Elastoplastic model of metals with smooth elastic–plastic transition
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The subloading surface model is based on the simple and natural postulate that the plastic strain rate develops as the stress approaches the yield surface. It therefore always describes the continuous variation of the tangent modulus. It requires no incorporation of an algorithm for the judgment of yielding, i.e., a judgment of whether or not the stress reaches the yield surface. Furthermore, the calculation is controlled to fulfill the consistency condition. Consequently, the stress is attracted automatically to the normal-yield surface in the plastic loading process even if it goes out from that surface. The model has been adopted widely to the description of deformation behavior of geomaterials and friction behavior. In this article, it is applied to the formulation of the constitutive equation of metals by modifying the past formulation of this model. This modification enables to avoid the indetermination of the subloading surface, to make the reloading curve recover promptly to the preceding loading curve, and to describe the cyclic stagnation of isotropic hardening. The applicability of the present model to the description of actual metal deformation behavior is verified through comparison with various cyclic loading test data.
The authors are grateful to Prof. N. Ohno, Nagoya University, and Prof. F. Yoshida, Hiroshima University, for providing the authors with papers related to the cyclic stagnation of isotropic hardening and the valuable discussions on this issue.
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
- 1.Armstrong, P.J., Frederick, C.O.: A Mathematical Representation of the Multiaxial Bauschinger Effect, G.E.G.B. Report RD/B/N 731 (1966)Google Scholar
- 3.Chaboche, J.L., Dang-Van, K., Cordier, G.: Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. In: Transactions of the 5th International Conference on SMiRT, Berlin, Division L., Paper No. L. 11/3 (1979)Google Scholar
- 6.Dafalias, Y.F., Herrmann, L.R.: A bounding surface soil plasticity model. In: Proceedings of the International Symposium on Soils under Cyclic and Transient Loading, Swansea, pp. 335–345 (1980)Google Scholar
- 11.Ellyin F.: Fracture Damage, Crack Growth and Life Prediction. Chapman & Hall, London (1997)Google Scholar
- 12.Hashiguchi, K., Ueno, M.: Elastoplastic constitutive laws of granular materials, constitutive equations of soils. In: Proceedings of the 9th International Conference on Soil Mechanics and Foundation Engineering, Specialty Session 9, Tokyo, JSSMFE, pp. 73–82 (1977)Google Scholar
- 27.Hashiguchi K.: Subloading surface model with tangential relaxation. In: Proceedings of the International Symposium of Plasticity 259–261 (2005)Google Scholar
- 29.Hashiguchi K., Tsutsumi S.: Gradient plasticity with the tangential subloading surface model and the prediction of shear band thickness of granular materials. Int. J. Plast. 22, 767–797 (2006)Google Scholar
- 32.Hashiguchi K.: Elastoplasticity Theory (Lecture Notes in Applied and Computational Mechanics). Springer, Berlin (2009)Google Scholar
- 34.Hill, R.: On the classical constitutive relations for elastic/plastic solids. Recent Prog. Appl. Mech. 241–249 (1967)Google Scholar
- 42.Masing, G.: Eigenspannungen und Verfestigung beim Messing. In: Proceedings of the 2nd International Congress for Applied Mechanics, Zürich, pp. 332–335 (1926)Google Scholar