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Physics Procedia 12 (2011) 431–439

www.elsevier.com/locate/procedia

LiM 2011

Analysis of Welding Zinc Coated Steel Sheets in Zero Gap Configuration by 3D Simulations and High Speed Imaging Holger Kocha,b*, Christian Kägelerb,c, Andreas Ottoa,b, Michael Schmidta,b,c a

b

University of Erlangen-Nürnberg, Chair of Photonic Technologies, Erlangen, 91052, Germany Erlangen Graduate School in Advanced Optical Technologies (SAOT) Erlangen, 91052, Germany c Bayerisches Laserzentrum GmbH, Erlangen, 91052, Germany

Abstract Welding of zinc coated sheets in zero gap configuration is of eminent interest for the automotive industry. This Laser welding process would enable the automotive industry to build auto bodies with a high durability in a plain manufacturing process. Today good welding results can only be achieved by expensive constructive procedures such as clamping devices to ensure a defined gad. The welding in zero gap configuration is a big challenge because of the vaporised zinc expelled from the interface between the two sheets. To find appropriate welding parameters for influencing the keyhole and melt pool dynamics, a three dimensional simulation and a high speed imaging system for laser keyhole welding have been developed. The obtained results help to understand the process of the melt pool perturbation caused by vaporised zinc. Keywords: Volume of Fluid; Laser Welding Simulation; Laser Keyhole Welding

1. Motivation / State of the Art For the automotive industry the laser beam welding of zinc coated steel sheets is of great economic importance. The corrosion protection of the car bodies can be significantly increased by the use of zinc coated steel sheets. To this day the laser beam welding process of zinc coated steel sheets is a challenge for a robust process control. The physical cause for the instabilities of the process lies in different melting and evaporation temperatures of zinc and steel. The dynamics of the welding process have been investigated by simulations and online monitoring systems. Present simulation models still use strong simplifications concerning the geometry or they concentrate on few specific physical effects. Thus, they do not describe the complex coupled physics including phase transitions, thermo and fluid dynamics and liquid-solid phase modelling of laser beam welding of zinc coated steel sheets. Within our present scientific work a complex multiphysical simulation model is being developed. The verification of the surface dynamics simulation in relation to the melt pool and the spatters can be done by high speed imaging.

* Corresponding author. Tel.: +49 9131 8523239; Fax: +49 9131 8523234 E-mail address: [email protected] 1875-3892 © 2011 Published by Elsevier Ltd. doi:10.1016/j.phpro.2011.03.153

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High speed imaging can further be used to gain a better understanding of the fluid dynamics of the melt pool and the spatter formation. 2. Simulation For the simulation OpenFOAM is used. This software is written in C++ and is based on the Finite Volume approach. To simulate the laser deep penetration welding process [1, 2 and 3] many coupled physical effects have to be considered. In a first step the governing physical effects have to be determined. The keyhole and melt pool dynamics strongly depend on the geometry and the heat flux of the melt pool (Fig. 1). The flow inside the melt pool and the energy dissipation inside the fluid and the solid phase are modelled as a system of coupled nonlinear partial differential equations. The flow characteristic of the molten steel is described as an incompressible fluid by the Navier-Stokes equation. The free surface of the molten steel is treated by the Volume of Fluid (VOF) method. The VOF method is a numerical approach for tracking and locating the free surface of the fluid-air interface [4]. Within the model the energy flux and the physics of the phase transformation are considered. The energy loss due to evaporating mass and the latent heat for melting and evaporation are calculated. Similar approaches are used in [5 and 6]. For the solution of the Navier-Stokes equation the PISO (Pressure Implicit with Splitting of Operators) scheme was used. The effects of the evaporating zinc layer are modelled by a gap of 50 μm between the two sheets. The pressure of the evaporating zinc in the gap is modelled by a given pressure at the boundary and initial conditions. Due to the transient temperature distribution the evaporation rate of the zinc coating and the pressure joining zone can only be estimated.

