# A Literature Survey on Electrical-Current-Assisted Friction Stir Welding
## 7 Simulation and Modelling of EA-FSW
The simulation procedure and results are presented in Figure 8. [PERSON] and [PERSON] [51] investigated EA-FSW numerically using finite element analysis. They reported reduced axial force in the penetration stage when an electrical current is applied, which may result in the promotion of tool wearing and a possibility to perform the welding with a speed that is twice that in conventional friction stir welding. [PERSON] et al. [48] also simulated current density distribution and associated resistance heating using COMSOL Multiphysics software. The basic finite element code used by them is the code that was used to simulate resistance spot welding. The code was modified to analyze the process in two stages: penetration and welding. They presented governing equations as follows. Analyzing this process includes electrical, thermal, and mechanical problems. The Fourier's 2 nd low heat transfer was used to model the heat transfer as follows:  
\[\rho c\frac{\partial T}{\partial t}=k\bigg{(}\frac{\partial^{2}T}{\partial x^{2 }}+\frac{\partial^{2}T}{\partial y^{2}}+\frac{\partial^{2}T}{\partial z^{2}} \bigg{)}+q_{0} \tag{7}\]  
where \(\rho\) is the material density, \(c\) is the heat capacity, \(T\) is temperature, \(t\) is time, \(k\) is thermal conductivity, and \(q_{0}\) is the inner heat source. \(c\) is a temperature-dependent material property. In this model, heat transfer attributed to the material motion is not considered. \(q_{0}\) includes three kinds of heat sources as follows:  
\[q_{0}=q_{0F}+q_{0P}+q_{0R} \tag{8}\]  
where \(q_{0F}\) is the friction heat, \(q_{0P}\) is plastic work heat, and \(q_{0R}\) is electrical resistance heat. There are two sources generating heat due to friction: contact of rotary tool shoulder with the workpiece and high strain rate plastic work dissipation by the pin stirring. The tool is tungsten in their model, and the workpiece is 304L stainless steel. Here, in addition to the frictional heat, another source in the EA-FSW is the heat generated due to the Joule effect. These heat sources are formulated as below. The main source of heat is on the upper part of the workpiece. If all the shearing work at the interface is converted into friction heat, the average heat input per unit area and time becomes  
\[Q_{Joule\ effect}=Q_{Increase\ temperature}\]0  
where \(q_{0F}\) is the net power, \(\mu\) is the friction coefficient, \(P\) is the pressure, \(N\) is the rotational speed, and \(R\) is the tool shoulder surface radius. The heat generated, in this case, is directly proportional to the friction coefficient which changes with the temperature. Thus, at high temperatures, the heat generation efficiency decreases due to changes in the material's physical properties. \[Q_{Joule\ effect}=Q_{Increase\ temperature}\]1 Numerical simulation of the current density distribution. (**a**) Geometrical model and mesh, (**b**) transversal cut view, (**c**) vectorial representation of the previous, and (**d**) top view. Reprinted with permission from ref. [29]. Copyright 2022 Elsevier. At the lower part of the workpiece, the main heat generation source is the plastic deformation due to pin stirring, which is given by the following equation:  
\[Q_{Joule\ effect}=Q_{Increase\ temperature}\]2  
where \(\mathbf{s_{ij}}\) is the deviatoric stress tensor, \(\dot{e}_{ij}^{p}\) is the incremental plastic strain rate tensor, and \(\eta\) is the energy input coefficient. The heat generated by the rotary friction and plastic deformation was applied as a heat flux on the tool shoulder and pin. The heat generated due to rotary friction could be calculated from Equation (9). However, due to the difficulty in calculating the heat generated using Equation (10), total energy input was used to calculate this fraction of heat generation. Tool pin experiences a high wear rate due to the lower temperature of the lower part of the workpiece. The temperature is raised in this zone when the electrical current is applied.