About the influence of a steady magnetic field on weld pool dynamics in partial penetration high power laser beam welding of thick aluminium parts

International Journal of Heat and Mass Transfer 60 (2013) 309–321

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About the influence of a steady magnetic field on weld pool dynamics in partial penetration high power laser beam welding of thick aluminium parts Marcel Bachmann ⇑, Vjaceslav Avilov, Andrey Gumenyuk, Michael Rethmeier BAM Federal Institute for Materials Research and Testing, Unter den Eichen 87, 12205 Berlin, Germany

a r t i c l e

i n f o

Article history: Received 17 October 2012 Received in revised form 10 December 2012 Accepted 9 January 2013 Available online 4 February 2013 Keywords: Electromagnetic weld pool control Hartmann effect Laser beam welding Lorentz force Marangoni flow Natural convection

a b s t r a c t A multi-physics numerical model was developed to investigate the influence of a steady magnetic field aligned perpendicular to the welding direction during partial penetration high power laser beam welding of aluminium in downhand position. Three-dimensional heat transfer, fluid dynamics including phase transition and electromagnetic field partial differential equations were successfully solved with the finite element differential equation solver COMSOL Multiphysics 4.2. The implemented material model used temperature-dependent properties up to evaporation temperature. Marangoni convection in the surface region of the weld pool, natural convection due to the gravitational field and latent heat of solid–liquid phase transition were taken into account. Solidification was modelled by the Carman–Kozeny equation for porous media morphology. The flow pattern in the melt as well as the weld bead geometry were significantly changed by the induced Lorentz force distribution in the liquid metal. It reveals that the application of a steady magnetic field to laser beam welding with corresponding Hartmann numbers Ha2  104 allows for a suppression of the characteristic wineglass-shape of the weld cross section caused by thermocapillary flow. The numerical results are in good agreement with experimental results obtained with welding of AlMg3 with a 16 kW disc laser. The steady magnetic field was delivered by permanent magnets mounted on both lateral sides of the weld specimen. The maximum magnetic flux density was around 500 mT. It shows, that the applied magnetic field has a predominant dissipating effect on the weld pool dynamics independently of its polarity. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction The development of modern laser systems for welding applications with output powers of up to 20 kW for CO2 and 50 kW for fibre lasers lead to the fact that the deep penetration welding found its way into a lot of industrial applications. Thick aluminium alloy plates to be welded are widespread in aerospace industry, shipyards and also for the construction of large vessels for the energy and food industry. The advantages of laser beam welding are obvious as there are the high quality of the welds at a high welding speed and its low heat input leading to less distortions of the workpiece compared to traditional arc welding methods [1]. The laser beam intensity is beyond the threshold to enforce the so-called keyhole mode welding, where a vapour-filled cavity develops by the evaporation of metal melt. The metal parts in thick-plate welding applications are very large and thus sometimes cannot be welded with the electron beam as that would require technical vacuum. ⇑ Corresponding author. Tel.: +49 3081042756. E-mail address: [email protected] (M. Bachmann). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.01.015

Nowadays, disc solid state and Yb fibre lasers are available. Their wavelength of around 1 lm is ten times shorter compared to CO2 lasers whose higher wavelength is the limiting factor for deep penetration welding processes above 20 mm due to intensive scattering and absorption of the laser light by the welding plasma plum and the plasma in the keyhole. In the case of laser systems with a wavelength of around 1 lm the interaction of the beam with the plasma plume is very low and a larger penetration into the material can be reached. It was shown, that full-penetration welding of 30 mm AlMg3 plates is possible with 15 kW laser power at relatively low welding speed to reach the desired penetration [2]. The heat conductivity of aluminium especially in its liquid state is very high. This leads to comparatively large weld bead widths in particular near the surfaces where thermocapillary (Marangoni) convection is the dominating driving mechanism for convective motions. A further consequence of that behaviour is the typical wineglass-shape of the weld cross sections. The strong curvature of the weld bead ends up in an inhomogeneous solidification front leading to heavy stresses in the workpiece and as a consequence in large bending and buckling distortions or residual stresses after cooling. That well-known characteristic [3] is of importance

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Nomenclature A B c1 c2 C eff p E fL FL F g Hf Ha2 j k L n Pk PL p t

T u x, y, z

magnetic vector potential magnetic flux density large computational constant small computational constant effective heat capacity electric field liquid fraction Lorentz force hydrodynamic volume force gravitational acceleration latent heat amount Hartmann number current density turbulent kinetic energy characteristic length (half width of the weld pool) normal vector turbulence production term laser power hydrodynamic pressure time

