Non-Monotonous Mechanical Behavior at the Nanoscale: Elastic and Plastic Properties

Abstract

The non-monotonous behavior of strength, activation volume, and pressure sensitivity parameter, as the grain size enters the nanoscale regime, is interpreted on the basis of a “rule of mixtures” argument, commonly used for composites. Grain interior and grain boundary spaces are treated as two independent “phases” with distinct mechanical properties. When the simple “rule of mixtures” argument is extended to incorporate concepts from the continuum theory of mixtures, the Laplacian of strain is generated in the local constitutive equation for each phase. A simple one-dimensional configuration for a nanopolycrystal is assumed and a related boundary value problem is solved to nterpret the dependence of the overall elastic modulus on the grain size.