ABSTRACT
In the context of designing a next-generation ultrasonic polar scan (UPS) measurement system for viscoelastic material characterization, a novel approach is proposed, which draws on a set of cylindrically focused emitters in conjunction with a circular phased array (C-PA) receiver in order to create a portable measurement system while improving the data quality and ease the data interpretation. To explore the potential of the new approach and determine its optimal design parameters, a 3-D analytical model is presented to numerically simulate UPS experiments with the proposed system. Furthermore, a postprocessing procedure is worked out to treat the acquired raw data with the aim to deal with the integrating effect of finite size transducers and directly reconstruct the angle-dependent plane wave reflection coefficients of the sample under study. As the accuracy of the reconstruction heavily depends on various design parameters, a parameter study focusing on the influence of three main experimental parameters is performed to guide the optimal design. For each of these parameter studies, the UPS simulation results have been inverted, and the errors on the estimated C-tensor parameters have been deduced. First, it is shown that, for a given frequency, the radius of the C-PA must be large enough to capture both the specular and nonspecular reflected field, which is crucial to assure a correct reconstruction of the plane wave characteristics and find proper estimates of the C-tensor parameters. Second, the impact of the emitter and receiver lengths on the quality of the reconstruction and the C-tensor parameters has been investigated, yielding superior results upon increasing either of them. Finally, a dedicated study of the pitch of the C-PA elements and the angular range of the cylindrically focused emitters shows that aliasing effects disturb the results if the pitch is too large. However, this effect can somewhat be mitigated by employing multiple emitters with a restricted angular range. Using the knowledge of the abovementioned parameter studies, a simulated UPS experiment using a proper set of design parameters is performed for a cross-ply carbon epoxy laminate. The postprocessed reconstruction based on these data shows an excellent agreement with the theoretical plane wave results.
ABSTRACT
Numerical finite-element (FE) simulations and postprocessing analysis methods are presented for ultrasonic polar scan (UPS) measurements involving a circular phased array (C-PA) to determine the plane-wave reflection coefficient of plates. Apodization weights for the C-PA elements are determined to assure the generation of a quasi-plane wave upon excitation at the plate surface and to mitigate bounded beam effects on the assessed reflection coefficient. In addition, postprocessing of the reflection signals is performed via the synthetic plane-wave technique to further filter out any bounded beam effects. Reflection coefficients are presented for three cases namely, an aluminum, a unidirectional carbon epoxy, and a cross-ply carbon epoxy plate. For all three cases, comparison with the analytical plane-wave theory shows excellent agreement with the reflection coefficients obtained by the C-PA and the additional postprocessing steps for both the pulsed and harmonic signals. It is also shown that the agreement becomes considerably worse if the nonspecular reflection field is disregarded in the postprocessing treatment, thus enforcing the need to capture the full reflected field via the PA whenever plane-wave reflection coefficients are needed.
