Simulation Of A Weld Pool Interface Motion By A Variational Inequality Approach
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D. D. Doan, F. Gabriel, Y. Jarny & P. Le Masson
This work deals with the numerical simulation of the temperature field within the solid part of a metallic piece during a welding process. By using an integral transformation such as the Duvaut’s transform, the direct heat transfer problem is formulated as a parabolic variational inequality in a fixed domain. It consists of determining the temperature distribution in the solid region, coupled with the location and the motion of the weld pool interface and the heat flow crossing it, which is modelled by a Stefan’s condition. The method is applied to numerically solve the solution of a phase change problem formulated in a 2-D cylindrical geometry. The computed temperature field is compared with results given by a standard method. Keywords: Stefan problem, front of fusion, heat source, Duvaut’s transform, variational inequality, finite element. 1 Introduction Fusion welding is the most frequently used metal joining method. It is a process by which the edges of two pieces of metal are melted and fused together. This is accomplished by using an intense local energy source. During the heating and cooling cycles while welding, thermal strains occur and generate residual stresses and distortions in the welded structure. One of the major industrial challenges is to predict these mechanical effects. Thus, in order to evaluate these mechanical effects with accuracy, it is necessary to have a thermal model which takes in to account the welding process.
Stefan problem, front of fusion, heat source, Duvaut’s transform, variational inequality, finite element.