stressrelaxation

Stress relaxation is the decrease in internal stress in a material held at a fixed deformation, or the corresponding decay of stress over time in viscoelastic solids under constant strain. In practice, a material is deformed to a fixed strain ε0 and the resulting stress σ(t) is monitored as it relaxes toward an equilibrium value. Conversely, under a fixed applied stress, strain increases with time, a phenomenon known as creep.

In viscoelastic materials such as polymers, asphalt, and some metals at elevated temperature, the relaxation behavior arises from time-dependent molecular or microstructural rearrangements. Branching polymer chains, diffusion of molecules, or reorientation of segments reduce the load carried by the elastic network, leading to a decay of stress. The characteristic times depend on temperature, composition, and molecular architecture.

The mathematical description frequently uses relaxation modulus G(t) or a spectrum of relaxation times. In a simple Maxwell model, stress decays exponentially as σ(t) = σ0 exp(-t/τ), with the relaxation time τ = η/G. More complex materials require a generalized Maxwell (a sum of exponential terms) or standard linear solid models to capture multiple relaxation processes. The time-temperature superposition principle is often employed to describe how relaxation shifts with temperature, via Arrhenius or WLF-type relationships.

Measurements are made with stress-relaxation tests (constant strain), creep tests (constant stress), or dynamic mechanical analysis that yields a spectrum of relaxation times. Applications span polymer processing, coatings and adhesives, bituminous materials, and high-temperature metals, where control of residual stresses affects performance and durability.