Properties of stress-strain curves generated by the nonlinear Maxwell-type viscoelastoplastic model under loading and unloading at constant stress rates

A. V. Khokhlov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 2, pp. 293-324.

Résumé

A physically nonlinear Maxwell-type constitutive relation for non-aging rheonomic materials is studied analytically to find out the set of basic rheological phenomena that it simulates, to indicate its application field and to develop identification techniques and ways of tuning and further modifications. Under minimal primary restrictions on two material functions of the relation, the general equation of theoretic stress-strain curves family produced by the model under loading and unloading at constant stress rates is derived and analyzed in uni-axial case. Intervals of monotonicity and convexity of loading and unloading curves, conditions for existence of extremum and inflection points, magnitudes of maximal strain, strain rate jumps and plastic strain arising as a result of loading- unloading cycle are considered and their dependences on material functions and on stress rate and maximal stress are examined. The main qualitative properties of stress-strain curves and unloading responses generated by the constitutive equation are compared to typical properties of test loading-unloading curves of viscoelastoplastic materials in order to elucidate capabilities of the model, to obtain necessary phenomenological restrictions which should be imposed on the material functions and to find convenient indicators of applicability (or non-applicability) that can (and should) be checked examining test data of a material.

Détail

Keywords: elastoviscoplasticity, stress-strain curves, stress rate, unloading response, rate sensitivity, instantaneous modulus, equilibrium stress-strain curve, tension compression asymmetry, superplasticity, polymers.

Bibliographie

[1] Khokhlov A. V., “Properties of a nonlinear viscoelastoplastic model of Maxwell type with two material functions”, Moscow University Mechanics Bulletin, 71:6 (2016), 132–136 | DOI | Zbl

[2] Khokhlov A. V., “The nonlinear Maxwell-type viscoelastoplastic model: Properties of creep curves at piecewise-constant stress and criterion for plastic strain accumulation”, Mashinostroenie i inzhenernoe obrazovanie, 2016, no. 3, 55–68 (In Russian)

[3] Khokhlov A. V., “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 (In Russian) | DOI | Zbl

[4] Khokhlov A.V., “Nonlinear Maxwell-type elastoviscoplastic model: General properties of stress relaxation curves and restrictions on the material functions”, Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2017, no. 6, 31–55 (In Russian) | DOI

[5] Khokhlov A. V., “Properties of stress-strain curves generated by the nonlinear Maxwell-type viscoelastoplastic model at constant stress rates”, Mashinostroenie i inzhenernoe obrazovanie, 2017, no. 1, 57–71 (In Russian)

[6] Khokhlov A. V., “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 (In Russian) | DOI

[7] “Nonlinear Maxwell-type viscoelastoplastic model: rate of plastic strain accumulation under cyclic loadings”, Deformatsiia i razrushenie materialov, 2017, no. 7, 7–19 (In Russian)

[8] Khokhlov A. V., “Identification methods of Maxwell-type nonlinear viscoelastoplastic model, based on creep curves with initial ramp loading. Part II. Methods”, Deformatsiia i razrushenie materialov, 2017, no. 10, 2–9 (In Russian)

[9] Kolarov D., Baltov A., Boncheva N., Mekhanika plasticheskikh sred [Mechanics of Plastic Media], Mir, Moscow, 1979, 304 pp. (In Russian)

[10] Koltunov M. A., Maiboroda V. P., Zubchaninov V. G., Prochnostnye raschety izdelii iz polimernykh materialov [Strength Calculations of Products Made of Polymer Materials], Mashinostroenie, Moscow, 1983, 239 pp. (In Russian)

[11] Kaibyshev O. A., Sverkhplastichnost' promyshlennykh splavov [Superplasticity of Industrial Alloys], Metallurgiia, Moscow, 1984, 264 pp. (In Russian)

[12] Vasin R. A., Enikeev F. U., Vvedenie v mekhaniku sverkhplastichnosti [Introduction to the Mechanics of Superplasticity], Gilem, Ufa, 1998, 280 pp. (In Russian)

[13] Nieh T. G., Wadsworth J., Sherby O. D., Superplasticity in metals and ceramics, Cambridge Univ. Press, Cambridge, 1997, 273+xiv pp. | DOI

[14] Segal V. M., Beyerlein I. J., Tome C. N., Chuvil'deev V. N., Kopylov V. I., Fundamentals and Engineering of Severe Plastic Deformation, Materials Science and Technologies Series, Nova Science Pub. Inc, New York, 2010, 542+xi pp.

