Non-destructive evaluation (NDE) in real time has important applications in the area of structural health monitoring (SHM). Examples include repair and rehabilitation of aerospace structures such as aircraft and space shuttles, civil infrastructures such as bridges and tall buildings, and heavy mechanical equipment. Healthy structures have the additional benefit that they are less expensive to maintain. A popular approach to NDE and SHM is to use ultrasonic sound waves to detect internal anomalies such as cracks, cavities, and inclusions (i.e., foreign materials) in a specimen. Several experimental techniques have been designed to investigate the patterns formed by these waves using signals generated by a transducer and sent to a receiver. Because it is difficult to interpret the results, researchers also want to develop an efficient numerical tool to simulate the experiments and make better sense of the findings. Progress has been hampered, however, by the lack of methods to accurately model the wave fields.
Efforts in ultrasonic field modeling typically rely on a pair of techniques called finite element and boundary element analysis, which are widely used to solve engineering problems. But detecting small cracks requires high frequencies, which cause spurious reflection of the waves at artificial boundaries. Moreover, elements must be very small, which leads to CPU-intensive packages. The few other techniques available, for example, the multi-Gaussian beam model, the multiple multipole program, and the charge simulation method, all have shortcomings—particularly in the case of complex structures—that have been addressed in detail elsewhere.1
Figure 1. Ultrasonic fields developed in a 10mm-thick aluminum plate with a horizontal cavity or crack for the Rayleigh angle of incidence when the guided wave propagates from the right to the left side of the plate: (a) normal stress, (b) shear stress, (c) normal stress, (d) normal displacement.
The distributed point source method (DPSM) avoids these shortcomings and thus is able to model ultrasonic wave fields in test specimens more efficiently.2 Over the last few years the approach has attracted increasing attention in the areas of ultrasonic, electrostatic, and electromagnetic field modeling.2,3 DPSM constitutes an alternative to standard techniques of ray tracing for ultrasonic waves. It eliminates the need for paraxial approximation and avoids having to compute transmission and reflection coefficients at the interface of the specimen. Unlike point sources with single-source strength, solid materials have point sources with three mutually-perpendicular source strengths that emit spherical wavefronts concentrically in isotropic materials (i.e., whose properties are the same in all directions) and 3D wavefronts of different shapes in anisotropic materials.
We have extended our original concept of DPSM to model the field generated by ultrasonic transducers of finite dimension in the vicinity of a solid plate when the plate and the transducers are immersed in a fluid.1 We also recently used DPSM to study the wave-scattering pattern produced by horizontally oriented internal cavities and cracks in a plate.4 We developed MATLAB (Math Works Inc.) software codes to model the ultrasonic field in an isotropic solid plate with such defects.
Figure 1 shows the ultrasonic fields developed in a 10mm-thick aluminum plate containing a horizontal cavity 1mm thick. The length of the cavity is 10mm. It is located at the central plane of the plate at the horizontal position −25mm≤ x≤ −15mm. The fields in Figure 1 are obtained by placing two ultrasonic transducers symmetrically on two sides of the plate at an inclination relative to the plate to generate guided waves through it. (Guided waves can propagate a significant distance in a structure without losing energy.) The angle between the transducer axis and the axis normal to the plate is 30.5°, the so-called Rayleigh critical angle. Figure 1(a–d) shows distributions of normal and shear stress and displacement along the x, y, and z axes inside the defective specimen. The figure illustrates nicely how the ultrasonic energy is scattered by the internal cavity.
In developing the DPSM method for solid media, we faced (and met) a number of challenges regarding defining a solid as a point source and calculating certain stress functions. Our next goal is to accurately model wave fields in structures containing multilayer ‘sandwiches’ of various isotropic and anisotropic materials. This problem has practical application in thermal protection systems for space shuttles.
Sourav Banerjee, Tribikram Kundu
Department of Civil Engineering and Engineering Mechanics
University of Arizona
Sourav Banerjee was born in Dhanbad, India, in 1977. He graduated with BE in civil engineering from Bengal Engineering College and with an MTech in structures from the Indian Institute of Technology, Mumbai. He earned a PhD in engineering mechanics from the University of Arizona, Tucson, in 2005, where he is currently a postdoctoral fellow. His broader research interests include intelligent infrastructure systems, structural health monitoring, and smart structures. His specific interests include analytical and computational ultrasonic field modeling in planar and nonplanar structures, acoustic frequency filtration, and structural band gap analysis. He is the author of a book chapter and 22 technical papers, 10 of which have been published in refereed scientific journals. He is a member of American Society of Mechanical Engineers.
Tribikram Kundu was born in Calcutta, India, in 1956. He graduated with a BTech in mechanical engineering in 1979 from the Indian Institute of Technology, Kharagpur. His MS (1980) and PhD (1983) are in solid mechanics from the University of California, Los Angeles, USA. He is a full professor at the University of Arizona in Tucson. He has edited 16 books (12 conference proceedings and four research monographs), and is the author of two textbooks, nine book chapters, and 200 technical papers, 100 of which have been published in refereed scientific journals. His fundamental research interests include the analysis of elastic wave propagation in solids, fracture mechanics, computational mechanics, geo- and bio-mechanics. He is a fellow of the American Society of Mechanical Engineers, the American Society of Civil Engineers, and SPIE, a member of the Acoustical Society of America, the American Society for Nondestructive Testing, the International Association for Computer Methods and Advances in Geomechanics, and the American Academy of Mechanics, and a life member of the Alexander von Humboldt Association of America. He was awarded the Humboldt Research Prize (Senior Scientist Award) in 2003.