A Simple One-Dimensional Model of Constrained Recovery in Shape Memory Alloys

Abstract

In elements made of shape memory alloys (SMAs), large stresses are generated if during heating, shape recovery associated with martensitic transformation, is constrained by an external element. This kind of recovery process is called constrained recovery. In this article, a simple one-dimensional model for the analysis of constrained recovery in SMA wire is presented. The model is based on the theory of generalized plasticity, which was developed by Lubliner and Auricchio. Despite the fact that the model considers an assumption of a non-constant Young's modulus of SMA wire, it remains simple and is well suited for further practical engineering applications and calculations. The regularity of the model is verified by comparing it to experimental results published by Kato, Inagaki, and Sasaki. It is shown that the assumption of non-constant Young's modulus significantly improves the agreement between theory and experiments.

Keywords:

• shape memory alloys
• NiTi wire
• constrained recovery
• generalized plasticity

Acknowledgment

The authors gratefully acknowledge the help of Prof. Hiroyuki Kato from Hokkaido University, who generously provided the experimental data.