Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors
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This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional (fractional-order) derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic (FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly. The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature (KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Time-dependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894 (2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.
Key wordscyclic visco-plastic constitutive fractional derivative fractional-order unified visco-plastic (FVP) model rate-dependent ratcheting
Chinese Library ClassificationO345
2010 Mathematics Subject Classification74C10
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- CHABOCHE, J. L., VAN DANG, K., and CORDIER, G. Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. The 5th International Conference on Structural Mechanics in Reactor Technology, IASMiRT, Berlin, 1–10 (1979)Google Scholar
- CHABOCHE, J. L. and NOUAILHAS, D. Constitutive modeling of ratchetting effects part I: experimental facts and properties of the classical models. Journal of Materials Science & Technology, 111(4), 384–392 (1989)Google Scholar
- CHABOCHE, J. L. and NOUAILHAS, D. Constitutive modeling of ratchetting effects part II: possibilities of some additional kinematic rules. Journal of Materials Science & Technology, 111(4), 409–416 (1989)Google Scholar
- DU, M. L., WANG, Z. H., and HU, H. Y. Measuring memory with the order of fractional derivative. Scientific Reports, 3, 1–3 (2013)Google Scholar
- PODLUBNY, I. Fractional Differetial Equations, Academic Press, San Diego, 78–81 (1999)Google Scholar