Time of flight improved thermally grown oxide thickness measurement with terahertz spectroscopy

Abstract

As a nondestructive testing technique, terahertz time-domain spectroscopy technology is commonly used to measure the thickness of ceramic coat in thermal barrier coatings (TBCs). However, the invisibility of ceramic/thermally grown oxide (TGO) reflective wave leads to the measurement failure of natural growth TGO whose thickness is below 10 μm in TBCs. To detect and monitor TGO in the emergence stage, a time of flight (TOF) improved TGO thickness measurement method is proposed. A simulative investigation on propagation characteristics of terahertz shows the linear relationship between TGO thickness and phase shift of feature wave. The accurate TOF increment could be acquired from wavelet soft threshold and cross-correlation function with negative effect reduction of environmental noise and system oscillation. Thus, the TGO thickness could be obtained efficiently from the TOF increment of the monitor area with different heating times. The averaged error of 1.61 μm in experimental results demonstrates the highly accurate and robust measurement of the proposed method, making it attractive for condition monitoring and life prediction of TBCs.

Graphical abstract

Keywords

thermal barrier coatings / thermally grown oxide / terahertz spectroscopy / time of flight

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Nomenclature

Abbreviations
SEM	Scanning electron microscope
TBC	Thermal barrier coating
TGO	Thermally grown oxide
THz-TDS	Terahertz time-domain spectroscopy
TOF	Time of flight
YSZ	Yttria-stabilized zirconia
Variables
a	Contraction−expansion factor
a0, b0	Extended steps in the discretization process of a and b, respectively
b	Translation factor
dc	Ceramic topcoat thickness
dT	TGO thickness
D	Signal points interval between reference signal and experimental signal in corss-correction process
E	Mathematic expectation
f(t)	Any function in wavelet transform process
f1(t)	Reference signal
f2(t)	Experimental signal
j	Number of discretized values
k	Discretization coefficient
nc, na	Refractive index of ceramic and air, respectively
nT	TGO refractive index
N	Signal length
R_{f_1{f}_2}	Cross-correction function between reference signal and experimental signal
R_{\mathrm{s}\mathrm{s}}	Autocorrelation function of the source signal
s(t)	Original signal without noise
s{n}_1(t), s{n}_2(t)	Uncorrelated noises in reference signal and experimental signal, respectively
t	Time in the signal sequence
Δt1	Time delay between air/ceramic reflective wave and ceramic/metal reflective wave
Δt2	Time delay between terahertz signals before and after TGO growth
wj,k	Discrete wavelet function coefficient
Wf	Continuous wavelet transform function
λ	Soft threshold in wavelet function
τ	Time in correction function
τd	Relative time delay between reference signal and experimental signal
α	Terahertz incident angle from air into ceramic
θ	Terahertz refractive angle from air into ceramic
\omega	Terahertz refractive angle from ceramic into TGO
ψ	Basic wavelet function

Acknowledgements

The authors acknowledge the funding they received from the National Natural Science Foundation of China (Grant Nos. 52275096 and 51905102), the Fujian Provincial Science and Technology Project, China (Grant No. 2019I0004), the State Key Laboratory of Mechanical Systems and Vibration, China (Grant No. MSV-2018-07), the Shanghai Natural Sciences Fund, China (Grant No. 18ZR1414200), and the China Postdoctoral Science Foundation (Grant No. 2019M662226).

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