Theory of inelasticity without loading surface and associated flow rule

Abstract


Based on the analysis of experimental hysteresis loops (cyclic diagram) of steel 40Х16Н9Г2С three sections are allocated describing the different behavior of the stress, i.e., three types of stresses. For each type of stress the authors have formulated appropriate evolutionary equations characterizing anisotropic hardening. To describe isotropic hardening, evolutionary equation for the parameter saturation stresses of the second type is introduced. In case of additional isotropic hardening under non-proportional cyclic loading we consider the stress saturation parameter of the second type dependent on the measure of disproportionality (complexity) of the loading process. To describe the phenomena of ratcheting under non-symmetric soft cyclic loading we consider the parameter, which is an evolutionary equation for the stress of the first type to be dependent on the accumulated strain. The stress deviator is defined as the sum of stress deviators of three types. To describe the nonlinear process of damage accumulation, the authors introduced the kinetic equation based on the energy principle, where energy equal to the work of stress of the second type on the deformations field is taken as energy spent on creating damage in the material. Kinetic equation for damage caused by stress of the first type on the field deformations is introduced under nonsymmetrical soft cyclic loading in case of ratcheting of the hysteresis loop. It became possible to assign material functions, close theory, formulate the basic experiment and the method of material functions identification. We have presented material functions of steel 40Х16Н9Г2С and the results of verification of the theory under proportional (simple) hard cyclic loading and disproportionate (complex) loading sweep deformations in the form of concentric circles with a common center at the origin of coordinates. Five turns of the trajectory, from the trajectory of the greater curvature to the average trajectory curvature, are considered. There is a reliable agreement between the results of calculations and experiments.

About the authors

V S Bondar

Moscow State University of Mechanical Engineering (MAMI)

V V Danshin

Moscow State University of Mechanical Engineering (MAMI)

References

  1. Бондарь В.С. Неупругость. Варианты теории. - М.: Физматлит, 2004. - 144 с.
  2. Бондарь В.С., Даншин В.В. Пластичность. Пропорциональные и непропорциональные нагружения. - М.: Физматлит, 2008. - 176 с.
  3. Bondar V.S. Inelasticity. Variants of the theory. - New York: Begell House, 2013. - 194 p.
  4. Волков И.А., Коротких Ю.Г. Уравнения состояния вязкоупругопластических сред с повреждениями. - М.: Физматлит, 2008. - 424 с.
  5. Bari S., Hassan T. An advancement in cyclic plasticity modeling for multiaxial ratcheting simulation // International Journal of Plasticity. - 2002. - Vol. 18. - P. 873-894.
  6. Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel: Damage evolution and damage-coupled viscoplastic constitutive model / G. Kang, Y. Liu, J. Ding, Q. Gao // Int. J. of Plasticity. - 2009. - Vol. 25. - P. 838-860.
  7. Kan Q., Kang G. Constitutive model for uniaxial transformation ratcheting of super-elastic NiTi shape memory alloy at room temperature // Int. J. of Plasticity. - 2009. doi: 10.1016/j.ijplas.2009.08.005.
  8. Chaboche J.-L. A review of some plasticity and viscoplasticity constitutive theories // Int. J. of Plasticity. - 2008. - Vol. 24. - P. 1642-1692.
  9. Rahman S.M., Hassan T., Corona E. Evaluation of cyclic plasticity models in ratcheting simulation of straight pipes under cyclic bending and steady internal pressure // Int. J. of Plasticity. - 2008. - Vol. 24. - P. 1756-1791.
  10. Abdel-Karim M. Modified kinematic hardening rules for simulations of ratchetting // Int. J. of Plasticity. - 2009. - Vol. 25. - P. 1560-1587.
  11. Abdel-Karim M. An evaluation for several kinematic hardening rules on prediction of multiaxial stress-controlled ratchetting // Int. J. of Plasticity. - 2010. - Vol. 26. - P. 711-730.
  12. Dafalias Y.F., Feigenbaum H.P. Biaxial ratchetting with novel variations of kinematic hardening // Int. J. of Plasticity. - 2011. - Vol. 27. - P. 479-491.
  13. Chaboche J.-L., Kanouté P., Azzouz F. Cyclic inelastic constitutive equations and their impact on the fatigue life predictions // Int. J. of Plasticity. - 2012. - Vol. 35. - P. 44-66.
  14. Бондарь В.С., Бурчаков С.В., Даншин В.В. Математическое моделирование процессов упругопластического деформирования и разрушения материалов при циклических нагружениях // Проблемы прочности и пластичности: межвуз. сб. Вып. 72. - Нижний Новгород: Изд-во Нижегород. гос. ун-та, 2010. - С. 18-27.
  15. Бондарь В.С., Даншин В.В., Макаров Д.А. Математическое моделирование процессов деформирования и накопления повреждений при циклических нагружениях // Вестник Пермского национального исследовательского политехнического университета. Механика. - 2014. - № 2. - С. 125-152.
  16. Охлопков Н.Л. Закономерности процессов упругопластического деформирования металлов при сложном напряженном состоянии и нагружении: автореф. … дис. д-ра техн. наук / Твер. гос. техн. ун-т. - Тверь, 1997. - 35 с.
  17. Ишлинский А.Ю. Общая теория пластичности с линейным упрочнением // Укр. матем. журн. - 1954. - Т. 6. - Вып. 3. - С. 314-324.
  18. Prager W. The theory of plasticity: A. Survey of Recent Achievements // Proc. Inst. Mech. Engrs. London. 1955. - 169.41.
  19. Amstrong P.J., Frederick C.O. A mathematical represention of the multiaxial bauscinger effect // CEGB Report No. RD/B/N/ 731. - 1966.
  20. Кадашевич Ю.И. О различных тензорно-линейных соотношениях в теории пластичности // Исследования по упругости и пластичности. - Л.: Изд-во ЛГУ, 1967. - Вып.6. - С. 39-45.
  21. Ohno N., Wang J.-D. Kinematic hardening rules with critical state of dynamic recovery, part 1: formulations and basic features for ratcheting behavior // International Journal of Plasticity. - 1993. - Vol. 9. - P. 375-390.
  22. Новожилов В.В. О сложном нагружении и перспективах феноменологического подхода к исследованию микронапряжений // ПММ. - 1964. - Т. 28. - Вып. 3. - С. 393-400.
  23. Chaboche J.-L., Dang-Van K., Cordier G. Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel // Proceedings of the 5th International Conference on SMiRT. Div L. - Berlin. Paper No. L. 11/3 - 1979.
  24. Ильюшин А.А. Механика сплошной среды. - М.: Изд-во МГУ, 1990. - 310 с.

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