Shear Band Formation in Bulk Metallic Glasses

In recent times, there has been a growing interest in the machining of amorphous metallic alloys, which are also called bulk metallic glasses (BMGs). These materials differ from common polycrystalline metallic alloys, because their atoms do not assemble on a crystalline lattice, and as a result, they have unique physical, mechanical, and chemical properties. A number of BMGs have been found to produce shear-localized chips during machining operations. Furthermore, a number of theoretical studies have argued that this strain localization is not controlled by rapid heating, but rather by a change in the concentration of free-volume in the material. In this work we study shear band formation in BMGs by studying a geometrically simple deformation of the material, a homogeneous shear flow. We perform a linear stability analysis of the homogeneous shear flow, obtaining a non-autonomous linear system of ODEs. Using numerical simulations of this system we show that free-volume instabilities dominate the growth of localized shear bands. Furthermore, we compare our results with simulations of the full system of PDEs. Finally, our simulations suggest that the simple shear model is not valid for long times and should only be used as an onset equation.