Figure 1: Schematic cross section of zinc coated steel sheets in overlap configuration

2.1 Governing Equations The presented simulation model was developed during the last years. The preceding simulation models are illustrated in [1, 2, 7, 8]. For the analysis of zinc coated steel sheets the laser is modelled by a Gaussian intensity distribution, given by Equ. (1):

QL

2 PL

Sw02



e

2( x 2  y 2 ) w0 2

(1)

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The energy is absorbed at the surface of the workpiece. At the melting temperature a phase transition takes place and at the boiling temperature the metal starts to evaporate and the formation of the keyhole begins. For modelling the energy absorption inside the keyhole a ray casting algorithm is used. The algorithm is based on an octal tree representation of the mesh. This leads to efficient and fast determination of the surface intersection with the rays. The absorption described by the Fresnel equation depends on the angle of incidence and the polarisation of the laser beam. The absorption coefficient for the intensity of the perpendicular polarised part of the laser beam is given by Equ. (2)

§ (n 2  k 2 )  cos 2 (D )  2n cos(D ) · ¸¸ AA (D ) 1  ¨¨ 2 2 2 © (n  k )  cos (D )  2n cos(D ) ¹

(2)

and for the parallel part is given by Equ. (3):

§ (n 2  k 2 ) cos 2 (D )  2n cos(D )  1 · ¸¸ A|| (D ) 1  ¨¨ 2 2 2 ( ) cos ( ) 2 cos( ) 1    n k D n D © ¹

(3)

In [9, 10 and 11] different formulations for the Fresnel absorption are given. The simplified equation of [7] for wavelengths over 0.5 μm is used. For the calculation of the absorption coefficient A0 is composed of the arithmetic average from A|| and AA :

A0 D

1  A|| (D )  AA (D ) 2

(4)

This proposal follows [12]. Modelling thermal processes involving phase changes needs to deal with free surfaces. To model the physical boundary conditions the position relative to the mesh has to be known. Mazumder et al. [13] used a Level Set approach. In the presented model the surface force is coupled by the forces resulting from the fluid dynamics by the VOF method. Further information about possible implementations can be found in [4, 13, 14 and 15]. For the solution of the Navier-Stokes equation the PISO scheme was used [14]. For the calculation of the fluid field for an incompressible medium the two governing equations are the mass conservation equation:

& wU  ’Uu wt

0

(5)

and the Navier-Stokes equation:

& & & wu  U u x ’u U wt

&  U ’p  K'u

(6)

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At the liquid-gas interface the atmospheric pressure p0, the vapour pressure pV and the pressure pL in the liquid interact with the surface tension caused by the curvature ț of the metal surface [16]:

 p0  pv  p L

2V N

(7)

The pressure pv emerging from evaporated steel [9] is given by the Equ. (8):

pv (T )

p0 e

'H § 1 1 · ¨  ¸ R ¨© Tv T ¸¹

(8)

The temperature field in the solid phase of the weld seam is calculated by the heat conduction Equ. (9):

U cL

§ w 2T w 2T w 2T wT  k ¨¨ 2  2  2 wt wy wz © wx

· ¸¸ Q T ¹

(9)

For the melt pool the convective heat transfer has to be taken into account. So the convection and conduction equation is used to determine the temperature field in the molten steel:

§ w 2T w 2T w 2T · wT  k ¨¨ 2  2  2 ¸¸ wz ¹ wy wt © wx § wT wT wT · ¸ v w QT  U cL ¨¨ u wy wz ¸¹ © wx

U cL

(10)

The laser power QT , which is absorbed at the surface, is determined by a ray casting algorithm. The latent heat due to the melting is simulated following the approaches in [17 and 18]. For the presented results the Enthalpy Method is used. The method can be easily extended to spatially multidimensional problems and the VOF method. The simulation model uses the approach of [19]. The enthalpy is calculated by:

h

­ cS T ® ¯ cLT  hM

for

T  Tm T ! Tm

(11)

The convective heat equation is than given by:

& & w ( U ˜ h)  U (’ ˜ (h ˜ u )  h ˜ ’ ˜ u )  ’ 2 (k ˜ T ) Q A wt

(12)

In [15] it was claimed that the formulation of treating the moving boundary with the enthalpy method performed better than the standard ¿nite difference representation but the computational cost was higher. In Fig. 2 the used adaptive mesh is pictured. The mesh is refined in regions of a strong temperature gradient, high

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velocities or at regions of phase transitions. The advantages of adaptive meshing are increased accuracy by high savings of the computation time. The temperature is indicated by colour. Blue corresponds to 300 K and red to 3100 K.

Figure 2: The process parameters for the simulation are: Ȝ = 1030 nm, PL = 3.6 kW, vo = 0.1 m/s, spot diameter 600 μm.

