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Cyclic Mechanical Fatigue Lifetime of Bi_{0.5}Na_{0.5}TiO_{3}-Based Eco-Piezoceramics

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{0.5}Na

_{0.5}TiO

_{3}and solid solutions based on it have surfaced in recent years as lead-free replacements for PZT ceramics [9,10]. As mentioned above, there have been some works on fatigue behavior of PZT piezoelectric ceramics. Studies have been carried out comparing various mechanical properties of lead-free materials, such as flexural strength, Young’s modulus, fracture toughness and R-curve behavior [11,12,13,14]. However, mechanical fatigue behavior analysis of lead-free piezoelectric ceramics has not been reported to date.

_{max}) vs. the number of cycles to failure (N). This method not only predicts the number of cycles in the given fatigue load but also shows the fatigue limit. Mechanical fatigue of the components does not occur in response to a stress level that is lower than a certain limit known as the fatigue limit, which represents the maximum cyclic stress that can be applied “infinitely” to the material without failure. Very few researchers reported the S-N diagrams of piezoceramics, since they are tedious and time consuming to obtain. However, they provide information that it is not possible to attain otherwise on the actual performance of the material in devices.

_{0.5}Na

_{0.5}TiO

_{3}-based eco-piezoceramics using unpoled and poled disks. Moreover, an attempt was made to interpret the influence of the polarization on their mechanical properties.

## 2. Materials and Methods

#### 2.1. Material

_{0.5}Na

_{0.5})TiO

_{3}-based, PIC700 ceramic, produced by PI Ceramic GmbH, Lederhose, Germany [25,26]. Thin ceramic disks of typically 1 mm thickness and 12 mm diameter were cut from unpoled cylinders of 10 mm height to ensure identical microstructural characteristics in all tested specimens.

#### 2.2. X-ray Diffraction (XRD) and Microstructural Analysis

#### 2.3. Electrical Characterization

#### 2.4. Mechanical Characterization

#### 2.4.1. Biaxial Flexural Strength

#### 2.4.2. Fatigue Behavior

_{max}is the maximum applied stress, N

_{f}is the cycles to failure, A is the fatigue strength coefficient and B is the fatigue strength exponent. The fatigue strength exponent represents the fatigue degradation rate of specimens during cyclic loading. Increased fatigue life is expected with an increase in the fatigue strength coefficient and a decrease in the fatigue strength exponent. For quality measurements of the regression model, we used the coefficient of determination (R

^{2}) [44]. The fractured surfaces of the specimens were observed with SEM to discern different microstructural behaviors after cyclic loading.

## 3. Results

_{0.5}Na

_{0.5})TiO

_{3}-xBaTiO

_{3}(BNBT) system near the MPB [32]. Noticeably, the peak intensity ratio for the doublets near 15 and 30° 2θ (001/100 and 002/200), which should be equal for a homogeneous sample from surface to bulk, is different. This is explained by a 001 surface texture, most probably developed during sample cutting [45], and it does not reveal a characteristic of the bulk of the ceramic.

_{eq}= 4(S/π)

^{1/2}, where S is the grain surface area) from the analysis of the lognormal distribution of measured equivalent diameters that is shown in Figure 3. Porosity (P) was quantified as the fraction of the analyzed surface area occupied by pores. Results of these measurements are given in Table 1.

_{0.5}Na

_{0.5})TiO

_{3}-based compositions, e.g., (1-x) (Bi

_{0.5}Na

_{0.5})TiO

_{3}-xBaTiO

_{3}(NBT-xBT) system.

_{max}, MPa) vs. cycles to failure (N

_{f}) derived from experimental data in Figure 5. The corresponding fitting results are shown. Additionally, the mean and standard deviation of flexural strength are illustrated for both types of samples in this figure at the maximum applied stress axis. The S-N curve showed that maximum applied cyclic stress gradually declined with the increasing number of cycles. The coefficients of determination (R

^{2}) values were 0.58 and 0.96 for poled and unpoled materials, respectively. The unpoled plot presents larger data scattering around the fitting line than the plot for poled samples. The fatigue strength exponents were −0.014 and −0.01 for poled and unpoled materials, respectively. Therefore, the unpoled samples showed a flatter S-N slope, which represents a lower fatigue degradation rate. In contrast, poled samples showed a steeper S-N diagram, which led to a more significant decrease in fatigue strength. The fatigue strength coefficients were 196 MPa and 169 MPa for poled and unpoled materials, respectively. Additionally, the fatigue strength (maximum applied load at each number of cycles) of unpoled ceramics is larger than that of poled ceramics at the same number of cycles, thereby indicating that the fatigue resistance is weakened by the poling effect. The arrows show that the fracture failure did not occur when the number of cycles reached 10

^{6}. As can be seen from Figure 5, the fatigue limits of unpoled samples were noticeably higher than those of poled samples. The fatigue limits at 10

^{6}cycles were 135 MPa for poled samples and 160 MPa for unpoled samples. The fatigue limit and fatigue strength exponent for all specimens are shown in Table 2.

## 4. Discussion

_{0.5}Na

_{0.5})TiO

_{3}-xBaTiO

_{3}(NBT-xBT) solid solution exhibits a morphotropic phase boundary (MPB) which spans a wide range of compositions from x = 5–11 mole% BT with varying degrees of average structural distortions (rhombohedral to pseudocubic to tetragonal with increasing BT content and in the absence of the electric field) [32]. The observed characteristics, as well as the temperatures in Figure 4, are in good agreement with those reported for x ≈ 0.10 in the Ba-rich tetragonal side of the undoped NBT-xBT system [46,47].

