Therefore, in any case a reflection is expected when the materials are in perfect selleck products contact. If, on the contrary, the fiber is totally debonded from the matrix, the reflection will be stronger since the impedance of air is negligible compared to that of the matrix. It is reasonable that for any intermediate condition of bonding quality the reflection will be in between the above-mentioned extreme cases. This role (quality of bonding) is played by the ��interphase�� material, which in our analysis obtains variable values of stiffness, as expressed by the different longitudinal wave velocities. The wave reflected by the fiber, which now may again include longitudinal components after the reflection on the circular surface, propagates back to the surface of the matrix (D), and a part is refracted within water as longitudinal wave following the opposite direction of the initial incident pulse.

This wave reaches the sensor as shown in Figure 2, point E. A typical waveform is seen in Figure 4 where the initial pulse and the reflection (window corresponding to point E of Figure 2) are shown, and in this part of the wave any analysis and evaluation should be focused to characterize the quality of the interphase.Figure 4Typical waveform after excitation of 25MHz. Figure 5 shows some indicative views of the displacement field for the frequency of 25MHz and for the stiff interphase with pulse velocity of 11770m/s. In the first case (a), the wave is propagating through water, while in Figure 5(b) the shear wave starts to be refracted in the matrix traveling on a higher speed than the wave in water.

In the last case of Figure 5(c), the clear reflection can be seen in water (see arrow) while the refracted wave propagates deep in the matrix. Figure 6 shows the field at approximately the same time but with loose interphase. It is obvious that no wave is transmitted through the fiber, while the reflection traveling back to the receiver is similar to the previous case. However, it contains critical differences that make characterization of the different interphases possible, as discussed next.Figure 5Consecutive snapshots of the displacement field for the case of stiff interphase.Figure 6Snapshot of the displacement field for the case of loose interphase.

Figure 7(a) shows the reflections (corresponding to window E of Figure 4) as recorded by the receiver for two extreme cases of interphase stiffness values, namely, equivalent to air (Ci = 330m/s) and fiber (Ci = 11770m/s). The waveforms are identical up to 1��s, since the initial part of the waveform is due to the GSK-3 direct reflection on the water/solid interface which is not influenced by the fiber. The wave packet of the reflection between the matrix/fiber interphase arrives slightly later since the fiber is at a depth of 100��m from the surface.