Table 1: Symbols and machining Parameters Physical property

symbol

unit

value 3

U

Kg/m

7860

cs / cL

J/(Kg K)

465

Thermal conductivity of steel

k

W/(m K)

67

Dynamic viscosity of molten steel

K

Ns/m2

5,5·10-3

Density of steel Specific heat of liquid and solid steel

Melting temperature of steel

TM

K

1893

Vaporization temperature

TV

K

3123

Surface tension coefficient

V

N/m

1.4

Laser power

PL

W

4200

Enthalpy of fusion

hM

kJ/kg

15,0

Heat of fusion

Hm

kJ/mol

13,8

Heat of vaporization

Hv

kJ/mol

340

nik

-

3.2 + i 4.6

w0

μm

200

m/s

0.1

Complex refraction index ( Ȝ = 1.064 μm) Focus radius Velocity vector

& u

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3. Experiments

For the experimental setup a Yb:Yag disc laser with an output of 3.6 kW and a wavelength of Ȝ = 1030 nm is used. The surface was illuminated by an additional light source. For this purpose a pulsed diode laser with the wavelength O = 890 nm was used. The combination of a pulsed illumination source and a synchronised high speed imaging system allows observation of the melt pool through the metal vapour (Fig. 3).

Figure 3: Overview of the system setup in the experiments.

The experimentally obtained data is transferred to a computer system. The computer system is able to control the laser source. The control of the laser power can be used to stabilise the welding process [15]. All the experiments are carried out using zinc-coated metal sheets as material. They consist of soft steel, galvanised with a zinc layer with a thickness of 10-15 μm [16]. 4. Results and Discussion

The pressure of the degassing zinc between the join partners is modelled by a pressure layer. The pressure is set to pG at the initial time step and at the boundaries as indicated in Fig. 4). In Fig. 5 the formation of the keyholes and the melt pool during laser beam deep penetration welding in overlap configuration can be seen. The colour of the simulation images on the left a), b) and c) indicates the temperature. Blue corresponds to 300 K and red to 3100 K. The feed direction points from the right to left. The comparison of the simulation with the high speed images shows a good agreement of the transient characteristics molten phase and the spatter formation. At the front of the keyhole oscillation can be observed. The effect of different pressure pG and laser power PL on the process can be seen in Fig. 6). In Fig. a) and b) the laser power PL is 3.9 kW and pG is 3 bar. In Fig. 6 a) after the upper join partner is penetrated the initiation of the influx inside the keyhole starts. The influx of the gas increases with the keyhole diameter. In Fig. c) and d) the laser power PL is 3.4 kW and pG is 4 bar. In Fig. 6 c) and e) the spatter formation is lower than in Fig. 6 a). This indicates that the laser power has a strong influence on the spatter formation at the process beginning. From Fig. 6 c) to d) a strong melt ejection develops during the course of the process. This strong melt ejection is driven by the pulse transmission of the gas influx. In Fig. 6 e) and f) the laser power PL is 3.4 kW and the pressure pG is decreased to 2 bar. Because of the comparable low laser power no spatter formation at the process beginning can be observed. The pressure in the pressure layer is too low to cause further spatters during the process progression. It emerges that the developed simulation model is a powerful tool to investigate the laser beam welding process, but to validate the simulation an elaborate imaging technique is needed, since qualitative attributes like spatter formation cannot be measured by other sensors.

Holger Koch et al. / Physics Procedia 12 (2011) 439–439

Figure 4: Modelling of the zinc layer by pressure layer with fixed boundary and initial conditions

d)

a)

v0 b)

t = 0.01 ms

e)

t = 1 ms

c)

f)

t = 1.5 ms Figure 5: Comparison of simulation and experiment. The process parameters for the simulation ( a), b) and c)) are: Ȝ = 1064 nm, PL = 3.6 kW, vo = 0.1 m/s, wo= 200 μm and width of zinc layer is 50 μm. The process parameters for the simulation ( d), e) and f)) are: Ȝ = 1030 nm, PL = 3.6 kW, vo = 0.1 m/s, spot diameter 600 μm.

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a) PL=3.9 kw pg=3 bar

b) PL=3.9 kw pg=3 bar

c) PL=3.4 kw pg=4 bar

d) PL=3.4 kw pg=4 bar

e) PL=3.4 kw pg=2 bar

f) PL=3.4 kw pg=2 bar

Figure 6: Comparison of varying simulation parameters: The constant process parameters for a) - f) are: Ȝ = 1064 nm, vo = 0.1 m/s, wo= 250 μm and width of zinc layer is 50 μm .

