Science Direct Science  Direct Science   Direct Science    Direct

Science     Direct

4.2. Rectangular defect

Table 1 Summary of the interaction of SH₀ and SH₁ modes with the rectangular defect for two thickness ranges

A further experiment was carried out with the rectangular defect, where the axial thickness change is absent and the situation is a little simpler. By machining, we made the defect deeper at many steps, keeping the flat face, the axial length of 50 mm, and the edges parallel to the axial and circumferential directions of the pipe. The amplitude and phase of the two modes are measured at each step at the center of the defect, the EMAT being placed opposite to the defects. The experimental results and summary are shown in Fig. 5 and Table 1, respectively. We observe that the amplitude and phase of the SH0 mode monotonously decrease with the minimum thickness, tmin. The decrease in phase can be explained by a reduction of the effective propagation distance due to the wall thinning from the outside. The amplitude ratio is proportional to tmin in the range of tmin , tC, which is the consequence of the uniform amplitude across the thickness and no mode conversion to the SH1
mode.
Those of the SH1 mode drastically respond to the wall thinning. The phase changes in a complicated way, but we always see an increase in phase and a very small amplitude for tmin , tC, where the received signal is made up with mode-converted (via the SH0 mode through the defect) and diffracted SH1 waves, and probably reflected waves (SH0 mode) from the defect edges. There is an interference among them and the phase delay indicates that the diffraction and reflection make a larger contribution. For tmin . tC, the through-transmitted SH1 mode also participates in addition to the above three to make the further complicated interference. We observe a clear difference of amplitude ratio between above and below tC. An amplitude ratio above 1 for tmin , 4 mm could be understood by a positive interference among the constituents.

Also important is the remarkable difference of the axial variation between the two thickness regions. Fig. 6 shows typical scanning results. Approaching the defect edges for tmin > tC, the amplitude first increases and then decreases around them. It considerably rises up and often exceeds the normal values at the midpoint. The phase is shifted down in most cases. In this thickness range, many mechanisms contribute to the response, including the mode conversion, the diffraction, the interference between the SH₀ and SH₁ modes, and their reflection at the side walls of the defect. We see no amplitude rise for tmin < tC, where the amplitude at the median portion is almost at the noise level. The increase in phase indicates that diffraction plays a role in transmitting the energy to the other side of the defect. It is noted that the circumferential length of defect changes accompanying the deepening, which varies the individual phases of the modes and can influence the interference between them. However, this is a secondary effect and has not been considered in the discussion.

Fig. 6. Axial scanning with the SH₁ mode and the response to the rectangular defect of two t_min.