Unveiling creep mechanisms in metallic glasses via fractional modeling under coupled thermo-mechanical loads

This study systematically investigates the creep behavior of Pd₂₀Pt₂₀Cu₂₀Ni₂₀P₂₀ metallic glass under varying temperatures and applied stresses. To accurately capture its time-dependent deformation response, a fractional Burgers model is proposed by extending the classical Burgers framework using fractional calculus. The model demonstrates excellent agreement with experimental data and offers physically interpretable parameters that describe the inelastic response of material. With increasing temperature, the quasi-steady-state creep strain rate increases significantly, accompanied by a notable reduction in the apparent viscosity. The viscosity-related parameters exhibit thermally activated behavior, while the fractional orders α_₁ and α_₂ also increase with temperature, indicating enhanced atomic mobility. The validity of the model is further supported by dynamic mechanical analysis, in which the temperature-dependent trends of storage and loss moduli align closely with model predictions. In contrast, increasing the stress primarily accelerates the creep rate but exerts only a limited influence on viscosity and the evolution of fractional parameters, suggesting that temperature plays a more dominant role than stress in determining creep kinetics. Creep experiments conducted on samples with different degrees of physical aging reveal that structural relaxation primarily suppresses the initial transient anelastic strain, while the quasi-steady-state stage remains largely unaffected. Finally, a comparative analysis among metallic glasses with different β relaxation features shows that alloys exhibiting more pronounced β relaxation tend to possess higher α_₁ and α_₂ values, underscoring the critical role of β relaxation in mediating intrinsic ductility and deformation behavior below the glass transition temperature in metallic glasses.