An upper bound to the free energy of n-variant polycrystalline shape memory alloys |
| |
Authors: | K Hackl R Heinen |
| |
Institution: | aLehrstuhl für Allgemeine Mechanik, Ruhr-Universität Bochum, Universitätsstr. 150, D-44780 Bochum, Germany;bWerkstoffkompetenzzentrum, Division Auto, ThyssenKrupp Steel AG, Kaiser-Wilhelm-Str. 100, D-47166 Duisburg, Germany |
| |
Abstract: | In the last two decades, the problem of computing the elastic energy of phase transforming materials has been studied by a variety of research groups. Due to the non-quasiconvexity of the underlying multi-well landscape, different relaxation methods have been used in order to estimate the quasiconvex envelope of the energy density, for which no explicit expression is known at present.This paper combines a recently developed lamination bound for monocrystalline shape memory alloys which relies on martensitic twinned microstructures with the work of Smyshlyaev and Willis 1998a. A ‘non-local’ variational approach to the elastic energy minimization of martensitic polycrystals. Proc. R. Soc. London A 454, 1573–1613]. As a result, a lamination upper bound for n-variant polycrystalline martensitic materials is obtained.The lamination bound is then compared with Reuß- and Taylor-type estimates. While, for given volume fractions, good agreement of lamination upper and convexification lower bounds is obtained, a comparison using energy-minimizing volume fractions computed from the various bounds yields larger differences. Finally, we also investigate the influence of the polycrystal's texture. For a strong ellipsoidal texture, we observe even better agreement of upper and lower bounds than for the case of isotropic statistics. |
| |
Keywords: | Lamination Microstructures Phase transformation Polycrystalline material Shape memory alloys |
本文献已被 ScienceDirect 等数据库收录! |
|