International Research Journal of Applied and Basic Sciences. Vol., 3 (8), 1624-1630, 2012 Available online at http:// www. irjabs.com ISSN 2251-838X 2012 Numerical simulation of weld pool shape during laser beam welding R.Daneshkhah 1, *, M.Najafi 1, H.Torabian 2 1- Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran 2- Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran *Corresponding Author Email: patientman2004@gmail.com Abstract A three-dimensional transient numerical model was developed to study the temperature field and molten pool shape during continuous laser keyhole welding. The volume-of-fluid (VOF) method was employed to track free surfaces. Melting and evaporation enthalpy, recoil pressure, surface tension, and energy loss due to evaporating materials were considered in this model. The enthalpy-porosity technique was employed to account for the latent heat during melting and solidification. Temperature fields and weld pool shape were calculated using FLUENT software. The calculated weld dimensions agreed reasonable well with the experimental results. The effectiveness of the developed computational procedure had been confirmed. Keywords: Energy, Laser, Simulation, Pool Shape Introduction Laser keyhole welding is widely used as machine tool to modify the surface of the engineering materials due to the high welding speed, high aspect ratio, and narrow heat affected zone (HAZ). During keyhole laser welding, when a laser beam with high intensity irradiates the surface, a keyhole is formed in the work piece. Since the early days of laser welding, much work had been carried out in order to understand the temperature field and molten pool behavior. Swift-Hook and Gick (Swift-Hook and Gick, 1973) formulated a model of keyhole mode of laser welding by treating the laser beam as a moving line source. Andrews and Atthey (Andrews and Atthey, 1976) extensively investigated three-dimensional convective flow in the weld pool. Mazumder and Steen (1980) developed a heat transfer model for a moving Gaussian heat source using the finite difference technique. Dowden et al. (Dowden et al., 1987) assumed a slim cylindrical keyhole of known radius in a molten pool that was almost cylindrical but not concentric to the keyhole due to the movement of the beam. Kross et al. (1993) developed a keyhole model that could predict the shape, position, and size of the keyhole based on the process parameters and the material properties used. Metzbower (1993) calculated the temperature distribution across the surface of the liquid and the keyhole considering laser power loss due to evaporation. Kaplan (1994) considered asymmetry of the keyhole by considering the different rates of heat transfer at different regions of the keyhole. Ki et al. (2002) described the keyhole by the level set method (Osher and Fedkiw, 2001) and showed an increase in the total laser absorptivity for both laser drilling and welding. Lee et al. (2002) showed the keyhole simulation in stationary laser welding with the VOF method (Hirt and Nichols, 1981). The Gaussian distribution of the laser beam, applied only on the top surface, is not adequate to describe this phenomenon. To overcome this limitation, a Gaussian rod type volumetric heat source was proposed a modified rotary Gaussian volumetric heat source and a Gaussian volumetric heat source was considered (Wang et al., 2006). Despite the investigations referenced above, a three-dimensional transient model for continuous keyhole welding that includes the simulation of temperature field, pressure balance, melt flow, free surface, and moving heat source based on volume heat source model has not yet been found. Our aim in this study is to simulate temperature field and continuous laser keyhole welding process using the presented model by
FLUENT software. Mathematical model The processing of a stainless steel sheet, sized 5 3 1 mm, was considered in this work. The heat source was located at point (0, 0, 0), and the material moved with a velocity of 0.05 m/s along the positive x- axis. Schematic representation of the geometry is shown in Fig. 1. In building the model, the basic assumptions were as follows: (1) The temperature of the work piece is initially at 300 K. (2) The flow pattern of weld pool is a laminar flow and incompressible. (3) The properties of the liquid metal are constant and independent of temperature. (4) A Boussinesq assumption is used. Figure1. Schematic representation of the geometry. Heat source model The most commonly used heat sources of this kind have a Gaussian distribution. Goldak et al. (1984) proposed a volumetric heat source. To simulate a realistic transfer of the energy to the workpiece, the volumetric heat source model was used. This heat source (Abderrazaket al., 2009) used in this present study can be expressed as Where P is the total power of laser beam. The parameters a and b are taken to be equal to the focal radius the laser beam, d is the max depth. Governing equations Complicated phenomena such as phase transition, heat and mass transfer, fluid flow, etc. were modeled mathematically and then we should establish the numerical simulation technique that could treat those complicated phenomena simultaneously. In the case of multi-phase fluids, governing equations (Fujii et al., 2000) were composed of the conservation of mass, conservation of momentum, conservation of energy, and a volume fraction function (Hirt and Nichols, 1981): (2) (1)
