Superelastic materials are a category of materials that present “plastic” strain way beyond their linear elastic regimes in response to applied stress, ideal for a variety of applications from sensors, actuators to dampers (14–16). The basic principle of superelasticity is the stress-driven transformation from parent phase to martensite during loading and vice versa during unloading (14–16). However, due to the structural incompatibility between the different phases, local mismatch stress will arise at their internal interfaces (1,2,6,8,10,15–18). This local mismatch stress combined with the applied stress, may exceed the dislocation activation stress or the strength of materials, resulting in an increase of residual plastic deformation and a variation of the stress-strain curves over loading cycles (functional fatigue) (6–8,14–16,19) or mechanical failure by fracture (structural fatigue) (10,15–19).
As the amplitude of the generated mismatch stress is roughly proportional to the area of the hysteresis loop (14–16,18,19), in specifically fabricated or designed superelastic materials with small hysteresis such as NiTi crystalline-amorphous nanocomposites (CAN) (2), [001]-oriented NiCoFeGa single crystals (3), additive manufactured NiTi alloys (4), and Au30Cu25Zn45 alloys (5), excellent reliability has been achieved. However, when large hysteresis is involved, superelastic materials still suffer poor fatigue (6,7,10). Although dedicated efforts have been made to address this issue, the achievement remains very limited. For instance, the fatigue life of shape memory ceramics designed using the concept of oligocrystalline can only sustain hundreds cycles before mechanical failure (10). For ductile shape memory alloys, the best results were reported in NiTiCu film with Ti2Cu precipitates (8), which presents repeatable transformation cycles of 107, but with limited hysteresis. While in some specific applications, e.g., microdampers to be used in micro- and nano-scale devices, large hysteresis and super-durability are both crucially required (20).
Ferroelectrics, another type of smart material, have been recently reported to present superelasticity, after tailoring the normally irreversible non-180o polarization switching (hereafter referred as ferroelastic switching) to be reversible, using external mechanisms such as restoring force (21,22), internal mechanisms such as defect pinning (23), or surface mechanisms such as surface energy and/or surface amorphous layer (24,25). Importantly, different from the traditional transformation superelastics, ferroelastic switching in ferroelectrics can be driven by stress less than 100 MPa and the mismatch stress between different ferroelectric variants is also limited, both are significantly smaller than the dislocation activation stress and the compressive strength of ferroelectrics (11–13). Thus, it is reasonably supposed that the long-standing challenge for superelastic materials, the attainment of large hysteresis and excellent durability simultaneously, could possibly be solved by using superelastic ferroelectrics.
Based on this assumption, we fabricated a series of cuboidal micropillars of various size using BaTiO3 (BT) crystal as a model material, and examined their constitutive behaviors and fatigue performance. As expected, we found the BT micropillars possess simultaneous large hysteresis and super-durability, sustaining up to 108 cycles without functional degradation and mechanical failure. The pillars were cut from the (001) surface of pre-poled BT bulk crystals using focus ion beam (FIB), as detailed in the Supplementary Materials (SM). The size of the pillars ranges from 0.5×0.5×1 µm3 to 5×5×10 µm3, with aspect ratios (height ‘h’ to side length of the top surface ‘d’) fixed at ~ 2 (Fig. 1A). The sides of the pillars’ top surface are along [110] and [011] crystallographic directions of BT. The mechanical responses of the pillars were characterized by compressing them along their long axis using a Hysitron TI-950 nanoindentor with a flat punch. Here cuboidal instead of cylindrical pillars were used as they have uniform cross-sectional area and thus have the uniform stress from top to bottom (2,6).
The measured stress-strain curves are displayed in Fig. 1B. Similar to the phenomena observed in BT pillars with cylindrical shape (11), the cuboidal pillars also show significant size effect. With relatively large d of 5 µm, the first cyclic stress-strain curve consists of an initial linear regime, a plateau regime corresponding to ferroelastic switching, and then a subsequent linear regime followed by the unloading curve with a slope similar to the second linear regime during loading, very similar to the response of bulk BT (21). The second cyclic stress-strain curve is drastically different from the first one, exhibiting linear elastic behavior since ferroelastic switching has been exhausted in the first cycle.