Greek symbols surface tension = @ c/@T surface tension coefficient turbulent dissipation rate dynamic viscosity k heat conductivity l0 permeability of vacuum lr relative magnetic permeability q mass density qel electrical resistivity r electric conductivity

c c0 e g

Sub- and evap liq, sol melt

especially for high penetration depths of the laser source associated to high power deep penetration welding. Another issue is the low viscosity of the aluminium melt which can promote highly dynamical processes near the surfaces leading to an unstable weld surface come along with strong spattering and the ejection of melt [4], see Fig. 1(a). For weld bead half widths of around 10 mm which are common for the welding of large aluminium alloy parts it shows that the Marangoni effect which occurs in a surface-near region becomes dominant. Additionally, natural convection in the melt due to the thermal expansion of the material when exposed to high temperature differences also plays an important role especially in deep regions of the weld pool. Both together can lead to an unstable behaviour of the weld pool surface. It is well-known that the application of magnetic fields in presence of electrically conducting liquids can have a significant effect on the dynamics of the flow behaviour [5]. The movement of such a fluid perpendicular to a magnetic field induces an electric current density

ju  ru  B:

ð1Þ

The induced electric currents interact with the externally applied magnetic field and a Lorentz force distribution arises that is directed against the fluid flow. Hence, a dissipating effect appears, see Fig. 1(b). In this paper the influence of the deceleration of the liquid metal dynamics in laser beam welding of aluminium by a steady magnetic field perpendicular to the processing direction (Hartmann effect) is investigated. This configuration works with permanent magnets without externally applied electric current. That means that no sliding contacts are necessary which is preferable for the welding of aluminium with a thick oxide layer and also for complex geometries. Permanent magnetic fields unlike ac magnetic fields can only generate a decelerating force following the second law of thermodynamics. A measure for the relative strength of magnetically induced and viscous drag gives the Hartmann number Ha2

Ha2 ¼

ðjBjLÞ2 r

g

;

temperature fluid velocity spatial coordinates

ð2Þ

where B is the magnetic flux density and r the electric conductivity. The Hartmann number for increasing weld bead widths is shown in

superscripts evaporation liquidus, solidus melting

Fig. 2 for a magnetic flux density of 0.5 T. The high values of Ha2 mean that the drag component due to electromagnetic braking is much larger than the viscous component. The application of steady, travelling and oscillatory magnetic fields is a common practice in many industrial processes (continuous casting, crystal growth, electrolysis) to obtain various aims, e.g. grain refinement, stabilization or even destabilization of liquid surfaces, acceleration or braking the flow of electrically-conducting fluids [6]. In welding, electromagnetically stirring metal melts by oscillating magnetic fields to obtain a homogeneous dilution in the weld pool [7,8] is well-known. Electromagnetic forces in the weld pool were also used to suppress the evolution of excessive porosity in the weld [9]. It was also shown, that oscillating electromagnetic fields can excess a magnetic pressure on the weld bead counteracting gravitational forces in downhand position [2,10,11]. Here, a suppression of the typical wineglass-shape was observed at the root surface within the penetration depth of the applied fields for aluminium. Although the Hartmann coefficient Ha2 in [2,11] was around 500 in the melt pool based on the effective magnetic flux value meaning that a notably effect of the electromagnetic influence was expected, computer simulations showed that strong convective motions in the weld pool could not be suppressed. An overview of different electromagnetic applications in arc and laser beam welding is presented in [12]. The importance of the Hartmann effect in further applications can be seen from [13,14]. The influence of a 200 mT steady magnetic field coaxially to the laser beam was studied in [15] for the welding of pure aluminium with a penetration of the keyhole into the material of around 5 mm. A notably effect in terms of reducing the weld pool dimensions and also a damping of the original melt flow was reported independently of the direction of the applied magnetic field. One of the first attempts to use the Hartmann effect in laser beam welding applications were experimentally conducted in [16] with a CO2 laser. A distinct smoothing of the weld seam for the welding of an aluminium alloy was reported for a weld half width of around 1 mm and a steady magnetic field of 40 mT with corresponding Hartmann numbers Ha2  100. However, a dependence of the polarity of the magnetic fields was observed which

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(a)

311

(b)

Fig. 1. (a) Sketch of the half-model of the partial penetration welding process influenced by permanent magnetic fields on both sides of the workpiece and (b) mechanism of induced Lorentz forces acting against the melt velocity.

