A fractal interpretation of size effects on the strength of metallic glasses

Yielding strength of metallic glasses in the uniaxial tensile and compressive tests is scale-dependent, which is attributed to the self-similar distribution of atomic cluster and free volume in the work. In contrast with the Weibull statistical theory previously employed in scaling phenomena of metallic glasses, fractal scaling laws are for the first time applied to describe the size effect inherent to the material disorder. Especially, the Multifractal Scaling Law (MFSL) originally proposed for quasi-brittle materials is used to interpret some experimental data in the literature. The best-fitted parameters (_fy$f_{\mathrm{y}}$ and l_ch) from the MFSL are in good consistency with the bulk yielding strength and the shear band size of metallic glasses observed in the alternative approaches or experiments. The fractal size effect laws provide insight into not only the scaling phenomena, but also further engineering strength predictions and designs.