## 2 The Physical Description of Surfacing by the Welding Process  
The purpose of the deposition is to restore the original shape of the element (rebuilding), or to obtain better surface properties (e.g., hardfacing). This technology involves applying a layer of the molten electrode material to the treated surface. The electric arc formed between the electrode and the welded object emits the thermal field which melts the electrode and melts the surface of the object. Droplets of the molten electrode material fall into the weld pool--the molten material of the welded object--and mix with this material to form padding weld. Thus, in this process, metallurgical melting of the base material occurs, whose share in the weld pad can go up to 60% [47]. In the GMA method, forces separating metal droplets from the electrode tip and transmitting them to the weld pool are different. The most important of them are [48]:  
- surface tension of the melted electrode droplet preventing it from detachment. - gravitational force,  
- Lorentz electromagnetic force (proportional to the square of the current intensity), which cuts the metal droplets from the electrode,  
- pressure of the gases released at the end of the electrode,  
- the electromagnetic interaction generated by changing the flow intensity of current in the arc plasma around the droplet. In the GMA method, metal may be transferred to the weld pool in three ways: short circuit, coarse droplet and spraying [49]. A unified model to simulate the transport phenomena occurring during the GMAW process by [PERSON] and [PERSON] [50; 51] has been presented. A coupling between arc plasma, melting of electrode, droplet formation, detachment, transfer and impingement onto the workpiece, as well as weld pool dynamics were considered. In [52], the authors conducted simulations to study the effects of current on the temperature distributions, velocity, pressure and current density in the droplet and arc plasma. The temperatures reached during heating, the hold time at each temperature, including the cooling rate in the temperature range of 800-500 \({}^{\circ}\)C, determine the nature of structures that occur in junction during and after welding. The above-mentioned transformations caused by a welding thermal cycle result in shaping distinctive structural zones of the surfaced area (Figure 1):  
- fusion zone which is completely melted and has a dendritic solidification structure,  
- full transformation, when there is a complete transformation of the primary structure in austenite,  
- partial transformation,  
- the parent material, when there have been no phase transformations. During heating, austenite transformation takes place whose beginning and end are limited by temperatures A\({}_{1}\) and A\({}_{3}\) resulting from the phase equilibrium Fe-C diagram. If the maximum heating temperature exceeds the temperature of the beginning of the austenite transformation A\({}_{1}\), but does not exceed A\({}_{3}\), there is incomplete austenitic transformation, i.e. only part of the original structure (parent material) is transformed into austenite. However, if the temperature exceeds A\({}_{3}\), then primary structure is completely transformed into austenite. Solidus temperature (above which the material begins to melt) defines the fusion line, and the area heated above this temperature creates a fusion zone. In modeling of a temperature field in welding processes in the vast majority of solutions, the assumed heat source model is characterized by a direct effect of the entire amount of generated electric arc heat on the welded or surfaced object. When welding, the weld execution takes place within the operation area of the welding arc and, by chamfering the edges of connected elements an area filled with liquid metal is determined. The fusion line is often of regular shape (usually parabolic) as well as isotherms in a heat-affected zone. However, during surfacing by welding of flat surfaces the fusion line shape is often irregular.