Nonlinear Acoustic NDT: Approaches, Methods, and Applications

Transcription

1 Nonlinear Acoustic NDT: Approaches, Methods, and Applications Igor Solodov Department of Non-Destructive Testing, Institute of Polymer Technology (IKT), University of Stuttgart, Stuttgart, Germany 5th International Workshop NDT in Progress October 12 14, 29 Prague, Czech Republic, Hotel and Congress center Floret

2 Conventional (linear) acoustic NDT: A Input spectrum A Output spectrum ω Amplitude and phase variation of input wave ω Nonlinear acoustic response A Input spectrum A Output spectrum ω ω Frequency conversion Nonlinear NDT (NNDT)

3 Outline Introduction: Classical nonlinear NDT& frequency conversion in homogeneous materials Mechanical diode and nonlinear resonance approaches to nonlinear spectra of planar defects Experimental nonlinear spectra of cracked defects Methods & case studies of multi-frequency NNDT Conclusions

4 Classical nonlinearity of homogeneous (intact) materials Lattice anharmonicity σ ( ε ) C (1 β ε β ε...) ε = II - generalized Hooke`s law Nonlinearity: Stiffness depends on strain c( ε) 3 2 = c (1 β 2ε β3ε 2...) velocity depends on local strain due to stiffness modulation

5 Classical NNDT & frequency conversion in homogeneous materials Saw-tooth waveform Waveform distortion and higher harmonic generation is a measure of material nonlinearity A Ultimate spectrum ~ 1/n n Power-law dynamics: ~ 2 3 U2ω Uω; U3 ω ~ U ω ε Second harmonic Fundamental wave 1% Classical NNDT is a second harmonic NDT

6 Nonlinear spectrum of a delamination in CFRP!? Planar defects exhibit specific nonlinearity: Contact Acoustic Nonlinearity (CAN)

7 Nonlinear spectra of planar defects Clapping CAN mechanism: Asymmetrical stiffness modulation σ σ ~ σ σ ε ( t) ε ε ε C t C ΙΙ ε out - τ 2 / + τ 2 / C(t) in τ - τ 2 / + τ 2 / 2Τ Τ / 2 t Mechanical diode model Pulse-type stiffness modulation

8 Clapping mechanism: higher harmonic generation by defects σ ( ε ) C = H ( ε ν t ) C C ( t ) = H cos ε τ C T NL ( t) C( t) ε = n 2 sinc cosnν n= 1 T higher harmonic amplitudes = ( ε ) cosν t ε ε ε = =,95,95 ε ε Harmonic number CAN non-classical features (clapping mechanism): τ higher harmonic amplitudes t,14,12,1,8,6,4,2, σ NL N N = 1 ( t) = A cos Nν t. 1, 1,1 1,2 1,3 1,4 1,5 1,6 Amplitude threshold Higher-order NLT Sinc-type spectrum modulation Both odd- & even HH Non-power dynamic behavior Rectified nonlinear waveform 5ω 4ω 2ω 3ω normalized amplitude (ε / ε ο )

9 Higher harmonics via micro-slip ε (t) Crack Rissufer-Klappern interface bei ε t Shear tangentialer wave Bewegung drive ε C(t) Symmetrical stiffness modulation (tangential clapping) σ τ / 2 τ / 2 T / 2 C t C ε ε ε ( t) = C(t ε = A cos( 2N ) σ NL ) 2N N = ν t

10 ,18,16,14,12,1,8,6,4,2 σ NL ( t) = 2 Cε sinc [( cos( 2n + 1) ν t + cos( 2n 1) ν t) ] N = A2 N + 1 Higher harmonics via micro-slip = A 2N + 1 ( N 1) τ 2Nτ 2 Cε sinc + sinc + T T T 2 ε n= 1 cos ( 2N + 1) ν t. =,95 ε, τ T Higher harmonic number 2nτ T τ Nonclassical features (micro-slip mechanism): Symmetrical waveform distortion Only odd harmonics Sinc-type spectrum modulation Non-power dynamics

11 σ Nonlinear friction mechanism ε 1 ε ε Stick-and-slip: Symmetrical nonlinearity Spectrum: σ NL ( t) = B cos( 2N 1) ν t. N = 2N B = ε[ τ f ( sinc ( N 1) τ f + sinc ( N + 1) τ f - N C s 2 ε sinc N τ ).5(1 ε ) sincn/2],,8 f N = 2 n +1 Harmonic amplitude,6,4,2 ε =.9 ε=.9, Harmonic number

12 Summary of CAN mechanisms CAN is due to local mechanical constraint of vibrations Crack Rissufer-Klappern interface bei tangentialer Bewegung Acoustic wave drive Strong step-wise stiffness variation: C II C C II C C II C ε ε ε ε ε ε Clapping Micro-slip (asperities) Stick-and slide CAN: - strong, high-order - local - no accumulation -specific nonlinear waveforms - non-power dynamics

13 Experimental spectra of planar defects Impact in CFRP Clapping mechanism 2 khz excitation Laser vibrometer detection σ ε C ΙΙ C ε out Time (µs) in

