Atomic-Scale Study of Plastic-Yield Criterion in Nanocrystalline Cu at High Strain Rates

Abstract

Large-scale molecular dynamics (MD) simulations are used to understand the macroscopic yield behavior of nanocrystalline Cu with an average grain size of 6 nm at high strain rates. The MD simulations at strain rates varying from 10⁹ s⁻¹ to 8 × 10⁹ s⁻¹ suggest an asymmetry in the flow stress values in tension and compression, with the nanocrystalline metal being stronger in compression than in tension. The tension-compression strength asymmetry is very small at 10⁹ s⁻¹, but increases with increasing strain rate. The calculated yield stresses and flow stresses under combined biaxial loading conditions (X-Y) gives a locus of points that can be described with a traditional ellipse. An asymmetry parameter is introduced that allows for the incorporation of the small tension-compression asymmetry. The biaxial yield surface (X-Y) is calculated for different values of stress in the Z direction, the superposition of which gives a full three-dimensional (3-D) yield surface. The 3-D yield surface shows a cylinder that is symmetric around the hydrostatic axis. These results suggest that a von Mises-type yield criterion can be used to understand the macroscopic deformation behavior of nanocrystalline Cu with a grain size in the inverse Hall–Petch regime at high strain rates.