Curing process and residual strain monitoring
By temperature compensation method, FBG-1 and FBG-2 achieved the real-time monitoring of temperature and residual strain during the curing process, as shown in Fig. 8. To avoid the FBG measuring deviation caused by the cross sensitivity of temperature and strain, researchers developed many techniques such as using special coating23, characterizing strain by bandwidth24, improving the demodulation method25 and so on. Setting temperature compensation sensor was a useful method to demodulate the temperature and strain26. The Bragg wavelength shift of FBG-1 represented the simultaneous change of temperature and residual strain, and FBG-2 only represented temperature change. As a result, the different value between them represented the residual strain change, illustrated by the blue line in Fig. 8. The glass transition temperature Tg after which the glass–ceramics would turn from the rubbery state to the vitreousness was detected. Based on the Eq. (2), the mean value of residual strain was estimated from the Bragg wavelength shift. The axial residual strain in glass–ceramics under the specific heating process was about 3,900 με.
Based on the finite element method (FEM) model in the “Finite element model” section, the residual strain at different temperature during the curing process was obtained as the red line shown in Fig. 8. The deviation between the monitored and numerical results was less than 5%, so the accuracy and reliability of this methodology were verified.
The results by grating length mismatched sensing method were presented and discussed. Given that the stress in glass–ceramics was non-uniform and high level shown in Fig. 3a, the origin spectrum of FBG-1 (Fig. 9a) would generate obvious distortions (see Fig. 9b,c) due to the chirped grating period when the residual strain began to formed27, so the softening point of the glass–ceramics was precisely monitored. As the temperature decreased to 100 °C, the residual strain in glass–ceramics increased, and the broadening and distortions of FBG-1 were more recognizable shown in Fig. 9c. This phenomenon was simulated by the transfer matrix method (TMM)28 based on the coupled mode theory as shown in Fig. 9c. The strain imposed to the grating region was the same as the strain distritbution of axial path 2 obtained by the FEM in “Finite element model” section. The spectra change of both experimental and simulated results was consistent. From the comparison between the experimental and simulated results of Fig. 9, the deviation of central wavelength was less than 5%, and the deviation of full width at half meduim (FWHM) was less than 15%. The measuring accuracy was validated, and the minor difference of FBG-1 was tolerated, because the mesh density of TMM method was much higher than the accuracy of the interrogator. To improve the accuracy of strain measuring, the Bragg wavelength of FBG-1 was extracted by Gaussian fitting method29.
The length of FBG-1 (12 mm) was mismatched with the glass–ceramics (5 mm), so part of the FBG-1 would stretch out of the glass–ceramics without the influence of residual strain. Therefore, the spectrum of FBG-1 was divided into two sections30. One was the chirped section due to the non-uniform axial strain distribution in glass–ceramics as shown in the red box in Fig. 9c. The other was the distinct single peak at the right side of spectrum, which was only affected by the environmental temperature, marked by the blue box in Fig. 9. This phenomenon was proposed to be a feasible method to demodulate the temperature and strain by a single FBG sensor. As simulated by TMM, when the embedded grating length was about half of the whole grating region (Fig. 10a), the spectrum of the FBG would split into two peaks (Fig. 10b). The right peak only indicated the temperature of the measured model, and the left peak indicated both temperature and strain inside the model.
In our previous research, the FWHM of FBG was only affected by the non-uniform strain distribution, which was also presented in Fig. 10c. For the type of FBG applied in our research, the relationship between average strain distribution and the Bragg wavelength was almost linear14. The experimental FWHM of FBG embedded in glass–ceramics after curing process (see Fig. 10d) was about 4.02 nm, and the corresponding strain was about 3,500 με. Compared with the FEM results in section Finite element model, the deviation between the measured and theoretical results was less than 12%, and it was also consistent with the strain (3,900 με) calculated obtained from the temperature compensation method with deviation around 10%. For the temperature measurement, the Bragg wavelength shift of the right peak was in according with the relationship between wavelength and temperature. Therefore, the spectrum analysing of single FBG in glass–ceramics with mismatched length would achieve the simultaneous discrimination of temperature and strain with good accuracy and easier operations compared with temperature compensation method.
