Dataset on reflection and transmission coefficients of ultrasonic shear horizontal guided waves in plates with wall thinning

This data article reports the data for reflection and transmission coefficients of the SH0 and SH1 ultrasonic guided waves modes due to their interaction with tapered wall thinning in aluminium plates. Several thinning depths and edge taper angles were machined, at the total of 35 different samples. Periodic permanent magnet array electromagnet acoustic transducers were used to generate and receive the waves. Both modes were individually generated and separated in the received signal by means of effective post-processing technique. Reflection and transmission coefficients were calculated at both the leading and trailing edges of the thinning region for mode-converted and non-mode converted signals; therefore, eight coefficients were calculated for each generated mode, at the total of sixteen coefficients for each sample. Additional finite-element model was used in order to obtain numerical values for the coefficients. These data were used in order to analyze the interaction of the SH0 and SH1 modes with wall thinning and the capabilities of using them in non-destructive evaluation of corrosion-like defects in the research paper entitled “Interaction of SH guided waves with wall thinning” (Kubrusly et al., 2019).


Specifications
Value of the data The data allow investigation on the interaction of the SH0 and SH1 guided wave modes with thinning regions that simulate wall loss due to corrosion in metallic plates, which is important for non-destructive tests of plates and pipes.
Up to now, detailed experimental data on the reflection and transmission coefficients for modeconverted and non-mode converted waves of the SH0 and SH1 guided wave modes were not reported.
The data allow one to address the capabilities and limitation on the use of ultrasonic SH guided wave to estimate and detect wall thinning.
The data can be used for developing and evaluating novel techniques in order to assess the amount and severity of wall loss by means of reflected and transmitted SH guided waves.

Data
The dataset within this data article provides the reflection and transmission coefficients of shear horizontal (SH) guided wave modes at both the leading and trailing edges of linearly tapered thinning regions. Each experimental sample had a different thinning depth and taper angle, 35 different samples were machined and experimentally analyzed. Coefficients for reflection at the leading edge, transmission to the thinning region, reflection at the trailing edge, and transmission out of the thinning region, were calculated. Either the SH0 or SH1 modes were individually generated; both modes were received in each generation case for each coefficient in order to obtain data on mode-converted and non-mode converted waves, therefore giving rise to a total of 16 different coefficients for each sample. Additional numerical data were obtained by means of a finite-element model for a wider collection of thinning geometry. The coefficient data are reported in Tables 1-8 and in Tables 9-16, for generation of the SH0 and SH1 mode, respectively.

