AIP Conference Proceedings 1806, 030015 (2017); https://doi.org/10.1063/1.4974583 1806, 030015
© 2017 Author(s).
Interaction of Higher Order Modes Cluster
(HOMC) guided waves with notch-like
defects in plates
Cite as: AIP Conference Proceedings 1806, 030015 (2017); https://doi.org/10.1063/1.4974583
Published Online: 16 February 2017
Sri Harsha Reddy K., Prabhu Rajagopal, Krishnan Balasubramaniam, et al.
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Interaction of Higher Order Modes Cluster (HOMC)
Guided Waves with Notch-like Defects in Plates
Sri Harsha Reddy K
1, a)
, Prabhu Rajagopal
1
, Krishnan Balasubramaniam
1
, Samuel Hill
2
, and Steve Dixon
2
1
Centre for Non-Destructive Evaluation, Department of Mechanical Engineering, Indian Institute of Technology
Madras, Chennai
2
Ultrasonics Group, Department of Physics, University of Warwick, United Kingdom
a)
Corresponding author: k.sriharsha85@gmail.com
Abstract. Guided ultrasonic waves are widely used for long range inspection. Higher Order Modes Cluster (HOMC),
discovered at the author’s research group [1-3] consist of multiple higher order guided wave modes that travel together as
a single wave-packet and without appreciable dispersion for distances in the range of meters. These waves not only
propagate along the length of the structure but also cover the entire thickness, and in view of the higher frequencies, they
can offer improved resolution over conventional low-frequency guided waves. This paper studies the sensitivity of axial
plate HOMC to notch-like defects, evaluated by calculating wave reflection co-efficient. The studies are carried out using
finite element models validated by experiments. Analysis is presented for better understanding of wave-defect interaction.
Advantages and limitations for practical realization of the above approach are also discussed.
INTRODUCTION
In-process inspection of structures in industrial processes such as welding is essential for maintaining its overall
integrity. Recently, ultrasonic guided waves based inspection has gained much attention, especially in the oil and gas
industry, as they offer several advantages such as the ability to scan relatively large structures from a single transducer
location and inspect both surface as well as internal defects due to their through-thickness modal nature. In addition
to this, they can be selectively used for inspecting parts of layered or coated surfaces.
Conventionally, guided wave based methods are used in low frequency regime with an emphasis on selectively
generating non-dispersive lower order modes in structures. However, the comparatively longer wavelength limits the
spatial resolution of inspection. This can be improved with high operating frequencies compromising on the inspection
range.
The recently discovered Higher Order Mode Cluster (HOMC) waves are attractive for this purpose, typically for
an inspection range less than a meter. HOMC waves consist of multiple higher order guided waves that travel together
as a cluster and without much dispersion for distances in the range of meters [1-3].
In this work, we demonstrate the interaction of HOMC waves with defects in the form of notches of different
depths in mild steel plate. Finite Element (FE) simulations are used to gain insight into the wave-defect interaction.
The reflection coefficient behavior study through simulations and experiments are then examined.
The outline of the paper is as follows. Initially, Lamb wave dispersion curves in mild steel plates are discussed,
helping to predict the propagation characteristics of HOMCs as well as providing insights on how they can be
generated. A description of the experimental set-up and procedure is then given, followed by the procedure for the
simulation studies. Results for HOMC waves scattered by the notches are then presented and discussed in sight along
with analytical validations, after which we conclude with directions for further work.
43rd Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 36
AIP Conf. Proc. 1806, 030015-1–030015-7; doi: 10.1063/1.4974583
Published by AIP Publishing. 978-0-7354-1474-7/$30.00
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GENERATION OF HOMC
Recently, a group of higher order guided wave modes in plates were discovered that travel over medium range
distances as a relatively non-dispersive cluster [1-3]. These Higher Order Modes Cluster (HOMC) waves are formed
at a frequency thickness of between 15 MHz-mm and 40 MHz-mm, and are composite waves formed from the
interference of several individual modes that travel with very similar speeds. In the high frequency-thickness region,
the excitation angles for multiple modes are converging to a similar value, multiple modes are generated and the
cluster of waves generated display properties different to the individual modes.
FIGURE 1. Variation of incidence angle with Frequency thickness for mild steel. Plotted using DISPERSE [4];
A - Dispersion region and B – non-dispersion region
Figure 1 shows the variation of incidence angle with the frequency-thickness product, for the Lamb modes that
can be supported by a mild steel plate. The curves were plotted using DISPERSE [4] for obtaining characteristics of
guided waves in simple waveguides. An optimal generation of HOMC waves occurs at about 52° and a wedge of this
angle can be used for generating them using the angle-beam technique [1].
