Shear Banding in Metallic Glasses: a mathematical perspective inspired by soil mechanics.

There have been many approaches to engineering toughness in metallic glasses. Some have worked in composites, such as the transformation-toughened examples developed recently. Others have delved into the fundamental nature of deformation in these systems. Here, a number of mathematical models from other fields are applied in order to shed light on some of these advances. A model of transformation toughening more typically used in ceramics is adapted to consider the question of whether martensitic transformation in CuZr austenitic nanocrystals can in fact toughen the surrounding glass by the same mechanism as is typically invoked for crystalline materials. The results draw that explanation into question - the volume change associated with transformation in that system is just too small to significantly modify the shear band tip stress state, and the shape strain terms are constrained by variant self-accommodation and matters of orientation. A model developed to describe dilatant shear banding in granular media is then adapted to draw new insight on the same problem in metallic glasses. By modelling the glassy system as made up of clusters that behave like particles in sand or gravel, arranged into load-bearing force chains that fail by buckling, the behaviour of the system is shown to depend on a series of spring constants that represent the local packing and bonding in the glass. These spring constants emerge as a new order parameter, promising the possibility of a direct quantitative link between the state of structural order and the degree of dilatation associated with deformation. The new order parameters represent a first step to bridging the gap between nanoscale bonding and structure, and larger-scale properties.