Khokhlov A.V. Сomparative Analysis of Creep Curves Properties Generated by Linear and Nonlinear Heredity Theories under Multi-Step Loadings

https://doi.org/10.15688/mpcm.jvolsu.2018.2.3

Andrey Vladimirovich Khokhlov
Candidate of Technical Sciences,
Senior Researcher, Laboratory for Elasticity and Plasticity,
Scientific Research Institute for Mechanics, Lomonosov Moscow State University
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Рrosp. Michurinskiy, 1, 119192 Moscow, Russian Federation

Abstract. The general equation and basic properties of theoretic creep curves generated by the linear integral constitutive relation of viscoelasticity or by the Rabotnov nonlinear (quasi-linear) constitutive relation under arbitrary multi-step uni-axial loadings have been studied analytically with the implication that material functions are arbitrary.

The Rabotnov constitutive relation generalizes the Boltzmann-Volterra linear relation in a uni-axial case by introducing the second material function (the non-linearity function) beside the creep compliance. The Rabotnov equation is aimed at adequate modeling of the rheological  phenomena  set  which  is  typical  for  isotropic  rheonomic  materials  exhibiting non-linear  hereditary  properties,  strong  strain  rate  sensitivity  and  tension-compression asymmetry. The model is applicable for simulation of mechanical behaviour of various polymers,  isotropic  composites,  metals  and  alloys,  ceramics  at  high  temperature,  biological tissues and so on.

The qualitative features of the theoretic creep curves produced by the relations mentioned above are examined and compared to each other and to basic properties of typical test creep curves of viscoelastoplastic materials under multi-step uni-axial loadings in order to find out inherited (from linear viscoelasticity) properties and additional capabilities of  the  non-linear  relation,  to  elucidate  and  compare  the  applicability  (or  non-applicability)  scopes  of  the  linear  and  quasi-linear  relations,  to  reveal  their  abilities  to provide an adequate description of basic rheological phenomena related to creep, recovery and cyclic creep, to find the zones of material functions influence and necessary phenomenological restrictions on material functions and to develop techniques for their identification and tuning. Assuming the material functions are arbitrary, we study analytically the theoretic creep curves properties dependence on creep compliance function, the non-linearity  function  and  parameters  of  loading  programs.  We  analyze  monotonicity  and convexity intervals of creep curves, conditions for existence of extrema or flexure points, asymptotic behavior at infinity and deviation from the associated creep curve at constant stress, conditions for memory fading, the formula for plastic strain after complete unloading (after recovery), influence of a stress steps permutation and the asymptotic commutativity phenomenon, ratcheting rate and a criterion for non-accumulation of plastic strain under  cyclic  loadings,  the  relations  for  strain  and  strain  rate  jumps  produced  by  given stress jumps and the phenomenon of elastic strain drift due to creep, etc. A number of effects are pointed out that the nonlinear model (and the linear theory as well) can’t simulate whatever material functions are taken.

Key words: elastoviscoplasticity, multi-step  loading, creep curves, asymptotics, recovery, memory decay, plastic strain accumulation, ratcheting, asymptotic commutativity, regular and singular models.

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Сomparative Analysis of Creep Curves Properties Generated by Linear and Nonlinear Heredity Theories under Multi-Step Loadings by Khokhlov A.V. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 21 No. 2 2018, pp. 27-51

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