The common creep laws are Norton-Bailey, Prandtl-Garofalo and Naumenko-Altenbach-Gorash constitutive models. The secondary creep constitutive model is the Norton-Bailey Law which gives a power law relationship between creep rate and stress.
Are the fractional generalizations for these creep laws known? Are there experimentally determined constants for these laws?
Creep equations like Norton-Bayley, Prandtl, Johnson etc. relate the minimum (or stationary) creep rate to the stress by a specific stress function like power law, exponent, double power law, etc.. In my view the fractional time derivative may be helpful to capture primary and/or tertiary creep effects, i.e. a non-linear dependency with respect to the time. However, in my experience with creep data, at least for metals, it is more reliable to formulate kinetic equations for hardening/softening/recovery and damage processes rather than to manipulate with time derivatives.
An interesting viewpoint, I'll think about it. May by you have some references for the applications of kinetic equations to creep in metals?
Here are our publications, regarding kinetic laws for hardening/recovery/softening and damage
Article A Combined Model for Hardening, Softening, and Damage Proces...
Article A constitutive model for inelastic behavior of casting mater...
Article Two-time-scales and time-averaging approaches for the analys...
Article A phase mixture model for anisotropic creep of forged Al–Cu–...
Best regards
Konstantin
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