Modeling Permanent Effects of Shape Memory Alloy: Recent Improvements and Case Studies

A macroscopic constitutive model of Shape memory Alloys, describing the thermo mechanical phase transformation and the onset and development of permanent effects has been recently developed starting from the model described in [1]. Permanent effects, microscopically due to the formation of lattice defects, macroscopically cause transformation temperature shift, reduction of the recoverable transformation deformation and plastic deformations. The proposed model aims at describing permanent phenomena by introducing two internal variables, the transformation strain tensor and the plasticity tensor q. Constitutive equations and internal variable flow rules are derived in the frame of Rajagopal theory [1] [2], by defining an energy density potential and a dissipation potential.

Focus of this work is the discussion of some case studies with the help of experimental data. In particular, tension cycles of superelastic wires at different temperatures and temperature cycles at different constant load of high temperature wires will be considered.  Through the comparison of experimental and numerical results, strengths and limitations of the present model will be discussed.

[1]	Auricchio, F. and A. Reali, U. Stefanelli. A three dimensional model describing stress induced solid phase traqnsformation with permanent inelasticity. Int. J. Plasticity, 23 (2007), 207-226.
[2]	Rajagopal, K. R. and Srinivasa, A. R. Mechanics of the inelastic behavior of materials - Part I, theoretical underpinnings. Int. J. Plasticity, 14 (1998), 945-967.
[3]	Rajagopal, K. R. and Srinivasa, A. R. Mechanics of the inelastic behavior of materials - Part II, Inelastic response. Int. J. Plasticity, 14 (1998), 969-995.