A variational material model for shape memory alloys under thermal cycling. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Waimann, Johanna; Hackl, Klaus; Junker, Philipp
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900052
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Due to their special material behavior– namely the superelasticity as well as the one‐way and two‐way effect– shape memory alloys are very attractive materials for industrial applications. The solid/solid phase transformation between austenite and martensite is however accompanied by a formation of dislocations which influence the cyclic behavior of this special class of smart materials. For mechanical cycling, the formed dislocations favor the transformation from austenite to martensite and delay the reverse transformation. But for thermal cycling, they have the opposite effect and thus result in a decrease of the transformation temperature and in a delayed transformation from austenite to martensite. We present a material model which is able to show both effects and hence displays microstructural evolution for a mechanically and thermally cycled material. Based on the variational method of the principle of the minimum of the dissipation potential, we model the so called effect of functional fatigue by storage of the transformation history of the observed material. In addition to that and for numerical efficiency, we use an evolving orientation distribution function to account for the polycrystalline structure of shape memory alloys, see [2]. Finally, we present first numerical results which verify the micromechanical model's functionality.