Theory of plasticity without loading surface and associated flow law

Abstract

Based on the analysis of a hysteresis loop (circular diagram), three areas were highlighted which characterize the different behavior of the stresses, i.e. three types of stress are revealed. For each type of stress corresponding evolution equations are formulated which describe the anisotropic hardening. To describe the isotropic hardening the author introduces an evolution equation for the fourth type stresses. A stress deviator is defined as the sum of the stresses of four types. To describe the non-linear process of stress accumulation there is introduced a kinetic damage equation, based on the energy principle where the energy consumed to create damage in material considers as energy equal to the work of the second type stresses on the total strain space. The material functions are shown, the basic experiment and the method of identification of material functions are formulated.

Keywords

plasticity / cyclic graph / accumulation of damage / basic experiment / identification of material functions

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. - V. 18. - pp. 873-894.

[6] Kang G., Liu Y., Ding J., Gao Q. Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel: Damage evolution and damage-coupled viscoplastic constitutive model. Int. J. of Plasticity. - 2009. V.25. - pp. 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. V.24. - pp.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. V.24. - pp.1756-1791.

[10] Abdel-Karim M. Modified kinematic hardening rules for simulations of ratchetting. Int. J. of Plasticity. - 2009. V.25. - pp. 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. V.26. - pp. 711-730.

[12] Dafalias Y.F., Feigenbaum H.P. Biaxial ratchetting with novel variations of kinematic hardening. Int. J. of Plasticity. - 2011. V.27. - pp. 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. V.35. - pp. 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: Межвузовский сборник. Вып.72. - Нижний Новгород: Изд-во Нижегородского госуниверситета, 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] Ишлинский А.Ю. Общая теория пластичности с линейным упрочнением // Укр. матем. журн. - 1954. Т. 6. Вып. 3. - С. 314-324.

[17] Prager W. The theory of plasticity: A. Survey of Recent Achievements // Proc. Inst. Mech. Engrs. London. 1955. - 169.41.

[18] Amstrong P.J., Frederick C.O. A mathematical represention of the multiaxial bauscinger effect // CEGB Report No. RD/B/N/ 731. - 1966.

[19] 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.

[20] 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. - V. 9. - pp. 375-390.

[21] Новожилов В.В. О сложном нагружении и перспективах феноменологического подхода к исследованию микронапряжений // ПММ. - 1964. - Т. 28, Вып.3. С. 393-400.

[22] 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.

RIGHTS & PERMISSIONS

Bondar V.S.