Numerical simulation of molten pool dynamics in high power disk laser welding

https://doi.org/10.1016/j.jmatprotec.2011.09.011Get rights and content

Abstract

A single-phase problem is solved rather than a multiphase problem for numerical simplicity: and the solution is based on the assumption that the region of gas or plasma can be treated as a void because solid or liquid steel has a greater density level than gas or plasma. The volume-of-fluid method, which can calculate the free surface shape of the keyhole, is used in conjunction with a ray-tracing algorithm to estimate the multiple reflections. Fresnel's reflection model is simplified by the Hagen–Rubens relation for handling a laser beam interaction with materials. Factors considered in the simulations include buoyancy force, Marangoni force and recoil pressure; furthermore, pore generation is simulated by means of an adiabatic bubble model, which can also lead to the phenomenon of a keyhole collapse. Models of the shear stress on the keyhole surface and of the heat transfer to the molten pool via a plasma plume are introduced in simulations of the weld pool dynamics. Analysis of the temperature profile characteristics of the weld bead and molten pool flow in the molten pool is based on the results of the numerical simulations. The simulation results are used to estimate the weld fusion zone shape; and the results of the simulated fusion zone formation are compared with the results of the experimental fusion zone formation and found to be in good agreement. The effects of laser beam profile (Gaussian vs. measured), vapor shear stress, vapor heat source and sulfur content on the molten pool behavior and fusion zone shape are analyzed.

Highlights

► This paper describes the modeling process of heat source and driving forces in disk laser welding to analyze the heat transfer and fluid flow in weld pool. ► Calculated fusion zone profile is in good agreement with the experimental result. ► The effects of laser beam profile (Gaussian vs. measured), vapor shear stress, vapor heat source and sulfur content are analyzed. ► The effects of beam profile, vapor shear stress and Marangoni flow by sulfur addition are insignificant. ► Vapor heat source has a profound effect on the upper part of the molten pool shape.

Introduction

The CO2 laser and the lamp pumped Nd:YAG laser have been commonly used in industrial welding applications for many years. High power welding is mainly realized with a CO2 laser but its 10.6 μm wavelength means it cannot be delivered via fiber-optic cable. The lamp pumped Nd:YAG laser is applied in various fields because it enables the beam to be delivered by fiber; however, it is limited to relatively low power welding and has the disadvantages of low efficiency and low beam quality due to problems with elevated temperatures, thermal lensing, and depolarization loss. Disk lasers have recently been commercialized; by using a diode-pumping method as well as a very thin disk (as the gain medium), disk lasers can achieve a high level of efficiency and a high beam quality at high power levels. Accordingly, besides being used for microprocessing, disk lasers can now be used as an alternative to CO2 lasers in multi-kilowatt applications for a thick plate range. In this case, Yb:YAG is used as the gain medium and the beam can therefore be delivered by fiber.

One of the goals of laser welding research is to determine optimal conditions by analyzing the effects of the welding conditions from the perspective of the process, metallurgy, and mechanics. The focus of such analysis should be the final weldment after cooling and the molten pool behavior during the welding process, like it is done for welding of zinc coated steels where a well-directed control of the process reduced the chaotic behavior (Schmidt et al., 2008). Also empirical methods like the Taguchi method can be used to optimize the laser welding process (Sathiya et al., 2010), but a high number of experiments is needed to get a deeper insight into the process characteristics. A better understanding of the latter could be helpful for determining the direct effect of driving forces on the molten pool under various welding conditions. Thus, the molten pool behavior is an important research topic. The related studies can be divided into experimental and numerical approaches. The experimental approach can be used to observe the molten pool flow and surface shape, though environmental limitations of the strong light and high temperature limit the availability of precise information. The X-ray transmission in situ observation method of the Joining and Welding Research Institute is the most developed way of observing the keyhole shape inside a molten pool (Seto et al., 2000). However, the application of this method is limited because the equipment is expensive and bulky. This paper is based on a numerical study because a numerical approach is favorable for comprehending how the driving forces affect the flow characteristics of a molten pool.

