Modelling of the Non Isothermal Cyclic Behaviour of a Polycrystalline Cu Zn Al Shape Memory Alloy

In this paper, a model describing the behaviour of Shape Memory Alloys (SMA) under constant applied stress and thermal cycling is developed. This is the first (and necessary) step to obtain a coherent modelling of the well-known Two Way Shape Memory Effect (TWSME) exhibited by SMA after a training process. Two different mechanisms characteristic to SMA are involved in the present description. The first one is related to training itself, whose macroscopic manifestation is the appearance of a permanent strain. The second one concerns the response of SMA to non-isothermal loading. It can be solved by the introduction of news variables in the internal variables set. There are the volume fraction of self-accommodating martensite (pure thermal effect) and the volume fraction of "oriented" martensite (thermo-mechanical effect). The comparison between simulation and our experimental results on Cu Zn Al polycrystals is fairly good

Plasticity Like Model of Martensite Phase Transition in Shape Memory Alloys

Many models simulating the behavior of Shape Memory Alloys (SMA) exist nowadays, in the one or three dimensional situation. In most of the cases they are not able to describe the non isothermal behavior of SMA due to the thermomechanical loadings. Indeed, the influence of the stress on the product phase leads to an orientation of the variants, when the temperature creates a self-accomodating martensite. The result of these two different influences is that the oriented product phase creates large deformations of phase transition, although the self-accomodating one does not produce any macroscopical deformation. In this paper, we develop a model of phase transition which takes into account the two types of martensite. Using this model allows us to simulate the behavior of SMA in isothermal or non isothermal loadings. Thus, the pseudoelasticity, the orientation of self-accomodating variants, the recovery stress or the thermal cycling at constant stress or strain can be simulated with a good agreement with experiments

A Finite Element Calculation for the Design of Devices Made of Shape Memory Alloys

In the first part of the paper a constitutive model for the pseudoelastic behavior of shape memory alloys (SMA) is presented in a finite element context. The model frame (state equation and phase transition kinetics) is rapidly described. Then the implementation of the model into a finite element code based on a fully implicit method consisting in an elastic prediction and phase transition correction is presented. Hence, the stress tensor and the tangent operator are calculated at each displacement increment. For a structural component as a thin plate subjected to bending loads, experimental data and finite element results are in a fair agreement. At last, an industrial application is treated for bronchial protheses used in medicine