[15] Lin Y. C., Chen X.-M., “A critical review of experimental results and constitutive descriptions for metals and alloys in hot working”, Materials and Design, 32:4 (2011), 1733–1759 | DOI

[16] McClung A. J. W., Ruggles-Wrenn M. B., “The rate (time)-dependent mechanical behavior of the PMR-15 thermoset polymer at elevated temperature”, Polymer Testing, 27:7 (2008), 908–914 | DOI

[17] Kästner M., Obst M., Brummund J., et al., “Inelastic material behavior of polymers – Experimental characterization, formulation and implementation of a material model”, Mech. Mater., 52 (2012), 40–57 | DOI

[18] Kim J.W., Medvedev G.A., Caruthers J.M., “Nonlinear stress relaxation in an epoxy glass and its relationship to deformation induced mobility”, Polymer, 54:15 (2013), 3949–3960 | DOI

[19] Yun K.-S., Park J.-B., Jung G.-D., Youn S.-K., “Viscoelastic constitutive modelling of solid propellant with damage”, Int. J. Sol. Struct., 34 (2016), 118–127 | DOI

[20] Xu J., Chen X., Wang H., Zheng J., Zhou C., “Thermo-damage-viscoelastic constitutive model of HTPB composite propellant”, Int. J. Sol. Struct., 51:18 (2014), 3209–3217 | DOI

[21] Krempl E., Khan F., “Rate (time)-dependent deformation behavior: an overview of some properties of metals and solid polymers”, Int. J. Plasticity, 19:7 (2003), 1069–1095 | DOI | Zbl

[22] Khan A. S., Farrokh B., “Thermo-mechanical response of nylon 101 under uniaxial and multi-axial loadings: Part I, Experimental results over wide ranges of temperatures and strain rates”, Int. J. Plasticity, 22:8 (2006), 1506–1529 | DOI | Zbl

[23] Taleb L., Cailletaud G., “Cyclic accumulation of the inelastic strain in the 304L SS under stress control at room temperature: Ratcheting or creep?”, Int. J. Plasticity, 27:12 (2011), 1936–1958 | DOI | Zbl

[24] Zhang J., Wang Y., Zan X., Wang Y., “The constitutive responses of Ti-6.6Al-3.3Mo-1.8Zr-0.29Si alloy at high strain rates and elevated temperatures”, J. All. Compounds, 647 (2015), 97–104 | DOI

[25] Bergstrom J. S., Mechanics of Solid Polymers. Theory and Computational Modeling, Elsevier, William Andrew, 2015, 509+xiv pp. | DOI

[26] Lee W.-S., Lin C.-R., “Deformation behavior and microstructural evolution of 7075-T6 aluminum alloy at cryogenic temperatures”, Cryogenics, 79 (2016), 26–34 | DOI

[27] Xiong Y., Yu Q., Jiang Y., “An experimental study of cyclic plastic deformation of extruded ZK60 magnesium alloy under uniaxial loading at room temperature”, Int. J. Plasticity, 53:2 (2014), 107–124 | DOI

[28] Launay A., Maitournam M. H.,. Marco Y., Raoult I., Szmytka F., “Cyclic behaviour of short glass fibre reinforced polyamide: Experimental study and constitutive equations”, Int. J. Plasticity, 27:8 (2011), 1267–1293 | DOI | Zbl

[29] Da Costa Mattos H. S., Reis J. M. L., De Medeiros L. G. M. O., Monteiro A. H., Teixeira S. C. S., Chaves E. G., “Analysis of the cyclic tensile behaviour of an elasto-viscoplastic polyamide”, Polymer Testing, 58 (2017), 40–47 | DOI

[30] Kujawski D., Kallianpur V., Krempl E., “An experimental study of uniaxial creep, cyclic creep and relaxation of aisi type 304 stainless steel at room temperature”, J. Mech. Phys. Solids, 28:2 (1980), 129–148 | DOI