Rosenthal (1941) used a simple heat conduction model to estimate the fusion zone shape; and heat conduction simulations were conducted until the early 1980s. Numerical simulations of the molten pool flow began in the mid-1980s for arc welding and in the late 1980s for laser welding. In laser welding, the recoil pressure forms a unique keyhole, and estimating the keyhole shape is a major research topic. In the early stages of laser welding simulation, however, the focus was on the conduction mode of laser welding and the simulation was similar to that of arc welding (Zacharia et al., 1989). Depending on the aim of the simulation, the usage of a Goldak heat source can be sufficient in laser welding simulation, e.g. in determination of the residual stresses and distortion (Huan et al., 2011). For some special tasks, even more simplified models than FEM can be helpful, see e.g. (van der Aa et al., 2008). On the other hand, other defects like pores demand more detailed description of the keyhole. To estimate the laser keyhole shape, Kaplan (1994) used an energy balance equation with a simple multiple reflection model. Multiple reflections were considered in a conical shape with an average angle of the keyhole wall; thus, only rough predictions could be made of the keyhole shape. Since then various numerical techniques have been used to track the free surface so that the precise keyhole shape can be calculated. Ki et al. (2001) used a level-set method (Osher and Sethian, 1988) to calculate the free surface of the keyhole for the purpose of realizing the multiple reflections inside the calculated keyhole shape. Lee et al. (2002) used a volume-of-fluid (VOF) method (Hirt and Nichols, 1981) to understand the mechanism of keyhole instability. Cho and Na (2006) also used the VOF method in conjunction with a ray-tracing algorithm to calculate the keyhole shape and realize the real-time multiple reflections. The same algorithm was used to estimate the results of the drilling process vis-à-vis the polarization of the laser beam (Cho and Na, 2007) as well as the results of laser-arc hybrid welding (Cho and Na, 2009). In addition, a laser model based on the optical geometry of a laser system and the theoretical laser- and material-dependent value which affects the reflectivity in the simplified Fresnel's reflection model was recently used in simulations of the laser-arc hybrid welding process (Cho et al., 2010).

In welding simulations, it is important to formulate reliable models based on actual welding phenomena. However, practical welding involves complex multi-physical phenomena, such as heat transfer, diffusion and electromagnetism, as well as solid, liquid, gas, and plasma phases. Thus, researchers have attempted to simplify the physical phenomena of welding through various assumptions.

This paper features a three-dimensional simulation of molten pool dynamics in multi-kilowatt disk laser welding. Molten metal is assumed to be an incompressible laminar fluid with Newtonian viscosity. The simulation considers the buoyancy force, the Marangoni force, the recoil pressure, the vapor-induced shear stress, and the vapor-induced heat transfer, and an adiabatic bubble model is used to simulate pore generation with a keyhole collapse. The effects of laser beam profile (Gaussian vs. measured), vapor shear stress, vapor heat source and sulfur content are analyzed.

Section snippets

Governing equations

For analysis of the heat transfer and fluid flow in relation to the tracking free surface in the weld, solutions are found for the governing equations of mass conservation, momentum conservation (Navier–Stokes), energy conservation and the VOF. In the simulation, the molten metal is assumed to be an incompressible laminar flow with Newtonian viscosity.

With these assumptions, the governing equations can be expressed in Cartesian coordinates as follows:

Mass conservation equation:v=0where v is

Results and discussion

Structural carbon steel (namely A36 (ASTM) or SS400 (JIS)) with a thickness of 12 mm is used in both the simulation and the experiment. The thermophysical material properties of the steel are listed in Table 2; the temperature-dependent properties are used for thermal conductivity (Cho et al., 2006). Fig. 7 shows a schematic of the simulation domain: the center domain (set at 36 mm in length, 6 mm in width, and 15.2 mm in height) is equally divided into fine cells, and the other domains are divided

Conclusions

The results of this work can be summarized as follows:

The simulation results of the fusion zone profile are in good agreement with the experimental results.

The upper part of the molten pool is extended in the opposite welding direction because hot molten metal is supplied to the rear upper part of the molten pool by the flow pattern of a clockwise vortex.

A cross section of the keyhole shows that the keyhole is widest at the top, narrow at the middle, but wide again at the bottom. Accordingly,

Acknowledgements

The authors gratefully acknowledge the support of the Brain Korea 21 project and the grant (No. 2010-0027749) from the National Research Foundation of Korea, which is funded by the Korean Ministry of Education, Science and Technology. They also gratefully acknowledge the support of the Alexander von Humboldt Foundation for the laser welding experiments at BIAS, University of Bremen. The authors are grateful to Mr. Stefan Gruenenwald from BIAS for conducting the experiments.

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