Modeling of transport phenomena and solidification cracking in laser spot bead-on-plate welding of AA6063-T6 alloy. Part I—the mathematical model

Abstract

In this study, a transient unified model including simulation of the temperature, velocity, solute (Mg2Si) concentration and stress fields, free surface, and laser-induced plasma, has been developed to predict the transport phenomena and solidification cracking susceptibility during laser spot bead-on-plate welding of aluminum alloy. The model consists of the modeling of heat, momentum and mass transports in the metal and plasma zones, thermomechanical modeling, and evaluation of solidification cracking. The full set of mathematical equations and numerical methods are presented. The main challenges and the corresponding solutions for the modeling are discussed. In this model, the lever-rule based on the phase diagram was used to deal with the macroscale segregation at the solid–liquid interface, while the solute transfer due to the diffusion and convection were calculated by the conservation equations for transport phenomena. The solute redistribution in the weldment is coupled with the changes of liquidus and solidus temperatures of the material. The total strain consists of the elastic, viscoplastic, and thermal parts that are coupled with the calculated temperature, velocity, and solute in the weldment. The criterion for the weld solidification cracking was established based on the strain theory, in which the cracking initiates only when the strain exceeds the threshold strain in the brittle temperature range (btr).