Measurement of Local Elastic Modulus of Thin Plates Using Lamb Wave Dual-Modal Resonance Motivated by Laser Ultrasound

Wang Jiang; Kaihua Sun

doi:10.3788/CJL221074

Chinese Journal of Lasers, Volume. 50, Issue 13, 1304004(2023)

Measurement of Local Elastic Modulus of Thin Plates Using Lamb Wave Dual-Modal Resonance Motivated by Laser Ultrasound

Wang Jiang and Kaihua Sun^*

Author Affiliations

Institute of Mechanical Manufacturing Process, China Academy of Engineering Physics, Mianyang 621999, Sichuan, China

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Abstract Get PDF(in Chinese)

Figures & Tables(16)

Fig. 1. Dispersion curves of 1 mm thick tungsten plate. (a) Dispersion curve of frequency-wavenumber; (b) dispersion curve of group velocity

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Fig. 2. Relationship between correction factor and Poisson's ratio. (a) Correction factor β₁ and Poisson's ratio υ; (b) correction factor β₂ and Poisson's ratio υ; (c) relationship between S₁-A₃ ZGV resonance frequency ratio f₂/f₁ and Poisson's ratio υ

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Fig. 3. Relationship between correction factor and Poisson's ratio. (a) Correction factor β₇ and Poisson's ratio υ; (b) correction factor β₆ and Poisson's ratio υ; (c) correction factor β₅ and Poisson's ratio υ

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Fig. 4. Relationship between resonant frequency ratio of dual-modal ZGV and Poisson's ratio. (a) f₇/f₁ and υ; (b) f₆/f₁ and υ; (c) f₅/f₁ and υ

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Fig. 5. Relationship between correction factor and Poisson's ratio under different conditions. (a) Formula about compressional wave $f_{1} = β_{1} \frac{V_{L}}{2 d}$ ; (b) formula about shear wave $f_{1} = β_{11} \frac{V_{T}}{d}$

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Fig. 6. Roadmap of laser ultrasonic inspection system

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Fig. 7. Identification of resonance modals in spectrum. (a) Spectrum of aluminum plate by single point detection; (b) theoretical (dotted line) and measured dispersion curves of thin aluminum 1060 plate

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Fig. 8. Measurement results of thin aluminum 1060 plate. (a) Time domain signal at initial position with resonance signal shown by box; (b) spectrum at initial position; (c) time domain B-scan map; (d) spectral B-scan map with noise shown by box

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Fig. 9. Measurement results of thin copper T2 plate. (a) Time domain signal at initial position; (b) spectrum at initial position; (c) time domain B-scan map; (d) spectral B-scan map

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Fig. 10. Measurement results of thin titanium TA2 plate. (a) Time domain signal at initial position; (b) spectrum at initial position; (c) time domain B-scan map; (d) spectral B-scan map

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Fig. 11. Measurement results of copper sheet nanoindentation. (a) Indentation of copper sheet; (b) loading-depth curve of copper sheet

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Table 1. Experimental sample parameters

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Table 1. Experimental sample parameters

Material	Theoretical parameter			Measured parameter
Material	Poisson's ratio υ /arb.units	Velocity of longitudinal wave V_L /（m·s^-1）	Velocity of shear wave V_T /（m·s^-1）	Thicknessd /mm	Densityρ /（g·cm^-3）
Aluminum-1060	0.33	6153.4	3099.6	0.983	2.716
Copper-T2	0.34	4555.5	2243.0	0.992	8.898
Titanium-TA2	0.36	6262.2	2928.9	0.992	4.500

Table 2. Resonance frequencies of three kinds of thin plates unit: MHz
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Table 2. Resonance frequencies of three kinds of thin plates unit: MHz
Material S₁-ZGV A₃- f_c A₂- f_c A₅- f_c S₆-ZGV
Aluminum-1060 2.940 4.780 6.565 7.982 9.495
Copper-T2 2.140 3.466 4.780 - 6.863
Titanium-TA2 2.640 4.363 - - 8.636

Table 3. Results of calculation and measurement of thin aluminum 1060 plate

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Table 3. Results of calculation and measurement of thin aluminum 1060 plate

Dual-modal resonance		Calculated parameter				Measured parameter
Dual-modal resonance		Poisson's ratio υ	Velocity of longitudinal wave V_L /（m·s^-1）	Velocity of shear waveV_T /（m·s^-1）	Elastic modulusE /GPa	Velocity of longitudinal wave by probe V_L /（m·s^-1）	Elastic modulus by nano-indenter E /GPa
	A₃-f_c and S₁-ZGV	0.3458	6452.1	3132.5	71.31	6461.79	71.44
	A₂-f_c and S₁-ZGV	0.3459	6453.4	3132.3	71.31
	A₅-f_c and S₁-ZGV	0.3443	6440.7	3138.5	71.51
	S₆-ZGV and S₁-ZGV	0.3493	6479.9	3117.7	70.85

Table 4. Results of calculation and measurement of thin copper T2 plate

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Table 4. Results of calculation and measurement of thin copper T2 plate

Dual-modal resonance		Calculated parameter				Measured parameter
Dual-modal resonance		Poisson's ratio υ	Velocity of longitudinal wave V_L /（m·s^-1）	Velocity of shear waveV_T /（m·s^-1）	Elastic modulusE /GPa	Velocity of longitudinal wave by probe V_L /（m·s^-1）	Elastic modulus by nano-indenter E /GPa
	A₃-f_c and S₁-ZGV	0.3488	4757.0	2292.2	126.12	4739.93	128.32
	A₂-f_c and S₁-ZGV	0.3463	4741.8	2299.3	126.66
	S₆-ZGV and S₁-ZGV	0.3563	4805.6	2270.7	124.44

Table 5. Results of calculation and measurement of thin titanium TA2 plate

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Table 5. Results of calculation and measurement of thin titanium TA2 plate

Dual-modal resonance

Calculated parameter

Measured parameter

Poisson's ratio υ

Velocity of longitudinal wave V_L /（m·s^-1）

Velocity of

shear waveV_T /（m·s^-1）

Elastic modulusE /GPa

Velocity of longitudinal wave by probe

V_L /（m·s^-1）

Elastic modulus by nano-indenter

E /GPa

A₃-f_c and S₁-ZGV

0.3332

5769.1

2885.4

99.90

5786.67

100.87

S₆-ZGV and S₁-ZGV

0.3336

5771.6

2884.2

99.84

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Wang Jiang, Kaihua Sun. Measurement of Local Elastic Modulus of Thin Plates Using Lamb Wave Dual-Modal Resonance Motivated by Laser Ultrasound[J]. Chinese Journal of Lasers, 2023, 50(13): 1304004

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