ABSTRACT
The transmission of Lamb waves across adhesively bonded lap joints is investigated using finite element analysis. The studies consider three modes for excitation and reception, s0, a0, and a1, applied to lap joints consisting of parallel aluminum sheets bonded with an epoxy adhesive. Transmission coefficient results for a two-dimensional range of bond thicknesses and bond overlap lengths are presented for all three modes. The transmission coefficients are calculated from the spectra of the received and transmitted signals using an approach which is insensitive to the presence of multimode signals and reverberated signals, and which approximates to a power transmission coefficient. Detailed analysis is then performed for one of the modes in order to investigate the nature of the mode conversion in the overlap region of the joint. It is found that the relative amplitudes of the different modes which propagate in the overlap region can be estimated reliably and simply from the properties of the incident wave mode. As well as demonstrating the physics of the mode conversion behavior, the study provides a basis for the selection of modes for nondestructive evaluation (NDE) of the bond region and for measuring the bond dimensions.
ABSTRACT
Analytical solutions of Lamb functions for symmetric and antisymmetric elastodynamic modes propagating within a solid layer embedded in an infinite medium are presented. Alternative theoretical analyses of such modes are performed, first in terms of the usual approach of harmonic heterogeneous plane waves (real frequency and complex slowness) and then in terms of transient homogeneous plane waves (complex frequency and real slowness). An example structure of a 0.1-mm-thick "alpha case" (an oxygen-rich phase of titanium that is relatively stiff) plate embedded in titanium is used for the study. A large difference between the usual dispersion curves calculated in real frequency and complex slowness and those calculated in complex frequency and real slowness is shown. Thus the choice between a spatial and a temporal parameter to describe the imaginary part of the guided waves is shown to be significant. The minima and the zeros of the longitudinal and shear plane-wave reflection coefficients are calculated and are compared with the dispersion curves. It is found that they do not match with the dispersion curves for complex slowness, but they do agree quite well with the dispersion curves for complex frequency. This implies that the complex frequency approach is better suited for the comparison of the modal properties with near-field reflection measurements.
