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. “Miner’s rule”). General formulas for cumulative damage (“Miner’s 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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/vsgtu1512
https://www.mathnet.ru/eng/vsgtu/v220/i3/p524
This publication is cited in the following 23 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, V. V. Gulin, “Families of Stress-Strain, Relaxation, and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 1. The model, Its Basic Properties, Integral Curves, and Phase Portraits”, Mech Compos Mater, 60:1 (2024), 49
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. V. Khokhlov, V. V. Gulin, “Families of Stress–Strain, Relaxation and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 2. Relaxation and Stress-Strain Curves”, Mech Compos Mater, 60:2 (2024), 259
A. V. Khokhlov, V. V. Gulin, “Families of Stress-Strain, Relaxation, and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 3. Creep Curves”, Mech Compos Mater, 60:3 (2024), 473
A. V. Khokhlov, “Creep curves generated by a nonlinear flow model of tixotropic viscoelastoplastic media taking into account structure evolution”, Moscow University Mеchanics Bulletin, 79:4 (2024), 119–129
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, A. V. Shaporev, O. N. Stolyarov, “Loading-Unloading-Recovery Curves for Polyester Yarns and Identification of the Nonlinear Maxwell-Type Viscoelastoplastic Model”, Mech Compos Mater, 59:1 (2023), 129
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, V. V. Gulin, “Analysis of the Properties of a Nonlinear Model for Shear Flow of Thixotropic Media Taking into Account the Mutual Influence of Structural Evolution and Deformation”, Phys Mesomech, 26:6 (2023), 621
A. V. Khokhlov, “Creep and Long-Term Strength of a Laminated Thick-Walled Tube of Nonlinear Viscoelastic Materials Loaded by External and Internal Pressures”, Mech Compos Mater, 57:6 (2022), 731
V. M. Mikhalevich, I. V. Abramchuk, “Maximum Accumulated Strain for Linear Two-Link Triangle-Like Deformation Trajectories”, Int Appl Mech, 57:6 (2021), 720
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
A. V. Khokhlov, “Applicability Indicators and Identification Techniques for a Nonlinear Maxwell–Type Elastoviscoplastic Model Using Loading–Unloading Curves”, Mechanics of Composite Materials, 55:2 (2019), 195–210
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
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
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, “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
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)
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