Dynamic electrical resistance during resistance spot welding has been quantitatively modeled and analyzed in this work. A determination of dynamic resistance is necessary for predicting the transport processes and monitoring the weld quality during resistance spot welding. In this study, dynamic resistance is obtained by taking the sum of temperature-dependent bulk resistance of the workpieces and contact resistances at the faying surface and electrode-workpiece interface within an effective area corresponding to the electrode tip where welding current primarily flows. A contact resistance is composed of constriction and film resistances, which are functions of hardness, temperature, electrode force, and surface conditions. The temperature is determined from the previous study in predicting unsteady, axisymmetric mass, momentum, heat, species transport, and magnetic field intensity with a mushy-zone phase change in workpieces, and temperature and magnetic fields in the electrodes of different geometries. The predicted nugget thickness and dynamic resistance versus time show quite good agreement with available experimental data. Excluding expulsion, the dynamic resistance curve can be divided into four stages. A rapid decrease of dynamic resistance in stage 1 is attributed to decreases in contact resistances at the faying surface and electrode-workpiece interface. In stage 2, the increase in dynamic resistance results from the primary increase of bulk resistance in the workpieces and an increase of the sum of contact resistances at the faying surface and electrode-workpiece interface. Dynamic resistance in stage 3 decreases, because increasing rate of bulk resistance in the workpieces and contact resistances decrease. In stage 4 the decrease of dynamic resistance is mainly due to the formation of the molten nugget at the faying surface. The molten nugget is found to occur in stage 4 rather than stage 2 or 3 as qualitatively proposed in the literature. The effects of different parameters on the dynamic resistance curve are also presented.

Unsteady, axisymmetric transport of mass, momentum, energy, species, and magnetic field intensity with a mushy-zone phase change in workpieces and temperature, and magnetic fields in electrodes during resistance spot welding, are systematically investigated. Electromagnetic force, joule heat, heat generation at the electrode–workpiece interface and faying surface between workpieces, different properties between phases, and geometries of electrodes are taken into account. The computed results show consistencies with observed nugget growth, electrical current, and temperature fields. The effects of the face radius and cone angle of the electrode, parameters governing welding current, electrical contact resistance, magnetic Prandtl number, electrical conductivity ratio, and workpiece thickness on transport phenomena are clearly provided.

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