Experiments were conducted for the welding of AlMg3 with a 16 kW disc laser leading to typical weld bead half widths of 10 mm. In contrast to the experiments in [16], the use of a disc laser eliminates the source of thermoelectric currents in the workpiece due to the CO2 laser-induced plasma. Furthermore, comparatively high magnetic fields of around 500 mT were used. Therefore, the Hartmann number becomes very large and dominates over all other effects in the weld pool, see Fig. 2. It is expected for high power disc laser beam welding, that the application of a steady magnetic field reduces the dynamics in the weld pool in terms of reduced weld pool extents and a smoother surface of the weld. This hypothesis is sketched in Fig. 3. 2. Mathematical modelling 2.1. Governing equations

Fig. 2. Dimensionless Hartmann number for aluminum for increasing half width L of the weld bead and a magnetic flux density of 0.5 T.

was explained by a net electric current flowing towards the weld pool end due to thermoelectric effects between cold base material and the liquid metal. As that current does not depend on the direction of the imposed magnetic field, it was reported to be the reason for the different effects according to the polarity of the magnetic field. Later, results of the same group showed that thermoelectric currents in the workpiece existed due to its interaction with the laser plume [17]. In this publication, it was found that this effect only exists for CO2 lasers with 10.6 lm wavelength whereas no electric current was measured for Nd:YAG lasers with 1.06 lm wavelength. That means that the influence of the Hartmann effect on laser deep penetration welding still remains unanswered. In the present investigation, the starting point are computer simulations with the FE package COMSOL Multiphysics to evaluate the critical Hartmann number for a suppression of convective motions in the weld pool. A steady magnetic field was applied to a partial penetration weld in a 500 mm  50 mm  40 mm aluminium plate. The magnetic flux density in the simulations was increased up to a value of 2 T. The goal was to clarify the extent of the influence of the Hartmann effect on the laser beam welding process of aluminium for high Hartmann numbers, where the electromagnetically induced drag component becomes dominant over viscous effects.

Since the physics of laser welding are highly demanding, it is necessary to break down the process to the most important physical aspects for the numerical calculations. The basic assumptions for the fluid flow and temperature field simulation were similar to those justified in detail in [11] for the case of an electromagnetic weld pool support. These are repeated briefly as follows.  Temporal oscillations of the weld pool or the keyhole were neglected [15,18,19].  The geometry of the free surfaces were fixed, cf. [18,19]. The curvature of the surface is less sensitive to strong changes in partial penetration welding of thick-walled workpieces than in the case of full penetration welding, where the melt can drop-out driven by gravitational forces.

Fig. 3. Sketch of effects of the application of a steady magnetic field perpendicular to the welding direction on the weld seam geometry.

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 The recoil pressure along the keyhole was assumed to be ideally balanced by surface tension forces. Therefore the keyhole geometry was fixed. The chosen keyhole radii were taken from twodimensional heat transfer calculations and scaled to obtain comparable results in terms of weld pool width, see Fig. 4. The radii depend on the depth according to the used laser type, laser power as well as its energy density distribution taking into account the heat fluxes due to absorption of laser energy, evaporation of material and heat conduction. Thus, oscillations of the keyhole and their possible influence on the flow field are neglected. The keyhole is subjected to free slip conditions. The keyhole diameter is much smaller than the width of the weld pool. Therefore, the influence of the keyhole shape on the flow field is relatively small (low Peclet number) whereas the heat input and the resulting amount of molten material depend on the keyhole radii. The temperature at the keyhole surface was set to evaporation temperature. In that configuration, the keyhole radii are a kind of free model parameter to obtain a good agreement with the experimental observations because of the chosen Dirichlet boundary conditions at the keyhole wall.  A turbulent flow pattern was assumed. Although there are no velocity boundary layers at the surfaces of the weld pool as well as at the keyhole wall there is a distinct influence of turbulence, especially at the rear weld pool wall, where the liquid metal solidifies and a no-slip condition applies. Therefore, the steady-state Reynolds averaged Navier Stokes (RANS) equations were solved combined with the standard k–e turbulence model.  The material properties were temperature-dependent up to evaporation temperature [20,21].  The natural convection influence was accounted for using Boussinesq approximation.  The solid–liquid phase transformation was modelled by an enthalpy-porosity approach [22] that uses a solidification range of the material.  The heat effect of the plasma was neglected due to the low heat absorption coefficient for the wavelength of around 1 lm of the used disc laser [23] and also the plasma temperature being close to the evaporation temperature of the material [24,25].

 Mass conservation

r  ðquÞ ¼ 0:

ð3Þ

Here, q and u = (u, v, w) are the mass density and fluid velocity.  Momentum conservation

h

qðu  rÞu ¼ r  pI þ ðg þ gT Þðru þ ðruÞT Þ  2 2  ðg þ gT Þðr  uÞI  qkI þ F 3 3

ð4Þ

with source term F

F ¼ qgbðT  T melt Þ  c1

ð1  fL Þ2 ðu  uweld Þ þ j  B: fL3 þ c2

ð5Þ

In (4) and (5), p, g, g, and b are pressure, dynamic viscosity, gravitational constant and the coefficient of thermal expansion. Two further equations for the turbulent kinetic energy k and the turbulent dissipation rate e were solved







gT rk þ Pk  qe; rk    g e e2 qðu  rÞe ¼ r  g þ T re þ C e1 Pk  C e2 q re k k qðu  rÞk ¼ r 

gþ

ð6Þ ð7Þ

with the turbulent viscosity gT and the turbulent production term Pk 2

gT ¼ qC g 

k

e

ð8Þ

;

