A Study on Lamb Wave Based Damage Identification and Detection on a Metallic Structure

A Study on Lamb Wave Based Damage Identification and Detection on a Metallic Structure

Sangeeta Patra 1, Avinash Nath Tiwari 2 Dept. of Mechanical Engineering 1, 2 Jagannath University

Jaipur, Rajasthan

Arunabha Datta3

Global Institute of Technology3

Dept. of Electronics & communication Engineering Jaipur, Rajasthan

AbstractDamage identification and detection on an engineering structure is an overwhelming need for several industrial applications. Lamb wave based damage identification and detection is an attractive choice for monitoring of the structural health monitoring (SHM) for structural safety and maintenances. Lamb waves are subset of ultrasonic waves family which disperse along the structure when it propagates. The interaction of Lamb wave with damage causes reflection, mode conversion and attenuation in the measured signal at the receiving end. The change in the received signal used to locate the size and position of the damage. In this work we have demonstrated damage detection using pitch catch configuration of Lamb wave propagation in 1-mm thick aluminum 2024-T3 plate. To simulate multimode guided waves interaction with damage we have used The WaveFormRevealer 3.0 software.

KeywordsLamb wave,PWAS, SHM, PWAS

1. INTRODUCTION

   Advanced Non-Destructive Techniques (NDT) are being used presently to detect damages and these methods are time consuming and expensive [1]. As inspections are planned at scheduled intervals, the damage could potentially exist on structure in the intervening period. Notwithstanding the fact that structures are designed based on damage tolerance philosophy for perceived threats, it is desirable to detect as it happens along with the location and size. In literature there are three methods exist to detect damage which are wave propagation based, vibration based and electromechanical impedance based method [2-4]. Lamb wave based ultrasonic method is a classic example for wave propagation based approach where propagation reflection and mode conversion of Lamb waves are measured, by which one can estimate position and the size of the damage. Typically, Lamb wave based method includes pitch catch and pulse echo techniques. In pulse echo method waves are generated through transmitting transducer and received at different location on the structure the severity of damage can be estimated based on attenuation and dispersion. In contrast to pitch catch, pulse echo method used same transducer for transmitting and receiving the wave, damage can be detected through reflection of wave and location can be detected through the time of flight distance travelled by the wave.

   Damage monitoring using different sensing methods like Resistance Strain Gauges and Fiber Bragg Gratings [5], Fiber Optic Interferometer [6], Fiber Optic Doppler Sensor [7], Piezoelectric sensor [8] are proposed in literature.

   Due to multimodal dispersion characteristics modelling of lamb wave is challenging problem. At certain plate thickness- frequency several mode exists and phase velocity varies with frequency [9]. To solve such problem using numerical methods such as finite element method (FEM) or boundary element method (BEM) usually adopted [10,11]. The transient analysis at high frequency requires small step size and mesh size which are time consuming and computational resource expensive. Analytical approach can give an alternative solution with less cost [12]. In this work, we have validated an analytical approach based on the 1D (straight crested) guided wave propagation analysis using MATLAB [13] and the WaveFormRevealer (WFR) graphical user interface (GUI) software develop by laboratory for active materials and smart structures (LMSS), University of South Carolina, USA [14]. The damage effect into the analytical model by considering wave transmission, reflection, mode conversion, and higher harmonics components described through damage interaction coefficients at the damage site are available either from literature or from FEM, BEM analysis performed separately in a separate computational module of the software.

2. LAMB WAVE PROPAGATION EQUATION

   In a thin isotropic and homogeneous plate shown in the figure-1, wave equation under plane strain condition described as [13]

   (1)

   (2)

   Equation 1 described governing longitudinal wave mode and equation 2 for governing transverse wave modes. cl and ct represents velocity of longitudinal and transverse waves respectively. Sinusoidal solutions to the wave equation were postulated, having x- and z-displacements of the form

   (3)

   (4)

   This form represents sinusoidal waves propagating in the x direction with wavelength 2/k and frequency /2.

   Displacement is a function of x, z, t only; there is no displacement in the y direction and no variation of any physical quantities in the y direction. The physical boundary condition for the free surfaces of the plate is that the component of stress in the z direction at z = ± d/2 is zero. Applying these two conditions to the above-formalized solutions to the wave equation, a pair of characteristic equations can be found.

   Figure 1: A thin plate of 2d thickness

3. LAMB WAVE PROPAGATION IN PRISTINE PLATE

   Figure 3 shows the pitch-catch active sensing method, where one transducer acts as the transmitter and sends out the guided waves, and another transducer acts as the receiver and pick up the sensing signal. In the pristine case (baseline), the interrogating waves are generated by the transmitter, propagate along the structure, and are picked up by the receiver. In the damaged case, the interrogating waves generated by the transmitter, propagate along the structure, interact with the damage, carry the damage information with them, and are finally picked up by the receiver. The subtraction between these two states reveals the damage scattering response, which may indicate the presence and severity of the damage.

   This section describes how an electrical tone burst applied to a transmitter Piezoelectric wafer active sensors transducer (T- PWAS) propagates through a structural waveguide to the receiver Piezoelectric wafer active sensors transducer (R- PWAS) in pitch-catch mode.

   Where

   (5)

   (6)

   Figure 3: Pitch catch configuration of Lamb wave propagation in pristine

   plate

   The propagation takes place through ultrasonic guided Lamb waves which are generated at the T-PWAS through

   Numerical methods are used to find the phase velocity cp= f

   /k, and the group velocity cg = d/dk, as functions of d/ or fd.

