# Laser-Ultrasound-Based Grain Size Gauge for the Hot Strip Mill
## 2 Materials and Methods
### The Generation Event Method
backward echo, but since the measured attenuation is then mainly due to grain scattering, most of the measured frequencies in the spectral analysis of the echo can be utilized in the attenuation analysis when fitting the data to Equation (3). Figure 3b displays the calculated attenuation (solid line) of one of the echoes presented in Figure 3a together with the result of the least square fit of the data to Equation (3) (dashed line with square markers). The result of the fit is only shown in the frequency region of consideration for the least square fitting. To translate the measured attenuation to a grain size, a calibration curve is required, which is established by measuring the frequency-dependent attenuation on several samples with LUS in the hot state, and then quenching the samples from which the prior austenite grain size (PAGS) can be determined. Several definitions of grain size are available, e.g., grain size by American Society for Testing and Materials (ASTM) number, equivalent circle diameter (ECD or EQAD) and mean circular intercept length, and additionally these methods can be area-weighted, depending on the interest. In the present work, the mean linear intercept (MLI), including annealing twin boundaries, is used as the definition of grain size. While the twin crystals have the same ultrasonic impedance for normally incident longitudinal waves, the grains have almost random orientation, so that only a very small fraction of all of the twin boundaries meet this condition. Hence, the twin boundary should be treated as all other boundaries in terms of ultrasonic propagation. The calibration curve is attained by comparing the known grain size to the LUS measurements at different temperatures, and a least square regression is performed to determine the function \(\Gamma(T)\) from Equation (5). The regression includes the austenite grain size determined with electron back scattering diffraction (EBSD) for the stainless steel samples that are austenitic at room temperature as well as in a hot state. The low alloying samples were also part of the regression, but since they underwent a phase transformation during quenching, their prior austenite grain size was analyzed with the martensite parent grain reconstruction (MPGR) technique [25]. The grain boundaries are defined in this work as a misorientation of \(>\)5\({}^{\circ}\). Various low-alloy steel and stainless steel samples were measured in the thermomechanical simulator GLEBLE 3800 at Swerim in Stockholm with the ancillary in-house laser ultrasonics GLUS\({}^{\circledR}\) for microstructure monitoring during thermal cycles. The samples had thicknesses between 3 and 5 mm, and most of them were flat, with a few exceptions, which were standard GLEBLE cylindrical compression samples with a diameter of 10 mm. Figure 3: (**a**) Plot of frequency content in the generation event and the consecutive echoes from the A-scans shown in Figure 2. (**b**) The calculated attenuation as a function of frequency (solid black line) for the 2 nd backwall echo of one of the A\(-\)scans in (**a**), The fitted 3 rd-order attenuation (dashed line with square markers) is also plotted. The fitting is only performed in the region where the SNR sufficiently large and the frequencies are high enough for the diffraction to be negligible. The samples were measured in either transmission or reflection mode, i.e., the lasers were directed at opposite sides or on the same side of the sample, respectively. For the GLUS measurements, the generation event could not be reliably measured, especially for the samples measured in transmission. Therefore, the reference spectrum used for the attenuation analysis of these samples was the average of the generation events measured in the mill during 2018 with the same lasers. The various samples were annealed between 900 and 1200 \({}^{\circ}\)C for 2-3 min, after which they were held at \(\sim\)900 \({}^{\circ}\)C for a few seconds before they were either quenched with air or naturally cooled down.