Tech Briefs

Thermo-mechanical Analysis of Electron Beam Welding

Electron beam welding is a fusion welding process that utilizes the kinetic energy of a high-velocity electron beam, which upon impact on the workpiece heats it up due to conversion of its kinetic energy to thermal energy.

In this Brief, we present the results of a numerical modeling of the electron beam welding process of two steel tubes with different diameters. The numerical results are also compared with the available experimental data (see Ref.). Figure 1 shows a representative specimen and a close-up of the welded region.

Figure 1  The welded specimen

One half of the finite element model used for modeling the welding process is depicted in Figure 2.

The movement of the heat source was simulated by applying the heat source to only one prism element along the circumference of the welding zone in each instance. There are 72 prisms along the circumference, each corresponding to 5° rotation of the heat source. The heat flux was applied in pulses, with an idle time between each pulse, to model the actual experimental condition.

Since the electron beam welding is usually performed in a vacuum, the convection coefficient was set to zero on the tube walls.

Each of the welding pulses was discretized by 100 time steps. Temperature-dependent thermal properties were used for modeling the thermal behavior of the tubes.

A temperature-dependent elasto-plastic material model, in which the yield stress and the strain hardening modulus are functions of temperature, was used in the stress analysis.

The movie above shows the evolution of the temperature field along the welding path as the heat source moves along the circumference of the tubes.

Figure 2  One half of the finite element model used in the analyses

Figure 3 presents the temperature variation as a function of time, for the welding speed of 10 mm/s, for the points located on the same plane perpendicular to the tube axis but at different depth through the thickness.

Figure 4 shows the temperature variation as a function of time for the points located at the same depth through the thickness but at different distances normal to the welding plane for the welding speed of 10 mm/s.

Figure 5 shows the temperature variation as a function of time for a single point but for different welding speeds.

Figure 3 Time variation of temperature in the weld zone (10 mm/s speed of welding)

Figure 4 Time variation of temperature in the weld zone (10 mm/s speed of welding)

Figure 5 Time variation of temperature at a single point, for different welding speeds

Figure 6 depicts the snapshots of the temperature variation as well as the thermal stresses in the tubes resulting from the coupled thermo-mechanical analysis at different times during the pulse period. It can be seen that the lowest values of effective stress occur in the molten pool while the highest values of effective stress occur around the molten pool.

Figure 7 presents a comparison between the numerical and experimental results. The isothermal lines obtained using the finite element method are superimposed on a picture of the welded region. A reasonable agreement is reported for the lower parts of the welded region. However, there is a discrepancy between the results for the upper portion. The main reason for the difference is that the specimen has undergone a secondary heat treatment to smooth out the weld face but this secondary heat treatment was not modeled in the numerical analysis.

Figure 6  Temperature field and effective stress band plots for (a) half of the pulse duration (b) end of the pulse (c) end of the idle period between pulses

Figure 7  Comparison between the temperature fields obtained using the FEA and experimental data

This study shows some of the capabilities of ADINA for solving industrial problems involving strong coupling between the thermal field and the mechanical deformations. For more information, please refer to our page on thermo-mechanical coupling capabilities of ADINA.


  • P. Lacki, K. Adamus, "Numerical simulation of the electron beam welding process", Computers and Structures, 89:977–985, 2011.

Electron beam welding, thermo-mechanical coupling, residual stress, thermo elasto-plastic material, moving heat source

Courtesy of P. Lacki and K. Adamus (Czestochowa University of Technology, Poland)