 2 2 P k ¼ gT ru : ðru þ ðruÞT Þ  ðr  uÞ2  qkr  u: 3 3

ð9Þ

The remaining constants were set according to Table 1.  Energy conservation

qC eff p u  rT ¼ r  ðkeff rTÞ:

ð10Þ

Here, C eff p ; T, and keff are heat capacity, temperature and heat conductivity. The latent heat of melting and solidification was accounted for using an effective heat capacity formulation:

The governing equations for mass conservation, momentum and energy transport in steady-state formulation are as follows as they are implemented within the simulation framework of COMSOL Multiphysics.

C eff p

  2  exp  TTdTmelt pffiffiffiffi  Hf ; ¼ C 0p þ pdT

ð11Þ

where C 0p is the temperature-dependent heat capacity and Hf is the latent heat amount which is normalized around the melting temperature with half width dT = 50 K. The effective heat conductivity keff accounts for the turbulent heat conductivity based on Kays–Crawford heat transport turbulence model [27]. The first term on the right-hand side (RHS) of (5) is the Boussinesq approximation accounting for the buoyancy force. The coefficient of thermal expansion reads

b¼

1 @q : q @T

ð12Þ

The second term refers to the Carman–Kozeny equation accounting for the resistance of the flow through the mushy region in the

Table 1 Model constants for the k–e turbulence model, see [26]. Constant

Fig. 4. Keyhole geometry used for the simulations.

Value

Cg

Ce1

Ce2

rk

re

0.09

1.44

1.92

1.0

1.3

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Fig. 5. Computational domains for the calculations.

region between the liquidus and solidus temperatures Tsol < T < Tliq. c1 is a large-valued constant accounting for the mushy region morphology whereas c2 is a small constant to avoid division by zero in the solid region. For pure materials with a fixed solidification temperature, it is necessary to introduce artificial solidus and liquidus temperatures Tsol and Tliq. The liquid fraction fL is assumed to vary linearly with temperature and then smoothed to avoid numerical issues:

fL ¼

8 0 > < > :

T < T sol ;

TT sol T liq T sol

T sol 6 T 6 T liq ;

1

T > T liq :

ð13Þ

The half interval between the numerical solidus and liquidus temperature for pure aluminium was chosen to be 50 K for easier convergence. The last term on the RHS of (5) is the Lorentz force contribution coupling the electromagnetic forces with the hydrodynamics in the weld pool. It builds up due to the magnetic flux density B of the applied permanent magnets and the electric current density j in the weld specimen that forms due to the movement of the electrical conducting media through the magnetic field. The Maxwell equations in stationary form for the magnetic field B and the electric field E are as follows:

r  B ¼ l0 j; r  E ¼ 0:

ð14Þ ð15Þ

The movement of conducting particles in the magnetic field, driven by the welding velocity and in particular by the highly dynamical processes in the pool of molten metal, induces a current density according to Ohm’s law. In absence of other sources, it reads:

j ¼ rðE þ u  BÞ;

ð16Þ

which couples fluid dynamic and electrodynamic processes. The current density j multiplied with the magnetic field B gives the Lorentz force FL. The resulting Lorentz force in that configuration with the magnetic field perpendicular to the welding direction has a component that acts against the original melt velocity thus reducing the dynamics in the weld pool. It is favourable to use a magnetic field that is homogeneously distributed over the weld pool and its vicinity to avoid the occurrence of non-uniform Lorentz forces. Therefore the magnet poles must be large enough to cover the whole weld pool length. 2.2. Computational domains The fluid dynamics as well as the heat equation were solved only in the weld specimen using the finite element solver COMSOL Multiphysics. The electromagnetic field equations were solved in the plate and additionally in the surrounding air environment,

see Fig. 5. The keyhole penetrates around 21 mm into the material. The complete mesh consists of around 900,000 tetrahedral elements and a subsequent number of degrees of freedom to be solved of 8,100,000. The calculation used linear elements for the solution of the heat equation as well as for the Navier–Stokes equations and quadratic elements for the Maxwell equations. The simulation was done by using a segregated solver that solves for the variables in groups: (1) magnetic vector potential and electric potential, (2) velocity and pressure, (3) turbulence variables, and (4) for the temperature. A two-iteration V-cycle geometric multigrid algorithm was used with the generalized minimal residual method (GMRES) iterative solver and a direct solver (PARDISO) on the coarsest grid level. 2.3. CFD boundary conditions The boundary condition set-up used in this study was as follows:  The keyhole surface was fixed, its temperature was set to the constant evaporation temperature of the material

T ¼ T evap :

ð17Þ

Flow normal to the keyhole wall was not allowed. The keyhole surface was subjected to a slip condition

u  n ¼ 0:

ð18Þ

 At the upper and lower surfaces: Surface tension variations with temperature were modelled by Marangoni shear stresses.

