A sharp-interface model for diffusional evolution of precipitates in visco-plastic materials

authored by: Lukas Munk, Silvia Reschka, Stefan Löhnert, Hans Jürgen Maier, Peter Wriggers
Abstract: This paper describes a 3D implementation of the sharp-interface theory for material heterogeneities and is, hence, able to identify equilibrium shapes of precipitates in superalloys. The theory is adopted from Morton E. Gurtin and extended by crystal plasticity in the bulk. Crystal plasticity relaxes stresses at the phase interface, which leads to subsequent coalescence of the precipitates. The fully implicit model employs the extended finite element method (XFEM) in conjunction with level sets. The level set is advected in a velocity field computed by the stress-modified Gibbs-Thomson interface condition. Mechanical equilibrium and level set update are solved in a staggered procedure. Jump quantities are treated by means of a suitable enriched least square smoothing. Multiple schemes for the computation of curvature of surfaces in the context of the XFEM are presented and compared. Equilibrium shapes at different levels of misfit are computed. A cuboidal equilibrium shape is retrieved in a rotated mesh in order to quantify mesh-independence, a linear volume-time relationship during Ostwald ripening is reproduced and merging of particles under tension is reported.
Organisation(s): Institute of Continuum Mechanics
Institute of Materials Science
External Organisation(s): Technische Universität Dresden
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 391
ISSN: 0045-7825
Publication date: 01.03.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2021.114440 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{6b41ade1a6144361896b848ac15cc9f5,
title = "A sharp-interface model for diffusional evolution of precipitates in visco-plastic materials",
abstract = "This paper describes a 3D implementation of the sharp-interface theory for material heterogeneities and is, hence, able to identify equilibrium shapes of precipitates in superalloys. The theory is adopted from Morton E. Gurtin and extended by crystal plasticity in the bulk. Crystal plasticity relaxes stresses at the phase interface, which leads to subsequent coalescence of the precipitates. The fully implicit model employs the extended finite element method (XFEM) in conjunction with level sets. The level set is advected in a velocity field computed by the stress-modified Gibbs-Thomson interface condition. Mechanical equilibrium and level set update are solved in a staggered procedure. Jump quantities are treated by means of a suitable enriched least square smoothing. Multiple schemes for the computation of curvature of surfaces in the context of the XFEM are presented and compared. Equilibrium shapes at different levels of misfit are computed. A cuboidal equilibrium shape is retrieved in a rotated mesh in order to quantify mesh-independence, a linear volume-time relationship during Ostwald ripening is reproduced and merging of particles under tension is reported.",
keywords = "Crystal plasticity, Curvature schemes, Heterogeneities, Phase transformation, Sharp-interface theory, XFEM",
author = "Lukas Munk and Silvia Reschka and Stefan L{\"o}hnert and Maier, {Hans J{\"u}rgen} and Peter Wriggers",
note = "Funding Information: The authors gratefully acknowledge financial support by the German Research Association (DFG) through grant no. 282253287 . The authors also thank Meisam Soleimani for valuable discussions on the subject. This work was supported by the LUH compute cluster, which is funded by the Leibniz Universit{\"a}t Hannover , the Lower Saxony Ministry of Science and Culture (MWK) and the German Research Association (DFG) .",
year = "2022",
month = mar,
day = "1",
doi = "10.1016/j.cma.2021.114440",
language = "English",
volume = "391",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}