## 5 Assessing the Impact of Welding Parameters on Ultrasonic Images
### 3D Effects--The Start and the Finish of the Arc  
The NDE community agreed several decades ago that the effect of the out-of-plane grain orientation angle is small [13], and it is often ignored when modelling the propagation of ultrasound or simulating acquisitions. In this part, we performed a 3D weld formation simulation based on the simplified modelling paradigm. This allowed for analysing the effect of the out-of-plane grain tilt, but also the arc start and arc end effects which relate to the robustness of a weld map determined at a single location for the remaining part of a weld. Figure 4c shows the FE mesh used in the weld formation model and the three locations along the weld axis used in the further comparison. While 3D simulations produces 3D orientations, we use a simplified approach in this paper, related to the common practice in the community, and use two angles for each cell--the angle in the plane of the cross-section, and the out-of-plane tilt along the weld axis. Let us first look at the resulting grain orientations predicted by the 3D model. The comparison focuses on the differences in angles read at the arc centre (Case 9) and those at arc extremities across both planes. First, Figures 24 and 25 show the angles over the plane of the cross-section for the arc start (Case 10) and arc finish (Case 11), respectively. They indicate no significant difference along the length of the weld, except for a few spot discrepancies. The out-of-plane grain angle tilt for the two locations is depicted in Figures 26 and 27. While the arc start shows approximately a constant angle difference against the arc centre across most of the weld (mainly in the range \(5^{\circ}\) to \(15^{\circ}\)), towards the end of the arc, the discrepancy tends to be more localised and slightly higher. Figure 24: Local grain orientation across the plane of the cross-section computed by the 3D model—arc centre (Case 9) vs. arc start (Case 10) location. Figure 25: Local grain orientation across the plane of the cross-section computed by the 3D model—arc centre (Case 9) vs. arc finish (Case 11) location. The FE simulations of ultrasonic acquisitions are in this case also in 2D, but 3D orientation angles are used to determine the local elastic tensor. Unlike in the previous cases, the \"reference\" image is now the image computed with delay laws based on the \"arc centre\" (Case 9) 3D orientations, including the out-of-plane component, analogous to the acquisition simulation. Figure 28 shows the images with the acquisition taken at the arc start location (Case 10). The top row of images acts as a reference. If we had only the 3D orientations computed at arc start, we would observe a decrease in the SNR of the defects increasing towards the backwall, as seen in the middle row. The notches are more severely affected--their signatures are not distinguishable any more. In the case when the TFM image was computed solely on the basis of the 2D delay laws from the simplified model used before in this paper, the defects close to the backwall and the right chamfer would not be legible any more. We now consider acquisition at the arc centre location in Figure 29. First, the middle row shows the effect of neglecting the out-of-plane tilt when computing delay laws. The SNR reduction reaches over 15 dB at the bottom of the right chamfer, suggesting that the out-of-plane tilt may play a significant role. The 2D orientations from the simplified model used at the beginning of the paper perform comparably and show very similar SNR reduction. These results question the common practice of neglecting the out-of-plane grain tilt, indicating that including this information may enhance the legibility of signatures located further from the array. Finally, the arc finish location (case 11) is addressed in Figure 30. While a small-to-moderate reduction in the SNR exists, all defect signatures retain their legibility, irrespective of the choice of the delay laws variant.