@u @ c @T ¼ ; @z @T @x @ v @ c @T : g ¼ @z @T @y

g

ð19Þ ð20Þ

Table 2 Material properties of pure aluminium at melting temperature Tmelt [20,21]. Material property Melting temperature Evaporation temperature Mass density Heat capacity Latent heat of fusion Heat conductivity Dynamic viscosity Surface tension Marangoni coefficient Electrical resistivity

Value

Unit

Tmelt Tevap

933 2700

K K

q

2380 1180 3.97  105 91 1.1  103 0.871 1.55  104 24.77  10 8

kg m3 J kg1 K1 J kg1 W m1 K1 Pa s N m1 N m1 K1 Xm

Cp Hf k

g c @ c/@T qel = r1

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transfer in the melt near the surfaces occurs mainly by convective energy transport. These surfaces were also subjected to a slip condition.  The inlet temperature was set to room temperature and the welding velocity uweld was constantly 0.5 m min1.  The solid–liquid phase transition was accounted for using the Carman–Kozeny equation [22]. Hereby, additional volume forces were introduced in the solid phase region to brake the fluid motion down to the welding speed of the process.  The symmetry plane was adiabatic and flow in wall-normal direction was not allowed.

2.4. Electromagnetic boundary conditions

Fig. 6. Normalized thermophysical properties of pure aluminium.

Here, c is the surface tension and u = (u, v, w) are the velocity components in the correspondent directions. Heat transport through the upper and lower walls was neglected (adiabatic walls) as heat

(a)

The weld specimen in the simulations consisted of aluminium with associated magnetic permeability lr = 1. The permanent magnets with a side length of 50 mm were shifted 20 mm in vertical direction and 10 mm in processing direction to ensure the maximum magnetic field strength in the region of the weld pool. The lateral distance between the permanent magnets was 40 mm. For simplicity, the magnetic field strength was chosen to be constant at the upper boundary of the magnet. Further boundary conditions for the electromagnetic part were as follows:

(b)

(c) Fig. 7. Temperature and velocity distributions as well as a sketch of the main flow directions in the symmetry plane for the reference case without applied magnetic fields. The solid line denotes the melting temperature, the dotted lines the artificial solidus and liquidus temperatures, respectively. Note that velocities above 0.1 m/s were cut.

M. Bachmann et al. / International Journal of Heat and Mass Transfer 60 (2013) 309–321

(a)

315

(b) Fig. 8. Temperature and velocity distributions in the symmetry plane for B = 0.5 T.

(a)

(b) Fig. 9. Temperature and velocity distributions in the symmetry plane for B = 1.0 T.

 The symmetry plane acted as a perfect magnetic conductor – the magnetic field at that plane was solely oriented normal to it.  At all the other outer air boundaries, the electric and magnetic fields were insulated, that means

n  j ¼ 0;

ð21Þ

n  A ¼ 0;

ð22Þ

3. Numerical results The present investigation was done with a welding speed of 0.5 m min1. The keyhole was assumed to intrude around 21 mm into the workpiece. The denoted magnetic flux density values were constant at the upper side of the permanent magnets. The applied magnetic flux density was increased stepwise up to 2 T.

where n denotes the normal vector on the outer surfaces.

3.1. Case I: magnet system off

2.5. Material model

The temperature and velocity fields for the partial penetration laser beam welding process of an aluminium plate are presented in Fig. 7(a) and (b). The solid line represents the melting isotherm of the material. It is clear that the surface tension variations at the upper surface cause a strong vortex flowing from hot regions near the laser spot associated with low values of the surface tension to

Table 2 as well as Fig. 6 give a summary of the material properties used in this study. The mass density is constant at the value of the melting point as its differences with temperature are neglected except for the buoyancy term itself.

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Fig. 10. Hartmann number Ha2 for increasing magnetic flux densities.

regions near the boundaries of the weld pool with corresponding higher values of the surface tension. This mechanism is wellknown and is the main reason for the formation of an elongated

weld bead at the surface. This mechanism is increased by an upward-directed flow near the keyhole due to natural convection caused by density differences in the melt. These effects lead to a

