Brittle and Ductile Character of Amorphous Solids (Advances in Applied Mathematics and Mechanics, 2018)
Common silicate glasses are among the most brittle of the materials. However,on warming beyond the glass transition temperature $T_g$ glass transforms intoone of the most plastic known materials. Bulk metallic glasses exhibit similar phenomenology,indicating that it rests on the disordered structure instead on the natureof the chemical bonds. The micromechanics of a solid with bulk amorphous structureis examined in order to determine the most basic conditions the system must satisfyto be able of plastic flow. The equations for the macroscopic flow, consistent with theconstrictions imposed at the atomic scale, prove that a randomly structured bulk materialmust be either a brittle solid or a liquid, but not a ductile solid. The theory permitsto identify a single parameter determining the difference between the brittle solid andthe liquid. However, the system is able of perfect ductility if the plastic flow proceedsin two dimensional plane layers that concentrate the strain. Insight is gained on thenature of the glass transition, and the phase occurring between glass transition andmelting.