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Correspondence principles for complex shear characteristics in a nonisothermal model of monoharmonic approximation for physically nonlinear materials

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The Bodner-Partom nonisothermal flow model and the generalized method of harmonic linearization are used to calculate the complex shear modulus and compliance for AMg-6 aluminum alloy. The strain-and stress-controlled cycles of loading in the temperature range 20–400°C are considered. The correspondence between the shear modulus and the compliance is studied. It is similar to the inverse proportionality condition in the theory of linear viscoelasticity. It is established that representing the modulus and compliance as functions of the strain amplitude is better than as functions of the stress amplitude due to the universal description of the characteristics for soft and hard cycles and high accuracy of correspondence

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References

  1. T. Alfrey, Jr., Mechanical Behavior of High Polymers, Interscience, New York (1948).

    Google Scholar 

  2. N. I. Bezukhov, V. L. Bazhanov, I. I. Gol'denblat, et al., High-Temperature Strength Analysis in Mechanical Engineering [in Russian], Mashinostroenie, Moscow (1965).

    Google Scholar 

  3. D. R. Bland, The Theory of Linear Viscoelasticity, Pergamon Press, New York (1960).

    MATH  Google Scholar 

  4. I. K. Senchenkov and V. G. Karnaukhov, “Thermomechanical behavior of nonlinearly viscoelastic materials under harmonic loading,” Int. Appl. Mech., 37, No. 11, 1400–1432 (2001).

    Article  MathSciNet  Google Scholar 

  5. I. K. Senchenkov and S. V. Novikov, “Spectral approach to the description of the cyclic deformation and dissipative heating of viscoplastic bodies,” Int. Appl. Mech., 26, No. 10, 985–991 (1990).

    MATH  Google Scholar 

  6. I. K. Senchenkov and G. A. Tabieva, “Determination of the parameters of the Bodner-Partom model for thermoviscoplastic deformation of materials,” Int. Appl. Mech., 32, No. 2, 132–139 (1996).

    Article  MATH  Google Scholar 

  7. I. K. Senchenkov, V. G. Karnaukhov, and V. I. Kozlov, “Toward a theory of governing equations of nonlinear thermoviscoelasticity for periodic deformation,” Int. Appl. Mech., 22, No. 8, 783–789 (1986).

    MATH  Google Scholar 

  8. I. K. Senchenkov, Ya. A. Zhuk, G. A. Tabieva, and O. P. Chervinko, “Generalized scleronomic model of the harmonic deformation of elastoviscoplastic bodies,” Int. Appl. Mech., 33, No. 6, 466–473 (1997).

    Article  Google Scholar 

  9. S. V. Serensen, Resistance of Materials to Fatigue and Brittle Fracture [in Russian], Atomizdat, Moscow (1975).

    Google Scholar 

  10. S. V. Serensen and R. M. Shneiderovich (eds.), Resistance to Deformation and Fracture under Low-Cycle Loading [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  11. J. D. Ferry, Viscoelastic Properties of Polymers, 3rd ed., Wiley, New York (1980).

    Google Scholar 

  12. O. P. Chervinko, “Modeling vibrations in vibroprotection systems with viscoplastic vibration isolators,” Mekh. Giroscop. Sist., 17–18, 218–226 (2001–2002).

    Google Scholar 

  13. O. P. Chervinko, “Modeling vibrations in vibroprotection systems with nonlinear viscoelastic vibration isolators,” Mekh. Giroscop. Sist., 17-18, 226–233 (2001–2002).

    Google Scholar 

  14. S. Bodner, Unified Plasticity—An Engineering Approach, Final Report, Technion, Haifa (2000).

    Google Scholar 

  15. O. P. Chervinko, I. K. Senchenkov, and N. N. Yakimenko, “Vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion,” Int. Appl. Mech., 43, No. 6, 647–653 (2007).

    Article  Google Scholar 

  16. L. J. Coffin, “Fatigue at high temperature—Prediction and interpretation,” in: Proc. Inst. Mech. Eng., 188, No. 9, 109–127 (1974).

    Article  Google Scholar 

  17. B. Gross, Mathematical Structure of Theory of Viscoelasticity, Herrman, Paris (1953).

    Google Scholar 

  18. V. G. Karnaukhov and Yu. V. Revenko, “Dissipative heating of a viscoelastic cylinder steadily rolling over a rigid foundation,” Int. Appl. Mech., 42, No. 1, 51–60 (2006).

    Article  Google Scholar 

  19. I. K. Senchenkov, Ya. A. Zhuк, and V. G. Karnaukhov, “Modeling the thermomechanical behavior of physically nonlinear materials under monoharmonical loading,” Int. Appl. Mech., 40, No. 9, 943–969 (2004).

    Article  Google Scholar 

  20. I. K. Senchenkov and N. F. Andrushko, “Thermomechanical coupling effects in a materially nonlinear disk under impulsive radial loading,” Int. Appl. Mech., 42, No. 8, 951–958 (2006).

    Article  Google Scholar 

  21. H. D. Dui and Q. S. Nguyen (eds.), Thermomechanical Couplings in Solids, Elsevier (1986).

  22. Ya. A. Zhuk and I. K. Senchenkov, “On linearization of the stiffness characteristics of flexible beams made of physically nonlinear materials,” Int. Appl. Mech., 42, No. 2, 196–202 (2006).

    Article  Google Scholar 

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Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 52–63, August 2008.

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Chervinko, O.P., Senchenkov, I.K. Correspondence principles for complex shear characteristics in a nonisothermal model of monoharmonic approximation for physically nonlinear materials. Int Appl Mech 44, 872–881 (2008). https://doi.org/10.1007/s10778-008-0103-5

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  • DOI: https://doi.org/10.1007/s10778-008-0103-5

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