On the power law description of low-stress uni-axial steady-state high-homologous-temperature deformation

The “power law” is often used to describe steady state/minimum creep rate as well as steady state superplastic deformation, both of which are observed under low-stress, high-homologous temperature conditions. In these cases, the activation energy, the proportionality constant in the strain rate equation and the stress exponent, n, change with the physical mechanism. Here a simpler alternative procedure for introducing a dimensionless stress term in the rate equation compared with the one used by materials scientists is advocated. The microstructure/crystal structure dependence of strain rate is introduced using the Buckingham Pi theorem. For the case where the contribution from the structure/microstructure terms to the isothermal deformation rate is constant, Laurent’s theorem helps generate a set of admissible values for n. The simplest solution of n being independent of stress, but a linear function of temperature, describes low stress, steady state creep rather well. (The case where n is independent of both stress and temperature follows as a special case of this solution.) The next simplest solution of n being a linear function of both temperature and stress corresponds to steady state superplasticity. Using the equations derived, the stress exponent, real and apparent activation energies for the rate controlling flow and strain rate values at different stresses and temperatures can be estimated. The equations are validated using experimental results pertaining to many systems. The implications of the findings are discussed.

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