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 DepartmentCranfield University

&

Graham Ball

AWE, Aldermaston

Project’s Objectives

Objective: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: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.

iiiii rUtFtrmtF

• 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

reservoirs

Reservoirs are thermostatted at 298K, and contained the same atoms as the bulk. PBC used in x and z direction.

The system is brought to equilibrium

Fn is 5.1GPa

Ft is an average force acting in such that atoms experience the same force at each time step. The atoms’ velocities remain constant

Ft

Fn

Fn

Up

Y

X

Plane

Up

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

a. 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)

b. Comparison with LANL1 system domain of (410, 320, 330)Å

c. Temperature variation across the interfaces at various speeds.

d. Microstructure characteristics at low and high speeds.

e. Mean square displacement plots (MSD)

f. 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

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)

The frictional force is representing by a power law:

vF g ~tan

Temperature and Velocity Variation Across the Interface

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

Video of 400 m/s Relative Speed

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.

N

i

rtrN

MSD1

201

MSD Plots at Various Speeds

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

Interfacial Region = 14 Å Interfacial Region = 24.5 Å

Concentration Gradient Plots

Interfacial Region = 91 ÅInterfacial Region = 38.5 Å

Concentration Gradient Plots

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.

Supplementary Slides

Centro-symmetry

6

1

2

6i

ii RRP

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.

A centrosymmetic material has pairs of equal and opposite bonds and to its nearest neighbour

Embedded Atom Method

N

i

N

ijj

ijijiitot rUFE1 12

1

Total Energy

Embedding Function, energy required to embed atom I into background electron density of ρi at site i.

Pair potential

Total Electron Density at an atom i. Calculated via linear superposition of the electron-density contribution from neighbor atoms.

N

ijj

ijji r1

EAM potentials do not take into account the s, p, d and f symmetries. Good for transition metals and noble metals.

• LANL’s Process:

1. Integration timestep used: 0.0027

2. 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.

3. The equilibrated system was then subjected to initial conditions (Temperature, PBC, sliding velocities, etc) and non-equilibrium steady state was achieved after 135ps.

4. Rougher surfaces were used for U>400m/s (smooth surfaces however show similar trend)

Process Used to Relax Interfaces and Sliding Conditions

Process Used to Relax Interfaces and Sliding Conditions

• Our Approach:

1. The same integration time step of 0.0027 was used

2. Significant larger equilibration times at P=5.1GPa which was 216ps, and further run at appropriate sliding velocities to achieve steady state (270ps)

3. 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.

Picture at sliding speed = 1000m/s

Non-equilibrium steady state

Relative velocity of 300m/s

Relative velocity of 800m/s