Coupled analysis of high and low frequency resonant ultrasound spectroscopy: Application to the detection of defects in ceramic balls

A coupled analysis of high and low frequency resonant ultrasound spectroscopy of spheroidal modes is presented in this paper. Experimentally, by using an ultrasonic probe for the excitation (piezoelectric transducer) and a heterodyne optic probe for the receiver (interferometer), it was possible to take spectroscopic measurements of spheroidal vibrations over a large frequency range of 100 kHz–45 MHz in a continuous regime. This wide analysis range enabled variations in velocity due to the presence of defects to be differentiated from the inherent characteristics of the balls and consequently, it offers the possibility of detecting cracks independently of production variations. This kind of defect is difficult to detect because the C-shaped surface crack is very small and narrow $(500×5μm2)$⁠, and its depth does not exceed $50μm$⁠. The proposed methodology can excite spheroidal vibrations in the ceramic balls and detect such vibrations over a large frequency range. On the one hand, low frequency resonances are used in order to estimate the elastic coefficients of the balls according to various inspection depths. This method has the advantage of providing highly accurate evaluations of the elastic coefficients over a wide frequency range. On the other hand, high frequency vibrations are considered because they are similar to the surface waves propagating in the surface zone of the ceramic balls and consequently can be used to detect C-crack defects.