   The Lamb waves propagate in two types of modes; the symmetrical (S) and the anti-symmetrical (A) modes which is shown in figure-2.

   Figure 2: Anti-symmetric and symmetric lamb wave modes

   In the S modes, the plate displacements are symmetrical with respect to its center plane while in the A mode, it is anti-symmetrical. There are infinite number of modes (S and A) existing in a plate. For a particular Lamb wave excitation, the available modes depend on the excitation frequencies and the thickness of the plate.

   piezoelectric transduction and then captured and converted back into electric signal at the R-PWAS. Since several Lamb wave modes traveling with different wave speeds exist simultaneously, the electrical tone-burst applied on the T- PWAS will generate several wave packets. These wave packets will travel independently through the waveguide and will arrive at different times at the RPWAS where they are converted back into electric signals through piezoelectric transduction. Three test cases were conducted:

4. incident S0 wave excitation

5. incident A0 wave excitation

6. incident S0 and A0 wave excitation

The transmitter PWAS (T-PWAS) and receiver PWAS (R- PWAS) are placed 500 mm away from each other on a 1-mm thick aluminum 2024-T3 plate. A 5-count Hanning window modulated tone burst centered at 150 kHz is used as the excitation which is given by

(7)

Received signal by R-PWAS, the dispersion curves; the excitation spectrum overlap with the S0 and A0 tuning curves

and the structure transfer shown in figure-4 for S0 excitation A0 excitation and (S0+A0) excitation.

Figure 4.a: Various parameter for S0 mode excitation: (a) Received signal by R-PWAS (b) The dispersion curves (c). The excitation spectrum overlap with the S0 and A0 tuning curves (d) structure transfer function

Figure 4.b: Various parameter for A0 mode excitation: (a) Received signal by R-PWAS (b) The dispersion curves (c). The excitation spectrum overlap with the S0 and A0 tuning curves (d) structure transfer function

In this work Structural Health Monitoring using active sensing is presented. Lamb wave based wave propagation model using WFR software has explored. In plate like structure pitch catch based model used for healthy and damaged metallic plate. The receiver and transmitter are separated by 500 mm and damage is present at 250 mm from the transmitter. Received signal by the receiver, dispersion curve, frequency spectrum of A0, S0 and excited tone burst and plate transfer function has presented for healthy case. In damaged case received signal and mode converted signal and its spectrogram is presented. The damage presented in this work is linear so there is no higher harmonics exist in the spectrogram.

REFERENCES

1. Charles Hellier (2003). Handbook of Nondestructive Evaluation. McGraw-Hill. p. 1.1. ISBN 0-07-028121-1.

2. Alleyne, D N, and P Cawley. 1992. The Interaction of Lamb Waves with Defects. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 39(3): 381-97.

3. Achenbach, J.D. 1973. Wave Propagation in Elastic Solids. Amsterdam, Londan, New York: North-Holland-American Elsevier.

4. Giurgiutiu, Victor. 2014. Structural Health Monitoring With Piezoelectric Wafer Active Sensors. Second Edi. Amsterdam, Boston, Heidelberg, London, New York, Oxford,Paris, San Diego, San Francisco, Singapore, Sydney, Tokyo: Elsevier.

5. G Zhou and L M Sim., Damage detection and assessment in fibre- reinforced composite structures with embedded fibre optic sensors review Institute Of Physics, Smart Materials and Structures . 11 (2002) 925939.

6. Fucai Li, Hideaki Murayama , Kazuro Kageyama , Guang Meng , Isamu Ohsawa andTakehiro Shirai., A Fiber Optic Doppler Sensor and Its Application in Debonding Detection for Composite Structures, Sensors 2010, 10, 5975-5993.

7. Y. G. Xu ,G. R. Liu., A Modified Electro-Mechanical Impedance Model of Piezoelectric Actuator-Sensors for Debonding Detection of Composite Patches, Journal of Intelligent Material Systems and Structures June 2002 vol. 13 no. 6 389-396.

8. Zhanjun Wu, Xinlin P. Qing and Fu-Kuo Chang., Damage Detection for Composite Laminate Plates with A Distributed Hybrid PZT/FBG Sensor Network , Journal of Intelligent Material Systems and Structures 2009 20: 1069.

9. Ramadas, C., Balasubramaniam, K., Joshi, M. and Krishnamurthy,

   C.V. (2008). Detection of transverse cracks in a composite beam using combined features of Lamb wave and vibration techniques in ANN environment. International Journal on Smart Sensing and Intelligent Systems, 1(4), 970984.

10. F. Moser, L. J. Jacobs and J. Qu, "Modeling elastic wave propagation in waveguides with the finite element method," NDT&E International, pp. 225-234, 1999.

11. M. Gresil, Y. Shen and V. Giurgiutiu, "Predictive modeling of ultrasonics SHM with PWAS transducers," in 8th International Workshop on Structural Health Monitoring, Stanford, CA, USA, 2011.

12. V. Giurgiutiu, M. Gresil, B. Lin, A. Cuc, Y. Shen and C. Roman, "Predictive Modeling of Piezoelectric Wafer Active Sensors Interaction with High-frequency Structural Waves and Vibration," Acta Mechanica, pp. 1681-1691, 2012.

13. https://in.mathworks.com/

14. http://www.me.sc.edu/research/lamss/html/people.html