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Eulerian Rate Model for Pseudoelastic NiTi Shape Memory Alloys
Author(s) -
Luig Patrick,
Bruhns Otto
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810439
Subject(s) - martensite , helmholtz free energy , austenite , shape memory alloy , materials science , nickel titanium , eulerian path , pseudoelasticity , deformation (meteorology) , cauchy stress tensor , thermodynamics , mechanics , metallurgy , mathematics , mathematical analysis , physics , composite material , microstructure , lagrangian
A phenomenological material model for the pseudoelastic material behavior of polycrystalline NiTi is presented. It is consistently derived within the Eulerian framework using the Kirchhoff stress (weighted Cauchy stress) and the stretching tensor. Deformation–like variables such as elastic or inelastic strains are omitted. The model is based on a non–convex Helmholtz free energy function for the phases austenite and martensite, which is formulated in terms of the Kirchhoff stress, temperature, mass fraction of martensite, and a tensorial internal variable accounting for the average orientation of the martensite variants. Evolution equations for the mass fraction of martensite as well as for the average orientation of the martensite variants are derived, taking into account the restrictions imposed by thermodynamics. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)