Physics-motivated fractional viscoelasticity model for dynamic relaxation in amorphous solids

Dynamic mechanical relaxation is an important metric to understand the mechanical/physical properties of amorphous solids which are of viscoelastic nature. Due to the heterogenous microstructure, the relaxation behavior of amorphous solids usually shows strong deviation from the Debye relaxation. The distribution of relaxation time derived from either the stretched exponential function (KWW function) or the power law form is probably the most adopted paradigm to describe the non-Debye relaxation. They are essentially the continuous spectrums given in analytical forms. However, whether a real amorphous material conforms to such distribution law remains to be discussed. Here we test the assumption in typical metallic glasses (MGs) as representatives of the general amorphous solids. The mechanical spectrum of a Cu₄₆Zr₄₇Al₇ MG in wide frequency domain is probed by the dynamic mechanical analysis technique. It is found that both the KWW function and the modified fractional (MF) model based on power law can well describe the experimental data. As a step forward, we combine the quasi-point defect theory with the MF model to theoretically reveal the feature of temperature-dependent structural evolution in MG. Finally, the distribution of relaxation time corresponding to the experimental data is discretized to argue the theoretically predicted microstructural heterogeneity in the MGs.