TY - JOUR

T1 - A sharp-interface model for diffusional evolution of precipitates in visco-plastic materials

AU - Munk, Lukas

AU - Reschka, Silvia

AU - Löhnert, Stefan

AU - Maier, Hans Jürgen

AU - Wriggers, Peter

N1 - 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 Universität Hannover , the Lower Saxony Ministry of Science and Culture (MWK) and the German Research Association (DFG) .

PY - 2022/3/1

Y1 - 2022/3/1

N2 - 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.

AB - 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.

KW - Crystal plasticity

KW - Curvature schemes

KW - Heterogeneities

KW - Phase transformation

KW - Sharp-interface theory

KW - XFEM

UR - http://www.scopus.com/inward/record.url?scp=85122649837&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2021.114440

DO - 10.1016/j.cma.2021.114440

M3 - Article

AN - SCOPUS:85122649837

VL - 391

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 114440

ER -