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A model of hybrid fillet welding is built and solved. No additional material (welding rod, etc.) is used. Heating of the welded parts is realized by laser beam with induction preheating and/or postheating. The purpose of these operations is to reduce the temperature gradient in welded parts in the course of both heating and cooling, which reduces the resultant hardness of the weld and its neighborhood and also reduces undesirable internal mechanical strains and stresses in material.

The complete mathematical model of the combined welding process is presented, taking into account all relevant nonlinearities. The model is then solved numerically by the finite element method. The methodology is illustrated with an example, the results of which are compared with experiment.

The proposed model provided satisfactory results even when some subtle phenomena were not taken into account (flow of melt in the pool after irradiation of the laser beam driven by the buoyancy and gravitational forces and evaporation of molten metal and influence of plasma cloud above the irradiated spot).

Accuracy of the results depends on the accuracy of physical parameters of materials entering the model and their temperature dependencies. These quantities are functions of chemical composition of the materials used, and may more or less differ from the values delivered by manufacturers. Also, the above subtle physical phenomena exhibit stochastic character and their modeling may be accompanied by non-negligible uncertainties.

The presented model and methodology of its solution may represent a basis for design of welding processes in various branches of industry.

The model of a complex multiphysics problem (induction-assisted laser welding) provides reasonable results confirmed by experiments.