The mechanical properties of glassy materials still pose challenges of great scientific and technological importance.
One such fundamental property is the fracture toughness – the ability of a material to resist failure in
the presence of a crack. Theoretically predicting the fracture toughness of materials, which is lacking in general,
is a particularly pressing problem in the context of metallic glasses, which constitute a promising
new class of materials, possessing superior properties, whose usage in structural applications is severely limited
by their relatively low fracture toughness. Here we use a simple model of plastic deformation in glasses, coupled to an advanced Eulerian level set formulation for solving complex free boundary problems, to calculate the fracture toughness of metallic glasses as a function of the degree of structural relaxation corresponding to different annealing times near the glass temperature. Our main result indicates the existence of an elasto-plastic crack tip instability for sufficiently relaxed glasses, resulting in a marked drop in the toughness, which we interpret as a ductile-to-brittle transition similar to experimental observations.