Calculation of Dispersion Curves in Bonded Joints Using Either Complex Frequency or Complex Slowness and Comparison of the Results with the Minima of the Plane Wave Reflection Coefficients

Bernard, A.
Lowe, M.
Deschamps, M.
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Oblique incidence methods using ultrasonic waves are often proposed for the inspection of multilayered plates. For example, during the bonding process between two plates of titanium, the possibility of the formation of a brittle layer of “Alpha case” (or “Hard Alpha” ) along the bondline has been established if nitrogen or oxygen is present [1]. Moreover, adhesive joints, which are widely used in industry, need to be inspected in order to confirm the properties of the adhesive layer (cohesion) and of its interfaces with the adherends (adhesion). One possible technique for inspection is to exploit the properties of guided waves which travel along the embedded layer. According to the coincidence angle principle, they can be excited by signals incident at a precise angle and there is an expectation that the generation of a plate mode is indicated by a minimum of the plane wave reflection coefficient. As plate modes are very sensitive to the properties of the embedded layer in which they travel, the waves which are excited within the adherent (adhesive joint) or within the bondline (diffusion bonded joint) would therefore give information on their properties [2]. This method of excitation and detection is practically valid in many circumstances such as immersed plates in water [3] as shown in Figure 1. However, when the surrounding medium has an impedance of similar order to the layer, minima of the reflection coefficient do not indicate the generation of guided modes in the layer [4–6].