# Experimental and Numerical Predictions of Cryogenic Leakages in Welded Steel Plates
## 4 Results and Discussion
### Numerical Analysis  
The nonuniform temperature distribution and rapid heating and cooling both increase the heterogeneous expansion and shrinkage of the fusion zone. It produces residual stresses and unexpected distortions. Similarly, during cryogenic leakage, the area endures a violent cooldown process, transitioning from ambient to ultralow temperatures in a short time. This area experiences alternating tension-compression thermal stresses, due to the variable temperature distribution during the cooldown process. Therefore, accurate simulation of the heat transfer analysis of the welding process and cryogenic leakage process represents a vital prerequisite to ensure the reliability of the residual stress, distortions, and thermal stresses. As expressed in Figure 13a-c, the residual stress distribution includes a three-axis stress model: the transverse stress \(\sigma_{x}\), longitudinal stress \(\sigma_{y}\), and normal stress \(\sigma_{z}\), which are perpendicular to the welded joint (X direction), parallel to the welded joint (Y direction) and along the thickness (Z direction), respectively. The transverse stress ranged from \(-711.9\) to \(749.2\) MPa and the longitudinal stress varied from \(-255.7\) to \(358.9\) MPa. The maximum and minimum of normal residual stress were \(-367.0\) MPa and \(799.0\) MPa, respectively. The transverse stress in the fusion zone (FZ) and the heat-affected zone (HAZ) reached a higher concentration than the other areas, as shown in Figure 13a. The stress profiles of von Mises equivalent stress were calculated as well, to consider the final residual stress state. Figure 13d highlights the equivalent stress distribution, in which there was a significant stress concentration in both the FZ and neighboring HAZ. The maximum value of the equivalent stress was \(502\) MPa, coupled with the appearance of a minor plastic deformation on the weld bead. Figure 12: The strain curves in the longitudinal and transverse directions: (**a**) Point 1, (**b**) Point 2, (**c**) Point 3, and (**d**) Point 4. Figure 14 displays comparisons of the temperature curves between the cryogenic leakage experimental measurements and FEM at various points. The figure presents that the simulation temperature at Point 1 matches the experimental temperature curve well, in terms of slope, trend, and value. Although there was a relative difference in the temperature curves' slopes (experiment and numerical simulation), both curves trended similarly, and their values are approximately equal. The temperatures were recorded at about \(-196\)\({}^{\circ}\)C at Point 1 and around \(-75\)\({}^{\circ}\)C at Point 2. The maximum temperature at Point 3 obtained from experimental measurements and numerical simulation was approximately \(-25\)\({}^{\circ}\)C. With this simplification, the predicted results from the FE analysis agreed with the experimental measurements. Figure 14: Validation of temperature distribution between simulation and experiment for (**a**) the measured points, and (**b**) comparing numerical results to experiment data. Figure 13: Simulated residual stress components in the weldment: (**a**) transverse stress, (**b**) longitudinal stress, (**c**) normal stress, and (**d**) von Mises equivalent residual stress. Stress simulation was also performed with directional and von Mises stresses. Unlike the relatively even distribution of Y-direction stress, Figure 15a illustrates that compressive stress was measured on the surface where LN\({}_{2}\) contacted, and tensile stress was measured on the opposite surface. This distribution reverses as the distance from the weld point increases. Z-direction and stress, as shown in Figure 15c, show compressive stress around the weld point and tensile stress at a distance from the surface. Additionally, von Mises stress exceeded the yield strength, as shown in Figure 15d. As shown in Figure 16, comparing the surface stress distribution with the X-direction stress measured using XRD yields a similar result.