14 Experimental spectra of planar defects Friction (hysteretic) mechanism d 5th 7th 9th Intact wood d 4th 6th 8th Frequency (khz) Damaged wood

15 Frequency conversion via CAN: subharmonic mode K Equation of motion 2 X& +ω NL X = f ( t) + F ( X ) K L X (1) = X + X (2) +... X (1) = Acosωt + B cosνt X& (2) +ω 2 X (2) = F NL ( X (1) ) F NL cos( ν ω )t ν out = / 2 ~ ω ω ω ω ν Higher-order NL terms mv nω ω ω mv/( n+ 1) ω mv/2 Ultra- subharmonics (USB)

16 Frequency conversion via CAN: frequency pair modes Combination resonance Resonance decay instability ν ω α ω β ν ωα ωβ ν ω β ω α frequency pairs ωα ωβ A ν ω α + ω β Higher-order NL terms F ωα NL ( ω) ~ ( nν + mω α + pωβ ) mn,, p ωβ ν Ultra- frequency pairs (UFP) (forerunner of chaos)

17 Dynamics of frequency conversion Bifurcation of USB - UFP decay frequency, khz driving amplitude, µm velocity amplitude, mm/s Excitation amplitude Excitation frequency ε > 1 3 Chaos Excitation amplitude ε Ultra-frequency pairs (UFP) Ultra-subharmonics (USB) ε ~ ε ~ ~ 1 1 Higher harmonics (HH) and frequency mixing UFP Threshold instability modes

18 Non-harmonic frequency conversion: examples Crack in `PMMA Impact in GFRP Ultra-subharmonic spectrum Ultra-frequency pair spectrum Delamination in C/C- SiC composite Frequency, khz Transition to chaos

19 Defect-selective localization of nonlinear vibrations A crack in polystyrene: Higher harmonic spectrum CAN frequency conversion is defect-selective

20 CAN applications: Defect-selective imaging via Nonlinear Laser Vibrometry (NLV) Scan area Defect (Crack) Scan-Tool Laser- Interferometer Excitation (Piezo-Stack) FFT of local acoustic field Delamination in C-C/SiC ceramic

21 Applications: Higher harmonic defect-selective imaging ω motor gear 3ω Gear clapping in commercial cutting tool ω 2ω 3ω Fatigue crack between rivets Oval delamination in GFRP Fatigue crack in riveted aviation component

22 CAN applications: Ultra-subharmonic NDE 5µm-fatigue crack in Νι-base super-alloy Delaminations in Glass fibre reinforced aluminum laminate (Glare ) 5 µm ω/2 7ω/2 11ω/2 12th USB 6%-plastic tensile deformation in a steel component 35 th ultra-subharmonic image

23 Ultra-frequency pair (UFP) NDE of impacts Impact in multi-ply GFRP UFP (198.8 khz) mage UFP- spectrum UFP- image Delamination area in GFR-concrete slab (15x3x1.5cm)

24 Nonlinear Air-Coupled Emission (NACE) M Spectrum analyzer Higher harmonics ½ condenser mic M 1 4 USB + UFP 4 khz 4 M UFP Airborne ultrasound radiated by nonlinear defect vibrations

25 Evidence for NACE via Air-Coupled Vibrometry Input voltage at frequency Ω Reflector 2D laser scan Specimen Scanning laser vibrometer crack FFT of output signal Image of NACE field

26 Evidence for NACE Damaged CFRP rod 4 khz flexural wave 4 khz flexural wave 4 khz airborne field 8 khz airborne field NDT & defect imaging via nonlinear listening?

27 NACE setup for defect imaging Input frequencies Ω = 2, 4 khz ACU output frequency ~ 4 khz C-scan Ω Amplitude, µm/s d HH 24th HH 9th HH 1th HH 11th HH Frequency, khz Frequency, khz

28 NACE vs Nonlinear Laser Vibrometry Impact damage in multi-ply ( ) CFRP Second harmonic NLV image 9 th 11 th harmonic NACE image Quite similar sensitivity and resolution

29 Applications: NACE for nonlinear NDE of defects (metals) 5µ crack in steel plate NACE-image Hammer peening area in steel

30 Applications: NACE for nonlinear NDE of defects (composites) NACE Delamination in GFRP 1 x 4 mm simulated subsurface delamination in 3mm-thick CFRP ACU-transmission image 9 th -11 th NACE image

31 Applications: NACE for nonlinear NDE of constructional materials NACE Surface-cutting crack in wooden plate NACE Laser welding line in steel Zoom-in: folded structure

32 Conclusions Highly nonlinear contact dynamics provides anomalously efficient frequency conversion by planar defects Nonlinear defects are localized sources of new frequency components that makes nonlinear NDT defect-selective NLV & NACE are sensitive and robust methods for NNDT and defect-selective imaging Analysis of multi-frequency spectra of planar defects improves reliability and quality of NDT

33 Nonlinear Acoustic NDT: Approaches, Methods, and Applications Igor Solodov Department of Non-Destructive Testing, Institute of Polymer Technology (IKT), University of Stuttgart, Stuttgart, Germany 5th International Workshop NDT in Progress October 12 14, 29 Prague, Czech Republic, Hotel and Congress center Floret