Normal pressure 5.1 GPa • MD code: SPaSM (Scalable Parallel Short-range Molecular Dynamics) Cranfield: • MD code: LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) • MD simulations using 1.3M atoms
Molecular Dynamics Results • Validation of Cu/Ag interfaces • Plots of frictional force per unit area against velocities i.e. Velocity weakening phenomenon at domain size of (300, 600, 100)Å (containing 1.3M atoms) • Comparison with LANL1 system domain of (410, 320, 330)Å • Temperature variation across the interfaces at various speeds. • Microstructure characteristics at low and high speeds. • Mean square displacement plots (MSD) • Concentration gradient plots 1. J. E. Hammerberg and T. C. Germann and B. L. Holian and R. Ravelo, Nanoscale Structure and High Velocity Sliding at Cu-Ag Interfaces, (2004)Materials Research Society Symposium Proceedings.
Plot of Velocity Dependence of Frictional Force The frictional force is representing by a power law: Domain size: Cranfield model x=300, y=600, z=100 (Å) (~1.3Million Atoms) LANL x=410, y=320, z=330 (Å) (~2.8Million Atoms)
Microstructure at Various Speeds • Our results confirm that there is a relation between structural transformation and velocity weakening at high velocities; the above are associated with the generation and localisation of plastic deformation. • At low speeds (up to 25m/s) there are no significant dislocations in both materials. • Defects are appearing in both slabs as speed is increasing (greater than 50 m/s) • At early times dislocations start to appear near the interface. • At later times dislocations are reaching the reservoirs.
Microstructure at Various Speeds • Blocks of Cu and Ag are visualised using VMD and AtomEye softwares. Atoms are coloured according to centrosymmetric parameter. Atoms with perfect FCC are excluded from the pictures. Speed of 25m/s 400m/s
VMD Snapshots 400m/s 200m/s
Mean Square Displacement (MSD) • MSD is a measure of the average distance a molecule travels. • The slope of MSD represents the diffusivity of the material.
MSD Plots at Various Speeds • Domain Size of (x,y,z) = (300,600,100) Å
Concentration Gradient Plots Interfacial Region = 14 Å Interfacial Region = 24.5 Å
Concentration Gradient Plots Interfacial Region = 38.5 Å Interfacial Region = 91 Å
Conclusions • The atomic modes of interfacial interaction operate at time and length scales far shorter than traditional experiments. Energy dissipation is still an issue in dynamic friction, this is because it is linked to time and spatial scales. • The nanoscale physics discussed through LANL and our simulations can be used as an input to mesoscale techniques. • Completing the model of friction requires further investigation of the energy dissipation using additional theories at the mesoscale. Future Work • Using the 1-D Hydrocode to study the materials of interest i.e. Cu/Ag at high speeds and compression forces. Compare with molecular dynamics studies • Coupling between MD and Hydrocode by performing simulation and comparing results with experimental studies, possibly using other materials of interest such as Al/Ta.
Centro-symmetry A centrosymmetic material has pairs of equal and opposite bonds and to its nearest neighbour Vectors connecting the six pairs of nearest neighbours surrounding a given atom in a relaxed FCC lattice. When material is distorted the bonds will change and this equal and opposite relation between the atoms will no longer hold for all the nearest neighbour pairs.
Embedded Atom Method Total Electron Density at an atom i. Calculated via linear superposition of the electron-density contribution from neighbor atoms. Total Energy Pair potential Embedding Function, energy required to embed atom I into background electron density of ρi at site i. EAM potentials do not take into account the s, p, d and f symmetries. Good for transition metals and noble metals.
Process Used to Relax Interfaces and Sliding Conditions • LANL’s Process: • Integration timestep used: 0.0027 • Samples were allowed to equilibrate and relax for 2.7 ps, which is sufficient to relax initial strains at pressure of 5.1GPa and Up=0. • The equilibrated system was then subjected to initial conditions (Temperature, PBC, sliding velocities, etc) and non-equilibrium steady state was achieved after 135ps. • Rougher surfaces were used for U>400m/s (smooth surfaces however show similar trend)
Process Used to Relax Interfaces and Sliding Conditions • Our Approach: • The same integration time step of 0.0027 was used • Significant larger equilibration times at P=5.1GPa which was 216ps, and further run at appropriate sliding velocities to achieve steady state (270ps) • Introduction of new command to insure that there is no movement in the z direction during sliding. The linear momentum zeroed by subtracting the centres of mass velocity of the group from each atom.