Experimental design, materials and methods
Aluminium plates were used as test samples with dimension of 8 mm thick, 800 mm long and 250 mm wide. A tapered thinner section was machined in each sample starting at position ℓ a ¼ 182 mm with a total length of ℓ d ¼ 150 mm, several different depths, d, and edge angles, α, of the thinned region were machined in order to analyze the coefficients as a function of d and α. Specimens were prepared at edge angles of 10°, 45°, 55°, and 90°; for each of these angles, depths from 1 mm down to 7 mm were machined in 1 mm step. Additional specimens were prepared with 6 mm and 7 mm depth at edge angles of 25°, 30°and 35°and 25°, 30°and 65°, respectively. Therefore, a total of 34 samples were machined plus one non-machined reference sample, all of which were experimentally evaluated. Fig. 1 shows the sample and machined thinning region drawing with dimension and Fig. 2 shows one machined test sample. The machined samples were experimentally evaluated using a RITEC s RPR-4000 Pulser/Receiver and periodic permanent magnet array electromagnet acoustic transducers (PPM EMATs) from Sonemat Ltd. (3cycle, 10 mm nominal wavelength) as transmitter and receiver. PPM EMATs are able to generate shear horizontal guided waves in metallic plates [2]. In order to generate either the SH0 or the SH1 mode an 8 cycle tone burst at 311 kHz or 367 kHz, respectively, were applied to the transmitter PPM EMAT according to dispersion curve of each mode [1]. Dual excitation and reception on both plate's surfaces was adopted in order to ensure that a single mode was generated and then to separate the two possible received modes due to mode conversion. Details on the dual transduction procedure and experimental setup are described in Refs. [3] and [1], respectively.
Transmitters were placed at position O whereas receiver was positioned at positions (1), (2) or (3), see Fig. 1, in order to receive signals before, at and after the thinning region, respectively. Signals acquired by the oscilloscope were averaged in order to diminish the noise level, also a digital low-pass filter at 400 kHz 3 dB cut-off frequency was applied to the raw signals. Signals acquired at both surfaces were combined following [3] in order to separate mode-converted and non-mode converted signals for each generation. Four coefficients were calculated, namely R ij , T ij , TR ij , TT ij , which denote the reflection at the thinning region leading edge, transmission to the region, reflection at the thinning region trailing edge, and transmission out of the far end of the region, respectively. The first subscript, i, denotes the generated mode, whereas the second one, j, denotes the received mode. Either i or j can be 0 or 1, here, corresponding to the SH0 or SH1 modes, respectively. These coefficients are defined by: where A is the peak-to-peak of the received signal inside a time gate in which the mode is expected to arrive, the superscripts þ andmean the forward and backward propagating waves, and (1), (2) and . Since the wave amplitude is increased when it is transmitted to a thinner region, due to the energy distribution across the thickness, it is necessary to include the square root in Eq. (1b) and (1c) in order to compensate it, where h is the plate's original thickness, and therefore h À d is the remaining thickness in the thinner region.
The time gate to select the amplitude A 1 ð Þþ i of the incident mode i before the thinning region, starts and ends, respectively at: due to the incident mode i, start and end instants are, respectively: ð Þ maxfc g j ðh À dÞ; c g i ðh ÀdÞg where c g j is the group velocity of the received mode, j, c g iorj h Àd ð Þ is the group velocity within the thinning region. It is necessary to consider velocity change at the thinning region because the SH1 mode is dispersive and its velocity is a function of the plate's thickness [4]. The minimum and maximum of the two possible modes within the thinner region length, in Eqs. (5a)-(6b), is considered because, at first, both modes can propagate in the thinning region due to mode conversion of any incident mode at the leading edge, and the coefficients TR ij and TT ij consider the two possible modes, SH0 or SH1, propagating inside the thinning region. This, however, only holds when the region remaining thickness is above the SH1 mode cut-off thickness. Otherwise, its group velocity is not defined and this mode cannot propagate inside the thinning. Thus, either minfc g j ðh À dÞ; c g i ðh À dÞg or maxfc g j ðhÀ dÞ; c g i ðh À dÞg should read c g 0 h À d ð Þ¼c g 0 h ð Þ ¼ c g 0 in this case, since the group velocity for the non-dispersive SH0 mode is constant for any thickness. Also, in this case, a time gate for T i1 or TR i1 cannot be defined, therefore no time gate restriction was applied and the whole SH1 signal on the region is considered to calculate the T i1 coefficient, whereas TR i1 is not calculated in this case.
Prior to calculating the experimental reflection and transmission coefficients, it is necessary to compensate for attenuation. The experimental attenuation of the guided wave modes was calculated by receiving the SH0 and SH1 signals in several positions in a non-machined sample and fitting the peak-to-peak of the signals versus the position with an exponential decay curve. The exponential coefficient was then used to compensate the values of the amplitudes,   Finally, the sixteen coefficients were calculated for each thinning depth and taper angle.
In addition to experiments, finite-element analysis was also performed using a commercial, timedomain, Finite-Element Method (FEM) solver, PZFlex©, which allows simulation of SH waves in twodimensional models. The numerical model was executed for thinning depth from 0.5 to 7.5 mm in 0.5 mm step with the following taper angles, 90°, 65°, 55°, 45°, 35°, 30°, 25°and 10°, therefore including all the experimental thinning geometries. Numerical simulation mimicked the PPM EMATs generation by applying forces in surface nodes along the transducer length according to the transducer spatial profile following the procedure used and validated previously [3,5], whereas reception  was done by numerically convolving the wave field on the surface of the model with the probe spatial profile. Then, likewise in the experiments, the dual excitation and reception procedure, filtering and time gating were applied. Therefore numerical and experimental data can be straightforwardly compared. The only procedure which was not included in the numerical data was attenuation compensation since damping was not included in the model. Figs. 3 and 4 show the experimental and numerical coefficients for generation of the SH0 and SH1 mode, respectively. This data not only helps on understanding the interaction of the SH0 and SH1 modes with wall thinning sections but also allows one to address the capabilities and limitation on the use of ultrasonic SH guided wave to estimate and detect wall thinning when both modes are allowed to propagate (see Ref. [1]).