Thermomechanical Model for Niti-Based Shape Memory Alloys Including R-Phase and Material Anisotropy Under Multi-Axial Loadings
Thermomechanical model for NiTi-based shape memory alloys covering macroscopic localization of martensitic transformation M. Frosta,b,∗, B. Beneˇsov´aa,c, H. Seinera, M. Kruˇz´ıkd, P. Sittnerˇ e,b, P. Sedl´aka,b aCzech Academy of Sciences, Institute of Thermomechanics, Dolejˇskova 5, 18200 Prague, Czech Republic bCzech Academy of Sciences, Nuclear Physics Institute, Husinec - Reˇz130,ˇ 250 68, Reˇz,ˇ Czech Republic cDepartment of Mathematical Analysis, Charles University, Sokolovsk´a83, 18600 Prague, Czech Republic dCzech Academy of Sciences, Institute of Information Theory and Automation, Pod Vod´arenskou vˇeˇz´ı4, 18200, Prague, Czech Republic eCzech Academy of Sciences, Institute of Physics, Na Slovance 2, 18221 Prague, Czech Republic Abstract The work presents a thermomechanical model for polycrystalline NiTi-based shape memory alloys developed within the framework of generalized standard solids, which is able to cover loading-mode dependent localization of the martensitic transformation. The key point is the introduction of a novel austenite-martensite interaction term responsible for strain-softening of the material. Mathematical properties of the model are analyzed and a suitable regularization and a time-discrete approximation for numerical implementation to the finite-element method are proposed. Model performance is illustrated on two numerical simulations: tension of a superelastic NiTi ribbon and bending of a superelastic NiTi tube. Keywords: NiTi shape memory alloys, constitutive modeling, localizaton, Mori-Tanaka method 1. Introduction Having found many applications in medicine, civil engineering or aerospace industry (Mohd Jani et al., 2014), NiTi-based alloys are a prominent class within shape memory alloys (SMAs) usually utilized in the form of thin structures, e.g.
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