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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2016, Volume 20, Number 3, Pages 524–543 (Mi vsgtu1512)  

This article is cited in 11 scientific papers (total in 11 papers)

Mechanics of Solids

Long-term strength curves generated by the nonlinear Maxwell-type model for viscoelastoplastic materials and the linear damage rule under step loading

A. V. Khokhlov

Lomonosov Moscow State University, Institute of Mechanics, Moscow, 119192, Russian Federation

Abstract: The nonlinear Maxwell-type constitutive relation with two arbitrary material functions is formulated for viscoelastoplastic materials and studied analytically in uni-axial case to reveal capabilities of the model and its applicability scope. Its coupling with a number of fracture criteria is analyzed in order to simulate creep rupture under constant and piecewise-constant loading and to compare creep life estimates arising as a result. The limit strain criterion, the critical dissipation criterion and two proposed new families of failure criteria taking into account a strain history (i.e. a whole creep curve) are considered. Long-term strength curves equations generated by each one of the four chosen failure criteria are derived. Their general qualitative properties are analyzed and compared to each other under minimal restrictions on material functions of the constitutive relation. It is proved that qualitative properties of all theoretic long-term strength curves coincide with basic properties of typical test long-term strength curves of viscoelastoplastic materials. For every failure criteria considered herein, rapture time under step-wise loading is evaluated for arbitrary material functions and compared to the lifetime yielding from the linear damage accumulation rule (i.e. “Miners rule”). General formulas for cumulative damage (“Miners sum”) deviations from unity are obtained for all failure criteria coupled with the nonlinear Maxwell-type constitutive relation. Their dependences on material functions and loading program parameters are examined. In particular, it is proved that the linear damage rule is exactly valid for the critical dissipation criterion whatever material functions, number of loading steps and stress levels are chosen. On the contrary, for the limit strain criterion, the linear damage rule is never valid for two-step loading and cumulative damage at rapture instant is greater or less than unity depending on the sign of stress jump.

Keywords: viscoelastoplasticity, creep curves, damage, failure criteria, dissipation, creep rupture, creep lifetime, long-term strength curves, superplasticity

DOI: https://doi.org/10.14498/vsgtu1512

Full text: PDF file (664 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 539.378
MSC: 74R20, 74D99, 74C99
Original article submitted 15/VII/2016
revision submitted – 04/IX/2016

Citation: A. V. Khokhlov, “Long-term strength curves generated by the nonlinear Maxwell-type model for viscoelastoplastic materials and the linear damage rule under step loading”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:3 (2016), 524–543

Citation in format AMSBIB
\Bibitem{Kho16}
\by A.~V.~Khokhlov
\paper Long-term strength curves generated by the nonlinear Maxwell-type model
for viscoelastoplastic materials and the linear damage rule under step loading
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 3
\pages 524--543
\mathnet{http://mi.mathnet.ru/vsgtu1512}
\crossref{https://doi.org/10.14498/vsgtu1512}
\zmath{https://zbmath.org/?q=an:06964524}
\elib{https://elibrary.ru/item.asp?id=28282247}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Khokhlov, “Nelineinaya model vyazkouprugoplastichnosti tipa Maksvella: modelirovanie vliyaniya temperatury na krivye deformirovaniya, relaksatsii i polzuchesti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:1 (2017), 160–179  mathnet  crossref  elib
    2. A. V. Khokhlov, “Analysis of general properties of creep curves generated by the rabotnov nonlinear hereditary relation under multi-step loadings”, Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2017, no. 3 (72), 93–123 (In Russian)  crossref  elib  scopus
    3. A. V. Khokhlov, “Analiz obschikh svoistv krivykh polzuchesti pri tsiklicheskikh stupenchatykh nagruzheniyakh, porozhdaemykh lineinoi teoriei nasledstvennosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:2 (2017), 326–361  mathnet  crossref  zmath  elib
    4. A. V. Khokhlov, “Nelineinaya model vyazkouprugoplastichnosti tipa maksvella: skorost nakopleniya plasticheskoi deformatsii pri tsiklicheskikh nagruzheniyakh”, Deformatsiya i razrushenie materialov, 2017, no. 7, 7–19  elib
    5. A. V. Khokhlov, “Svoistva semeistva krivykh nagruzheniya s postoyannoi skorostyu, porozhdaemykh nelineinoi modelyu vyazkouprugoplastichnosti tipa Maksvella”, Mashinostroenie i inzhenernoe obrazovanie, 2017, no. 1 (50), 57–71  elib
    6. A. V. Khokhlov, “A nonlinear Maxwell-type model for rheonomous materials: stability under symmetric cyclic loadings”, Moscow University Mechanics Bulletin, 73:2 (2018), 39–42  mathnet  crossref  zmath  isi
    7. A. V. Khokhlov, “Cvoistva diagramm nagruzheniya i razgruzki, porozhdaemykh nelineinym opredelyayuschim sootnosheniem tipa Maksvella dlya reonomnykh materialov”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:2 (2018), 293–324  mathnet  crossref  zmath  elib
    8. 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  crossref  elib
    9. 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  mathnet  crossref
    10. A. V. Khokhlov, “Applicability Indicators and Identification Techniques for a Nonlinear MaxwellType Elastoviscoplastic Model Using LoadingUnloading Curves”, Mechanics of Composite Materials, 55:2 (2019), 195–210  crossref  scopus
    11. A. V. Khokhlov, “Deformation and long-term strength of a thick-walled tube of a physically non-linear viscoelastic material under constant pressure”, Russ. Metall., 2020:10 (2020), 1079–1087  crossref  isi  scopus
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