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Relaxation and creep in twist and flexure

V. Kobelev (Department of Natural Sciences, University of Siegen, Siegen, Germany)

Multidiscipline Modeling in Materials and Structures

ISSN: 1573-6105

Article publication date: 7 October 2014




The purpose of this paper is to derive the exact analytical expressions for torsion and bending creep of rods with the Norton-Bailey, Garofalo and Naumenko-Altenbach-Gorash constitutive models. These simple constitutive models, for example, the time- and strain-hardening constitutive equations, were based on adaptations for time-varying stress of equally simple models for the secondary creep stage from constant load/stress uniaxial tests where minimum creep rate is constant. The analytical solution is studied for Norton-Bailey and Garofalo laws in uniaxial states of stress.


The creep component of strain rate is defined by material-specific creep law. In this paper the authors adopt, following the common procedure Betten, an isotropic stress function. The paper derives the expressions for strain rate for uniaxial and shear stress states for the definite representations of stress function. First, in this paper the authors investigate the creep for the total deformation that remains constant in time.


The exact analytical expressions giving the torque and bending moment as a function of the time were derived.

Research limitations/implications

The material isotropy and homogeneity preimposed. The secondary creep phase is considered.

Practical implications

The results of creep simulation are applied to practically important problem of engineering, namely for simulation of creep and relaxation of helical and disk springs.


The new, closed form solutions with commonly accepted creep models allow a deeper understanding of such a constitutive model's effect on stress and deformation and the implications for high temperature design. The application of the original solutions allows accurate analytic description of creep and relaxation of practically important problems in mechanical engineering. Following the procedure the paper establishes closed form solutions for creep and relaxation in helical, leaf and disk springs.



Kobelev, V. (2014), "Relaxation and creep in twist and flexure", Multidiscipline Modeling in Materials and Structures, Vol. 10 No. 3, pp. 304-327.



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