## 5 Numerical Results and Discussion  
### Simulation and Experimental Verification  
In welding numerical simulation, the heat transfer in the workpiece and around the surrounding environment should be considered, which is shown in Figure 6. The source of the arc inputs a large amount of heat into the workpiece in the heating process, which rises temperature rapidly in the welding seam zone. In the heating process, the heat transfers from the center zone of the workpiece to the lower temperature zone, which inevitably causes changes within the metal microstructure due to the thermal expansion effect. The heating effect from the source of the arc is over in the cooling process, the heat transfer between the workpiece and the surrounding environment is continuing, the temperature of the workpiece gradually becomes lower, with cooling contraction in the metal microstructure. In both the processes, the thermal crack may initiate or change dynamically in the welding seam zone over which the moving heat source moves. Therefore, the heating and cooling processes are necessarily considered to calculate the temperature field, displacement field and the dynamic response in the welding workpiece. Figure 6: The geometry and welding heating and cooling processes, (**a**) heating process; (**b**) cooling process. The finite element model of the thin plate hardfacing welding is adopted to be simulated and analyzed. The welding material is 2024 aluminum alloy, the welding geometry size is 80 mm \(\times\) 60 mm \(\times\) 2 mm, the welding joint is located in the center line of the \(x\)-\(y\) plane and the arc center moves along the \(x\) axis with a speed of \(v=2\) mm/s. In numerical calculations, the heat source model (3) is used with the thermal efficiency \(\eta=0.9\), the effective heating radius of the arc \(R=3.0\) mm, the welding voltage \(U=20\) V, the welding current \(I=160\) A, the welding speed \(v=2\) mm/s. The calculation times of the heating and cooling processes are 40 and 140 s respectively. The coefficient of the heat transfer \(a_{\mathrm{k}}=50\) W/(m\({}^{2}\cdot\)K), \(\theta=\varepsilon\times\Phi\), \(\varepsilon\) is the radiation coefficient with the value of 0.5; \(\Phi\) is the [PERSON] constant with the value of 5.670373 \(\times\) 10\({}^{-8}\) kg\(\cdot\)s\({}^{-3}\cdot\)K\({}^{-4}\). Material properties' parameters include the thermal conductivity coefficient \(\lambda\) (W/(m\(\cdot\)\({}^{\circ}\)C)), density \(\rho\) (Kg/m\({}^{3}\)), specific heat \(c\) (J/(Kg\(\cdot\)\({}^{\circ}\)C)), coefficient of thermal expansion \(\alpha\) (\({}^{\circ}\)C\({}^{-1}\)) and elastic modulus \(E\) (GPa). The material parameters can be treated as a function of temperature with isotropic property. Initial temperature of aluminum alloy sheet is chosen by 20 \({}^{\circ}\)C; the material performance parameters at different temperatures are shown in Table 1; the data that are more than 400 \({}^{\circ}\)C in Table 1 are obtained by the extrapolation method. The linear elastic stress-strain relation is not satisfied when the temperature of the material is heated above the melt temperature. In the welding process, when the temperatures of the elements in the XFEM model exceed the upper limit temperature value of the solid-liquid zone, the elements are not involved in the calculation of the thermal stress in the welding process. When the temperatures of the elements are lower than the upper limit temperature value of the solid-liquid zone, the elements are involved in the calculation of the thermal stress in the welding process. The first example is of a plate without an isothermal crack in the heating and cooling processes. The distributions of the temperature at different times in the heating process are shown in Figure 7. The distributions of the temperature at different times in the cooling process are shown in Figure 8.