This paper gives an overview about a 3D simulation model for welding zinc coated steel sheets in overlap configuration. As far as the authors know it is the first time that a fluid dynamical model for welding of zinc coated steel sheets in overlap configuration was developed. The zinc coating was modelled by a pressure layer between the joint partners. This pressure layer was given through the boundary and initial conditions. For the simulation of the work piece a multiphysical approach was used. For a future simulation the indirect modelling of the zinc coating by a pressure layer should be brought forward to realistic material model of the zinc coating.

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Acknowledgements

The authors gratefully acknowledge the funding of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German National Science Foundation (DFG) in the frame work of the excellence initiative. The authors also acknowledge the support of the project “Fehlerfreies Laserstrahlschweißen verzinkter Stahlbleche durch frequenzmodulierte, resonante Anregung – FM-LaB“ by the BMBF. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]

Koch, H.; Leitz, K.-H.; Otto A.: A Three Dimensional Simulation of Laser Keyhole Welding, Proceedings of LANE 2007, Meisenbach Verlag, Bamberg, 2007, 251-260 Geiger, M.; Leitz K.-H.; Koch H.; Otto A.: A 3D Transient Model of Keyhole and Melt Pool Dynamics in Laser Beam Welding applied to the joining of zinc coated sheets. Production Engineering, Springer, (2009) Beyer, E. : Schweißen mit Laser. Grundlagen, Springer Berlin, (1995) Ferziger, J.; Peric, M.: Numerische Strömungsmechanik. Springer, Berlin, (2008) Ki, H.; Mohanty, P. S.; Mazumder, J.: Modelling of high-density laser-material interaction using fast level set method, Journal of Physics D: Applied Physics, 34 (2001) 364-372 Mackwood, A.P.; Crafer, R.C.: Thermal Modelling of laser welding and related processes: a literature review, In: Optics & Laser Technology 37 (2005) 99-115 Koch, H.; Leitz, K.-H.; Otto A.; Schmidt, M.: A Process Analysis of Laser Beam Welding Steel Sheets in Overlap Configuration by Using a 3D Transient Simulation Model, Proceedings of LiM 2009, AT-Fachverlag GmbH, Stuttgart, (2009), 777-782 Otto A.; Schmidt, M.: Towards a Universal Numerical Simulation Model for Laser Material Processing, Physics Procedia 5 (2010) 35–46 Dowden, J. M.: The Theory of Laser Material Processing, Wiesbaden, (2009) Hügel, H.; Graf, T.: Laser in der Fertigung, Vieweg+Teubner Verlag, Berlin, (1995) Prokhorov, A. M.: Laser Heating of Metals, Adam Hilger, Bristol, (1990) Wang, H; Shi, Y; Gong, S: Numerical simulation of laser keyhole welding processes based on control volume methods, In: Journal of Physics D: Applied Physics, 39 (2006) 4722-4730 Ki, H.; Mohanty, P.S.; Mazumder, J.: Modelling of high-density laser-material interaction using fast level set method, Journal of Physics D: Applied Physics, 34 (2001) 364-372 Brackbill, J.U.; Kothe, D.B.; Zemach, C.: A Continuum method for Modelling Surface Tension, In: Journal of Computational Physics 100 (1992) 335-354 Versteeg, H. K; Malalasekera, W: An Introduction to computational fluid dynamics-The Finite Volume Method, Pearson Education Limited, Harlow, (2006) Kägeler, C.; Grimm, A; Otto, A. , Schmidt, M.: Frequency-modulated zero-gap laser beam welding of zinc-coated steel sheets in an overlap joint configuration, Proceedings of LiM 2009 , AT-Fachverlag GmbH, Stuttgart, (2009),1-8 Mackwood, A.P.; Crafer, R.C.: Thermal Modelling of laser welding and related processes: a literature review, In: Optics & Laser Technology 37 (2005) 99-115 Hu, H.; Argyropoulos, S.: Mathematical modelling of solidi¿cation and melting: a review, Modelling Simul. Mater. Sci. Eng. 4 (1996) 371–396. Tacke, K.-H.: Discretization of the Explicit Enthalpy Method for Planar Phase Change, International Jouranl for Numercial Methods in Engineering, Vol. 21, 543- 554 (1985)