M. Bachmann et al. / International Journal of Heat and Mass Transfer 60 (2013) 309–321

typical shape of the weld bead in both the longitudinal as well as the transversal cross section similar to a wineglass. Moreover, the vertical flow near the keyhole causes convective heat transfer mainly to the upper surface in its vicinity followed by a downwards directed flow at the weld pool rear. Thus, the temperature gradients become very high in welding direction. From Fig. 7(b), it becomes evident that the maximum velocities occur near the surfaces under the influence of thermocapillary convection. Further local maxima of the velocity in the symmetry plane are situated at the place where the flow reversal of the surface jet occurs and also near the keyhole under the influence of gravity-driven natural convection. In the lower part of the weld bead, the flow pattern is dominated by the flow of molten metal around the keyhole in horizontal direction and a downwards directed flow at the rear of the melt. 3.2. Case II: magnet system on Figs. 8 and 9 show the temperature distribution and flow velocities in the symmetry section of the weld bead for increasing magnetic flux densities. The upper part of the weld bead is still dominated by the strong thermocapillary convection present at the upper surface although its influence is minimized to a comparably thin layer, cf. Fig. 7. The influence of the Lorentz forces causes changes in the solidification front at the rear side of the weld pool and also in the cross sectional size. The reason for this modification lies in the braking of the dynamics especially in the rear of the weld pool. This can clearly be observed in the course to higher magnetic flux densities and corresponding higher Lorentz forces in Figs. 7(b), 8(b) and 9(b) showing the velocity distributions. The magnitudes and the extent of the local maximum of the velocity behind the keyhole is clearly diminished under the action of the applied magnetic field. In the end, the velocities inside the weld pool remain on welding speed level. Furthermore, the region at the surface that is highly influenced by Marangoni stresses becomes thinner. Increasing the extent of electromagnetic control leads to a less pronounced convexity of the weld bead shape in the cross section and a shortened weld bead at the rear side. The same tendencies can be observed at the front side of the weld pool. Fig. 10 shows, that a qualitative effect of the electromagnetic forces on the weld pool shape in this configuration is observable not before Ha2  104. Here, the Hartmann number Ha2 was calculated using the effective dynamic viscosity consisting of the (laminar) viscosity gL from the material properties and an additional contribution accounting for the turbulent flow pattern gT thus increasing the effective viscosity:

g ¼ gL þ gT :

317

much lower than in the solid material. As the Hartmann number only depends on the strength of the magnetic field and not on its spatial orientation, it should only be seen as a rough estimate for the quality of flow control. For example, in the case of an oscillatory magnetic field perpendicular to the welding direction, which can be used to push the liquid melt (cf. [10,11]) at working frequencies of some hundreds to thousands Hertz, the induced electric current density due to the movement of conducting media perpendicular to the magnetic field (similar to Fig. 11) is superimposed by eddy currents which can be an order of magnitude larger thus forcing the net current density on streamlines being parallel aligned to the welding direction. It is worth remarking, that the current density distribution in the solid material in Fig. 11 especially in the solid phase is caused by the inlet boundary conditions in the numerical calculations, that means a constant relative velocity between the workpiece and the

Fig. 11. Exemplary electric current distribution in the weld specimen for B = 1 T.

ð23Þ

It shows, that up to a magnetic flux density of around B = 0.3 T, the flow pattern is dominated by strong turbulence. Accordingly, the Hartmann number is relatively small in regions of high turbulence compared to its respective maximum value for each simulation case. This occurs especially in the upper rear of the weld pool where the flow reversal of the Marangoni vortex happens. Beginning with B = 0.4 T the Hartmann number jumps to higher values predominantly homogeneously distributed in the whole weld pool, which indicates a more laminar flow. Furthermore, a shortening of the weld pool dimensions in terms of width and length begins. The need for high applied magnetic flux densities to produce a remarkable effect on the weld pool shape (cf. [7]) might also be caused by the orientation of the induced electric current density. The location of the permanent magnets perpendicular to the welding direction leads to two counter-rotating vortices of the electric current density in the half-plane of the weld specimen whose rotational direction depends on the direction of the applied magnetic field, see Fig. 11. The electric conductivity inside the weld pool is

Fig. 12. Velocity streamlines in the specimen for increasing magnetic flux densities.

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M. Bachmann et al. / International Journal of Heat and Mass Transfer 60 (2013) 309–321 Table 3 Laser beam welding processing parameters. Laser type Laser power PL Welding speed uweld Fibre diameter Wave length Laser torch angle Focal length Focus position Shielding gas nozzle angle Shielding gas

Disc laser Trumpf TruDisc 16002 16 kW 0.5 m min1 200 lm 1030 nm 18° 300 mm 4 mm 45° 30 l min1 Ar

stresses at the surface remains only noticeable in a very thin layer near the surface. The rest of the liquid metal in the weld bead moves with the processing speed synchronous to the solid phase. The extent of damping the dynamics especially near the upper surface which is dominated by strong Marangoni convection can be expressed in terms of Weber number We: Fig. 13. Weber number for different magnetic flux densities applied at 3 mm behind the keyhole at the upper surface.

