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Abstract
A large number of applications could benefit from the remarkable properties of shape memory alloys but up to now, a relatively limited number have been brought to the market. This can be attributed in part to the lack of numerical tools dedicated to the computer aided design of shape memory devices. The actual design process of shape memory components is mostly based on trial-and-error and most of the time, several prototypes must be built in order to meet the functional requirements. Apart from being an expensive practice, sometimes a whole project is abandoned because the optimal performance was never attained. Therefore, it is mandatory to develop computer aided design software in order to facilitate the emergence of new shape memory industrial applications.
The development of a general material law is the first important step before reliable design calculations can be carried out. This thesis presents a new phenomenological constitutive law based on dual kriging, which is a powerful mathematical tool used here as an interpolation method. From a few isothermal experimental force-deflection curves at different temperatures. two surfaces are constructed which describe the loading and unloading behavior of the material. The response of the material subjected to complex thermomechanical loadings is calculated by successive interpolations on these surfaces via dual kriging. For hysteretic subcycles, the response is calculated through the volume delimited by the two surfaces in such way that any recursive thermomechanical subcycle can be simulated. This methodology yields a uniaxial material law for shape memory alloys that includes in a single formulation superelasticity, pseudo-plasticity, one way shape memory effect and assisted two way shape memory effect.
The modeling of three-dimensional devices is performed by finite elements. The geometrical nonlinearities are taken into account by an updated-Lagrangian formulation. The material nonlinearities are calculated by the material law based on kriging connected to the finite element program. The relationship between the three-dimensional stress states of the finite element program and the one-dimensional states of the material law is achieved by the definition of equivalent stress and strain values based on Prager type criterion. Such a criterion seems to be more realistic for the shape memory behavior.
Finally, two industrial applications of shape memory devices are analyzed. The first application is a Belleville spring disk mounted in bolted joint for electrical contact. When a bolted joint is not properly assembled, an increasing temperature is observed. The Belleville spring disk is introduced in order to increase the force in the assembly by shape recovery during heating. The finite element results point out an important deficiency. The Belleville disk works properly during heating, but a loss of the generated force is calculated after a subsequent cooling. Therefore, the entire concept based on the shape recovery of the Belleville disk should be revised. The other industrial application studied in this thesis is a superelastic shape memory medical stent. A stent is a device inserted in the human body via a catheter to increase the diameter of partially obstructed blood vessels. Afterward, the stent is extracted from the catheter in the body and deployed by superelasticity. The validity of the superelastic stent concept is verified by finite elements and the minimal radius of the catheter until plastification of the stent is determined.
