Abstract
A one-dimensional model is proposed for the simulations of resistance spot
welding, which is a common industrial method used to join metallic plates by electrical
heating. The model consists of the Stefan problem, in enthalpy form, coupled with
the equation of charge conservation for the electrical potential. The temperature
dependence of the density, thermal conductivity, specific heat, and electrical
conductivity are taken into account, since the process generally involves a large
temperature range, on the order of 1000 K. The model is general enough to
allow for the welding of plates of different thicknesses or dissimilar materials and
to account for variations in the Joule heating through the material
thickness due to the dependence of electrical resistivity on the
temperature. A novel feature in the model is the inclusion of the effects of interface
resistance between the plates which is also assumed to be temperature dependent.
In addition to constructing the model, a finite difference scheme for its numerical
approximations is described, and representative computer simulations are depicted.
These describe welding processes involving different interface resistances,
different thicknesses, different materials, and different voltage forms.
The differences in the process due to AC or DC currents are depicted as well.