R. Heinen

Variational modeling of shape memory alloys – an overview

Abstract Shape memory alloys can be described in a uniform way relying on energetic considerations only. We present micromechanically motivated models for single and polycrystals. The approach studied here is based on energy minimization and includes hysteretic effects via a simple dissipation ansatz. It is capable of reproducing important aspects of the material behavior such as pseudoelasticity and pseudoplasticity. The influence of anisotropies in the crystalline texture as well as in the elastic constants of the austenite and the martensitic variants is also discussed. Furthermore, regularization is applied in order to receive localized but still mesh independent results for phase distributions in a finite element implementation. The entire presentation emphasizes the usage of variational methods leading to the notion of relaxed potentials. Interrelations to various other applications of these concepts will be highlighted.

ASSESSMENT OF THE INFLUENCE OF R-PHASE FORMATION ON THE MATERIAL BEHAVIOR OF NiTi USING A MICROMECHANICAL MODEL

Shape memory alloys (SMA) show several interesting features in their material behavior which are due to martensitic phase transformation. In NiTi, this transformation covers the three crystallographic phases of austenite, martensite, and R-phase. This publication analyzes the influence of the R-phase formation on the overall material behavior by means of a micromechanical model. The model is based on energy minimization with the assumption of a certain energy dissipation when martensite is formed. To simplify the formulation, the dissipation associated with the transformation between austenite and R-phase is neglected, since the geometrical change in unit cell geometry is relatively small in this case. Numerical simulations show that especially the slope reduction in the stress–strain curve, which is known from experiments, can be explained by R-phase formation.

A Micromechanical Model for Polycrystalline Shape Memory Alloys – Formulation and Numerical Validation

The specific material properties of shape memory alloys are due to the formation of martensitic microstructures. In this contribution, we develop a strategy to model the material behavior based on energy considerations: we first present narrow bounds to the elastic energy obtained by lamination of the multi-well problem in the monocrystalline case. These considerations are then extended to polycrystals and compared to a convexification bound. Due to the acceptably low difference between convexification lower and lamination upper bound,we use the convexification bound to establish a micromechanical model which, on the basis of physically well motivated parameters such as elastic constants and transformation strains, is able to represent a variety of aspects of the material behavior such as pseudoelasticity, pseudoplasticity and martensite reorientation.