Fig. 1. Schematic of the design concept of the large linear elasticity with a wide temperature range. (a) Conventional stress-strain diagram of twinning-detwinning deformation. (b) Large linear elasticity assisted by the concurrency of elastic deformation and twinning deformation.

Fig. 2. Microstructures of NC-NiTi wire. (a) TEM bright-field image of annealed specimen. (b) 1D HE-XRD pattern of the annealed specimen. Insert is its corresponding 2D HE-XRD pattern. (c) 14 % tensile loading-unloading curve of the annealed specimen at 20 °C. (d) 1D HE-XRD pattern of the pre-deformed specimen. Insert is its corresponding 2D HE-XRD pattern. (e) Evolution of HE-XRD intensity for multiple planes of B19′-NiTi phase along the Debye-Scherrer rings (insert of Fig. 1(d)). (f) TEM bright-field image of the pre-deformed specimen.

Fig. 3. Mechanical response of NC-NiTi wire. (a) Tensile stress-strain curves at -197 °C and 20 °C. (b) Tensile loading-unloading curves at -197 °C, -100 °C, -50 °C, 20 °C and 70 °C. (c) Comparison of recovery strain between the NC-NiTi and other bulk metal materials with large elastic strains [10,45,46]. (d) Comparison of mechanical energy storage density and storage efficiency between the NC-NiTi (tested at -197 °C) and other various advanced materials [10,31,[47], [48], [49], [50], [51]].

Fig. 4. (a-c) In-situ synchrotron X-ray diffraction of NC-NiTi wire at 20 °C. (a) Evolution of in-situ HE-XRD patterns during a tensile loading-unloading deformation to 4.3 % macroscopic strain. (b) The d-spacing strain and calculated twinning-detwinning strain with respect to macroscopic strain perpendicular to the loading direction. (c) The plot of the d-spacing for (002) and (03) versus the azimuthal angle, the wire longitudinal direction is 90° and the transverse direction is 0°. (d) Microstructure evolution diagram of subsequent tensile loading-unloading for the pre-deformed sample, where the pink grains are in tension and the blue ones are in compression.

Fig. 5. Schematic representation for the formation of residual internal stress in NC-NiTi. (a) Stress-free microstructure of NC-NiTi (set PA and PB as the two grains of B2 phase) before pre-deformation, grains with different colors represent grains of different orientations. (b) Diagram of tensile loading of 14 %, where $\varepsilon _{\text{P}-\text{M}}^{\text{A}}$< $\varepsilon _{\text{P}-\text{M}}^{\text{B}}$, $\varepsilon _{e}^{\text{MA}}$>$\varepsilon _{\text{e}}^{\text{MB}}$. (c) Stress states of the two grains inside NC-NiTi (set MA and MB as the two grains of B19′ phase) after unloaded, where the red arrows represent the direction of internal stress.

Fig. 6. Linear elastic mechanical characteristics of the NiTi samples with varying mean grain sizes between 15 nm and 350 nm at 20 °C. (a) Tensile loading-unloading curves. (b) Grain-size dependence of yield stress and recovery strain. (c) Comparison of d-spacing strain and twinning-detwinning strain.

Fig. 7. Linear elastic mechanical characteristics of the NiTi with mean grain size of 15 nm and 350 nm from -150 °C to 70 °C. Testing temperature effect on (a) yield stress as well as (b) recovery strain. (c) Storage modulus change as a function of testing temperature. (d) Testing temperature effect on d-spacing strain and twinning-detwinning strain.