(3) (4) (5) (6) Where E, F sa,, F re,, Q, p,, T, t,,, and are internal energy, surface tension, recoil pressure, gravitional acceleration, heat flux, pressure, velocity, temperature, time, volume fraction function, thermal conductivity, kinematic viscosity, and density,respectively. The last term of the momentum equation represents the resistance to the liquid flow through the mushy region. It is in the form of a Darcy-like resistant source, and tends to zero as liquid volume fraction in its end. Permeability K is the related to the liquid volume fraction via the Kozeny Carman (1991) equation (Abderrazak et al., 2009). 2.3. Boundary conditions Boundary conditions employed in this study are as follows: 1) At top free surface inside the keyhole: The temperature- dependent Margoni shear stress on the free surface in the direction tangential to the surface is given by Fan et al. (2001): Where is the surface tension, which varies linearly according to the temperature. It is modeled using the following relationship (Zacharia et al., 1989): Where is the surface tension at melting temperature and the surface tension gradient. (2) In the solid region, u w is the velocity of work piece along the positive x-axis. (3) Along the longitudinal section plane of symmetry (y=0), the boundary conditions for the velocity components were defined as (7) (8) ) (9) (10) (11) Results and discussion The base metal was assumed to be Type 304 stainless steel. The values of the material properties (Zhou and Tsai, 2007) used in this study are shown in Table 1. The following welding conditions were assumed in the model: laser power is 2500 W, the radius at focus was 200 m, and the volumetric heat source was used in this study. In Fig. 2a h simulation results of the continuous laser deep penetration welding process can be seen. Part of the absorbed energy is being used to melt the metal and part of it is being conducted into the solid base metal. Heat conduction is the major mode of heat transfer in the initial stage. In the intermediate stage, the metal melts up and the recoil pressure leads to a deformation of the free surface of the weld pool.
Table1. The material physical properties and process parameters (Zhou and Tsai, 2007). Material Properties Value Specific heat of liquid phase, C (J kg -1 K -1 ) 780 Specific heat of plasma, C pl (J kg -1 K -1 ) 49.0 Latent heat of fusion, H(j kg -1 ) 2.47 10 5 Latent heat of vaporization, H v (j kg -1 ) 6.34 10 6 Thermal conductivity of liquid phase, k l (W m -1 K - 1 ) Thermal conductivity of plasma, k pl (W m -1 K -1 ) 3.74 Density of liquid phase, l(kg m -3 ) 6900 Density of plasma, pl(kg m -3 ) 0.06 Dynamic viscosity,!(kg m -1 s -1 ) 0.006 Solidus temperature, T s (K) 1670 Liquidus temperature, T m (K) 1727 Boiling temperature, T " (K) 3200 Thermal expansivity,#(k -1 ) 4.95 10-5 Surface tension at T m, $ m (N m -1 ) 1.2 Surface tension gradient,a $ (N m -1 K -1 ) -0.43 10-3 22 During continuous laser deep penetration welding, a keyhole is generated and maintains the balance between surface tension and the recoil pressure boundary condition. When time is greater than 2.0 ms the melt pool has reached about one third of the depth of the sheet. The recoil pressure thrusts away the molten metal under the laser beam and the surface of the melt pool gets curved. After 5.0 ms the weld pool has already reached about half the depth of the workpiece. Owing to liquid melt flowing down the keyhole, hot liquid melt is transported to the end of the keyhole. This is in line with the experimental observations (Semak et al., 1999). The melt pool growth further and further and finally reaches a length of about 2.0 mm. During continuous laser deep penetration welding process the length of the weld pool in the upper part is bigger than in the lower part. Finally the melt pool size stabilizes and the back wall surface becomes steep (Geiger et al., 2009). In Fig. 2 it is shown that the temperature at laser beam center is much higher than the rest of the workpiece. The large temperature gradients occur in the front vicinity of the keyhole. Verification of the mathematical modeling was carried out by comparing the simulation results to the experimental data. The experiment was performed with 2500 W laser power and 0.05 m/s welding speed parameters. Fig. 3 shows weld pool profile at cross section. The geometry of the pool was measured by recording the depth and width of penetration, is shown in Table 2. From Fig. 3, it can be seen that the shape is somewhat different: the fusion line turns gradually to left, but prediction gives upward direction. The somewhat difference between the model prediction and experimental results may be due to the different of the input values of parameters (laser power, welding speed, welding time, etc.). Overall, the weld bead geometry predicted by the model agrees well with that from the experiment.
