# A Literature Survey on Electrical-Current-Assisted Friction Stir Welding
## 7 Simulation and Modelling of EA-FSW  
Modeling is essential when a manufacturing process is to be investigated [49]. In these processes, generally, many parameters should be considered and evaluated. Analytical models are beneficial; however, due to the complexity of manufacturing processes, the numerical model could be more precise [50]. Friction stir welding and resistance welding, as two popular welding procedures, are investigated widely. However, electrically assisted friction stir welding could be considered a hybrid process where resistance welding and friction stir welding are jointly applied, because it is a new procedure, and very few investigations have been carried out. [PERSON] et al. [28] developed an analytical model together with a numerical one to investigate electrically assisted friction stir welding of the AA6082-T6 alloy. In their analytical model, the temperature rise due to the Joule effect is calculated considering the two following assumptions:  
Figure 7: Cross-section view of Al-Mg joint welded by (**a**) 0 A, (**b**) 300 A, and (**c**) 500 A electrical current. Reprinted with permission from ref. [40]. Copyright 2022 Elsevier. 1. The electric current \(I\) (A) flows within the copper core of the probe, as depicted in Figure 6, with a diameter \(\phi\) (m) at a distance \(h\) (m) from the back plate, closing the electric circuit;
2. The increase in the temperature that occurs due to the Joule effect under adiabatic conditions, that is, energy losses to adjacent materials (back plate, base materials, and tool) is negligible. Thus, in the control volume, the temperature is raised using all heat generated by the Joule effect according to the fundamental calorimetric equation (Equation (2)): \[Q_{Joule\ effect}=Q_{Increase\ temperature}\] (1) \[R\cdot I^{2}\cdot t=m\cdot C_{p}\cdot\Delta T\] (2) where \(R\) [\(\Omega\)] is the material electrical resistance, \(I\) [A] is the current intensity, \(t\) [s] is the time for passing the current, \(m\) [kg] is the mass dissipating heat, \(C_{p}\) [J/kg\({}^{\circ}\)C] is the specific heat of the material, and \(\Delta T\) [\({}^{\circ}\)C] is the increment in temperature. Equation (3) could be used to calculate the electrical resistance: \[R=\frac{h\cdot\rho_{e}}{\pi\phi^{2}/4}\] (3) where \(h\) [m] is the inherent gap distance, \(\rho_{e}\) [\(\Omega\)m] is the electrical resistivity, and \(\phi\) [m] is the diameter of the conducting copper core. The interaction time \(t\) [s] is related to the welding speed \((V_{x})\)[m/s] and can be calculated by Equation (4), considering that there is no complete overlapping between the copper core and the material interaction area during time \(t\). The mass \(m\) [kg] is given by Equation (5), considering the geometrical features of the copper core (\(\phi\)), gap distance \((h)\), and the material density \(\rho\) [kg/m\({}^{3}\)]: \[t=\frac{\phi}{V_{x}}\] (4) \[m=\rho\cdot h\cdot\frac{\pi\phi^{2}}{4}\] (5) Thus, the temperature increase considering the Joule effect could be written as follows: \[\Delta T=\frac{16}{\pi^{2}}\cdot\frac{\rho_{e}}{\rho\cdot C_{p}}\cdot\frac{1} {V_{x}}\cdot\frac{1}{\phi^{3}}\cdot I^{2}\] (6) where the four affecting properties are as follows: \(\frac{\rho_{e}}{\rho\cdot C_{p}}\) is the material properties, FSW travel speed \(V_{x}\), geometric features of copper core diameter \(\phi^{3}\), and electrical current intensity \(I^{2}\). This heat source (Joule effect) is the third source in addition to the friction and plastic deformation that exists in the conventional FSW. Thus, a smaller probe diameter and higher current intensity results in a higher temperature raise in the nugget. The temperature raise, in practice, is higher compared with the values predicted by the model due to the decrease in the electrical conductivity of copper by the temperature raise. [PERSON] et al. [28] also simulated the process using the CST-EM Studio Suit software. They included that the current intensity flows the layer below the probe tip by 70%.