Modified CEL method for determination of defect formation mechanism in underwater stationary shoulder FSW based on softened pressure-overclosure contact relationship

The Coupled Eulerian-Lagrangian (CEL) method was employed to simulate underwater friction stir welding with a stationary shoulder tool (USSFSW). The governing equations in the CEL method were formulated for FSW based on the immersed boundary method. A new softened pressure-overclosure model was introduced to define contact pressure within the overclosure zone, and an initial nodal clearance control method was implemented to prevent the penetration of Eulerian elements into the Lagrangian domain. For modeling the mechanical and thermal interactions between surfaces, the VUINTERACTION subroutine was utilized. The study focused on the defect formation mechanisms during USSFSW, highlighting the roles of material flow velocity and nodal forces. Simulation results demonstrated close alignment with experimental data, revealing three flow paths that developed during the process, merging in the empty area behind the pin and generating upward material flow. Notably, the maximum flow velocity at the boundary of the third and fourth quadrants ranged from 0.189 to 0.495 m/s, while the overall maximum material flow velocity varied from 0.193 to 0.502 m/s. The nodal force was found to vary between 180 and 600 N; notably, when this force dropped below 200 N, the driving force for material flow decreased, resulting in the inability to fill the cavity behind the tool. Conversely, increasing the nodal force enhanced both backward flow (BF) and horizontal flow (HF), promoting higher material extrusion into the cavity. ​Ultimately, when the flow velocity fell below approximately 0.25 mm/s and the nodal force dropped below about 200 N, cavity defects in USSFSW became inevitable.