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Atomic Simulation of Grain boundary sliding

Atomic Simulation of Grain boundary sliding. Sirish Namilae Advisor: Prof. Namas Chandra. Molecular Statics Energy Minimization T=0 K. Molecular Dynamics. Newtonian Mechanics to Solve Eqns of Motion Finite Stress and Temperature. Interatomic Potentials (We Use EAM Potentials).

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Atomic Simulation of Grain boundary sliding

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  1. Atomic Simulation of Grain boundary sliding Sirish Namilae Advisor: Prof. Namas Chandra

  2. MolecularStatics • Energy Minimization • T=0 K Molecular Dynamics • Newtonian Mechanics to Solve Eqns of Motion • Finite Stress and Temperature Interatomic Potentials (We Use EAM Potentials) Input Xi Input Xi ,T,,time (t) Positions and energies of all atoms after application of T,  for time t Equilibrium positions and energies of all atoms Atomic Simulation Method

  3. Molecular Dynamics - Introduction • A Classical mechanics based study of dynamics • of atoms and molecules • Ignores uncertainty principle and is completely deterministic • Numerically solving the Equations of motion (Newton’s • Second law) of multi-body system • Interaction of atoms based on interatomic potential U(r) • The objective of Molecular statics is to find the minimum • energy configuration

  4. Apply Boundary conditions, Stresses, Vol Change, Thermostat Based on requirement Move Atoms one Step Ahead - Integration Schemes Analysis and Visualization Flow Chart of Typical MD code Initialization Calculate forces/energies for each atom

  5. Calculation of Force/energy For any potential U(r) ,force exerted on atom i due to Atom j is given by: Then we have total force exerted on a particular atom • Potential energy of atom i directly given by the potential

  6. Potentials Pair Potentials • Totally empirical, only pair interactions considered • example • - Lennard Jones Embedded Atom Method Potentials • Implicitly include many body effects and metallic bond F is energy to embed an atom i into electron density I, f is contribution to electron density of atom i due to atom j and is two body central potential or repulsion term E-A force matching potentials for Al used in this work

  7. Symmetric Tilt Grain Boundaries • Random grain boundaries have both tilt and twist components, typically have 5 degrees of freedom corresponding to unit normals of the two grains and angle of rotation. • Symmetric tilt grain boundaries have only the tilt component. They can be specified by two degrees of freedom

  8. Construction of Computational Crystal Periodic in X and Z plane

  9. Equilibrium Grain Boundary Structures • [110]3 and [110]11 are low energy boundaries, [001]5 • and [110]9 are high energy boundaries GB GB [110]3 (1,1,1) [001]5(2,1,0) GB GB [110]9(2,21) [110]11(1,1,3)

  10. Grain Boundary Energy Computation Our Calculation Experimental Results1 GBE = (Eatoms in GB configuration) – N  Eeq(of single atom) 1Proceeding Symposium on grain boundary structure and related phenomenon, 1986 p789

  11. Energy Distribution at Grain Boundaries for Different STGB Configurations       • It can be observed that there is no difference in energy across the grain • boundary for 3 special boundary

  12. Grain Boundary Sliding • Grains remain equiaxed after superplastic deformation • This suggests that grain boundary sliding is the major • Strain contributing mechanism in sliding. • Atomic scale details of sliding not clearly understood. Few studies on Atomic simulation of sliding • Deymier P and Kalonji G, Scripta. Mat. 20 13 (1984) • Molteni et al , Phy. Rev. lett, 76 1284 (1996) • Chandra N and Dang P J. of Mater. Sci.34 655 (1999) • Kurtz, RJ et al , Phil. Mag. A79, No.3 665, (1999)

  13. Generation of crystal for simulation of sliding. Free boundary conditions in X and Y directions, periodic boundary condition in Z direction. Boundary Conditions • Most of the experiments on bicrystal sliding grain boundary • oriented at 45 degrees to the tensile (or compressive) axis. • Grain boundaries for MD also with similar boundary conditions. • Simulation cell contains about 14000 to 15000 atoms. Grain boundaries studied: 3(1 1 1), 9(2 2 1), 11 ( 1 1 3 ), 17 (3 3 4 ), 43 (5 5 6 ) and 51 (5 5 1)

  14. Boundary Conditions Y’ A state of shear stress is applied on the grain boundary by applying an external stress  X’ Stresses about 10% of Voigt average shear modulus for the potential The amount of sliding is calculated as difference between the average X displacements in the bottom and top crystals in (X’ Y’ Z’) reference frame

  15. Fig.6 Extent of sliding and Grain boundary energy Vs misorientation angle Sliding Results Variation of grain boundary sliding with grain boundary energy is shown below Grain boundary sliding is more in the boundary, which has higher grain boundary energy Monzen et al1 observed a similar variation of energy and tendency to slide by measuring nanometer scale sliding in copper Monzen, R; Futakuchi, M; Suzuki, T Scr. Met. Mater., 32, No. 8, pp. 1277, (1995) Monzen, R; Sumi, Y Phil. Mag. A, 70, No. 5, 805, (1994) Monzen, R; Sumi, Y; Kitagawa, K; Mori, T Acta Met. Mater. 38, No. 12, 2553 (1990) 1

  16. EGB For Pure Al =0.65 x 10-2 (eV/A2) Position 2 Position 1 Mg Segregation in Al Grain Boundaries Grain Boundary segregation of impurity atoms plays major role In deformation and sliding of material Mg atoms were placed at various locations in Al grain boundaries And energetics was analyzed using statics Figs show variation of grain boundary energy

  17. Mg Segregation in Al Grain Boundaries Al y Y GB Distribution of atoms around impurity atom in 9 STGB Segregation of Mg Atoms to particular Locations in grain boundary is based on Size effect and Hydrostatic pressure

  18. Hydrostatic Stress and Segregation Energy There is a almost a one to one correlation between hydrostatic stress and segregation energy Effect of Mg on sliding Simulation results also indicate that there is an increase In grain boundary sliding when Mg atoms are present

  19. Summary • There is a definite correlation between sliding and grain • boundary energy in Aluminum STGB. • Higher disorder boundaries, which have higher grain • boundary energy exhibit more sliding. • There is an increase in grain boundary energy in Al • bicrystals with the presence of magnesium. However, this • increase is dependant on the position of Mg atom. • Presence of Mg at grain boundary tends to increase • sliding in some of the grain boundaries studied in this • work. S Namilae, N Chandra and TG Nieh, Scripta. Mater. 46 Jan 2002 S Namilae, C Shet,N Chandra and TG Nieh, MatSci Forum Vol-357 1999

  20. Application of Homogenization to Atomic scale Asymptotic Homogenization (AEH) has been used in composite used to study heterogeneous materials with two natural scales e.g composites Decouples the boundary value problem into macro and micro problem By expanding field variables asymptotically with scaling parameter  Application of AEH to atomic scale. The idea is that macro scale is described by hyperelastic FEM while the microscale is described by Molecular statics

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