1. MOLECULAR DYNAMICS SIMULATION OF STRESS INDUCED GRAIN BOUNDARY MIGRATION IN NICKEL Hao Zhang, Mikhail I. Mendelev, David J. Srolovitz Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08540 Background Goal: Determine grain boundary mobility from atomistic simulations Methods based upon capillarity driving force are useful, but not sufficient gives reduced mobility, M * =M   ”), rather than M boundary stiffness  ” not readily available from atomistic simulations average over all inclinations Flat boundary geometry can be used to directly determine mobility, but subtle ( Schönfelder, et al.) Molecular Dynamics Velocity Verlet Voter-Chen EAM potential for Ni Periodic BC in X, Y, free BC in Z Hoover-Holian thermostat and velocity rescaling 12,000 - 48,000 atoms, 0.5-10 ns Application of Driving Force Ideally, we want constant driving force during simulation avoid NEMD no boundary sliding Use elastic driving force even cubic crystals are elastically anisotropic – equal strain  different strain energy driving force for boundary migration: difference in strain energy density between two grains Apply strain apply constant biaxial strain in x and y free surface normal to z provides zero stress in z X Y Z Grain Boundary Free Surface Grain 2 Grain 1 11 22 33 11 22 33  Linear Elastic Estimate of Driving Force Non-symmetric tilt boundary [010] tilt axis boundary plane (lower grain) is (001) Present case:  5 (36.8º) Strain energy density determine using linear elasticity Conclusion Developed new method that allows for the accurate determination of grain boundary mobility as a function of misorientation, inclination and temperature Activation energy for grain boundary migration is finite; grain boundary motion is a thermally activated process Activation energy is much smaller than found in experiment (present results 0.26 eV in Ni, experiment 2-3 eV in Al) The relation between driving force and applied strain 2 and the relation between velocity and driving force are all non-linear Why is the velocity larger in tension than in compression? ε σ ** Strain energy density Apply strain ε xx =ε yy =ε 0 and σ zz =0 to perfect crystals, measure stress vs. strain and integrate to get the strain contribution to free energy Includes non-linear contributions to elastic energy Grain1Grain2 Typical strains as large as 4% (Schönfelder et al.) 1-2% here Expand stress in powers of strain: Non-Linear Stress-Strain Response Fluctuations get larger as T ↑ GB Motion at Zero Strain At high T, fluctuations can be large Velocity from mean slope Average over long time (large boundary displacement) Steady State Migration (Typical) Velocity vs. Driving Force Velocity under tension is larger than under compression (even after we account for elastic non-linearity) Difference decreases as T ↑ 800K 1200K1400K 1000K Mobility Activation energy for GB migration is ~ 0.26 ±0.08eV p v/p Determination of Mobility Determine mobility by extrapolation to zero driving force Tension (compression) data approaches from above (below) Non-linear dependence of driving force on strain 2 Driving forces are larger in tension than compression for same strain (up to 13% at  0 =0.02) Compression and tension give same driving force at small strain (linearity) Driving Force Non-Linear Driving Force Implies driving force of form: