A general class of non-linear kinematic models to predict mean stress relaxation and multiaxial ratcheting in fatigue problems – Part II: Generalized surface translation rule

Abstract

Part I of this work introduced efficient reduced-order five-dimensional (5D) stress and strain spaces that can be used to predict ratcheting and mean stress relaxation phenomena at a much lower computation cost than in traditional 6D formulations. These 5D spaces were then applied to the qualitative study of uniaxial ratcheting, multiaxial ratcheting, and mean stress relaxation. Several non-linear kinematic (NLK) hardening models have been proposed to capture these effects in incremental plasticity simulations. In this Part II, an incremental plasticity formulation is proposed in the adopted 5D spaces, while its advantages over the classical 6D formulation are discussed. The 5D version of the main NLK models proposed in the literature are presented, which allows the definition of a unified generalized equation. The physical and geometrical interpretation of the hardening, dynamic recovery, and radial return terms from the proposed generalized equation are presented. Several surface translation rules can be represented as a particular case of the proposed model, including the ones by Chaboche (1979), Burlet–Cailletaud (1986), Ohno–Wang (1993), Jiang–Sehitoglu (1996), Bari–Hassan (2001) and Chen–Jiao (2004), among others. The adopted hardening surface representation can be used not only for the studied NLK models, but also to reproduce the Mróz–Garud multi-surface approach. Uniaxial ratcheting, multiaxial ratcheting, and mean stress relaxation experiments with 316L and 1020 steel tubular and cylindrical specimens are conducted to validate the proposed models.