magnetic field, that is not present when using permanent magnets mounted on the workpiece. In real experiments that case corresponds to the application of a steady magnetic field delivered by a DC electromagnet being moved synchronous with the laser beam. For the electric currents inside the weld pool, the influence of this assumption is small as the maximum liquid metal velocities in the weld pool especially at the surface can be up to two orders of magnitude larger than the processing speed [11] and the largest effect of the Lorentz forces in the weld pool is expected in that region. The influence of the magnetic fields becomes large enough to cause significant changes in the flow pattern and also the weld pool geometry. Arbitrarily chosen three-dimensional streamlines of the velocity field are presented in Fig. 12. Note the pronounced three-dimensionality of the prevailing flow pattern without electromagnetic control system. It is clearly observable that the flow especially in the lower part of the weld pool becomes more uniform heading to a purely horizontal flow around the keyhole with magnetic fields applied. For B = 1 T, the influence of the Marangoni

(a)

We ¼

qU 2 L ; c

ð24Þ

where U is the velocity magnitude and c is the surface tension of the liquid aluminium. This number relates the kinetic energy and the surface tension of the fluid at the interface between the liquid metal and the gaseous phase. As deep-penetration aluminium weld surface quality is very susceptible to suffer from the dynamics in the weld pool, the Weber number gives an estimate of its stability. Fig. 13 shows the Weber number at the upper surface at a position 3 mm behind the keyhole for different magnetic flux densities applied. It yields that the dynamics of the weld pool corresponding to high values of We mitigates the higher the applied magnetic field is which is because of the much lower flow velocities. 3.3. Case III: comparative case with constant velocity Fig. 14(a) shows a theoretical case without simulation of electromagnetic fields and fluid flow. Instead, a constant welding velocity is assumed throughout the whole plate and only a thermal simulation with constant convective transport term was done. A comparison with Figs. 8(a) and 9(a) reveals the stepwise approach from fully turbulent three-dimensional flow inside the molten pool

(b)

Fig. 14. (a) Temperature distribution in the symmetry plane for the case of constant velocity in the whole calculation domain. (b) Weld pool widths and lengths for different magnetic flux densities and for the case without calculating the fluid dynamics in the melt.

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4. Experimental conditions

Fig. 15. Experimental setup.

Fig. 16. Magnetic flux density measured in the middle plane between the permanent magnets. The black frame denotes the magnet geometry.

to the case without any convection except from processing speed inside the melt seen in Fig. 14(a). This yields that an increase of the magnetic field above Hartmann number of around 105 would not result in further qualitative changes of the weld pool geometry. For higher Hartmann numbers, the weld pool width and length converge to the theoretical case without additional convection in the melt, see Fig. 14(b).

The welding experiments were performed with a disc laser TruDisc 16002 with an output laser power of 16 kW in downhand position. To avoid reflections to the optical system, the laser incident angle was chosen to be 18° from the vertical. The experiments were done with AlMg3 with a cross sectional width of 40 mm and a height of 50 mm. An overview of the parameters of the welding process can be found in Table 3. Two permanent magnets were mounted stationary on both lateral sides of the workpiece, a water-cooled plate made from ferromagnetic steel was attached in between to prevent the magnets from being heated above the Curie temperature, see Fig. 1(a). The magnets have a cross section of 50 mm  50 mm. Their vertical offset to the upper surface of the specimen was 20 mm to ensure the maximum magnetic flux density in the region of the weld pool. Their lateral distance was 40 mm according to the width of the workpiece. The welds were performed by traversing the laser torch linearly along the long axis of the specimen. Shielding gas was provided at the upper side behind the laser beam with a nozzle angle of around 45°, see Fig. 15. A splash guard was used to avoid heavy spattering of the process, especially in the reference case without magnetic field applied. They were made of the same material as the workpiece to avoid thermoelectric effects on the contact surfaces between the sample and the splash guard. The permanent magnets are made of neodymium iron boron with a nickel finish. As aluminium and air have the same magnetic properties (lr = 1), it was possible to measure the magnetic flux density before starting the welding tests by mounting the permanent magnets on a test stand in the welding configuration but without the workpiece. The results can be seen in Fig. 16 proving that the magnetic flux distribution is approximately constant over the inner 20 mm  20 mm where the weld pool is developing thus justifying the assumption of a constant magnetic field boundary condition in the calculations. 5. Comparison between simulation and experimental results The comparison between the experimental results and the computer simulations of the process shows a good agreement of the observed trends in terms of a reduction of the weld pool extent

Fig. 17. Comparison of the macro sections of the welds produced experimentally and in computer simulations. The solid line marks the melting temperature whereas the region inside the dotted lines is the solidification interval.

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Fig. 18. Macro sections at different positions relative to the mounted permanent magnets.

