Buckling and recovery of NiTi tubes under axial compression

Abstract

Experiment and analysis are used to investigate the buckling and recovery of pseudoelastic NiTi tubes with a diameter-to-thickness ratio of 23.6 under compression and the associated energy absorption. At a stress level corresponding to the onset of transformation to martensite, the tube initially buckles into a periodic axisymmetric wrinkling mode. The wrinkled structure remains stable despite the loss in stiffness, but at larger strain levels wrinkling gives way to an unstable non-axisymmetric buckling mode, characterized by three circumferential waves. With the load decreasing, this mode localizes first into a single lobe followed progressively by others. Unlike elastoplastic material behavior, transformation terminates into a stiff, saturation-type response with the linear elastic modulus of the M-phase. This stiffening of the material limits the growth of deformation in the mode-3 lobes preventing them from folding up. As a consequence, this progressive collapse occurs at a much higher stress level relative to that at the onset of collapse, than in concertina folding observed in typical structural metal energy absorbers. Even more importantly, on unloading the material transforms back to the A-phase resulting in recovery of deformation, erasure of the buckles, and a nearly closed hysteresis. The buckling and recovery phenomena are simulated numerically using a finite element model coupled to a J2-type nonlinear kinematic hardening model. The model is customized to the primarily compressive stress state of the problem at hand and is calibrated to the compressive hysteresis of the material. The analysis captures the onset of wrinkling, the switch to mode-3, and its localization first into a single lobe followed by a second and subsequent ones. The recovery on unloading is also reproduced by the analysis resulting in a completely closed hysteresis. Idealizations made in the present version of the constitutive model resulted in an unloading stress that is at a higher level than that observed in the experiment. Despite this discrepancy, the results demonstrate the overall veracity of the constitutive model developed.