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An energy-barrier-based computational micro-sphere model for phase-transformations interacting with plasticity

Ostwald, Richard; Bartel, Thorsten and Menzel, Andreas LU (2015) In Computer Methods in Applied Mechanics and Engineering 293. p.232-265
Abstract
We extend a newly introduced framework for the simulation of shape memory alloys undergoing martensite-austenite phase-transformations by allowing for the evolution of individual plastic deformations in each phase considered. The goal is to obtain a generalised model which will facilitate the reflection of the characteristic macroscopic behaviour of SMA as well as TRIP steels. Particularly, we show that the incorporation of plasticity effects interacting with phase-transformations allows to capture the typical multi-cyclic stress-strain responses. As a basis, we use a scalar-valued phase-transformation model where a Helmholtz free energy function depending on volumetric and deviatoric strain measures is assigned to each phase. The... (More)
We extend a newly introduced framework for the simulation of shape memory alloys undergoing martensite-austenite phase-transformations by allowing for the evolution of individual plastic deformations in each phase considered. The goal is to obtain a generalised model which will facilitate the reflection of the characteristic macroscopic behaviour of SMA as well as TRIP steels. Particularly, we show that the incorporation of plasticity effects interacting with phase-transformations allows to capture the typical multi-cyclic stress-strain responses. As a basis, we use a scalar-valued phase-transformation model where a Helmholtz free energy function depending on volumetric and deviatoric strain measures is assigned to each phase. The incorporation of plasticity phenomena is established by enhancing the deviatoric contributions of the Helmholtz free energy functions of the material phases considered, where the plastic driving forces acting in each phase are derived from the overall free energy potential of the mixture. The resulting energy landscape of the constitutive model is obtained from the contributions of the individual constituents, where the actual energy barriers are computed by minimising parametric intersection curves of elliptic paraboloids. With the energy barriers at hand, we use a statistical physics based approach to determine the resulting evolution of volume fractions due to acting thermo-mechanical loads. Though the model allows to take into account an arbitrary number of solid phases of the underlying material, we restrict the investigations to the simulation of phase-transformations between an austenitic parent phase and a martensitic tension and compression phase. The scalar-valued model is embedded into a computational micro-sphere formulation in order to simulate three-dimensional boundary value problems. The systems of evolution equations are solved in a staggered manner, where a newly proposed, physically motivated plasticity inheritance law accounts for the inheritance of plastic deformations due to evolving phases. (C) 2015 Elsevier B.V. All rights reserved. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Phase-transformations, Plasticity, SMA, TRIP steel, Micro-sphere model, Finite elements
in
Computer Methods in Applied Mechanics and Engineering
volume
293
pages
232 - 265
publisher
Elsevier
external identifiers
  • wos:000361475900012
  • scopus:84930227015
ISSN
0045-7825
DOI
10.1016/j.cma.2015.04.008
language
English
LU publication?
yes
id
01550d27-ce9c-4d33-87f5-d7ec49825f45 (old id 8074125)
date added to LUP
2015-10-22 15:22:02
date last changed
2017-03-05 03:55:41
@article{01550d27-ce9c-4d33-87f5-d7ec49825f45,
  abstract     = {We extend a newly introduced framework for the simulation of shape memory alloys undergoing martensite-austenite phase-transformations by allowing for the evolution of individual plastic deformations in each phase considered. The goal is to obtain a generalised model which will facilitate the reflection of the characteristic macroscopic behaviour of SMA as well as TRIP steels. Particularly, we show that the incorporation of plasticity effects interacting with phase-transformations allows to capture the typical multi-cyclic stress-strain responses. As a basis, we use a scalar-valued phase-transformation model where a Helmholtz free energy function depending on volumetric and deviatoric strain measures is assigned to each phase. The incorporation of plasticity phenomena is established by enhancing the deviatoric contributions of the Helmholtz free energy functions of the material phases considered, where the plastic driving forces acting in each phase are derived from the overall free energy potential of the mixture. The resulting energy landscape of the constitutive model is obtained from the contributions of the individual constituents, where the actual energy barriers are computed by minimising parametric intersection curves of elliptic paraboloids. With the energy barriers at hand, we use a statistical physics based approach to determine the resulting evolution of volume fractions due to acting thermo-mechanical loads. Though the model allows to take into account an arbitrary number of solid phases of the underlying material, we restrict the investigations to the simulation of phase-transformations between an austenitic parent phase and a martensitic tension and compression phase. The scalar-valued model is embedded into a computational micro-sphere formulation in order to simulate three-dimensional boundary value problems. The systems of evolution equations are solved in a staggered manner, where a newly proposed, physically motivated plasticity inheritance law accounts for the inheritance of plastic deformations due to evolving phases. (C) 2015 Elsevier B.V. All rights reserved.},
  author       = {Ostwald, Richard and Bartel, Thorsten and Menzel, Andreas},
  issn         = {0045-7825},
  keyword      = {Phase-transformations,Plasticity,SMA,TRIP steel,Micro-sphere model,Finite elements},
  language     = {eng},
  pages        = {232--265},
  publisher    = {Elsevier},
  series       = {Computer Methods in Applied Mechanics and Engineering},
  title        = {An energy-barrier-based computational micro-sphere model for phase-transformations interacting with plasticity},
  url          = {http://dx.doi.org/10.1016/j.cma.2015.04.008},
  volume       = {293},
  year         = {2015},
}