With d decreasing, the measured stress-strain curves no longer follows the linear slope during unloading. Instead, the unloading curve goes through a plateau (via reversed ferroelastic switching) followed by another linear regime, resulting in partial recovery of the strain for pillar with d of 4 µm, and almost complete recovery for pillars with d smaller than 4 µm. Thus for pillars with d from 3 to 0.5 µm, their second cyclic stress-strain curves closely follow the first cycle, and that is superelasticity.
We extracted the critical stress (\({\sigma }_{c}\)) required to drive ferroelastic switching by the transition between the initial linear and stress plateau regime (Fig. 1C). When d decreases from 5 to 1 µm (for pillar with d of 0.5 µm, \({\sigma }_{c}\) becomes less well defined), \({\sigma }_{c}\) roughly increases linearly from 16 MPa to 43 MPa, but significantly smaller than the dislocation nucleation activation stress (\({\tau }_{a}\)) of BT (11–12).
In order to quantitatively compare the hysteresis characteristics of BT pillar with other materials, we calculated their damping coefficient \(\psi\) (\(\psi =\varDelta W/{W}_{max}\)) from the second cyclic stress-strain curves (Fig. 1C). Here \(\varDelta W\) is the dissipated energy over the loading-unloading cycle; \({W}_{max}\) is the maximum stored energy per unit volume over the cycle. With the decrease of d, the calculated \(\psi\) first increases and then decreases. The largest \(\psi\) of 0.38 was observed in pillar with d of 2 µm, which is smaller than CuAlNi pillars of ~ 0.63 (1,26) and ZrO2-based ceramic particles of ~ 0.78 (27,28), comparable to NiTi pillars of ~ 0.37 (6) and ZrO2-based ceramic pillars of 0.44 (10), and larger than NiTi crystalline-amorphous nanocomposite (CAN) pillars of 0.06 (2), NiTiCu film of 0.16 (8), and FeMnAlCrNi alloys of 0.26 (7).
We then characterized the fatigue performance of the pillar with d of 2 µm (Hereafter, all the characterization was conducted on pillars with d of 2 µm). After 102 loading cycles, the measured stress-strain curves nearly overlap with each other, and only show slight difference from that of the as-fabricated pillar (Fig. 2A). Remarkably, even after 108 cycles (run out), no appreciable plastic deformation was found on surface of the pillar (Insets of Fig. 2A and Fig. S2).
Following the fatigue test, we characterized the stress-strain curves of the same pillar after 1 month and 3 months. The overlap of the measured stress-strain curves demonstrates that BT pillar possesses long-term performance (Fig. S3A).
We also examined the response of BT pillar with varying frequencies from 0.1 Hz to 10 Hz. Results demonstrate that the measured stress-strain curves are nearly unchanged (Fig. S3B). Note that limited by instrument, here the maximum loading frequency of 10 Hz was used. However, inferred from the actuating performance of bulk BT we reported under the action of high-frequency electric field (29), it is believed BT pillar would possess similar hysteretic performance at higher mechanical loading frequency.
Figure 2B highlights the remarkable fatigue performance of BT pillar in comparison with other superelastic materials. After 108 loading cycles, \(\psi\) of BT pillar maintains at ~ 0.35. While for other superelastic materials, comparable fatigue resistance was only achieved in NiTiCu film and NiTi CAN pillars with much smaller \(\psi\) (2,8). When large \(\psi\) is involved, e.g., for NiTi and CeO2-ZrO2 ceramic pillars, \(\psi\) decreases quickly as a function of \(log\left(N\right)\) (6,7,10,27,28).
The residual strain of BT pillar, which is important for practical applications, is also smaller than other superelastic materials that with large hysteresis (Fig. S4). Except in the first cycle where a residual strain of 0.05% was observed possibly due to plastic deformation on the top surface or a small volume of domains that cannot switch back after unloading, in the subsequent loading cycles, the measured residual strains remain almost unchanged. In comparison, for NiTi pillar, its residual strains reach 3% after 106 loading cycles (6); for FeMnAlCrNi alloy, its residual strains reach 2.5% after 50 loading cycles (7).
