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Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

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Abstract

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.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China

    Wenjie Zhao, Guilin Wen & Xuehong Ren

  2. State Key Laboratory of Mechanical Behavior in Traffic Engineering Structure and System Safety, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Shaopu Yang

Authors
  1. Wenjie Zhao
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  2. Shaopu Yang
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  3. Guilin Wen
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  4. Xuehong Ren
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Correspondence to Shaopu Yang.

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Project supported by the National Natural Science Foundation of China (Nos. 11790282, U1534204, and 11472179) and the Natural Science Foundation of Hebei Province of China (No. A2016210099)

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Zhao, W., Yang, S., Wen, G. et al. Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors. Appl. Math. Mech.-Engl. Ed. 40, 49–62 (2019). https://doi.org/10.1007/s10483-019-2413-8

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