The first image was taken at 1.75ms after the beam impinged on the material, and then others were taken every 0.22ms. This is the first keyhole formed during the weld. There is no pore at the bottom of the keyhole in the first image. The keyhole was collapsed in the second image, and a pore was trapped at the bottom of the keyhole after 0.22ms since the complete keyhole formed. This was the first pore seen since the laser beam impinged on the edge of the sample. In the third image the pore suddenly disappeared because the continuous laser beam broke through the bridge and reopened the keyhole. The keyhole diameter increased and did not collapse in the fourth image. The keyhole was still in a stable state.

In the fifth image the protrusion appeared on the wall of the keyhole. Simulation results of shown later that the protrusion forms because of the collision the flow of the molten metals due to the recoil pressure acting upward and the surface tension acting downward. The protrusions on the keyhole walls were obviously growing toward the center of the keyhole and were almost connected each other. This is the beginning point of the keyhole collapse. Finally, the bridge was completely built and the pore was trapped at the bottom of the keyhole in the sixth image.

The complete keyhole was found 1.75ms after the laser beam impinged on the plain carbon steel. After 1.97ms, the first keyhole collapse was observed and then the keyhole reopened by the continuous laser beam irradiation after 0.22ms. The period of the periodical collapse time is about 0.88ms.

The surface profile, flow velocities and temperature distributions corresponding to a 500W laser power are shown in Figure 4. The recoil pressure is significantly higher and keyhole exists at a time of 10ms. Simulation results between 10 and 13ms show molten metal oscillating upward and downward along the keyhole wall, a mode which contributes to the keyhole instability. Upward flow from the bottom of the keyhole, caused by the high recoil pressure at that location, delivers heat and molten material to the periphery. The surface profile at the periphery becomes a convex (e.g. at 13ms), increasing the inward pressure due to surface tension. This pressure induces a downward flow, opposite to that induced by recoil pressure. As the opposing flows collide at 13.2ms, an inward protrusion is formed near z = 0.1mm. This protrusion becomes unstable, since the smaller keyhole radius at that location increases the inward radial component of surface tension pressure. Hence, the protruding liquid is accelerated inward and the keyhole collapsed shortly after 13.2 ms.

The keyhole profile from the simulation at 13.2ms is similar to the keyhole shape from the x-ray experiment at the fifth image in Figure3. Also, it takes 0.2ms for the keyhole to collapse since the protrusion is generated in both cases, which are the x-ray videography experiment and the simulation.

Figure 4: Surface profiles, temperature, and flow pattern for 500W laser

That the cylindrical keyhole geometry is prone to instability of this type is not surprising. Conceptually, the dynamics of the keyhole configuration are related to that of a submerged gas jet in a liquid, first analyzed by Rayleigh.' In that work, it was found that the cylindrical jet was unstable when the wavelength of a varicose perturbation was greater than its circumference. The maximum exponent, q, of the rate of increase in the amplitude of a varicose perturbation e" was calculated as

where a is the radius of the jet, y is the surface tension, and p is the density of the steel. For the simulated keyholes, this amounts to the time constant of about 1.8x10 s. This growth rate compares well to the time elapsed from protrusion formation to keyhole collapse in both the 500W keyhole simulations and the direct x-ray keyhole observation experiment of the 500W laser weld.

CONCLUSION

The direct observation of the keyhole dynamics by the x-ray transmission imaging system showed the dynamic behavior of keyholes generated with a 500W CO2 laser beam. The keyhole formation was monitored and instability of the keyhole was observed by the analysis of images. Additionally the dynamic behavior of the keyhole was simulated and it was compared to the experimental results. Surface tension caused growth of protrusions on the keyhole wall. This caused instability of the keyhole and led to the collapse of the keyhole. In both cases the time for the complete collapse of keyhole when the protrusion appeared was about 0.2ms. This number shows reasonable correlation between the experiment and the simulation.

REFERENCE

1. Welding Handbook, Eighth Edition, Vol. 2. Miami: American Welding society, 1991:723725.

2. Shigeki Fujinaga, Hiroo Takenaka, Toru Narikiyo, Seiji Katayama and Akira Matsunawa. Direct observation of keyhole behaviour during pulse modulated high-power Nd:YAG laser irradiation. J. Phys. D: Appl. Phys. 33 492-497.: November 1999.