_{F-R}, as observed in Figure 3 for the unpoled sample under study. That material showed a slight increase in T

_{F-R}in the poled state, which was related to the stabilization of the ferroelectric long-range order due to the aligned polarization vectors in the oriented domains. As a result, in the poled NBT-xBT tetragonal ferroelectric at room temperature, the remnant strain at the strain-stress unipolar cycle under uniaxial compressive test was about twice as high as in the unpoled state for x = 0.12 [12]. Due to the thickness poling of the specimens, more non-180° ferroelectric-ferroelastic domains have the polarization vector aligned parallel to the loading direction. Therefore, more domains can switch under the action of a mechanical load.

^{2}= 0.58 vs. poled samples: R

^{2}= 0.96). This is because such defect distributions are narrowed due to the systematic action of the tensile stress at grain boundaries and domain walls produced by the poling effect.

_{0.5}Na

_{0.5}TiO

_{3}-based ceramics is not only related to the microstructure (porosity and other inhomogeneities) but is also involved with the stress induced by the ferroelectric-ferroelastic domain orientation, either on cyclic loading or anisotropically during poling.

## 5. Conclusions

- −
- The biaxial bending strength and fatigue strength for the unpoled samples are about 10% and 15% higher than for the poled samples, respectively.
- −
- The fatigue lifetime of the poled samples is much shorter than that of unpoled ones when subjected to the same external stress, which indicates a lower cyclic fatigue resistance.
- −
- The different fatigue crack growth behavior produces a different fracture pattern, with flat transgranular-based fractures in the unpoled samples and a mixture of transgranular and intergranular wavy fractures in the poled ones.
- −
- The poling process decreases the mechanical strength and further deteriorates the cyclic fatigue properties due to the domain orientation that generates an anisotropic residual stress field; crack propagation occurs mainly along the domain walls and the grain boundaries.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic of the piston-on-3-ball set-up (P is the applied load, σ

_{1}and σ

_{2}are the applied biaxial tensile stresses localized at the center of the bottom surface of specimen).

**Figure 2.**PIC700 synchrotron X-ray diffraction patterns observed (red line) from the Rietveld analysis using a P4 mm model (black line). Reliability factors: R

_{p}= 8.11, χ

^{2}= 7.22.

**Figure 4.**Dielectric permittivity: (

**a**) real part and (

**b**) loss of unpoled PIC700 ceramic samples on heating (red curves) and on cooling (blue curves).

**Figure 5.**S-N curves for unpoled (green color) and poled (blue color) specimens showing maximum load as a function of the number of cycles to failure. Arrows indicate run out. Bar graphs illustrating the mean and standard deviation of flexural strength values are also plotted in the figure.

**Figure 6.**SEM photographs of the fracture surfaces showing grain and domain structures: (

**a**)only transgranular fracture is observed in the unpoled specimen; (

**b**) wavy surface with a mixture of transgranular and intergranular fractures of the poled specimen.

**Figure 7.**Schematic of the stress field under biaxial flexural loading test on: (

**a**) an unpoled specimen and (

**b**) a poled specimen with anisotropic internal stress distribution after poling.

**Table 1.**Some ceramic properties and the catalog density [25] of the PIC700 ceramic. Data are provided only with significant digits.

PIC700 Perovskite-Type Structure | Density ρ (g.cm ^{−3}) | Mean Grain Size <G> (μm) | <G>’s Standard Deviation σ _{<G>} (μm) | Porosity p (%) |
---|---|---|---|---|

5.76 | 2.12 ± 0.09 | 0.20 ± 0.03 | 3.2 ± 0.3 | |

Symmetry | S.G. | a (Å) | c (Å) | c/a |

Tetragonal | P4 mm | 3.9024 (1) | 3.9747 (2) | 1.019 (1) |

Material | Bending Strength (MPa) | Fatigue Limit (MPa) | Fatigue Exponent (B) | Fatigue Coefficient (A) (MPa) |
---|---|---|---|---|

Unpoled | 220 ± 20 | 160 | −0.010 | 196 |

Poled | 200 ± 13 | 135 | −0.014 | 169 |

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**MDPI and ACS Style**

Bartolomé, J.F.; Fuentes-Cobas, L.E.; García, Á.; Jacas, A.; Pardo, L.
Cyclic Mechanical Fatigue Lifetime of Bi_{0.5}Na_{0.5}TiO_{3}-Based Eco-Piezoceramics. *Materials* **2021**, *14*, 4113.
https://doi.org/10.3390/ma14154113

**AMA Style**

Bartolomé JF, Fuentes-Cobas LE, García Á, Jacas A, Pardo L.
Cyclic Mechanical Fatigue Lifetime of Bi_{0.5}Na_{0.5}TiO_{3}-Based Eco-Piezoceramics. *Materials*. 2021; 14(15):4113.
https://doi.org/10.3390/ma14154113

**Chicago/Turabian Style**

Bartolomé, José F., Luis E. Fuentes-Cobas, Álvaro García, Alfredo Jacas, and Lorena Pardo.
2021. "Cyclic Mechanical Fatigue Lifetime of Bi_{0.5}Na_{0.5}TiO_{3}-Based Eco-Piezoceramics" *Materials* 14, no. 15: 4113.
https://doi.org/10.3390/ma14154113