An explanation for the power-law scaling of size effect on strength in micro-specimens

The power-law scaling of size effect of strength in micro-crystals is explained in terms of an assumed fractal geometry of the initial dislocation network. The size effect arises from the Taylor-type resistance in such a network. The power exponent of the size effect is predicted to be 3/(q + n), where q is the fractal dimension of the dislocation network, and n is the stress exponent of dislocation velocity. The theory is verified by a set of experimental strength data of Al micro-pillars.