Averaging Molecular Dynamics simulations to study the slow-strain rate behavior of metals

Abstract

The application of molecular dynamics (MD) simulations to quasistatic loading is severely limited by the large separation between atomic vibration timescales and experimentally relevant deformation rates. In this work we employ the Practical Time Averaging (PTA) framework to overcome this limitation and enable atomistic simulations of crystalline solids under quasistatic loading conditions. PTA exploits the intrinsic separation of timescales by defining slow variables as time-averaged observables of the fast atomistic dynamics and their evolution on the slow loading timescale, thereby avoiding explicit integration of the fast dynamics. Using this approach, we simulate uniaxial deformation, in both tension and compression, of 4 to 20 nm cubic specimens of face centered cubic aluminum nanocrystals at applied strain rates approaching quasistatic conditions. We define slow variables as the averaged kinetic energy, potential energy, and normal stress in the loading direction, and track their evolution on the slow timescale. The stress-strain curves show yielding close to the theoretical stress for homogeneous nucleation, followed by successive load drops and rises caused by dislocation nucleation, motion, and exit from free surfaces. The "smaller is harder" effect is evident from the stress-strain response and from the variation of yield stress with sample size. Serrations in the response are more pronounced for smaller samples. The effects of applied strain rate and initial temperature are also studied. The method also captures the evolution of intricate dislocation microstructures on the slow timescale by tracking time-averaged atomic positions. The PTA framework enables simulations at strain rates several orders of magnitude lower than those accessible to conventional MD, demonstrating significant speedup in computational time while retaining full atomistic resolution.

Figures (7)

• Figure 1: MD Box and Sample.
• Figure 2: Boundary conditions (BCs) applied on the sample corresponding to uniaxial tension/compression in the $x$ direction. To obtain the converged running time average $R^m_t$ at slow time $t$, MD is run with the left boundary atoms $\partial B_l$ fixed at zero displacement while the right boundary atoms $\partial B_r$ are fixed at $u_x(t)=\varepsilon(t) \, L_s=\dot{\varepsilon} \, t \, L_s$ while $u_y=u_z=0$, where $\dot{\varepsilon}$ is the applied strain rate and $t$ is the slow time.
• Figure 22: Evolution of dislocation microstructure in slow time, at different strains for $20 \, nm$ sample under uniaxial compression. Different types of dislocations are indicated using the colors shown in the legend.
• Figure 23: Mean atomic positions at $5 \, \%$ and $11 \, \%$ strain for $20 \, nm$ sample under uniaxial compression.
• Figure 24: Mean atomic position at $5 \, \%$ strain for $20 \, nm$ sample under uniaxial compression. Atoms are colored as FCC, HCP or others. Only FCC atoms in green are at their regular lattice positions. Atoms which are not in their lattice positions such as the HCP atoms in red and other atoms in white result from slip caused by dislocation motion. A defective zone of the crystal is zoomed in to show the atoms which are out of their lattice positions.