3. Akira Matsunawa, Jong-Do Kim, Naoki Seto, Masami Mizutani and Seiji Katayama. Porosity Formation and Solidification Cracking in Laser Welding. Taiwan International Welding Conference.: September 1998.

4. Milewski J O and Barbe M B 1999 Modeling and analysis of laser melting within a narrow groove welding Welding J. 78 109-115s

5. Hirt C W and Nichols B D 1981 Volume of fluid (VOF) method for the dynamics of free boundaries J. of Computational Phys. 39 201-225

6. von Allmen M and Blatter M 1995 Laser-beam interactions with materials 2nd ed (Springer) 7. Ko S H, Choi S K and Yoo C D 2001 Effects of surface depression on pool convection and geometry in stationary GTAW Welding J. 80 39-45s

8. Fan H G and Kovacevic R 1999 Keyhole formation and collapse in plasma arc welding J. Phys. D: Appl. Phys. 32 2902-2909

9. Rayleigh J WS 1892 "On the stability of cylindrical fluid surfaces", Phil. Mag. s.5 v.34 177180.

FINITE ELEMENT MODELLING ON WELDING PROCESSES AND

WELDING PHENOMENA

B. Palotas*

ABSTRACT

The Finite Element Modelling is a wide applicable method in the field of welding as well. The paper shows application examples of modelling of resistance welding processes, modelling of cold pressure welding and some possibilities of FEM application.

The results of FEM can be used in the field of Computer Aided Process Planning applied in the field of welding processes.

The application of Finite Element Modelling helps to understand the welding processes, the welding phenomena and it is an effective tool of Welding Specialists and Researchers in our time.

KEYWORDS

Welding, Computer Aided Welding, Modelling of Welding, Finite Element Modelling

INTRODUCTION

The Welding Engineer is often faced with the task of developing a welding technology, after he has first selected the welding procedure in accordance with the prescribed characteristics and the geometrical requirements of the weld. Then it is necessary to calculate the course of the welding process, the criteria for optimisation being the weld form, the quality stability and the weldability of the material under pre-established physical, technical and economical conditions. The physical processes should be described by natural laws, such as the conservation, transmission and conversation of energy. The technical and economic conditions, on the other hand, such as time, output and cost can be influenced. They therefore form the basis for the optimisation problem. This complicated problem can be solved theoretically or empirically. Less and less time available for project planning tasks makes it increasingly necessary to avoid empirical test methods and to search for more effective methods of studying and developing welding technologies. Automated preparation of the technological data increases the labour productivity of the engineer, but basically does not change the quality of the design work. This is due to the fact that the welding parameters are prescribed on the basis of empirical information.

Associate Professor, Department of Materials Science and Engineering, Budapest University of Technology and Economics, Bertalan L. u. 7. Budapest, H-1111, Hungary, Tel: +36 (1) 463 1115, e-mail: palotasb@eik.bme.hu

The quality of the design work can, however, be improved considerably using the theory of welding process in the form of certain mathematical models. These models should as far as possible contain complete information about the process to be calculated. It would be advantageous to create universal models for the form of the welds and the weld defects. The software for the mathematical model is only produced once and can be rendered more precise as knowledge of the process to be studied increases (Ref. 1.).

MATHEMATICAL MODELLING OF WELDING PHENOMENA

The welding phenomena should be written by differential equations given in the Table 1. on the basis of (Ref. 2.). The general solution of these equations can be given by Gauss-Ostrogradsky's theorem:

where q is a flow through a Σ surface (flux of q) when its source is written with its divergent (div) in V volume bordered by Σ surface. The equation (1) can be used for analysis of phenomena occurring in solid, liquid, solid-liquid and gas agent during welding.

Unfortunately, the analytical solution of equations (Tab.1.) is very difficult and it requires a lot of neglect and we have to know all the processes occurring during welding. Of course all the processes are not known that occur during welding and negligence lead to information losses.