On the thermodynamically consistent modeling of distortional hardening: A novel generalized framework

Abstract

a b s t r a c tMany important physical effects of materials undergoing plasticity at the macroscale cannot be captured realistically by isotropic and kinematic hardening only. For instance, the evolution of the texture in polycrystals results macroscopically in a distorted yield surface. This paper deals with adequate hardening models for such a distortion. To be more precise, a novel general frame for finite strain plasticity models is elaborated. To the best knowledge of the authors, it is the first one combining the following features: (1) proof of thermodynamical consistency; (2) decomposition of distortional hardening into dynamic hardening (due to currently active dislocations) and latent hardening (due to currently inactive dislocations); (3) difference of the yield surface's curvature in loading direction and in the opposite direction. The cornerstone of this model is a new plastic potential for the evolution equations governing distortional hardening. Although this type of hardening is characterized through a fourth-order tensor as internal variable, the structure of the aforementioned potential is surprisingly simple. Even though the final model is rather complex, it requires only few model parameters. For these parameters, in turn, physically sound bounds based on the convexity condition of the yield surface can be derived. Three different examples demonstrate the predictive capabilities of the novel framework.

A generalized thermodynamically consistent distortional hardening model for Mg alloys

“…The dissipation inequality (6) is fulfilled directly for elastic unloading (L p = 0 andα = 0). Concerning on plastic loading, in contrast to the introduction of convex and non-negative plastic potential g in Shi and Mosler (2013); Shi et al (2014), the dissipation is to be decomposed directly into four parts (the first and second parts corresponding to isotropic and kinematic hardening, while the third and fourth parts together corresponding to distortional hardening). In order to fulfill the dissipation inequality, each part is simply assumed as non-negative quadratic forms in line with the method in Feigenbaum and Dafalias (2007) and the evolution equations are derived.…”

“…This effect is modeled precisely by the coefficient N r : Q kin , cf. Shi and Mosler (2013); Feigenbaum and Dafalias (2007); Shi et al (2014). In line with the original work carried out in Feigenbaum and Dafalias (2007), the plastic Helmholtz energy is split as:…”

“…However, the evolution equations of distortional hardening kept same and the yield functions were changed from the original model (Hill-type) to the extended one (CPB06), hence, the extended model was not thermodynamically consistent analytically in Shi and Mosler (2013). After that work, a unified framework for dynamic and latent distortional hardening was elaborated, in which, the second law of thermodynamics was fulfilled and the stress space was bounded by the convexity condition, see Shi et al (2014).…”

Capturing yield surface evolution with a multilinear anisotropic kinematic hardening model

“…Some of the models are phenomenological Miller, 1987, 1988;Kurtyka and Zyczkowski, 1996;Voyiadjis and Foroozesh, 1990;Francois, 2001;Liu et al, 2011;Wu and Hong, 2011;Lee et al, 2012;Radi and Abdul-Latif, 2012;Barlat et al, 2013;Shi et al (2014)) and some of http://dx.doi.Org/10.1016/j.ijsolstr.2015.ll.030 0020-7683/© 2015 Elsevier Ltd. All rights reserved. them micromechanically-based or motivated (Zattarin et al, 2004;Kabirian and Khan, 2015;Yoshida et al, 2014;Hu et al, 2015).…”

Constitutive and friction modeling for accurate springback analysis of advanced high strength steel sheets

“…The role of the constitutive model is especially important for AHSS sheets, which exhibit characteristic features during deformation under reverse loading, for instance, the Bauschinger effect, transient hardening and permanent softening. Because the conventional isotropic hardening model cannot describe such phenomena, kinematic hardening and other types of models have been generally recommended for the prediction of springback (Carvalho Resende et al, 2013;Clausmeyer et al, 2014;Geng and Wagoner, 2000;Lee et al, 2012bLee et al, , 2005Shi et al, 2014;Vladimirov et al, 2009;Yoshida and Uemori, 2003). Another major characteristic of AHSS is the nonlinear and history-dependent elastic modulus.…”