Center for Mechanics of Solids, Structures and Materials

Localization in NiTi Tubes

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Research Objectives

Nearly equiatomic NiTi exhibits two very interesting mechanical responses – the shape memory effect and pseudoelasticity – both due to a reversible solid-to-solid phase transformation. Under certain manufacturing conditions, bulk NiTi will exhibit pseudoelasticity at ambient temperatures. The goals of this project are to: (1) Develop the experimental methodology to characterize the complex highly asymmetric pseudoelastic material response of bulk NiTi; (2) Develop the necessary modeling framework to represent all aspects of bulk pseudoelastic NiTi calibrated with the aforementioned experimental work.


Nathan Bechle, S. Kyriakides, Dongjie Jiang, Chad M. Landis


In tension, the transformation leads to localized deformation of several percent that tends to spread at nearly constant stress under isothermal conditions. For tubular specimen geometries, the localized deformation takes the form of angled fingers that traverse the tube in a helical manner. Under compression, while still pseudoelastic, the transformation strains are smaller, the stress is higher, the response is monotonic, and the deformation is essentially homogeneous.

This project seeks to examine how this texture-driven, complex material asymmetry affects a simple structure: the bending of a tube. To this end, NiTi tubes are bent in a custom four-point bending facility under rotation control isothermally. The phase transformations lead to a closed moment-rotation hysteresis comprised of loading and unloading moment plateaus. During loading, localized nucleation of martensite results in a high curvature for the transformed sections of the tube and low curvature for the untransformed. The nucleation of martensite is in the form of bands inclined to the axis of the tube that organize themselves into diamond shaped deformation patterns on the tensioned side of the structure. The patterns are similar to those observed in bending of steel tubes with Lüders bands, however, for NiTi they develop only to the tensioned side due to the material asymmetry. This complex behavior was found to repeat for a number of temperatures in the pseudoelastic regime of the material.


Buckling Experiment

This movie shows an experiment in which an initially austenitic NiTi tube with diameter-to-thickness ratio 23.6 was axially compressed and unloaded between two plates in a very slow loading rate. The nominal stress - normalized shortening response of the tube followed the elastic modulus of Austenite up to about 700 MPa, after which the response entered a plateau. As the plateau ends, the deformation of the tube was localized into a buckling lobe with three circumferential waves and subsequently into another one, associated with two subsequent stress drops. Upon unloading, the deformation of the two buckling lobes recovered, as well as the two lobes. The hysteresis was closed, with a small amount of permanent deformation left.



The response of a NiTi tube subjected to uniaxial tension under isothermal conditions. Transformation leads to localized deformation in the form of inclined helical bands and the coexistence of two deformation regimes. The bands propagate across the specimen at a relatively constant stress for both loading and unloading.



The response of a relatively thick-walled NiTi tube (D/t = 8) subjected to uniaxial compression under isothermal conditions. The behavior differs significantly from tension with a higher transformation stress, smaller transformation strain, and the deformation is homogeneous. The corresponding nominal stress vs. normalized displacement response is monotonic indicative of a stable material response.



The response of a NiTi tube subjected to pure bending under isothermal conditions. Transformation leads to localized deformation in the form of inclined bands that coalesce into diamond-shaped patterns. This deformation leads to localized curvature and the coexistence of two structural deformation regimes. The deformation propagates across the specimen at a relatively constant moment for both loading and unloading. This is visualized in the video by tracking the top and bottom edges of the deformed tube and computing the pointwise rotation with respect to the arc length. The rotation is the derivative of the bending curvature, thus the clear linear regions represent the constant curvature regimes. The structural response is inhomogeneous, however the localized deformation patterns only appear on tensioned side of the bent tube.


Selected Publications
  • Jiang, D., Bechle, N.J., Landis, C.M., Kyriakides, S., 2016. Buckling and recovery of NiTi tubes under axial compression, International Journal of Solids and Structures, Volume 80, February 2016, Pages 52-63, ISSN 0020-7683,

  • Bechle, N.J., Kyriakides, S., 2014. Localization in NiTi tubes under bending, International Journal of Solids and Structures, Volume 51, Issue 5, 1 March 2014, Pages 967-980, ISSN 0020-7683,