## 4 Extension of the MINA Model to Gas Tungsten Arc Welding  
Gas tungsten arc welding (GTAW) is often operated in addition to shielded metal arc welding (SMAW) for industrial applications. Some experimental investigation with ultrasounds has been conducted on plates welded using these two welding processes to compare their inspectability [64]. In this study, the ultrasonic time-of-flight diffraction (TOFD) technique is investigated to compare the resulting images, as each process creates a specific grain structure and, as a consequence, creates a material with a different anisotropic behaviour. It is shown that the GTAW sample is more isotropic than the SMAW sample. It is demonstrated that the GTAW material exhibits a stronger wave attenuation. It is easier to detect flaws with Bscans for the SMAW sample. It is also noticed that the time of flight of diffraction (TOFD) technique works with better efficiency for SMAW welds than for GTAW welds. Recently, [PERSON] et al. proposed an extension of the MINA model [65]. As there are significant differences in the welding parameters between the SMAW process and the GTAW process, the authors choose to apply the MINA main guidelines. If some phenomenological input parameters are obtained from welding notebook data, a new approach is used to define some phenomenological parameters. This approach uses analysis and measurement of the dimensions of simple beads on plate. These kinds of beads are generally available because they have been made for each weld before complete welding in order to adapt welding settings. The welds have been manufactured in a downhand position using GTAW with arc voltage control (AVC). The Figure 5 shows that the pass morphology is different from that obtained with the SMAW process, as seen in Figure 5a. In Figure 5b, a sketch of a weld bead is drawn, with four measured geometrical parameters: the bead width \(W_{b}\), the bead height \(H_{b}\), the reinforcement \(R_{b}\) and the bead penetration depth \(D_{b}\). Figure 5c represents the simplified geometric model for a pass in the GTAW weld: a \"U-flat\" type. Marsac has tested various welding parameters, and obtained in any case this type of pass morphology. Remelting parameter \(R_{p}\) is the ratio of \(D_{b}\) to \(H_{b}\); this ratio depends on the welding power. For small powers, the average of \(R_{p}\) values is 0.39, and for high powers, it is 0.61. The \(R_{L}\) parameter cannot be evaluated simply from the measurements of the widths and the heights on the beads. The study shows that \(R_{L}\) values are also related to several other parameters such as the layer width, the number of passes per layer and the width of each pass [65]. \(R_{L}\) keeps an identical value within the same layer, but can be modified from one layer to another. Following previous MINA model guidelines, grain growth is closely connected to the temperature gradient. The new model considers three areas, as shown in Figure 5b. Black arrows represent grain growth directions, which are considered symmetric about the vertical axis. The central area is defined as a rectangle and the lateral zones are defined with a quarter circle. These lateral zones contain continuously varying grain growth orientations. In the central zone the grain growth direction is mainly vertical. Figure 5c shows with black arrows that the grain growth at boundaries is assumed to be orthogonal to boundaries. This principle follows MINA basic rules, that is, it considers that boundaries correspond to an isotherm and the temperature gradient is perpendicular to these lines. Grains within a bead are straight; it is thus assumed that the temperature gradient is also straight. The grains do not cross each other within a pass, and so selective growth is rarely observed. Using these hypotheses and considering the \"U-flat\" geometry, it is possible to automatically calculate the thermal gradient directions \(\alpha_{g}\).