A two-phase model of large-strain plasticity in covalent nanostructures

We present a continuum model describing the extreme plastic behavior of nanostructured materials with covalent bonding, drawing inspiration both from recent experiments on Si nanowires, and atomic-scale molecular dynamics simulations. Building on the observations of such works it is proposed that deformation in a nanostructure made of randomly oriented nanocrystals embedded in an amorphous layer, proceeds by transferring the deformation energy to and from three distinct regions: a crystalline phase, corresponding to the bulk-like interior of each nano grain; a constrained amorphous phase, the percolative connecting network between different nano grains; and a defect accumulation zone, a thin shell surrounding each nano grain, where matter is turned from one phase into another. We formulate a free energy functional to describe the energy balance among the phases under steady non–equilibrium loading conditions. Strain and stress partial differential equations are derived, which are solved numerically to follow the evolution of the concentrations of the material phases, and the overall mechanical response of the system at constant input of external work. Matter transport is also included in the model, to account for stress-assisted diffusion, leading to accretion and non-constant volume and mass of the nanostructure during the mechanical deformation. A remarkable agreement with recent experiments on Si nanowires under extreme tensile deformation is obtained.