  Quantitative understanding of the fracture toughness of metallic glasses,
including the associated ductile-to-brittle transitions, is not yet available.
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.
