Some basic solutions for nonlinear creep

AbstractThe aim of the paper is to derive the exact analytical expressions for torsion and bending creep of rods that obey the Norton–Bailey, Prandtl–Garofalo and Naumenko–Altenbach–Gorash constitutive models. The common secondary creep constitutive model is the Norton–Bailey law which gives a power law relationship between creep rate and stress. The closed form solutions for fractional Norton–Bailey creep law are derived. The analytical formulas express the torque and bending moment as functions of the time for the period of relaxation. Other formulas express the twist rate and curvature as functions of the time for the duration of engineering creep experiment. The derived formulas are suitable for the practically important problems of machinery. Namely, the formulas are relevant for calculation of hereditary effects for helical, leaf and disk springs and twisted shafts