Meaning
Mathematical stretched exponential equations describe the non-exponential relaxation behavior of disordered molecular systems over time. The kohlrausch-williams-watts function models how polymer chains release internal energy when subjected to mechanical deformation or thermal changes. This formulation is highly useful for characterizing amorphous resins.
Relaxation Function
Stretched exponential decay is governed by a characteristic relaxation time and a stretching parameter between zero and one. When applied to polymer dynamics, the kohlrausch-williams-watts equation captures the broad distribution of relaxation processes. A smaller stretching parameter indicates a wider distribution of molecular environments within the material.
Glass Transition
Polymeric materials cooled rapidly from the melt exhibit a slow return to thermodynamic equilibrium. The kohlrausch-williams-watts model calculates the structural recovery of the glass as it undergoes physical aging. This aging increases the density and yields higher yield stresses in the moulded part.
Viscoelastic Prediction
Predicting the long-term creep performance of injection moulded parts requires a clear understanding of the relaxation spectrum. By utilizing the kohlrausch-williams-watts approach, engineers can simulate how a thermoplastic structural component will deform under continuous load over several years. This capability prevents premature part failure in applications such as pressurized fluid housings or snap-fit assemblies where stress relaxation might cause a loss of sealing force.
It replaces simple single-exponential models that typically underestimate the creep rate at extended timescales.
