AIP Conference Proceedings 1806, 090011 (2017); https://doi.org/10.1063/1.4974655 1806, 090011
© 2017 Author(s).
Sub-wavelength resolution of cracks in
metallic materials
Cite as: AIP Conference Proceedings 1806, 090011 (2017); https://doi.org/10.1063/1.4974655
Published Online: 16 February 2017
Kiran Kumar Amireddy, Prabhu Rajagopal and Krishnan Balasubramaniam
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Sub-wavelength Resolution of Cracks in Metallic Materials
Kiran Kumar Amireddy
a
, Prabhu Rajagopal, and Krishnan Balasubramaniam
Centre for Non-destructive Evaluation, Department of Mechanical Engineering,
Indian Institute of Technology- Madras, Chennai 600036, Tamil Nadu, India
a
amireddykiran@gmail.com
Abstract. In recent years, various types of acoustic metamaterials have been proposed with capabilities for overcoming
the diffraction limit. However, typically such developments only consider the acoustic regime or imaging in liquid media.
In this paper we show the application of a holey structured metamaterial lens for sub-wavelength imaging of defects in a
metallic sample, in the ultrasonic regime. Finite Element (FE) simulations are used to study longitudinal wave interaction
with ideal cracks in isotropic elastic materials. Holey-structured meta-lenses are then used to transmit the scattered waves.
We present a super resolution RI Ȝ ZLWK D subwavelength crack in an aluminium sample, which to the best of our
knowledge this is the highest resolution achieved in the ultrasonic regime.
INTRODUCTION
Ultrasonic imaging is one of the popular tools used to detect and characterize the defects that are presented in the
metallic materials by Non-Destructive testing (NDT). Wave scattering effects such as diffraction establishes a tradeoff
between the depth of image and the range. Due to this the resolution of an imaging system is restricted to half the
wavelength of the wave used for the imaging [1]. To overcome the diffraction limit requires the information from the
evanescent waves, which carries the information of fine features of the object but decays exponentially in all natural
materials away from the source [1, 2]. Research in recent years, finds solution to overcome the diffraction limit by
artificial metamaterials, Viz. Photonic [3], Phononic crystals [4] and Negative indexed materials [5]. Much attention
has been paid to perforated metallic materials with periodic hole arrays [6-8] for extraordinary optical transmission
[9]. Recent research in this area reveals possibilities for extraordinary transmission [10-12] as well as to explore
applications to sensing and super resolution [1, 13]. In this paper we present numerical results showing super resolution
of subwavelength cracks in metallic materials using periodic holey-structured metamaterial lens.
This paper is organized as follows. We begin with a brief description of ultrasonic imaging and its limitation for
resolution, then the solutions to overcoming the resolution limit by holey structured metamaterial lens, after which we
define our problem of interest. This is followed by a detailed procedure followed for numerical (FE) studies to model
the metamaterial lens. Finally results are presented to demonstrate the subwavelength resolution in to the ultrasonic
regime, after which we conclude with an outline on implications and further work.
BACKGROUND
In the holey structured metamaterial lens each ‘hole’ acts as a pixel for imaging and improves resolution by
amplifying the decaying evanescent waves through Fabry-Perot resonant modes [2]. At the resonance all the waves
constructively interfere with each other and transmission coefficient becomes 1 and hence the metamaterial lens
transfers all the waves from object plane to image plane without any loss. Evanescent waves also transfer with them
without much loss, and hence the subwavelength information carried by them will construct the image with high
resolution.
43rd Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 36
AIP Conf. Proc. 1806, 090011-1–090011-4; doi: 10.1063/1.4974655
Published by AIP Publishing. 978-0-7354-1474-7/$30.00
090011-1
Problem Studied
We consider an aluminium sample having a notch or crack of length 1.8 mm as shown in the Figure 1(a). The
crack present in the aluminium sample is considered as the defect for imaging purpose. The length of the crack (1.8
PPLVDERXWȜIRUDIUHTXHQF\RIN+]7KLVREMHFWis imaged with ultrasonic immersion C-scan technique with
through transmission mode to resolve the subwavelength crack dimensions in its image with the help of periodic
holey-structured metamaterial lens.
FIGURE 1. Aluminum sample with the details of crack presented in it.
METHODS
FE Simulations
Commercially available FE package [14] is used for modeling. A 2D- FE model was created with dimensions
200x100 mm
2
, chosen to avoid reflections from the boundaries. The overall model consists of one part each for the
defective sample (aluminium block with crack in it) and the metamaterial immersed in the water respectively, as
shown in Figure 2. For both parts 4-noded quadrilateral mesh with a seed size of 0.1 mm was used. For the model of
defective sample, mechanical properties of aluminium were assigned, with density ȡ = 2700 kg/m
3
, Young’s modulus
of elasticity E= 69 GPa and the poison’s ratio ȣ = 0.334. To create crack in the aluminium sample, a node set of length
= 1.8 mm is chosen and setting rigid (displacement is zero) boundary conditions on the selected nodal line.
For modeling of metamaterial lens immersed in water, 2-D model of 240x120 mm
2
was created and assigned
acoustic media (water) properties, with density ȡ = 1000 kg/m
3
and bulk modulus K = 2.2 GPa. A 2-D holey structured
metamaterial of length 13 mm with a hole thickness of 1.5mm and a periodicity of 2mm is created as shown in figure
2. The aluminum block with crack and metamaterial lens immersed in water are assembled and a tie constraint is given
at the interface to allow the wave propagation from one media to other. Waves are generated in the aluminum sample
by exciting the source (left node set in the aluminum block) in horizontal direction by 3 cycle Hanning windowed tone
burst signal of central frequency at 500 kHz. Wave propagation in the model was simulated using the explicit FE
algorithm provided in the commercial package [14]. This was run for a total time period of 90 ȝV which is sufficient
for longitudinal waves to reach other end of the model. The transmitted waves from the metamaterial lens were
collected at the monitor set on the time trace.
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FIGURE 2. Snapshot of FE model with mesh.
RESULTS AND DISCUSSIONS
The maximum amplitude variation from the each A-scan (amplitude variation on time trace) as obtained from the
simulations is then plotted against monitored positions as shown in the Figure 3. At the crack position the amplitude
drop is observed and it is indicated with dashed lines in the plot. Diffractions from the both edges of the crack are
clearly resolved in its image. This shows that the periodic holey-structured metamaterial lens helps to effectively
UHVROYHWKHVXEZDYHOHQJWKȜFUDFNLQWKHDOXPLQXPsample to the ultrasonic regime.
FIGURE 3. Simulated results for normalized amplitude variation with the measurement position across the sample with the
meta-lens. The dashed lines represent WKHSRVLWLRQRIWKHVXEZDYHOHQJWKȜFUDFNLQDQaluminum sample.
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CONCLUSIONS
Our results show that a periodic holey-structured metamaterial can act as a perfect lens for subwavelength imaging
in the ultrasonic regime. This device operates at set of frequencies of Fabry-Perot resonant modes. Reduction of the
geometrical parameters like, hole diameter, periodicity and the length of the meta-lens will further improves its
resolution capacity.
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Manual. Version 6.10-1; accessed 28 July, 2015.
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