Non-Newtonian rheology in stress relaxation of metallic glasses

Traditional rheological models of viscoelastic materials, like generalized Maxwell and Burgers models, often require numerous fitting parameters, leading to potential overfitting particularly for complex behaviors below the glass transition temperature. Here we propose a modified viscoelastic model incorporating a non-Newtonian element to quantitatively describe the thermodynamic behavior and structural evolution of metallic glasses. By employing a modified Maxwell model with an Eyring-type non-Newtonian element, it achieves satisfactory prediction of stress relaxation. It is found that strain amplitude has minimal impact on relaxation kinetics, while temperature plays a dominant role in driving stability. At low temperatures, even rejuvenation is achieved. We further find that cyclic loading leads to hardening and subsequent stabilization, consistent with molecular dynamics simulations. The reference strain rate in the non-Newtonian rheological model effectively captures both internal energy dissipation and rearrangement of atoms, offering a quantitative metric for assessing the dynamic properties of metallic glasses and their responses to thermo-mechanical loading.