Absolute Measurement and Relative Measurement of Ultrasonic Nonlinear Parameter

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Cory Blair
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Jhang Department of Mechanical Convergence Engineering, Hanyang

1 Absolute Measurement and Relative Measurement of Ultrasonic Nonlinear Parameter Jongbeom Kim, Dong-Gi Song, Kyoung-Jun Lee, Kyoung Young Jhang Department of Mechanical Convergence Engineering, Hanyang University School of Mechanical Engineering of Hanyang University

Ultrasonic Nonlinear Parameter Higher Harmonic Generation Input Signal Spectrum A A Output Signal Specturm f 0 σε ( ) = Eε ( βε + γε + ) f 0 f 0 3 E : Young s modulus / k : Wave number / x :

2 Ultrasonic Nonlinear Parameter Higher Harmonic Generation Input Signal Spectrum A A Output Signal Specturm f 0 σε ( ) = Eε ( βε + γε + ) f 0 f 0 3 E : Young s modulus / k : Wave number / x : Propagation distance A : Displacement amplitude of fundamental frequency A : Displacement amplitude of second order harmonic / A3 : Displacement amplitude of third order harmonic β : Second order ultrasonic nonlinear parameter / γ : Third order ultrasonic nonlinear parameter A A 3 β = 8A A k x 3f 0 γ = 33A3 A 3 k 4 x - -

3 Measurement of Ultrasonic Nonlinear Parameter Direct measurement of displacement amplitudes of harmonic components is difficult. (< nm) Measure relative nonlinear parameter instead of absolute one. A β = A, A : Detected ultrasonic signal amplitudes A Measurement conditions should be all kept in constant. (e.g. equipment, frequency, thickness of specimen) β can be used for relative comparison of ultrasonic nonlinearity. Material Ⅰ (Intact) Material Ⅱ (Damaged) β Ⅰ β Ⅱ β' β' Ⅱ Ⅰ? = βⅡ β Ⅰ - 3-

4 Objectives ) Verification of the relationship between absolute nonlinear parameter and relative nonlinear parameter β' β' Ⅱ Ⅰ βⅡ = β Ⅰ ) Verification of the relationship between second- and third- order ultrasonic nonlinear parameters γ = β γ II β γ β II = I I 3-4-

Specimen and Experimental Procedures Fused Silica and Al 606-T6 (Thickness : 0 mm ) Fused Silica Al606-T6 Absolute nonlinear parameter and relative nonlinear parameter β AAAAAA TT β

5 Specimen and Experimental Procedures Fused Silica and Al 606-T6 (Thickness : 0 mm ) Fused Silica Al606-T6 Absolute nonlinear parameter and relative nonlinear parameter β AAAAAA TT β fffff ssssss β AAAAAA TT β fuuuu ssssss Second- and third- order ultrasonic nonlinear parameter γ = β (fffff ssssss) Absolute 3 γ II β II = γ I β I - 5- (AAAAAA TT, Heat treatment) Relative

Experimental Set-up Oscilloscope (Lecroy

Transducer (0 MH) tone burst signal Measure

6 Experimental Set-up Oscilloscope (Lecroy WS45) Tone burst generation Current probe LiNbO3 transducer(0mhz) I ooo (ω) RITEC RAM-5000 SNAP Trigger RITEC RAM-5000 SNAP LiNbO3 transducer (5 MH) 0mm LiNbO3 transducer(5mh) Oscilloscope LiNbO3 Transducer (0 MH) tone burst signal Measure current ssssss I ooo (ω) Calculate displacement amplitude A(ω)= H(ω) I ooo (ω) - 6-

Results Fused silica Al606-T6 Ratio ( AAAAAA TT fffff ssssss ) Absolute 0.

36 ~ 0.66 Ref) G. E. Dace, R. B. Thompson and O.

Characterization using Contact Transducer", Review of Progress in

7 Results Fused silica Al606-T6 Ratio ( AAAAAA TT fffff ssssss ) Absolute Relative Reference 8.67 ~ ~ ~ 0.66 Ref) G. E. Dace, R. B. Thompson and O. Buck, Measurement of The Acoustic Harmonic Generation for Materials Characterization using Contact Transducer", Review of Progress in Quantitative Nondestructive Evaluation, 99, pp β AAAAAA TT β fffff SSSSSS β AAAAAA TT β fffff SSSSSS Ratio was almost same - 7-

Results x 0-0 A vs A x 0 - A 3 vs A3 0.8.5 A [m] 0.6 0.4 R = 0. 99 A 3 [m] R = 0. 99 0. 0.5 0 0 0.5.5 A x 0-6 [m ] 0 3 4 3 3 A [m ] x 0-3 Nonlinear parameter β : 0.06 ± 0.45 Nonlinear parameter γ : 0.

8 Results x 0-0 A vs A x 0 - A 3 vs A A [m] R = A 3 [m] R = A x 0-6 [m ] A [m ] x 0-3 Nonlinear parameter β : 0.06 ± 0.45 Nonlinear parameter γ : 0.7 ± 9.63 Average Reference β ~.4 γ γ β.08 Ref) G. E. Dace, R. B. Thompson and O. Buck, Measurement of The Acoustic Harmonic Generation for Materials Characterization using Contact Transducer", Review of Progress in Quantitative Nondestructive Evaluation, 99, pp Ref) R. Bruce Thompson, O. Buck, and D. O. Thompson Higher Harmonics of Finite Amplitude Ultrasonic Waves in Solids", Journal of Acoustics, 976, pp γ fffff ssssss β fffff ssssss Relationship between second- and third-order nonlinear parameter was verified - 8-

9 Results 3 Heat Temperature: 0 Heat Treatment Times: 0, 0, 40, 60, 0, 600, 6000 Ref) G. Ren, J. Kim, and K. Y. Jhnag Relationship between second- and thirdorder acoustic nonlinear parameters in relative measurement", Ultrasonics, 05, pp γ γ 0 β β 0-9-

Conclusions Ratio of absolute parameter β and ratio of relative parameter β is identical, - when the detected signal amplitude is proportional to the ultrasonic displacement amplitude and measurement

10 Conclusions Ratio of absolute parameter β and ratio of relative parameter β is identical, - when the detected signal amplitude is proportional to the ultrasonic displacement amplitude and measurement conditions are all kept in constant. - β and β can be applied for relative comparison of two materials equally. Second- and third-order nonlinear parameters (β, γ) satisfy the theoretical relationship (γ β ) - Third-order nonlinear parameter can be estimated by secondorder nonlinear parameter. - 0-

Absolute Measurement and Relative Measurement of Ultrasonic Nonlinear Parameters

More info about this article: http://www.ndt.net/?id=20778 RESEARCH IN NONDESTRUCTIVE EVALUATION http://dx.doi.org/10.1080/09349847.2016.1174322 Absolute Measurement and Relative Measurement of Ultrasonic