Time–temperature superposition

Time–temperature superposition shifts viscoelastic measurements made at different temperatures along the time or frequency axis to construct a master curve. It relies on temperature changing relaxation rates in a way that preserves the material’s underlying response shape.

Connect

Master curve: A curve assembled from measurements across conditions to represent behavior over a wider range than any single measurement. Time–temperature superposition builds this extended response curve by joining temperature-shifted data.
Viscoelasticity: The combination of elastic energy storage and viscous energy dissipation in a material’s response to deformation. Time–temperature superposition organizes measurements of this time-dependent material behavior.
Polymer rheology: The study of how polymer materials flow and deform under applied forces. Time–temperature superposition is a standard way to extend polymer response measurements across timescales.
Thermorheological complexity: Behavior in which different relaxation processes respond differently to changes in temperature. Distinct shift factors prevent all measurements from collapsing onto one master curve.
Shift factor: A multiplicative factor that translates a measured response along an independent variable such as time or frequency. It specifies how far each temperature’s data move to align with the reference curve.
Stress relaxation: The decrease in stress over time after a material is held at a fixed deformation. Its temperature-dependent timescales can be shifted to extend the observed relaxation window.
Asphalt binder: The bituminous material that binds mineral aggregates in asphalt mixtures. Its temperature-dependent viscoelasticity is evaluated with shifted modulus and creep data.
Time–temperature equivalence: The principle that changing temperature can produce effects resembling a change in observation time. It is the physical idea underlying the method, but does not guarantee successful superposition for every material.
Reduced time: A time coordinate rescaled to account for changes in a system’s rate of evolution. The method interprets temperature-dependent relaxation as a change in the effective time scale.
Creep (deformation): The time-dependent increase in deformation under a sustained applied stress. Creep compliance measurements can form a master curve using the same shifting principle.