Resistance spot welding simulation: a general finite element formulation of electrothermal contact conditions

Spot welding is an usual joining process for assembling steel sheets but its simulation requires the modelling of complex interactions between electrical, thermal, metallurgical and mechanical phenomena. From the physical point of view, the simulation of such a process needs a high coupling level to take account of the interactions between electrical and thermal phenomena coming from the Joule effect and the temperature dependence of the electrical conductivity. Moreover, contact conditions between sheets and electrodes need to be carefully accounted for. Most finite element studies taking the electrothermal contact conditions into account use the assumption that both contact surfaces are close enough to consider a normal flux exchange. From the numerical point of view, it is generally assumed with this kind of models that contact conditions are ensured through elements linking two nodes face to face and therefore, only small relative displacements are considered. In order to accurately account for the relative displacements of contact surfaces, a general finite element formulation of the electrothermal contact is proposed in this paper. The electrothermal model is described and the general formulation of electrical and thermal contact conditions is detailed. A finite element simulation of the welding of three steel sheets is presented. The results are discussed and compared to a micrographic cut.