[31] Drozdov A. D., Klitkou R., Christiansen J., “Multi-cycle deformation of semicrystalline polymers: Observations and constitutive modeling”, Mech. Res. Commun., 48 (2013), 70–75 | DOI

[32] Jiang Y., Zhang J., “Benchmark experiments and characteristic cyclic plasticity deformation”, Int. J. Plasticity, 24:9 (2008), 1481–1515 | DOI | Zbl

[33] Fung Y. C., Biomechanics. Mechanical Properties of Living Tissues, Springer-Verlag, New York, 1993, 568+xviii pp. | DOI

[34] Lakes R. S., Viscoelastic Materials, Cambridge Univ. Press, Cambridge, 2009, 461+xvi pp. | DOI

[35] Diani J., Fayolle B., Gilormini P., “A review on the Mullins effect”, Eur. Polym. J., 45 (2009), 601–612 | DOI

[36] Machado G., Chagnon G., Favier D., “Induced anisotropy by the Mullins effect in filled silicone rubber”, Mech. Mater., 50 (2012), 70–80 | DOI

[37] Fernandes V. A., De Focatiis D. S., “The role of deformation history on stress relaxation and stress memory of filled rubber”, Polymer Testing, 40 (2014), 124–132 | DOI

[38] Zhu Y., Kang G., Yu C., Poh L. H., “Logarithmic rate based elasto-viscoplastic cyclic constitutive model for soft biological tissues”, J. Mech. Behav. Biomed. Mater., 61 (2016), 397–409 | DOI

[39] Drozdov A. D., Dusunceli N., “Unusual mechanical response of carbon black-filled thermoplastic elastomers”, Mech. Mater., 69:1 (2014), 116–131 | DOI

[40] Hassan T., Kyriakides S., “Ratcheting of cyclically hardening and softening materials: I. Uniaxial behavior”, Int. J. Plasticity, 10:2 (1994), 149–184 | DOI | MR

[41] Kang G., Kan Q., Zhang J., Sun Y., “Time-dependent ratchetting experiments of SS304 stainless steel”, Int. J. Plasticity, 22:5 (2006), 858–894 | DOI

[42] Kang G., “Ratchetting: recent progresses in phenomenon observation, constitutive modeling and application”, Int. J. Fatigue, 30:8 (2008), 1448–1472 | DOI

[43] Cao W., Kim Y. R., “A viscoplastic model for the confined permanent deformation of asphalt concrete in compression”, Mech. Mater., 92 (2016), 235–247 | DOI

[44] Kregers A. F., Vilks U. K., Leitane M. Ya., “Forward and reverse creep of a physically nonlinear polymer material”, Polymer Mechanics, 9:5 (1973), 696–703 | DOI

[45] Khan A. S., Lopez-Pamies O., “Time and temperature dependent response and relaxation of a soft polymer”, Int. J. Plasticity, 18:10 (2002), 1359–1372 | DOI

[46] Dorfmann A., Ogde R. W., “A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber”, Int. J. Sol. Struct., 41:7 (2004), 1855–1878 | DOI | Zbl

[47] Qi H., Boyce M., “Stress–strain behavior of thermoplastic polyurethanes”, Mech. Mater., 37:8 (2005), 817–839 | DOI

[48] Drozdov A. D., “Time-dependent response of polypropylene after strain reversal”, Int. J. Sol. Struct., 47:24 (2010), 3221–3233 | DOI | Zbl

[49] Khan F., Yeakle C., “Experimental investigation and modeling of non-monotonic creep behavior in polymers”, Int. J. Plasticity, 27:4 (2011), 512–521 | DOI | Zbl

[50] Khan F., Yeakle C., Gomaa S., “Characterization of the mechanical properties of a new grade of ultra high molecular weight polyethylene and modeling with the viscoplasticity based on overstress”, J. Mech. Behav. Biomed. Mater., 6:2 (2012), 174–180 | DOI

[51] Khohlov A.V., “The Qualitative Analysis of Theoretic Curves Generated by Linear Viscoelasticity Constitutive Equation”, Science and Education, 2016, no. 5, 187–245 (In Russian) | DOI

[52] Khokhlov A. V., “Specific features of stress-strain curves at constant stress rate or strain rate yielding from linear viscoelasticity”, Problemy prochnosti i plastichnosti, 77:2 (2015), 139–154 (In Russian)