Universality of the Phenomenology of Structural Superplasticity

The equation σ=Kέm, where σ is the applied stress, έ is the strain rate, K and m are material constants that depend on stress / strain rate, temperature and grain size is often used to describe structural superplasticity. The general shape of the logσ-logέ curve is sigmoidal. Based on limited data, it was suggested by us earlier that a universal σ-έ curve could exist in a properly normalized space. έ and m are normalized with respect to έopt and mmax, the strain rate at which m is a maximum and the maximum m value respectively. Here a multi-dimensional relationship involving σ/σopt-έ/έopt-m/mmax-ΔF0/kT-η/ηopt is developed; σopt corresponds to έopt, ΔF0 is the free energy of activation for the rate controlling mechanism, k the Boltzmann constant, T the absolute test temperature, η the (apparent) viscosity of the superplastic alloy and ηopt is the viscosity of the same alloy for m=1 in a dimensionless σ-έ space. Using data concerning many systems, the phenomenology of structural superplasticity in all classes of materials is shown to be unique.