Modeling of Cyclic Ratchetting Plasticity, Part I: Development of Constitutive Relations

Abstract

The existing plasticity models recognize that ratchetting direction strongly depends on the loading path, the stress amplitude, and the mean stresses, but their predictions deviate from experiments for a number of materials. We propose an Armstrong-Frederick type hardening rule utilizing the concept of a limiting surface for the backstresses. The model predicts long-term ratchetting rate decay as well as constant ratchetting rate for both proportional and nonproportional loadings. To represent the transient behavior, the model encompasses a memory surface in the deviatoric stress space which recalls the maximum stress level of the prior loading history. The coefficients in the hardening rule, varying as a function of the accumulated plastic strain, serve to represent the cyclic hardening or softening. The stress level effect on ratchetting and non-Masing behavior are realized with the size of the introduced memory surface. Simulations with the model checked favorably with nonproportional multiaxial experiments which are outlined in Part 2 of this paper.

Recent Progress in Constitutive Modeling for Ratchetting

“…3 (a) Incidentally, Jiang et al [35,36] showed that the material constants ƒÄi and ƒÁi in Eqs. (8), (10) and (11) can be determined systematically using the following equations if rate-independent plasticity with no isotropic hardening is assumed:…”

Phenomenological Modelling of Cyclic Plasticity

“…For correct description of ratcheting in proportional and non-proportional loading more and more authors introduced a nonproportional parameter, which enables simultaneous correct description of uniaxial and multiaxial ratcheting (Chen & Jiao 2004;Chen, 2005;Halama, 2008). Significant improvements of prediction capability can be reached by using memory surfaces Sehitoglu, 1996 andDöring, 2003). Presented models should be compared in terms of nonlinearity, established for each backstress in the case of uniaxial loading.…”

Material parameter optimisation of Ohno-Wang kinematic hardening model using multi objective genetic algorithm

“…The hysteresis loading curve (σ -ε p ) is divided into 12 segments. The corresponding kinematic hardening parameters (C (1) to C (12) and γ (1) to γ (12) ) are determined by the following equations as described by Bari and Hassan (2000) and Jiang and Sehitoglu (1996).…”

“…Many advanced constitutive models have been developed to simulate the cyclic and time independent behaviours of the material. Armstrong and Frederick (1966), Abdel Ohno (2000a, 2000b), Bari and Hassan (2000, Chaboche (1986a), Chaboche et al (1979), Chaboche andRousselier (1986b, 1986c), Ohno and Wang (1991, 1993, 1994, Ohno (1998), Yoshida (2000), Yoshida and Uemori (2002), Ellyin and Xia (1989), Trampczynski and Mroz (1992), Haupt and Kamlah (1995), Jiang and Sehitoglu (1996), Kobayashi and Ohno (2002), Khutia et al (2013) and many others developed improved constitutive models for representing cyclic non-linear responses including ratcheting.…”