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Interlaminar Fracture Toughness Measurement of Multilayered 2D Thermoelectric Materials Bi2Te3 by a Tapered Cantilever Bending Experiment

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Abstract

Background

Multilayered thermoelectric material bismuth telluride (Bi2Te3) is widely used in engineering owing to its exceptional thermoelectric performance at room temperature. However, Bi2Te3 is prone to cracks, voids, or other defects due to its multilayered structure, leading to decreased device lifetime and reliability.

Objective

This paper aims at stably and precisely measuring the interlaminar fracture toughness (IFT) of multilayered Bi2Te3 for the reliability evaluation of Bi2Te3-based thermoelectric devices. In addition, we seek a method to stably measure the IFT even for very brittle materials.

Methods

We developed a tapered cantilever bending (TCB) experiment to obtain the IFT. The experimental specimens were fabricated using a focused ion beam (FIB) technique at the micro scale, and the initial interlaminar crack was introduced by the notch method.

Results

By performing the TCB experiment, we created an ideally sharp pre-crack and observed stable crack propagation. The critical energy release rate (ERR) for crack propagation obtained in the present paper is around 0.51–0.53 J/m2, which agrees reasonably with theoretical van der Waals (vdW) interlaminar interaction energy.

Conclusions

The proposed method can be well-applied in assessing IFTs of multilayered materials, even for very brittle multilayered 2D materials.

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Acknowledgements

This research was supported by Research Innovation Fund of Shenzhen City of China (project nos. JCYJ20170811160538023), the National Natural Science Foundation of China (project nos. 11972137, 11972133, 11672084, 12090033, 12002036, 12041202, 12102043), the China Postdoctoral Science Foundation (2019M660476, 2020T130056, 2021M690403), and JSPS KAKENHI Grant Number JP21K18674. Experiments in FESEM were technically supported by Mr. K. Ishikawa (Kyoto University).

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Appendix: Design Philosophy of the Specimen Size Dimensions

Appendix: Design Philosophy of the Specimen Size Dimensions

As shown in Fig. 14(a), the specimen design can be characterized by 8 size parameters in total, where \({l}_{1}\) often takes a large value to ensure the cantilever property of the beam, \({l}_{2}\) and \({h}_{2}\) are the beam length and thickness, and among these parameters, the tapered angle \(\alpha\) and notch depth \(h{}_{n}\) are of most importance for the performance of stable interlaminar crack growth. Therefore, before the start of the fracture test, we have to carry out some preliminary investigation on the specimen design philosophy.

Fig. 14
figure 14

(a) Dimensions of the specimen for measuring interlaminar fracture toughness; (b) the boundary conditions and model mesh with a crack length of 1 μm

The preliminary study is performed based on a FEM simulation through ANSYS, where the model size takes the measured specimen size of \({h}_{1} = 9.02\), \({h}_{2} = 3.89\), \(h = 18.5\), \({h}_{n} = 1.73\), \({l}_{1} = 49.6\), \({l}_{2} = 5.97\), \({l}_{3} = 3.14\), \({l}_{n} = 1.78\), and \(t = 10.7\) (all units in μm). The lower base is fixed and the beam end is subjected to an area load of 1 mN distributed on the center 1/3 length of \({l}_{3}\), the crack region and crack tip mesh are refined as shown in Fig. 14(b). On this basis, we separately change the length of \({h}_{1}\) and \({h}_{n}\), to analyze the effect of tapered angel \(\alpha\) (where \(\alpha =\mathrm{arccot}[({l}_{2}+{l}_{n}+{l}_{3})/(h-{h}_{1}-{h}_{2})]\) and normalized notch depth \(r\) (where \(r ={h}_{n}/{h}_{2}\)) on the energy release rate (ERR) \(G\) at different crack length. The applied load is \(P = 1\) mN and the loading displacement is calculated by FEM, denoted as \(D\). The G-a curve for different structure shapes are shown in Figs. 15-16, where \(G(a)\) is fitted as a quadratic function for each case. For a good specimen shape in this work, decreasing energy release rate (ERR) is expected to creating the stable crack propagation.

Figure 15 shows the variation of ERR with crack length under different tapered angle, the comparison results show that when α is small, the tapered beam is similar to a rectangle beam, leading to an increasing ERR and instant crack propagation. When \(\alpha\) is large, ERR decreases as crack length rises, so that a stable crack growth can be expected. However, when the \(\alpha\) angle gets larger, the structure becomes stiffer, and stronger loading is needed for the interface cracking. This may lead to significant local stress concentration as shown in Fig. 17(b). Therefore, a proper tapered angle for the experiment may be \(\alpha = 20^\circ - 40^\circ\).

Fig. 15
figure 15

FEM simulation results of \(G\) versus crack length subjected to different tapered angle: (a) \(\alpha = 3^\circ\), (b) \(\alpha = 13^\circ\), (c) \(\alpha = 23^\circ\), (d) \(\alpha = 31^\circ\), (e) \(\alpha = 41^\circ\), and (f) \(\alpha = 51^\circ\), under a normalized notch depth \(r = 0.51\)

Figure 16 shows the FEM simulation results of ERR versus crack length subjected to different notch depth \(r ={h}_{n}/{h}_{2}\). Similar to the analysis of Fig. 15, the results show that higher notch depth makes the specimen more suitable for the fracture test. However, higher notch depth may also enhance the local stress concentration, as shown in Fig. 17(c). Hence, higher \(\alpha\) or \(r\) may lead to un-desired plastic deformation or specimen failure of such layered 2D materials, as discussed in Material and Specimen. Hence, the recommended specimen size dimensions for fracture test are about \(\alpha = 20^\circ - 40^\circ\) and \(r = 0.4-0.6\).

Fig. 16
figure 16

FEM simulation results of \(G\) versus crack length subjected to different notch depth \(r ={h}_{n}/{h}_{2}\): (a) \(r = 0.13\), (b) \(r = 0.26\), (c) \(r = 0.38\), (d) \(r = 0.64\), (e) \(r = 0.77\), and (f) \(r = 0.9\), under a tapered angle of \(\alpha = 27^\circ\)

Fig. 17
figure 17

The contour plot of specimen stress intensity under identical loading of (a) original state \(\alpha = 27^\circ\), \(r = 0.51\); (b) large tapered angle \(\alpha = 51^\circ\), \(r = 0.51\); (c) deep notch \(\alpha = 27^\circ\), \(r = 0.9\). Large \(\alpha\) may enhance the local stress intensity around the base corner at and deep notch may produce extra beam damage since the beam gets thicker

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Wang, P., Wang, K.F., Wang, B.L. et al. Interlaminar Fracture Toughness Measurement of Multilayered 2D Thermoelectric Materials Bi2Te3 by a Tapered Cantilever Bending Experiment. Exp Mech 62, 165–180 (2022). https://doi.org/10.1007/s11340-021-00761-2

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