Molecular Dynamics Simulations of Dynamic Friction and Mixing at Rapidly Moving Material Interfaces

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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

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Projects 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.

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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.

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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
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LANL and Cranfields (FMCS) MD models

• LANL
• Sliding of Cu (010) on Ag(010) in the lt100gt
  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

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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.
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Plot of Velocity Dependence of Frictional Force
The frictional force is representing by a power
law
Domain size Cranfield model
? x300, y600, z100 (Å) (1.3Million Atoms)
LANL
? x410, y320, z330 (Å)
(2.8Million Atoms)
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Temperature and Velocity Variation Across the
Interface
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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.

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Microstructure at Various Speeds
Speed of 25m/s
400m/s

• 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.

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VMD Snapshots
400m/s
200m/s
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Video of 400 m/s Relative Speed
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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.

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MSD Plots at Various Speeds

• Domain Size of (x,y,z) (300,600,100) Å

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Concentration Gradient Plots
Interfacial Region 14 Å
Interfacial Region 24.5 Å
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Concentration Gradient Plots
Interfacial Region 91 Å
Interfacial Region 38.5 Å
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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.

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Supplementary Slides
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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.
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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 ?i at site
i.
EAM potentials do not take into account the s, p,
d and f symmetries. Good for transition metals
and noble metals.
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Process Used to Relax Interfaces and Sliding
Conditions

• LANLs 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 Up0.
• 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 Ugt400m/s (smooth
  surfaces however show similar trend)

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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
  P5.1GPa 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.

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Picture at sliding speed 1000m/s
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Non-equilibrium steady state
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Relative velocity of 300m/s
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Relative velocity of 800m/s