  The yielding transition, structural relaxation, and mechanical properties of
metallic glasses subjected to repeated loading are examined using molecular
dynamics simulations. We consider a poorly-annealed Cu-Zr amorphous alloy
periodically deformed in a wide range of strain amplitudes at room temperature.
It is found that low-amplitude cyclic loading leads to a logarithmic decay of
the potential energy, and lower energy states are attained when the strain
amplitude approaches a critical point from below. Moreover, the potential
energy after several thousand loading cycles is a linear function of the peak
value of the stress overshoot during startup continuous shear deformation of
the annealed sample. We show that the process of structural relaxation involves
collective, irreversible rearrangements of groups of atoms whose spatial extent
is most pronounced at the initial stage of loading and higher strain
amplitudes. At the critical amplitude, the glass becomes mechanically annealed
for a number of transient cycles and then yields via formation of a shear band.
The yielding transition is clearly marked by abrupt changes in the potential
energy, storage modulus, and fraction of atoms with large nonaffine
displacements.
