A simplified analytical model to simulate martensite reorientation and plasticity in shape memory alloy ring couplers

Recent studies on Shape Memory Alloy rings have been undertaken at the European Organization for Nuclear Research (CERN) to develop smart and leak-tight couplers for Ultra High Vacuum systems of particle accelerators. A special thermo-mechanical process (training) is needed to provide SMA rings with proper functional properties, that is to allow thermal mounting, dismounting, and leak tight coupling within a given service temperature window. Low temperature ring expansion is a crucial part of the training process as it gives suitable size, shape recovery properties, and thermal stability range to the SMA element. An analytical model, based on simplified elastic-plastic axisymmetric concepts, has been developed and implemented in a commercial software to simulate isothermal SMA rings expansions. It is particularly useful to predict the final size of a martensitic SMA coupler as a function of the initial dimensions and of the pre-deformation parameters. The effectiveness of the model has been demonstrated by analyzing the stress/deformation field occurring in a wide range of ring geometries for different load cases including martensite reorientation and plasticity. The predictions of the analytical model have been systematically compared with those obtained by axisymmetric finite element (FE) analyses based on elastic-plastic constitutive models and experimental measurements.