Abstract:
The nonlinear Maxwell-type constitutive relation with two arbitrary material functions for viscoelastoplastic multi-modulus materials is studied analytically in uniaxial isothermic case to reveal the model abilities and applicability scope and to develop techniques of its identification, tuning and fitting. The constitutive equation is aimed at adequate modeling of the rheological phenomena set which is typical for reonomic materials exhibiting non-linear hereditary properties, strong strain rate sensitivity, secondary creep, yielding at constant stress, tension compression asymmetry and such temperature effects as increase of material compliance, strain rate sensitivity and rates of dissipation, relaxation, creep and plastic strain accumulation with temperature growth. The model is applicable for simulation of mechanical behaviour of various polymers, their solutions and melts, solid propellants, sand-asphalt concretes, composite materials, titanium and aluminum alloys, ceramics at high temperature and so on.
To describe the influence of temperature on material mechanical behavior (under isothermic conditions), two scalar material parameters of the model (viscosity coefficient and “modulus of elasticity”) are considered as a functions of temperature level. The general restrictions on their properties which are necessary and sufficient for adequate qualitative description of the basic thermomechanical phenomena related to typical temperature influence on creep and relaxation curves, creep recovery curves, creep curves under step-wise loading and quasi-static stress-strain curves of viscoelastoplastic materials are obtained. The restrictions are derived using systematic analytical study of general qualitative features of the theoretic creep and relaxation curves, creep curves under step-wise loading, long-term strength curves and stress-strain curves at constant strain or stress rates generated by the constitutive equation (under minimal restrictions on material functions) and their comparison to typical test curves of stable viscoelastoplastic materials. It is proved that the viscosity coefficient and the “modulus of elasticity” of the model and their ratio (i.e. relaxation time of the associated linear Maxwell model) should be decreasing functions of temperature. This requirements are proved to provide an adequate qualitative simulation of a dozen basic phenomena expressing an increase of material compliance (a decrease of tangent modulus and yield stress, in particular), strengthening of strain rate sensitivity and acceleration of dissipation, relaxation, creep and plastic strain accumulation with temperature growth.
Citation:
A. V. Khokhlov, “The nonlinear Maxwell-type model for viscoelastoplastic materials:
simulation of temperature influence on creep, relaxation and strain-stress curves”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:1 (2017), 160–179
\Bibitem{Kho17}
\by A.~V.~Khokhlov
\paper The nonlinear Maxwell-type model for viscoelastoplastic materials:
simulation of temperature influence on creep, relaxation and~strain-stress curves
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 1
\pages 160--179
\mathnet{http://mi.mathnet.ru/vsgtu1524}
\crossref{https://doi.org/10.14498/vsgtu1524}
\elib{https://elibrary.ru/item.asp?id=29245103}
Linking options:
https://www.mathnet.ru/eng/vsgtu1524
https://www.mathnet.ru/eng/vsgtu/v221/i1/p160
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, 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, “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, “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, “Equilibruim point and phase portrait of flow model for thixotropic media with consideration of the structure evolution”, Moscow University Mеchanics Bulletin, 78:4 (2023), 91–101
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, 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, “Generalization of a Nonlinear Maxwell-Type Viscoelastoplastic Model and Simulation of Creep and Recovery Curves”, Mech Compos Mater, 59:3 (2023), 441
A. M. Stolin, A. V. Khokhlov, “Nonlinear model of shear flow of thixotropic viscoelastoplastic continua taking into account the evolution of the structure and its analysis”, Moscow University Mechanics Bulletin, 77:5 (2022), 127–135
G. Kurt, A. Kasgoz, “Effects of molecular weight and molecular weight distribution on creep properties of polypropylene homopolymer”, J. Appl. Polym. Sci., 138:30 (2021), e50722
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
K. N. Galimzyanova, L. V. Kovtanyuk, G. L. Panchenko, “Polzuchest i plasticheskoe techenie materiala sfericheskogo vyazkouprugoplasticheskogo sloya pri ego nagruzke i razgruzke”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:2 (2019), 270–283
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, “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
T. Bobyleva, A. Shamaev, “The averaged model of layered elastic-creeping composite materials”, IOP Conference Series-Materials Science and Engineering, 365 (2018), UNSP 042078
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
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