Understanding scale-dependent yield stress of metals at micrometre scales

The mechanical softening behaviour of micrometre-scale metals (free-standing metal foils and wires) with decreasing either the geometrical or the microstructural scale (i.e. the smaller, the weaker) has recently been reported. Here, we present a mechanism-based model to understand the softening behaviour, which is based on competition between the effects of surface grain relaxation and the interior grain strengthening effect. The model describes well the yield stress of Cu foils with different ratios of the thickness to grain size.