## 1 Introduction
The first extensive analysis of the conventional friction welding process was conducted in references [4; 5]. The temperature distribution and uniform heat flow in the friction welding process of carbon steel bars with a constant friction coefficient and thermal properties were presented. The first numerical analysis of the friction welding process using the finite differences method was carried out by the authors of papers [6; 7]. The authors analyzed the time-varying heat input, axial shortening and plastic deformation of welding materials. A two-dimensional finite-difference model for conducting simulations of the temperature fields of the friction welding process was also developed in references [8; 9]. The results show a visible difference in the temperature distribution between the conventional and inertia friction welding (IFW) methods. The friction welding of steel bars with identical properties using the finite element method, along with the conditions of element contacts, was proposed in references [10; 11]. Moreover, the temperature distribution and final shape of the welds were determined in references [12; 13]. A thermo-mechanical finite element model of IFW of two bars as a viscoplastic material was proposed in reference [14]. The FEM model considered the plastic deformation of the joined workpiece and a heat flow analysis was conducted [15]. The effective stress, strain and temperature field for nickel-based alloy friction welded joints were determined. An FEM simulation of the IFW of materials with different physical properties that assumed mechanical and thermal dependencies and the elastic-viscoplastic behavior of the material was completed [16]. A new friction law for the modelling of the continuous drive friction welding (CDFW) of steel was proposed [17]. A FEM method for the friction welding of ceramic-metal [18] and refractory metals [19] was also used. The numerical model for a steady-state flow and the analysis of a coupled thermo-mechanical problem in friction welding was presented [20]. An investigation of the temperature distribution, axial shortening, flash formation and microstructure using inverse heat flow analysis can be found in reference [21]. Due to its high density, high strength, good toughness and other excellent properties, tungsten heavy alloy material has become the first choice for many kinds of kinetic energy armor-piercing bullets. Tungsten alloy penetrator bullets have a high penetration ability thanks to the high-density tungsten alloy, which makes the projectile fly at high speed and with high energy. Recently, tungsten heavy alloy projectile cores have been used as kinetic energy penetrators (KEPs) for sub-caliber bullets. These THA cores can be joined to a ballistic cap made of an aluminum alloy. This cap protects the projectile against ricochets when it hits the armor plate. These materials are often joined by threads, which require milling. This is problematic because tungsten is difficult to cut due to its relatively high hardness and strength. Therefore, the authors of references [22; 23] have proposed the friction welding method for joining these materials. Friction welding is an effective solid-state joining method for various materials. Compared to the conventional joining method, rotary friction welding is a simple, cheap and very fast process. Moreover, it makes it possible to join metals and alloys that are very difficult to join or are not joinable at all using other methods. This is why friction welding is a very attractive method and is studied in many laboratories across the world. However, there are some difficulties in joining dissimilar materials. These difficulties are caused by very different melting points, different thermal expansion coefficients, the forming of hard precipitates that are usually intermetallic phases, or problems caused by difficulties in the reaching of an appropriate temperature.