Size-dependent transformation patterns in NiTi tubes under tension and bending: Stereo digital image correlation experiments and modeling

Abstract

The dependence of transformation pattern in superelastic NiTi tubes on tube outer diameter D and wall-thickness t is investigated through quasi-static uniaxial tension and large-rotation bending experiments. The evolution of outer-surface strain fields is synchronized with global stress-strain and moment-curvature responses using a multi-magnification, high-resolution stereo digital image correlation system at 0.5-2x magnifications. The transformation patterns exhibit systematic size-dependent behaviors. Under tension and for a specific D, as the diameter-to-thickness ratio D/t decreases, a decreasing number of fat/diffuse helical bands emerge, in contrast to sharp/slim bands in thin tubes. Consequently, the austenite-martensite front morphology transitions from finely-fingered to coarsely-fingered with decreasing D/t. Below a characteristic D/t, front morphology no longer exhibits patterning and phase transformation proceeds via propagation of a finger-less front. Moreover, the transformation pattern exhibits an interrelation between D and D/t, where a front possessing diffuse fingers is observed in a thin but small tube. Under bending, both the global moment-curvature response and transformation pattern exhibit D- and D/t-dependence. While wedge-like martensite domains consistently form across all tube sizes, their growth is noticeably limited in smaller and thicker tubes due to geometrical constraints. A gradient-enhanced model of superelasticity is employed to analyze the distinct transformation patterns observed in tubes of various dimensions. The size-dependent behavior is explained based on the competition between bulk and interfacial energies, and the energetic cost of accommodating martensite fingers. By leveraging an axisymmetric tube configuration as a reference energy state, the extra energy associated with the formation of fingers is quantified.

Figures (13)

• Figure 1: (a) Cross-sectional dimensions of the NiTi tubes used in the experiments. (b,c) Typical speckle patterns applied on the surface of (b) a $D = 2.5$ mm tube, imaged at $0.53\times$ magnification, and (c) a $D = 1.2$ mm tube, imaged at $1\times$ magnification. (d,e) Photographs of the experimental setups and stereo-DIC rigs for measuring mechanical responses and capturing transformation patterns under (d) quasi-static tensile setup, and (e) large-rotation bending setup.
• Figure 2: Quasi-static stress--strain responses of superelastic NiTi tubes with different dimensions at $T_\text{test}=22~^\circ$C. The alignment of the responses from the T1 and T2 tests, corresponding to slightly different $L_\text{e}$ (see Table S1), demonstrate the repeatability of the experiments.
• Figure 3: Surface evolution of axial strain field ($e_\text{zz}$) corresponding to the circled numbers $\rightarrow$on tensile curves (Fig. \ref{['fig:mechsize']}): (a) 3.0/0.1/30, T2, (b) 2.5/0.13/19.23, T1, (c) 2.5/0.28/8.93, T1, and (d) 1.2/0.1/12, T1.
• Figure 4: Surface evolution of axial strain field ($e_\text{zz}$) corresponding to the circled numbers $\rightarrow$on tensile curves: (a) 1.2/0.2/6.0, (b) 0.8/0.13/6.15, and (c) 0.43/0.09/4.78 tubes, all pertaining to T1 tests.
• Figure 5: Magnified views of $e_\text{zz}$ at two selected time instants for T1 (blue box) and T2 (red box) tests. In each box, the upper set of images is representative of a time instant (strain) at the early stage of stress-induced PT (nucleation) and the lower set of images represents a time instant corresponding to the propagation of austenite--martensite interface.