Abstract:
Basic qualitative properties of the creep curves generated by the linear integral constitutive relation of viscoelasticity (with an arbitrary creep compliance) under cyclic piecewise-constant uni-axial loadings (with an arbitrary asymmetry stress ratio) are studied analytically. General formulas and a number of exact two-sided bounds are obtained for maximal, minimal and ratcheting strain values during each cycle, for their sequences limits, for the rate of plastic (non-recoverable) strain accumulation and for cyclic creep curve deviation from the creep curve at constant stress which is equal to the cycle mean stress. Their dependence on loading cycle parameters and creep compliance properties are analyzed. Monotonicity and convexity intervals of cyclic creep curves, sequences of maximal and minimal strain values and ratcheting strain sequence, their evolution with cycle number growth and conditions for their boundedness, monotonicity and convergence are examined. The linear viscoelasticity theory abilities for simulation of ratcheting, creep acceleration, cyclic hardening or softening and cyclic stability under symmetric cyclic loadings are considered. The analysis carried out revealed the importance of convexity restriction imposed on a creep compliance and the governing role of its derivative limit value at infinity. It is proved that the limit value equality to zero is the criterion for non-accumulation of plastic strain, for memory fading and for asymptotic symmetrization of cyclic creep curve deviation from the creep curve at the mean stress. The qualitative features of theoretic cyclic creep curves are compared to basic properties of typical test creep curves of viscoelastoplastic materials under cyclic multi-step uni-axial loadings in order to elucidate the linear theory applicability scope, to reveal its abilities to provide an adequate description of basic rheological phenomena related to cyclic creep and to develop techniques of identification and tuning of the linear constitutive relation. In particular, it is proved that the linear constitutive relation with an arbitrary (increasing convex-up) creep compliance function provides the absence of ratcheting and cyclic softening under symmetric cyclic multi-step loadings and the absence of creep acceleration whenever a symmetric cyclic loading is added to a constant load.
Keywords:
linear viscoelasticity, cyclic creep, creep curves at piecewise-constant loading, asymmetry stress ratio, mean stress, creep acceleration, plastic strain, ratcheting, cyclic stability.
Citation:
A. V. Khokhlov, “Analysis of creep curves produced by the linear viscoelasticity theory under cyclic stepwise loadings”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:2 (2017), 326–361
\Bibitem{Kho17}
\by A.~V.~Khokhlov
\paper Analysis of creep curves produced by the linear viscoelasticity theory under cyclic stepwise loadings
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 2
\pages 326--361
\mathnet{http://mi.mathnet.ru/vsgtu1533}
\crossref{https://doi.org/10.14498/vsgtu1533}
\zmath{https://zbmath.org/?q=an:06964677}
\elib{https://elibrary.ru/item.asp?id=30039932}
Linking options:
https://www.mathnet.ru/eng/vsgtu1533
https://www.mathnet.ru/eng/vsgtu/v221/i2/p326
This publication is cited in the following 16 articles:
A. V. Khokhlov, V. V. Gulin, “Influence of Structural Evolution and Load Level on the Properties of Creep and Recovery Curves Generated by a Nonlinear Model for Thixotropic Viscoelastoplastic Media”, Phys Mesomech, 28:1 (2025), 66
A. V. Khokhlov, “Hybridization of a Linear Viscoelastic Constitutive Equation and a Nonlinear Maxwell-Type Viscoelastoplastic Model, and Analysis of Poisson's Ratio Evolution Scenarios under Creep”, Phys Mesomech, 27:3 (2024), 229
A. S. Stolyarchuk, M. D. Romanenko, “Phenomenological Approach to Assessing the Low-Cycle Damageability of Metal Materials under Stationary and Nonstationary Loading”, Steel Transl., 54:3 (2024), 177
A.V. KHOKHLOV, V.V. GULIN, “INFLUENCE OF STRUCTURE EVOLUTION AND LOAD LEVEL ON THE PROPERTIES OF CREEP AND RECOVERY CURVES PRODUCED BY A NONLINEAR MODEL FOR THIXOTROPIC VISCOELASTOPLASTIC MEDIA”, FM, 27:5 (2024)
A. V. Khokhlov, “Generalization of a Nonlinear Maxwell-Type Viscoelastoplastic Model and Simulation of Creep and Recovery Curves”, Mech Compos Mater, 59:3 (2023), 441
A. V. Khokhlov, “On the capability of linear viscoelasticity theory to describe the effect of extending region of material linearity as the hydrostatic pressure grows”, Moscow University Mechanics Bulletin, 76:1 (2021), 7–14
A. V. Khokhlov, “Obschie svoistva pokazatelya skorostnoi chuvstvitelnosti diagramm deformirovaniya, porozhdaemykh lineinoi teoriei vyazkouprugosti i suschestvovanie maksimuma u ego zavisimosti ot skorosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 24:3 (2020), 469–505
A. V. Khokhlov, “Reshenie zadachi o napryazhenno-deformirovannom sostoyanii pologo tsilindra iz nelineino nasledstvennogo materiala pod deistviem vnutrennego i vneshnego davlenii”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 12:1 (2020), 44–54
A. V. Khokhlov, “Analiz vozmozhnostei opisaniya vliyaniya gidrostaticheskogo davleniya na krivye polzuchesti i koeffitsient poperechnoi deformatsii reonomnykh materialov v ramkakh lineinoi teorii vyazkouprugosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:2 (2019), 304–340
A. V. Khokhlov, “Analiz vliyaniya ob'emnoi polzuchesti na krivye nagruzheniya s postoyannoi skorostyu i evolyutsiyu koeffitsienta poperechnoi deformatsii v ramkakh lineinoi teorii vyazkouprugosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:4 (2019), 671–704
A. V. Khokhlov, “Monotonnoe vozrastanie pokazatelya skorostnoi chuvstvitelnosti lyubykh parallelnykh soedinenii lineinykh modelei vyazkouprugosti so stepennymi funktsiyami relaksatsii”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 11:3 (2019), 56–67
A. V. Khokhlov, “Properties of the set of strain diagrams produced by rabotnov nonlinear equation for rheonomous materials”, Mech. Sol., 54:3 (2019), 384–399
A. V. Khokhlov, “Osobennosti povedeniya poperechnoi deformatsii i koeffitsienta Puassona izotropnykh reonomnykh materialov pri polzuchesti, opisyvaemye lineinoi teoriei vyazkouprugosti”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 10:4 (2018), 65–77
A. V. Khokhlov, “Indikatory primenimosti i metodiki identifikatsii nelineinoi modeli tipa maksvella dlya reonomnykh materialov po krivym polzuchesti pri stupenchatykh nagruzheniyakh”, Vestnik Moskovskogo gosudarstvennogo tekhnicheskogo universiteta im. N. E. Baumana. Seriya: Estestvennye nauki, 2018, no. 6 (81), 92–112
A. V. Khokhlov, “Sravnitelnyi analiz svoistv krivykh polzuchesti, porozhdaemykh lineinoi i nelineinoi teoriyami nasledstvennosti pri stupenchatykh nagruzheniyakh”, Matematicheskaya fizika i kompyuternoe modelirovanie, 21:2 (2018), 27–51
A. V. Khokhlov, “Two-sided estimates for the relaxation function of the linear theory of heredity via the relaxation curves during the ramp-deformation and the methodology of identification”, Mech. Sol., 53:3 (2018), 307–328
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