A theoretical study of the structure–property relations in ultra-fine metallic materials with fractal microstructures

Nanostructured and ultra-fine grained metals have higher strength than coarse-grained metals, but suffer from the extremely limited ductility. It has been shown that in some metals the ductility can be improved via the introduction of a specific range of grain sizes at the micro-level while in other metals this does not occur. The present work relates the multi-scale microstructures in metals to their overall structure–property behavior using a fractal law where microstructural parameters such as grain size and fractal dimension are introduced and, thus, mechanical properties such as strength and ductility are presented as a function of these microstructural parameters. The effect of fractal dimension on the mechanical properties is theoretically studied. The applicability of the Considère and the Hart criteria to predict the uniform elongation in materials with fractal microstructures (MFMs) is investigated. Possible mechanisms affecting the plastic deformation of MFMs are further considered. Advantages and shortcomings of the application of the fractal law to study the structure–property relationships in materials with multi-modal microstructures are discussed.