Deformation gradient based kinematic hardening model

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Abstract

A kinematic hardening model applicable to finite strains is presented. The kinematic hardening concept is based on the residual stresses that evolve due to different obstacles that are present in a polycrystalline material, such as grain boundaries, cross slips, etc. Since these residual stresses are a manifestation of the distortion of the crystal lattice a corresponding deformation gradient is introduced to represent this distortion. The residual stresses are interpreted in terms of the form of a back-stress tensor, i.e. the kinematic hardening model is based on a deformation gradient which determines the back-stress tensor. A set of evolution equations is used to describe the evolution of the deforrnation gradient. Non-dissipative quantities are allowed in the model and the implications of these are discussed. Von Mises plasticity for which the uniaxial stress-strain relation can be obtained in closed form serves as a model problem. For uniaxial loading, this model yields: a kinematic hardening identical to the hardening produced by isotropic exponential hardening. The numerical implementation of the model is discussed. Finite element simulations showing the capabilities of the model are presented.

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Subject classification (UKÄ)

  • Mechanical Engineering

Keywords

  • finite strain plasticity, non-linear kinematic hardening, exponential, update
Original languageEnglish
Pages (from-to)2025-2050
JournalInternational Journal of Plasticity
Volume21
Issue number10
Publication statusPublished - 2005
Publication categoryResearch
Peer-reviewedYes