## 4 Example of Calculations  
Calculations of the transient temperature field are conducted for a steel element with a length of 500 mm, width of 200 mm, and thickness of 30 mm, made with commonly used weldable construction steel S235. Numerical simulations were performed with the author's program created in Borland Delphi environment using Borland Pascal language. In the program, the integration procedure over time is implemented according to the trapezoidal method. Near the control area (cross-section--\(x\) = 0.25 m) calculations were performed at 0.01 s with division of the integration interval at 0.0002 s. Calculations with such a time increase and with the division of the integration interval are necessary due to the high heating rates, as well as reaching maximum temperature at particular points of surfaced object at different times of the deposition process. In the anticipated areas and the heat-affected zone, temperature calculations were made at points in the distances of 1 mm, increasing the distance further from the HAZ--at the edges of the plate calculation were performed every 1 cm. Thermal properties of the welded material and electrode are determined by \(a\) = 8 \(\times\) 10\({}^{-6}\) m\({}^{2}\)/s, \(C_{p}\) = 670 J/kg K, \(\rho\) = 7800 kg/m\({}^{3}\) and \(L\) = 268 kJ/kg. In the simulation, five welds are applied in the middle part of a welded element (the coordinate of weld beginning \(x_{0}\) = 0.15 m) of length \(l\) = 0.2 m. The surfaced area on the top surface of the plate with sequence of the weld padding is presented in Figure 7, where a dashed line denotes the location of a cross-section, at which the analysis of the temperature distribution and welding thermal cycles was performed. The numerical simulation is conducted for the welding heat source of power 3500 W, which corresponds to the parameters \(U\) = 24.3 V, \(I\) = 232 A, \(\eta\) = 0.6 applied in trials of single-pass GMA surfacing conducted by [PERSON] et al. (2016). The source connected with the activity of an electric arc with Gaussian distributed power density is characterized by \(z_{0}\) = 0.0062 m and \(t_{0}\) = 0.001 s. Likewise, in calculations for an experiment, welding speed \(v\) = 0.007 m/s, electrode wire diameter \(d\) = 1.2 mm, wire feed speed \(v_{e}\) = 0.013 m/s and bead dimensions \(h_{w}\) = 2.77 mm, \(w_{w}\) = 11.93 mm (\(d_{p}\) = 0) are assumed. In the calculations, the assumed chemical composition and properties of the electrode material (wire SG3 DIN 8559) are similar to the material of the overlaid object. Accordingly, the content of the article has been completed. Additionally, there are initial values of the temperature of electrode \(T_{e}\) = 100 \({}^{\circ}\)C and temperature \(T_{L}\) = 2500 \({}^{\circ}\)C assumed. The weld overlap is obtained assuming the distance between axes of particular beads equal to 8 mm. Figure 7: The scheme of Gas Metal Arc Welding (GMAW) surfaced area on the top surface of the plate with the sequence of the weld padding. In Figures 8 and 10, one can observe a strong influence of the weld reinforcement heat on temperature isotherm in neighboring, previously created padding welds. The temporal temperature field during the application of the third weld at time \(t=83\) s (electrode's position \(x=y=0.1\) m) is presented in Figure 12 (in longitudinal section on the axis of third weld) and in Figure 13 (on the top surface of a surfaced element \(z=0\)). The obtained shapes of the heat-affected zone determined by isotherms are confirmed in the literature, for example [31; 41]. Isotherms of maximum temperature obtained during the whole surfacing process in the cross-section of the element (the peak temperature contour experienced for all welds) and in the heat-affected zone are illustrated in Figures 14 and 15. The field of maximum temperature shows clear asymmetry outside the heat-affected zone. Figure 11: Temperature field (\({}^{\circ}\)C) in cross-section during the application of fourth weld 0.5 s after passage of the electrode over this cross-section.