## 1 Introduction  
The modeling of thermo-mechanical phenomena in welding processes is usually treated as an interdisciplinary problem. An analysis of these phenomena requires knowledge from thermodynamics, metallurgy, material science and continuum mechanics (solid and fluid) among others. The description of thermo-mechanical states requires the temperature field, which is variable in time and space, to be determined. Further analysis of strains and stresses requires consideration of material properties that change depending on the temperature as well as structural changes in the material caused by phase changes. Analysis of thermo-mechanical phenomena requires deep knowledge and understanding of the welding processes, as well as easy use of the mathematical apparatus or numerical methods, especially for creating original programs. Thermo-mechanical states in welding processes are analyzed using analytical and numerical methods. The analytical solutions [1; 2; 3; 4; 5; 6] allow us to estimate the searched values and to determine their dependence on various factors quicker, but for more complex problems these solutions are difficult or even impossible to apply. Some problems can be solved only with numerical methods, for instance, the finite element method, which is commonly used [7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. Thermal-mechanical phenomena occurring in joints during welding are not only the result of the temperature influence (heat source). The process and the quality of welding joints are significantly influenced by a number of factors, including properties and chemical composition of the welded material and electrodes [17], technological parameters [18; 19] and welding conditions [20], as well as heat treatment after welding [21; 22]. Among the various criteria for assessing the quality of welded joints, it is important to assess the tendency to crack [23] and the susceptibility to corrosion [24; 25]. In the paper [17], the weldability, mechanical and plastic properties of S700 MC steel, as well as the precipitation hardening characterized by a high yield, were obtained using the thermomechanical control process. The influence of high-speed cutting parameters on the surface roughness and cutting forces of machined AL/SiC composite has been investigated in [18]. [PERSON] et al. [19] proposed a new method for the rapid and economical production of 'nutless' bolted joins, using a combination of two hole-making techniques, namely, form drilling and form tapping. [PERSON] et al. [20] reported the effect of underwater wet welding parameters and conditions on the diffusible hydrogen content in deposited metal for welding with a self-shielded flux-cored wire. [PERSON] et al. [21] conducted analysis of the tempering effect on the microstructure and properties of SAW (submerged arc welding) layers of H13 steel. Tempering causes the surfacing layer to undergo reversion and recrystallization, resulting in the formation of a finer microstructure and a reduction in the number of welding defects, with martensite and residual austenite transformed into fine-tempered martensite, and carbide precipitation occurring at higher temperatures. In the study [22], the effect of post-weld heat treatment and TiAlSiN coating on tensile, bending strength, hardness and corrosion of duplex stainless steel and super austenite stainless steel-joined materials in plasma arc welding has been shown. The evaluated fatigue cracks' growth rates in welding metals with heat input higher than 10 kJ/mm made of the new submerged arc welding (SAW) technique, called the integrated cold electrode with the addition of non-energized (cold) wire, was analyzed in [23]. The main goal of [24] was the creation and evaluation a micro-arc oxidation coating in order to enhance the corrosion resistance of additively manufacture NiTi medical devices. [PERSON] et al. [25] studied the effect of the Mo content on the mechanical and corrosion properties of hyper duplex stainless-steel welds that are subjected to flux-cored arc welding.