Issue 33

M.A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 33 (2015) 357-367; DOI: 10.3221/IGF-ESIS.33.39 357 Focussed on multiaxial fatigue On the applicability of multi-surface, two-surface and non-linear kinematic hardening models in multiaxial fatigue M.A. Meggiolaro, J.T.P. Castro Pontifical Catholic University of Rio de Janeiro meggi@puc-rio.br , jtcastro@puc-rio.br H. Wu Tongji University in Shanghai wuhao@tongji.edu.cn A BSTRACT . In this work, a comparison between NLK and Mróz-Garud’s multi-surface formulations is presented. A unified common notation is introduced to describe the involved equations, showing that the Mróz-Garud model can be regarded as a particular case of the NLK formulation. It is also shown that the classic two-surface model, which is an unconventional simplified plasticity model based on the translation of only two surfaces, can also be represented using this formulation. Such common notation allows a direct quantitative comparison among multi-surface, two-surface, and NLK hardening models. K EYWORDS . Multiaxial fatigue; Incremental plasticity; Kinematic hardening; Non-proportional variable amplitude loads. I NTRODUCTION he Bauschinger effect, commonly called kinematic hardening , can be modeled in stress spaces by allowing the yield surface to translate with no change in its size or shape. So, in the deviatoric stress space, kinematic hardening maintains the radius S of the yield surface fixed while its center is translated, changing the associated generalized plastic modulus P that defines the slope between stress and plastic strain increments in the Prandtl-Reuss plastic flow rule, also known as the normality rule. There are several models to calculate the current value of P as the yield surface translates, as well as the direction of such translation, to obtain the associated plastic strain increments. Most of these hardening models can be divided into three classes: Mróz multi-surface (or multi-linear), non-linear, and two-surface kinematic models. Mróz [1] defined in 1967 the first multi-surface kinematic hardening model to approximately describe the behavior of elastoplastic solids through a family of nested surfaces in the stress space, the innermost being the yield surface associated with the material yield strength. It assumes that P is piecewise constant, resulting in a multi-linear description of the stress- strain curve, i.e. the non-linear shape of the elastoplastic stress-strain relation is approximated by several linear segments. The Mróz model can induce a few numerical problems, which can result in hardening surfaces improperly intersecting in more than one point under finite strain increments. Garud [2] proposed a geometrical correction that avoids intersection problems even for coarse integration increments. In spite of its limitations, several multiaxial fatigue works use the Mróz-Garud model to predict the stress-strain behavior under combined loading, especially due to its ability to store plastic memory effects under variable amplitude loading. This T