  The effect of periodic shear on strain localization in disordered solids is
investigated using molecular dynamics simulations. We consider a binary mixture
of one million atoms annealed to a low temperature with different cooling rates
and then subjected to oscillatory shear deformation with a strain amplitude
slightly above the critical value. It is found that the yielding transition
occurs during one cycle but the accumulation of irreversible displacements and
initiation of the shear band proceed over larger number of cycles for more
slowly annealed glasses. The spatial distribution and correlation function of
nonaffine displacements reveal that their collective dynamics changes from
homogeneously distributed small clusters to a system-spanning shear band. The
analysis of spatially averaged profiles of nonaffine displacements indicates
that the location of a shear band in periodically loaded glasses can be
identified at least several cycles before yielding. These insights are
important for development of novel processing methods and prediction of the
fatigue lifetime of metallic glasses.
