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Анализ общих свойств кривых ползучести при ступенчатых нагружениях…
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2017. № 3
119
ANALYSIS OF GENERAL PROPERTIES OF CREEP CURVES GENERATED
BY THE RABOTNOV NONLINEAR HEREDITARY RELATION UNDER
MULTI-STEP LOADINGS
A.V. Khokhlov
andrey-khokhlov@ya.ruInstitute of Mechanics, Lomonosov Moscow State University,
Moscow, Russian Federation
Abstract
Keywords
We analyze basic properties of the theoretic creep curves
under arbitrary piecewise-constant uniaxial stress histories
generated by the Rabotnov constitutive relation with two
material functions for elastoviscoplastic materials which
exhibit a pronounced nonlinear heredity, rate sensitivity
and multi-modulus behavior. Under minimal primary
restrictions on the material functions of the relation, we
study analytically the creep curves properties dependence
on creep compliance function and loading program pa-
rameters, their asymptotic behavior at infinity, conditions
of memory fading, formula for plastic strain after complete
unloading (after recovery), influence of stress steps permu-
tation, relations for strain and strain rate jumps produced
by given stress jumps, etc. We compare the qualitative
features of theoretic creep curves to typical test creep
curves properties of rheonomous materials under multi-
step uniaxial loadings in order to examine the Rabotnov
relation abilities to provide an adequate description of
basic rheological phenomena related to creep and recovery,
to find the zones of material functions influence and neces-
sary phenomenological restrictions on material functions,
to indicate the field of applicability or non-applicability of
the model and to develop techniques for its identification
and tuning. We compare the arsenal of capabilities of the
Rabotnov nonlinear constitutive relation and its applicabi-
lity scope to capabilities of the Boltzmann — Volterra
linear viscoelasticity theory which was generalized to state
the Rabotnov relation. We elucidate the inherited proper-
ties and the acquired properties due to the introduction of
the second material function providing a sort of physical
non-linearity
Elastoviscoplasticity, tension compres-
sion asymmetry, piecewise-constant
loading, creep curves, asymptotics,
recovery, fading memory, plastic
strain accumulation, regular and
singular models
REFERENCES
[1] Rabotnov Yu.N. Creep problems in structural members. Amsterdam, London, North-
Holland Publ. Co., 1969. 822 p.
[2] Bugakov I.I. Polzuchest' polimernykh materialov [Polymer materials creep]. Moscow, Nauka
Publ., 1973. 287 p.