The development of undercut and bulge on a solidified surface

Abstract This study numerically investigates the development of undercuts and bulges parallel to the scanning direction on the surface solidified from a thermocapillary molten pool. The analysis considers various parameters, including power-off time, active solute concentration, beam power and radius, surface tension, liquid thermal conductivity, viscosity, and density. The formation and shapes of undercuts and bulges directly impact the yield, fatigue, fracture strength, and stress concentration in the solidified region. Unsteady two-dimensional fluid flow and heat transfer, which drive surface deformation in metals containing surface-active solutes (e.g., iron with sulfur), are solved using COMSOL Multiphase version 5.6. The development of the undercut, bulge, and molten pool is identified in six stages, based on whether the peak temperature is below the melting temperature, between the melting and critical temperatures, or above the critical temperature during heating and power-off periods. The critical temperature, determined as a function of solute content and temperature, leads to inward surface flow in the undercut near the pool edge, while the bulge in the central region can form due to either inward or outward surface flow. The predicted undercut depth and bulge height align well with previous scaling analyses and experimental data from laser polishing. These findings are relevant to various processes, including welding, additive manufacturing, polishing, melting, and solidification.