Figure 2. Continuous laser keyhole welding process. Figure 3. Comparison of weld shape by experiment with that by calculation. Table 2. The comparison between simulative size and measured size. Depth of penetration(h/mm) Width of penetration(b/mm) Measured Value 0.84 0.86 Simulative Value 0.83 0.82
Conclusions In this study, a three-dimensional transient model for simulating continuous laser keyhole welding process of 304 stainless steel sheet has been developed. Good agreement has been found between the numerical simulation and experimental data. The results clearly demonstrate the simulation model is useful for predicting heat and mass transfer and melt flow during continuous laser deep penetration welding. According to the simulated and experimental results, the main conclusions can be summarized as follows: (1) According to the simulated results, the large temperature gradients occur in the front vicinity of the keyhole. (2) The recoil pressure plays a key role in the keyhole formation, which pushes down the liquid in the weld pool and acts as the main driving force for the keyhole formation. (3) The 3D numerical model predicts well the transient temperature distribution and molten pool formation, which are in good agreement with the experiment results. Acknowledgements The authors acknowledge the support of Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran. References Abderrazak K, Bannour S, Mhiri H, Lepalec G, Autric M. 2009. Numerical and experimental study of molten pool formation during continuous laser welding of AZ91 magnesium alloy. Comput Mater Sci 44:858 66. Abderrazak K, Kriaa W, Salem WB, Mhiri H, Lepalec G, Autric M. 2009. Numerical and experimental studies of molten pool formation during an interaction of a pulse laser (Nd:YAG) with a magnesium alloy. Optics Laser Technol 41:470 80. Andrews JG, Atthey DR. 1976. Hydrodynamic limit to penetration of a material by a high-power beam. J Phys D. 9:2181 94. Chang WS, Na SJ. 2002. A study on the prediction of the laser weld shape with varying heat source equations and the thermal distortion of a small structure in micro- joining. Matter Process Technol 120:208 14. Dowden J, Postacioglu N, Davis M, Kapadia P. 1987. A keyhole model in penetration welding with a laser. J Phys D. 20:36 44. Fan HG, Tsai HL, Na SJ. 2001. Heat transfer and fluid flow in a partially or fully penetrated weld pool in gas tungsten arc welding. Int J Heat Mass Transfer 44:417 28. Frewin MR, Scocc DA. 1991. Finite element mode of pulsed laser welding. Welding Res 78(Suppl):15 22. Fujii S, Takahashi N, Sakai S, Nakabayashi T, Muro M. 2000. Development of 2D simulation model for laser welding. In: Proceedings of the SPIE, vol. 3888. Geiger M, Leitz KH, Koch HA. 2009. 3D transient model of keyhole and melt pool dynamics in laser beam welding applied to the joining of zinc coated sheets. Prod Eng Res Dev 3:127-36. Goldak J, Chakravarti A, Bibby M. 1984. A new finite element model for welding heat sources. Metall Trans B 15:299 305. Hirt CW, Nichols BD. 1981. Volume of fluid method for the dynamics of free boundaries. J Comput Phys 39:201 25. Kaplan A.1994. A model of deep penetration laser welding based on calculation of the keyhole profile. J Phys D 27:1805 14. Ki H, Mohanty PS, Mazumder J. 2002. Modelling of laser keyhole welding: Part I. Mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections and free surface evolution. Metall Mater Trans A 33: 1817 30. Ki H, Mohanty PS, Mazumder J. 2002. Modelling of laser keyhole welding: Part II. Simulation of keyhole evolution, velocity, temperature profile, and experi- mental verification. Metall Mater Trans A 33:1831 42. Kross J, Gratzke U, Simon G. 1993. Towards a self-consistent model of the keyhole in penetration laser beam welding. J Phys D 26:474 80. Lee JY, Ko SH, Farson DF, Yoo CD. 2002. Mechanism of keyhole formation and stability in stationary laser welding. J Phys D 35:1570 6. Mazumder J, Steen WM. 1980. Heat transfer model for CW laser material processing. J Appl Phys. 51:941-7 Metzbower EA. 1993. Keyhole formation. Metall Trans B 24:875 80.
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