Proposal and analysis of a non-collinear wave mixing technique for the detection of micro-cracks using phased arrays

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May, Max Philipp
Jacobs, Laurence J.
Kim, Jin-Yeon
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In this thesis, a new ultrasonic measurement setup for the detection of micro-scale damage in cement based materials is proposed and analyzed. The idea is to use the nonlinear phenomenon of wave mixing to characterize third order elastic behavior of a material. By wave mixing, the nonlinear interaction between two ultrasound waves creating a third resonant wave inside a material is meant. The amplitude of this third wave is dependent on the third order nonlinear constants of a material, which in turn are influenced by micro-scale damage inside the material structure. Furthermore, a nonlinear technique is especially needed in the case of attenuative materials, which prevent the use of higher frequencies to get good resolution with linear approaches. Recent measurement results using a wave mixing technique are designed in a fixed setup to evalute a single point inside the material or scan line regions by moving the ultrasonic equipment. This limitation originates from the use of common ultrasonic transducer elements generating an ultrasound wave at a fixed angle by using the refraction of wedges. As a remedy to this limitation, phased arrays can be used as a source for the incident waves instead. Thus, having the advantage to change the beam angle without changing the physical measurement configuration. Two phased arrays are used on one side of the specimen to generate incident shear waves. If the the beams intersect inside the material at a point fulfilling certain mixing conditions, a longitudinal resonant wave is generated which amplitude is proportional to the amount of nonlinearity inherent to the mixing volume. This resonant wave can be measured by a receiver on the other side of the material to asses, e.g., micro-crack density in the mixing volume. \par In this thesis, necessary and sufficient conditions for this non-collinear shear wave mixing are derived. Furthermore, the basic laws for beam steering with phased arrays are explained and the mixing volume is modeled. Finally, advantages and limitations of this measurement technique as well as design specifics for the practical construction of a measurement setup are discussed.
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