·Table of Contents
·Workshop - Guided Wave
Quantitative Guided Wave NDE
J. L. Rose, S. P. Pelts, Jian Li
Department of Engineering Science and Mechanics
The Pennsylvania State University
212 Earth & Engineering Science Building
University Park, PA 16802
Guided waves have demonstrated their value in flaw detection over long distances from just a single probe position. Inspection under coatings, fluids, and insulation is often possible. By way of phase velocity and frequency tuning, defect detection sensitivity and location analysis can be superb despite distance and environmental constraints. The ability to go beyond detection and location to classification and sizing, however, is extremely difficult. The use of the Boundary Element Method for defect characterization through guided wave mode conversion is considered in this paper. An outline of the approaches used, and sample results showing features that might be useful in classification and sizing analysis is covered. The question of which mode and frequency should be selected to impinge onto a defect and have the best chance of classifying or sizing that defect is addressed.
Ultrasonic guided waves are being used extensively for defect and materials characterization; some theoretical and experimental results that using BEM are presented in [1-5]. The finite element method (FEM) for Lamb and SH wave scattering problem has been analyzed in [6-9]. An electromagnetic-acoustic transducer (EMAT) technique for SH wave excitation is presented in . The defect within an incident guided wave path impacts the signature of the scattered fields by exciting all possible modes for the given frequency value. The study of the scattered field (reflected and transmitted) provides essential features for defect characterization. Efficiency of this approach can be improved by selecting propagating modes sensitive to the different kinds of defects.
MODELING ANALYSIS AND SAMPLE RESULTS
Let us consider the incident guided wave that propagates in an infinite elastic plate by striking a surface breaking elliptical defect with the geometry shown in Figure 1.
Fig 1: Modeling statement of a guided wave striking an elliptical defect.|
Two different cases of an elastic field are considered: the first is for Lamb wave propagation modes and the second for a shear horizontal (SH) field. BEM results are presented for a 10 mm steel plate and elliptical wastage parameters of 2a=6.35 mm and various b values.
Sample phase and group velocity dispersion curve results are shown in Figure 2. Details of the computational process and explanations of dispersion curve generation and BEM development can be found in . To illustrate the process of BEM utility for wave scattering in a wave guide, a sample problem of S0 mode impingement onto a series of different depth elliptical defects is illustrated in Figure 3. Even though reflected and transmitted modes are numerous including A0, S0, A1, S1, A2, S2, etc., whatever modes can exist at the incoming mode frequency value, emphasis is placed on the A1 reflected and transmitted values. The A1 and other modes can be identified experimentally by group velocity, as an example, and measurement or adjustment of an angle beam transducer receiving angle. The most interesting results are shown over specific frequency values. Note that there is a monotonic increase in the A1 mode reflection factor amplitude with defect depths around 0.25 MHz and around 0.5 MHz also. In the transmission factor amplitude, there is a monotonic decrease with defect depth around 0.3 MHz.
Fig 2: Lamb wave phase (a) and group (b) velocity dispersion curves for a 10 mm thick Steel plate (cL=5.9 km/sec, cT=3.2 km/sec)|
Fig 3: Variation of reflection (a) and transmission (b) coefficients of the A1 mode for different cases of the ellipse parameter b, that is equal to 10%, 30%, 50% of the wall thickness for an S0 incident mode. (Areas of monotonic behavior of R(A1) and T(A1) are marked with a rectangle.)|
We'll now consider shear horizontal impingement onto the same elliptical defect. Dispersion curves for the steel plate are shown in Figure 4. See  for computational details. To illustrate BEM utility for SH wave scattering in a wave guide, a sample problem of n=1 mode impingement onto a series of different depth elliptical defects is illustrated in Figure 5. Note in through transmission the monotonic decrease in amplitude as defect thru wall size increases for almost the entire frequency range 0.25 to 0.8 MHz. Transmitted amplitude as a function of frequency is approximately constant which is also a useful result.
Fig 4: SH phase (a) and group (b) velocity dispersion curves for a 10 mm thick Steel plate (cL=5.9 km/sec, cT=3.2 km/sec)|
Fig 5: Variation of reflection (a) and transmission (b) coefficients of the n=1 mode for different cases of the ellipse parameter b, that is equal to 10%, 30%, 50% of the wall thickness for the n=1 incident mode|
Some interesting results are presented here to show that defect quantification analysis can be carried out for guided wave impingement onto a defect in a wave guide. In particular, note the monotonic increase in amplitude with defect thru wall size. Both Lamb and SH wave have potential. Much more additional work is necessary, however, to handle both defect shape and size for complete quantification analysis. Presented BEM results can be used to establish data acquisition and analysis guidelines for development of a test protocol and quantification algorithm development program.
Figure 5. Variation of reflection (a) and transmission (b) coefficients of the n=1 mode for different cases of the ellipse parameter b, that is equal to 10%, 30%, 50% of the wall thickness for the n=1 incident mode
Thanks are given to the Gas Research Institute, Chicago IL for the support of this work and in particular to Dr's Harvey Haines and Albert Teitsma.
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