Localization instabilities in pseudoelastic NiTi tubes under multiaxial stress states




Kazinakis, Karlos Thomas Leonidas

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Nearly equiatomic NiTi has a unique property called pseudoelasticity in that strain of several percent is recoverable at room temperatures. This characteristic is attainable due to solid-state transformations between the austenite and martensite phases. It is well established that the transformation in tension is associated with localization during the loading/unloading stress plateaus of its hysteresis. By contrast, the transformation in compression is essentially homogeneous and occurs at much higher stresses and lower strains. Recently conducted biaxial experiments on NiTi tubes revealed, in addition to tension/compression asymmetry, an inherent anisotropic behavior. The interaction of these material nonlinearities with geometric instabilities results in challenging structural problems and the need for adept constitutive models is vital. Hence, a J₂-type kinematic hardening model was developed by our group, which incorporates asymmetry and is now extended to include anisotropy. Two numerical studies of NiTi tubular structures incorporate this framework within a finite element analysis aiming to reproduce the experimental responses and the transformation-induced strain patterns. The first problem investigates the buckling and collapse of a thin-walled NiTi tube under pure bending. The analysis captures the moment-end rotation response and the distinct diamond patterns that develop demonstrating how their interaction with ovalization leads to buckling and collapse. Parametric sensitivity studies illustrate the roles of the diameter-to-thickness ratio, geometric imperfections, and some key aspects of the model to the stability of the structure. The second problem examines thin-walled NiTi tubes under combined axial force and internal pressure. The simulations reproduce well the stress-average strain responses and the transformation stress loci, while for hoop dominant stress paths the extents of the transformation strains are somewhat overpredicted. The evolution of localization in the form of high or low strain helical bands, the variation of helix angles with the stress ratio, and the dissipated energy compare favorably. The hardening response and essentially homogeneous deformation exhibited in the neighborhood of the equibiaxial stress state is reproduced, but with reduced hardening and weak deformation patterns. The special case of equibiaxial tension is studied further as it highlights the effects of asymmetry and anisotropy in the constitutive model on structural behaviors


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