Continuum nanomechanics for nanocrystalline and ultrafine grain materials

An extension of the classical continuum mechanics model is provided for the solution of boundary value problems at the nanoscale. The resulting continuum nano-mechanical model is based on the introduction of new terms to account for the interaction of bulk and surface points of the medium, which becomes significant as the specimen size is reduced down to the nanometer level. The model can be used to interpret deformation and diffusion phenomena in nanocrystalline (NC) and ultrafine grain (UFG) polycrystals, where a large number of internal surfaces (e.g. grain/twin boundaries) are present. When small material volumes are considered, random effects of the underlying microstructure become pronounced and their interpretation cannot be addressed with deterministic models alone. In this case, the continuum nanomechanics model may be enhanced with stochastic terms accounting for their competition with their deterministic gradient counterparts. The resulting combined gradient-stochastic model can be used to interpret intermittent plasticity and size-dependent serrated stress-strain curves in micro/nano pillars. These ideas have been applied to address certain benchmark problems and configurations of nanoelasticity, nanodiffusion and nanoplasticity. Non-singular expressions can be derived for stresses and strains in the neighborhood of dislocation lines and crack tips contained in a nanograin. Non-linear concentration depth profiles for diffusion in NCs are obtained in agreement with experiments. Corresponding results are obtained herein for coupled elasto-diffusion processes and related size-dependent phase transformation diagrams. When differential equations are not available, deformation features may be revealed through a statistical analysis of the relevant experimental data. This is done here for the interpretation of statistical features of deformed UFG alloys exhibiting serrated stress-strain curves and fractal shear bands. © Published under licence by IOP Publishing Ltd