To understand the fatigue performance of BT pillar as a function of stress amplitude, we estimated its stress-life (S-N) curve by measuring their strength (Fig. 3A) and their fatigue life under cyclic compressive stress of 900 MPa (Fig. 3B). Here the failure was defined by the presence of unrecoverable plastic strain, which occurred at ~ 1.3 GPa during strength characterization, and after ~ 5×103 loading cycles at 900 MPa. Accompanied with the strain burst, shear bands with direction along the dislocation slip systems {101}<101 > of BT appeared on the pillar’ surface (insets in Fig. 3A and 3B) (12).
By fitting the measured data with power function, we obtain \({\sigma }^{26.9}N={10}^{83.2}\) (Fig. 3C). According to the consensus of researchers working on mechanics, the stress fatigue limit (\({\sigma }_{FL}\)) of BT pillar was assumed to correspond to the loading cycle of 107 (30). Then we have \({\sigma }_{FL}=680 \text{M}\text{P}\text{a}\). That is, when the applied stress is smaller than \(680 \text{M}\text{P}\text{a}\), BT pillars will be fatigue-free. To verify this conclusion, we characterized the fatigue life of a new BT pillar under cyclic compressive stress of 600 MPa. From 107 to 107+5 cycles, the measured stress-strain curves are nearly the same as that measured in the initial 5 loading cycles, and after test, no plastic deformation appeared on the pillar’ surface (Fig. 3D), demonstrating the obtained S-N curve is valid.
We further characterized the plastic deformed pillars with higher magnification SEM (Fig. 4A and Fig. S5). For the pillars shown in Fig. 3A and Fig. 3B, there are 6 and ~ 1.6 shear bands appeared on their surface, with numbers corresponding to the strain burst of ~ 2.1% and 0.4%, respectively. The distance between the shear bands are ~ 30 nm. Here 1.6 means that there is one shear band only sweeps part of the pillar (Fig. S5B).
We cut a thin slice from the pillar illustrated in Fig. 3A by FIB, and characterized the microstructure in the shear bands using transmission electron microscopy (TEM). The dispersed dislocation heads revealed in Fig. 4B-4E directly prove that the shear bands were induced by dislocations. Additionally, a crack appeared at the bottom of the pillar (Fig. 4E), possibly induced by plastic deformation accumulation.
These dislocations, obviously, are induced by the applied compressive stress, not by the mismatch stress between different ferroelectric variants. Under stress of 70 MPa, ferroelastic switching has nearly completed. Thus if the dislocations were caused by the mismatch stress, plastic deformation would occur under stress lower than 70 MPa. Additionally, by assuming the unit cells in ferroelectric 90° domain walls as cubic, the upper limit of the mismatch shear stress can be estimated using the elastic mechanics, resulting in values of ~ 1.2 GPa (31,32), with amplitude significantly smaller than the \({\tau }_{a}\) of BT, with values of 7.5 ~ 8.2 GPa determined by nanoindentation technique (Fig. 4F) (33). This again, proves that the mismatch stress cannot induce dislocation nucleation.
Note that the measured strength of ~ 1.3 GPa is significantly smaller than the determined \({\tau }_{a}\). To explain this disparity, we calculated the stress field distribution in BT pillar by 3-dimensional finite element (FE) calculation, as detailed in SM. Results show that stress concentration exists at the corner between the pillar and base, with intensity depending on the curvature radius (R) of the fillet. Under compressive stress of 1.37 GPa, the maximum shear stress (\({\tau }_{max}\)) along the BT dislocation slip direction can reach ~ 8 GPa with R of ~ 0.02 µm (Fig. 4G), large enough to drive dislocation nucleation. The rationality of the FE calculation, also, is indirectly proved by the observed partial shear band (Fig. S5B).
In summary, we have shown that large hysteresis and super-durability could be achieved simultaneously in BT pillar, and we believe that similar performance will also likely exist in other ferroelectric materials as well, e.g., in PbTiO3 (34). Given that ferroelastic switching can also be driven by electric field, thus under electromechanical loading, the hysteretic performance of ferroelectric pillars is thought to be tunable, as that observed in bulk BT (21). And moreover, by applying constant stress and cyclic electric field on ferroelectric pillars, realization of activation with large strain output is also possible (29). For the coming applications of the superelasticity of ferroelectrics, although much work is still required, these findings reported here, aspire a strong motivation to pursue their development.