Material length scale of strain gradient plasticity: A physical interpretation

The physical basis and the magnitude of the material length scale in theories of strain gradient plasticity are crucial for accounting for size effects in the plastic behavior of metals at small scales. However, the underlying physics of the length scale is ambiguous. The length scales in strain gradient plasticity theories in which the plastic work density can be expressed as a function of the gradient-enhanced plastic strain are here derived from known physical quantities via critical thickness theory. A connection between the length scale and the fundamental physical quantities is elucidated. The combination of the strain and strain-gradient terms within the deformation theory of strain gradient plasticity is addressed. It is shown that, compared with the harmonic sum of the strain and strain-gradient terms in Fleck-Hutchinson theory, the linear combination gives a more reasonable value of length scale, several micrometers, which is close to that in the gradient theory of Aifantis. In contrast, the value of length scale in Nix-Gao theory is much larger, in the millimeter range. The length scales determined by critical thickness theory are in good agreement with those obtained by fitting to experimental data of wire torsion.