On phase transformation models for thermo-mechanically coupled response of nitinol
type: Item
instance of: scholarly article
title: On phase transformation models for thermo-mechanically coupled response of nitinol
zbMATH Open document ID: 1273.74369
author: Arkaprabha Sengupta
author: P. Papadopoulos
author: Aaron Kueck
author: Alan R. Pelton
published in: Computational Mechanics
publication date: 2012-01-16T00:00:00Z
review text: The paper presents two constitutive models for the fully coupled thermomechanical behavior of shape-memory alloys. One of the models is based on a physically motivated multiplicative decomposition of the total deformation gradient at mesoscale. Another model constitutes an extension to the purely mechanical approach. That is, the first includes the effect of local rotations (at grain level) induced by the transformation strain, whereas the second neglects this effect altogether. First, the backgrounds on the kinematics and kinetics of phase transformation at the grain level are presented. The constitutive developments are stated using a Helmholtz free energy proposed for the phase transformation of nitinol by adding all relevant entropic, thermomechanical and chemical contributions. The study of the two models allows one to assess the significance of including the above-mentioned rotations in the prediction of stresses and temperatures during the phase transformation. A second alternative model is obtained by adding a thermomechanical, coupling and entropic terms to the Helmholtz free energy. Then an incremental method is proposed for the solution of the transformation equations subjected to constraints. Starting with a set of potentially active variants, this scheme uses a predictor-corrector approach which iteratively solves the constraint equations simultaneously with the transformation equations until both are exactly satisfied. The finite element formulation of the coupled thermomechanical problem is based on the use of the Galerkin method to solve the momentum and energy equations using a Newton-Raphson scheme. The evolution of temperature under mechanical loading at moderate strain rates and its effects on the constitutive response are investigated. Experiments on thin-walled tubes at different strain rates are used to estimate some material parameters and the heat transfer coefficient due to convection between the specimen and air. Finally, the finite elemen…
Mathematics Subject Classification ID: 74N05
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 5997846
zbMATH Keywords: finite element method
zbMATH Keywords: Newton-Raphson scheme
zbMATH Keywords: shape-memory alloys
zbMATH Keywords: Helmholtz free energy
reviewed by: Ivan A. Parinov
describes a project that uses: FEAP
MaRDI profile type: Publication
full work available at URL: s00466-011-0587-4
OpenAlex ID: W2087495323
cites work: Constitutive equations for polycrystalline thermoelastic shape memory alloys. I: Intragranular interactions and behavior of the grain
cites work: A multivariant micromechanical model for SMAs. I: Crystallographic issues for single crystal model. II: Polycrystal model
cites work: A multi-variant martensitic phase transformation model: Formulation and numerical implementation
cites work: Thermal effects in the superelasticity of crystalline shape-memory materials
cites work: A multiscale thermomechanical model for cubic to tetragonal martensitic phase transformations
cites work: Theory and finite element computation of cyclic martensitic phase transformation at finite strain
cites work: A computational model for shape memory alloys
cites work: Constitutive modelling and numerical simulation of multivariant phase transformation in superelastic shape-memory alloys
cites work: A finite element model for shape memory alloys considering thermomechanical couplings at large strains
cites work: Polycrystalline shape-memory materials: Effect of crystallographic texture
cites work: Strain rate sensitivity in superelasticity
cites work: On the viscous and strain rate-dependent behavior of polycrystalline NiTi
cites work: Shape memory behaviour: Modelling within continuum thermomechanics
cites work: Constitutive modeling and finite element approximation of B2-R-B19\(^{\prime}\) phase transformations in Nitinol polycrystals
DOI: 10.1007/S00466-011-0587-4
description: scientific article; zbMATH DE number 5997846