Nondestructive determination of elasticity constants of composite plates by the acousto-ultrasonic method

A nondestructive, reliable, and fast method for estimating the elasticity constants that characterize a fiber-reinforced polymer matrix composite plate is proposed. The proposed acousto-ultrasonic technique, which takes advantage of the spectral analysis of the ultrasonic plate waves, allows for the calculation and measurement of the dispersion curves of a plate wave propagating in the lowest symmetric mode. A dispersion curve is a plot of phase velocity versus frequency or wavelength. A narrow-spectrum ultrasonic pulse is applied to the surface of a plate by a broad-band ultrasonic transducer. Time signals captured with two piezoelectric transducers in contact with the plate are first transformed to the frequency domain. The cross phase spectra is then calculated to obtain the phase shift, which in turn yields the phase velocity. The processing of the recorded signals involves a Fourier transform analysis to estimate the cross power spectrum of the received waves. The phase cross spectrum provides the phase shift over a frequency spectrum determined by the input pulse shape. The phase shift at each frequency is proportional to the distance between receivers and to the phase velocity of the ultrasonic wave. Since the receiver separation is known, the dispersion curve can be constructed in the frequency range where the input pulse contains significant energy. From the experimental dispersion curve, the stiffness constants of the plate are estimated. A theoretical dispersion curve is fitted to the measured dispersion curve using a plate model. The model relates the plate elasticity constants and thickness to the phase velocity of plate waves. An inversion algorithm was developed based on the general inverse theory which rapidly converges to the desired elasticity constants. The experimental set up automatically and in real-time acquires the data through a digitizing oscilloscope. The accuracy of phase velocity measurements in aluminum plates was found to be, on the average, within ±1% when compared to the theoretical dispersion curves, and the inversion process yielded elasticity constants that were within 1% of the nominal values