Geometrical Critical Thickness Theory for the Size Effect at the Initiation of Plasticity

Recently, size effects in the initiation of plasticity have been clearly observed and reported in different geometries; e.g., bending (Ehrler et al. Phil. Mag. 2008), twisting (Ehrler et al., MRS, Spring Meeting 2009) and indentation (Zhu et al. J. Mech. Phys. Sol. 56, 1170, 2008). Strain gradient plasticity theory is the principal approach for explaining size effects during plastic deformation in these geometries. However, it fails to account for any size effect at the initial yield. Geometrical critical thickness theory was proposed to explain the yield size effect in bending and torsion (Dunstan and Bushby, Proc. Roy. Soc. A460, 2781, 2004). The theory shows that the initial yield strength is scaled with the inverse square root of the characteristic length scale without requiring any free fitting parameters. Here, we extend the theory to describe the yield size effect in indentation. The theory agrees fairly well with experimental observations in micro-torsion (Ehrler et al., MRS, Spring Meeting 2009) and nanoindentation (Zhu et al., J. Mech. Phys. Solid, 2008).