Delayed elasticity of metallic glasses: Loading time and temperature dependences of the anelastic relaxation

Abstract

One of the hallmarks of disordered matter is the large amplitude of the anelastic deformation, i.e., the fraction of reversible deformation that is not instantaneously recovered after the release of load but is delayed in time. In this paper, this delayed elasticity is studied for the glass-forming ${\mathrm{Zr}}_{46.25}{\mathrm{Ti}}_{8.25}{\mathrm{Cu}}_{7.5}{\mathrm{Ni}}_{10}{\mathrm{Be}}_{27.5}$ alloy by means of stress step and recovery experiments. Even at high temperatures, not far from the glass transition, the delayed elasticity can recover an important fraction of the deformation and endure for a long time. Analyzing the effects of loading time and waiting time on the strain evolution, we reveal the presence of an anelastic response with a timescale dependent on loading time and an invariant shape, which indicates the presence of a distribution of reversible relaxation modes following a ${\ensuremath{\tau}}^{\ensuremath{-}n}$ law with exponent $n$ between 0.5 and 1. The underlying distribution of energy barriers activated at different temperatures is accordingly shape invariant. Moreover, we found that a distribution of reversible modes corresponding to the high-frequency side of the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{relaxation}$ peak can reproduce the experimental results. The results establish a direct link between the dynamical spectrum and the distribution of activation energies, revealing the origin of the transient creep and anelastic recovery behaviors of metallic glasses.