Structural health monitoring of thermal cycling aging
The on-line monitoring results of 22 thermal cycles were shown in Fig. 11. The methodology based on femto-laser inscribed FBG was effective and the monitoring was consecutive in the thermal cycling aging. The monitored trend of residual strain was much more important than the exact magnitude. The cooling rate before 14th cycle (5 °C/min) was 2 times faster than that of 15th to 22nd cycles (1.5 °C/min). From the demodulated strain change in Fig. 11b extracted from Fig. 11a, the cooling rate introduced a small effect on the residual strain value. The strain would grow when the cooling rate was faster. Besides, the number of thermal cycles would give a insignificant positive correlation with the residual strain (less than 10%).
The influence factors of residual strain in glass–ceramics contained the crystallization properties (volume fraction, crystal shape, etc.) and the mechanical properties (Young’s modulus, CTE, etc.)6. The cooling rate before the softening point of glass–ceramics (> 600 °C) played an important role on the crystallization properties and the permanent strain value. Because the maximum temperature in thermal cycling was 450 °C and less than the Tg of glass–ceramics, the permanent strain wouldn’t generate distinct variations for this reason. Moreover, the enlarging of non-homogenous cooling rate would intensify the thermal gradient and strain rate of the MTGC-EPA. The residual strain reached a relatively constant value as the MTGC-EPA model was cycled further, and no severe strain relaxation of this model was observed in the thermal cycling aging. Hence, the appropriate amount of thermal cycles wouldn’t decrease the mechanical strength and lead to the stress relaxation in MTGC-EPA model, based on the monitoring result of temperature compensation method.
The spectra of FBG-1 and FBG-2 at each stage of 22 thermal cycles were extracted as shown in Fig. 12. The Bragg wavelength of FBG-2 were almost the same wavelength around 1555.40 nm (± 0.05 nm), indicating that the ultimate temperature of each thermal cycle was constant nearby 100 °C (± 2 °C). The FWHM of the right peak of FBG-1 changed from 4.02 to 4.18 nm after 22 thermal cycles, representing the strain increased marginally from 3,500 to 3,700 με, which was in good accordance with the strain demodulated by temperature compensation method, and the fitted central wavelength (illustrated in Fig. 12) showed little deviation. Both these results proved that the residual stress maintained a stable value and there was no strain relaxation in glass–ceramics. Consequently, the mechanical robusticity and hermetic reliability of glass–ceramics sustained after several extreme temperature change in nuclear reactors, validated by the chirped spectra of embedded length-mismatched FBG-1.
Results of SEM and leakage rate detecting
The microstructure images of EPA cross-section before and after thermal cycling aging were respectively shown in Fig. 13. The interface between fiber and glass–ceramics showed no gaps (Fig. 13a), because the constituents of them were mainly SiO2 and they could be fused together easily. After thermal cycling aging, the appearance of fiber was almost intact with insignificant defects generated on the interface (Fig. 13b). This guaranteed the measuring accuracy of residual strain in glass–ceramics. It was observed that some pores developed after 22 thermal cycles, causing the glass–ceramics turn from smooth to uneven (see Fig. 13c,d). The microstructure of the cross section was preserved and bonded.
The leakage rate of MTGC-EPA models was detected at vacuum helium environment from 100 to 450 °C as shown in Fig. 14. The leakage of the model before and after thermal cycling aging showed similar trend with temperature rising. The leakage rate was almost unchanged (less than 1e−11 Pa·m3/s) before the temperature reached 310 °C. The leakage rate rose sharply when the temperature was larger than 310 °C.
It appeared that the leakage rate of model increased insignificantly after thermal cycling aging, and the hermeticity was still intact (less than 1e-7 Pa·m3/s) from 100 to 450 °C, so the model was able to bear the effect caused by several severe temperature variations in nuclear reactors (100–450 °C). The rising point of leakage rate delayed slightly after thermal cycling aging, due to the incremental residual strain explained in “MTGC-EPA” section.