EXPERIMENTAL STUDIES
Experimental Setup
Experiments were performed on a mild steel plate of 10 mm thickness, 1 m length and 0.6 m width. HOMC waves
were generated using a piezoelectric crystal mounted on a plexi-JODVVZHGJHZLWKDQDQJOHRIࡈUHODWLYHWRWKHSODWH
surface, and driven using a RITEC pulser receiver (RITEC Inc. USA, RPR-4000) at a frequency of 2 MHz. An
ultrasonic couplant gel was used to effectively couple ultrasonic energy to the plate. A photograph of the experimental
setup is shown in Fig. 2(a).
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(a) (b)
FIGURE 2. Photograph of (a) experimental setup; (b) Plate showing the machined notches as a percentage of thickness.
Pulse echo configuration is used to capture the signals which are observed and recorded for subsequent analysis
on a digital storage oscilloscope (Agilent Technologies DSX2012-A). Rectangular notches 5 different depths (5%,
10%, 20%, 30% and 50% of plate thickness) were machined on the plate through milling process. The notches are of
10 mm length and 2 mm width as shown in Fig. 2(b). The notches are located 10 cm away from one end of the plate.
The distance is to ensure proper separation of the wave echoes from the notch and the plate end.
Experimental Procedure
The PZT Plexiglas-wedge transducer was excited using a 3 cycle tone-burst, with a center frequency of 2 MHz,
generated by the RITEC pulser-receiver in a pulse-echo configuration. The transducer was placed on a perpendicular
line bisecting each of the 5 notches, at a distance of 400 mm from the notch location, in different measurement runs.
Waves scattered by the notches were received using a digital oscilloscope and were recorded for further analysis.
Signals received were averaged using 128 ensembles for each reading to improve the signal to noise ratio. Also, the
measurements were repeated five times for each notch depth case, in order to account for variability and ensure
repeatable results. The performance of the HOMC modes waves is compared quantitatively through the reflection
coefficient, which is the spectral ratio of displacement of the reflected signal to that of the incident signal in frequency
domain. The incident signal is taken as the reflection from the plate edge; Separate readings were taken for this purpose
with the wedge at a distance of 400 mm from the edge.
A frequency analysis of the signal recorded on the oscilloscope was done. The Fast Fourier Transform was applied
to the signal to get the distribution of the signal across the frequency spectrum. The peak amplitude for each run,
which occurred about the center-frequency excited, was noted and a mean value was calculated for the 5 readings
taken for each notch depth case. This procedure was repeated for the incident signal. In order to understand the
underlying wave mechanics, the reflection coefficient is plotted as a function of notch depth to wavelength.
FINITE ELEMENT SIMULATIONS
In order to gain more insight into the propagation and scattering of the high-frequency guided waves, finite element
simulation implemented in the commercial package ABAQUS 6.12 [5] was used. A 2D plane strain model was created
for the studies, with the wedge and the plate modeled separately and connected using continuity conditions. The wedge
was modeled as Plexiglas and the plate was modeled as mild steel. A 3 cycle Hanning windowed tone-burst signal
centered at a frequency of 2 MHz was used as the force input to excite the system. A finite line source was used to
model a one inch diameter probe for the HOMC waves, in order to mimic the experimental conditions. The material
properties, as well as the other FE parameters, used in the simulations are listed in Table 1.
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TABLE 1. Finite element parameters used in simulations
FE Parameter Plate Wedge
Material
Density
Young’s Modulus
Poisson’s ratio
Model Type
Element Size
Element Type
Mild Steel
7850 kg/m
3
210 GPa
0.28
2D Plane Strain
Ȝ
Linear Quadrilateral
Acrylic/Plexiglas
1180 kg/m
3
4.5 GPa
0.37
2D Plane Strain
Ȝ
Linear Triangular
A 10 mm by 600 mm mild steel plate is modeled as a test specimen using Absorbing Layers with Increasing
Damping (ALID) [6] at both ends of the plate. The transducer wedge is placed at a distance of 400 mm from the notch.
The excitation signal is generated from the wedge. Outputs requested are the displacements U
x
and U
y
of the
monitoring points. The incident signal was obtained in the FE simulations the same way as in the experiments, by
noting the wave reflected from the plate edge. The schematic representation of the model used for FE simulations is
shown in Fig. 3.
FIGURE 3. The schematic representation of the 2D model for FE simulations
The simulation is conducted for higher order mode cluster (HOMC) waves. The goal is to study the variation of
reflection coefficient (RC) with variation in the notch depth. For this case the defect depths are varied from 5% to
50%, and the variation of RC for different notch depths will be calculated.
RESULTS
HOMC Scattering for Notches
For the FE simulations, the output was obtained by monitoring the displacement of a point on the transmitting
surface of the wedge as pulse-echo method was performed. The output obtained in the 50% notch depth case is shown
in Fig. 4(a). There are different regimes in the plot, including the incident wave and reflection from the defect. The
reflection from the plate edge will not be present here as an ALID was used at both ends of the plates. The reflection
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