Analysis of the inverse square-root size effect in the plasticity of metals

Abstract

Small-scale mechanical behaviour shows significant departures from classical elastic-plastic theory. In a remarkable number of instances, the strength of a material appears to scale as the reciprocal square root of the smallest length scale. There are several recent experimental and modeling results in the literature that show an interaction between dimensional (extrinsic) size and microstructural (intrinsic) size effects. In this paper, we present a mechanical model that naturally produces the inverse square root strengthening and derive an expression for the effective length when both the extrinsic and intrinsic size effects are significant. The theory fits well to data from a wide range of deformation geometries and includes the interaction between the microstructural and dimensional size effects. Furthermore, this approach is able to predict the size effect under uniform deformation without strain gradient.