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Constitutive modeling and finite element analysis of the dynamic behavior of shape memory alloys Azadi Borujeni, Bijan


Previous experimental observations have shown that the pseudoelastic response of NiTi shape memory alloys (SMA) is localized in nature and proceeds through nucleation and propagation of localized deformation bands. It has also been observed that the mechanical response of SMAs is strongly affected by loading rate and cyclic degradation. These behaviors significantly limit the accurate modeling of SMA elements used in various devices and applications. The aim of this work is to provide engineers with a constitutive model that can accurately describe the dynamic, unstable pseudoelastic response of SMAs, including their cyclic response, and facilitate the reliable design of SMA elements. A 1-D phenomenological model is developed to simulate the localized phase transformations in NiTi wires during both loading and unloading. In this model, it is assumed that the untransformed particles located close to the transformed regions are less stable than those further away from the transformed regions. By consideration of the thermomechanical coupling among the stress, temperature, and latent heat of transformation, the analysis can account for strain-rate effects. Inspired by the deformation theory of plasticity, the 1-D model is extended to a 3-D macromechanical model of localized unstable pseudoelasticity. An important feature of this model is the reorientation of the transformation strain tensor with changes in stress tensor. Unlike previous modeling efforts, the present model can also capture the propagation of localized deformation during unloading. The constitutive model is implemented within a 2-D finite element framework to allow numerical investigation of the effect of strain rate and boundary conditions on the overall mechanical response and evolution of localized transformation bands in NiTi strips. The model successfully captures the features of the transformation front morphology, and pseudoelastic response of NiTi strip samples observed in previous experiments. The 1-D and 3-D constitutive models are further extended to include the plastic deformation and degradation of material properties as a result of cyclic loading.

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