Fig. 19. Macro sections of two welds, shown are both the reference case without magnetic field (left) as well as the case with magnetic field applied and changed polarity (right).

and also the attenuation of the influence of the thermocapillary flow at the upper surface, see Fig. 17. The weld surface as well as macro sections at different positions from an experimentally obtained weld are shown in Fig. 18. The welding parameters were according to Table 3. The macro sections far away from the permanent magnets show a strong convexity due to strong Marangoni convection. Furthermore, the weld seam surface is very wavy as it is highly influenced by the dynamics inside the weld pool and no reasonable weld was obtained. The macro sections under the influence of the magnetic field show a regular weld pool without strong convexity of the solidification front and with an approximately flat upper surface, cf. Fig. 3. The weld pool depth remains the same for every position at around 25 mm whereas the width at the upper surface becomes smaller when a magnetic field perpendicular to the welding direction is applied. The reason is the induced Lorentz force distribution that mitigates the strong thermocapillary surface flow as it is directed against the original flow direction in wide areas of the weld pool.

This mechanism increases drastically for the welding with high power laser systems as the corresponding Hartmann number rises quadratically with the half width of the welds. This yields that the magnetic braking of the metal melts works the better the more laser output power was used and the lower the welding speed was both ending in an increase of the weld pool size. To confirm that the observed effects are really result of the Hartmann effect, test welds were performed with different polarity of the applied magnetic field using Ar shielding gas at a flow rate of 20 l min1, see Fig. 19. The very wide weld pools are very susceptible to the shielding conditions and show a more curved upper surface than the welds in Fig. 18. High speed videos of the process show the formation of a very thick oxide layer on the surface. Therefore, the pores cannot escape from the weld pool and remain in the vicinity of the surface. Nevertheless, the curvature of the magnetically controlled welds is much lower independently of the polarity of the applied magnetic field which indicates a strong influence of the applied braking Lorentz forces in the melt. In contrast to [16], in the experiments with a disc laser system with around ten times smaller optical wavelength of the laser radiation shown in this paper, an influence of the polarity of the magnetic field on the weld shape was not observed. That means that the reason for the difference between the cases with and without applied magnetic fields can only be the Hartmann effect with sufficient high Hartmann numbers. Independently on the direction of the applied magnetic field, the resulting Lorentz force is directed against the original melt velocity thus lowering the dynamics in the weld pool significantly.

6. Conclusions The purpose of the present investigation was to work out the influence of a magnetic field on a weld pool during high power thick section partial penetration laser beam welding of aluminium based on the Hartmann effect. It was shown, that the application of an external magnetic field perpendicular to the welding direction induces electric currents, which in combination with the applied magnetic field built a Lorentz force distribution that is directed against the melt flow. Thus a braking of the flow velocities in the weld pool was observed. The simulations as well as the experimental work show a severe influence of the applied magnetic fields beginning with Hartmann

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numbers Ha2  104. Hereby, the polarity of the applied magnetic field was found to be irrelevant as the resulting Lorentz force is directed against the melt velocity as long as the magnetic field is aligned perpendicular to the welding direction. The modifications in the flow field in the molten pool also change the local temperature distribution. Therefore, also the heat transfer changes in the weld pool as heat conduction gains more influence compared to convective energy transport. The decelerating nature of the applied electromagnetic forces leads to a shortening of the weld bead in longitudinal as well as in transversal directions. The significant mitigation of the flow velocities especially near the surface of the weld bead is favourable in terms of also reducing the evolution of spatter and melt ejections. It was observable that the influence of thermocapillary flow, namely a wineglass shape of the weld bead, on the weld cross section could almost completely be eliminated. The resulting smaller curvature of the solidification front related to a V-shape of the weld cross section benefits a more uniform stress distribution inside the weld specimen which in effect leads to smaller deformations of the workpiece after cooling down. Acknowledgements Financial funding of the Deutsche Forschungsgemeinschaft DFG (Bonn, Germany) under Grant No. DFG GU 1211/2-1 and the German Allianz Industrie Forschung (AiF), Grant No. 17.265N is gratefully acknowledged. References [1] J.F. Ready, D.F. Farson, LIA Handbook of Laser Materials Processing, Laser Institute of America/Magnolia Publishing/Springer, Berlin, 2001. [2] V. Avilov, A. Gumenyuk, M. Lammers, M. Rethmeier, PA position full penetration high power laser beam welding of up to 30 mm thick AlMg3 plates using electromagnetic weld pool support, Sci. Technol. Weld. Joining 17 (2012) 128–133. [3] D. Radaj, Welding Residual Stresses and Distortion. Calculation and Measurement, DVS-Verlag, 2003. [4] A. Matsunawa, Problems and solutions in deep penetration laser welding, Sci. Technol. Weld. Joining 6 (2001) 351–354. [5] R. Moreau, Magnetohydrodynamics, Kluwer Academic Publisher, 1990. [6] Proceedings 6th International Conference on Electromagnetic Processing of Materials, Dresden, Germany, 2009.

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