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Numerical simulation of temperature field, fluid flow and weld bead formation in oscillating single mode laser-GMA hybrid welding
Journal of Materials Processing Technology 242 (2017) 147–159
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Numerical simulation of temperature field, fluid flow and weld bead formation in oscillating single mode laser-GMA hybrid welding X.S. Gao a , C.S. Wu a,∗ , S.F. Goecke b , H. Kügler c a b c
MOE Key Lab for Liquid-Solid Structure Evolution and Materials Processing, Institute of Materials Joining, Shandong University, Jinan 250061, China Technische Hochschule Brandenburg, Brandenburg an der Havel, D-14770, Germany BIAS- Bremer Institut fuer Angewandte Strahltechnik, Bremen, D-28359, Germany
a r t i c l e
i n f o
Article history: Received 25 October 2016 Received in revised form 22 November 2016 Accepted 23 November 2016 Available online 24 November 2016 Keywords: Oscillating laser-GMA hybrid welding Lap joint Three dimensional numerical model Droplet impingement Weld pool behavior
a b s t r a c t A three dimensional numerical model of oscillating single mode laser-GMA hybrid welding process with lap joint and arc inclination configuration has been developed for the first time. The model is used to investigate the temperature field and fluid flow corresponding to the aforesaid welding process and weld configuration. An asymmetric distribution of arc heat and a cylindrical volumetric distribution of laser heat are established to describe the heat transfer from the combined heat source to the workpieces. The droplet with predefined temperature and velocity is impinged on the weld pool at a given fillet weld angle. Arc pressure, electromagnetic force, Marangoni force and buoyancy are also considered in the model with some modifications with respect to the lap joint and arc inclination configuration. Results show that the droplet impingement process has a significant influence on the weld geometry, temperature field and fluid flow pattern due to the transfer of mass, energy and momentum into the weld pool. These unique temperature fields and flow patterns are characteristic to the lap joint and arc inclination configuration. The proposed model exhibits close correspondence with the experimental results with respect to weld geometry. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Press-hardened steels are candidate materials for crashresistance applications in automobile industry. However, their efficient welding is an issue. Rossini et al. (2015) have found that laser butt welding successfully joins dissimilar advanced high strength steels such as TRIP steel, DP steel and 22MnB5 steel combinations and this process is an effective solution to assemble car body parts. Oscillating single mode laser welding has the advantages of high welding speed and excellent concentrated heat density. In the oscillating single mode laser welding of 22MnB5 steels, Chsel et al. (2013) have reported a 10% loss in tensile strength of weld joint as compared to the parent metal. In addition, the above process is involved with strict demands for workpiece alignment and no feeding wire, which limit application of the process in the automobile industry where welding of various joint types with inevitable gaps is essential. On the other hand, the gas metal arc (GMA) welding process is widely used in the current automobile industry because of its excellent gap-bridge ability, meeting the
∗ Corresponding author. E-mail address: [email protected] (C.S. Wu). http://dx.doi.org/10.1016/j.jmatprotec.2016.11.028 0924-0136/© 2016 Elsevier B.V. All rights reserved.
demands of most weld joint types and welding positions. However, high welding speeds make the GMA welding process unstable, so relatively low welding speeds are recommended. It appears that introduction of laser to stabilize the arc process at higher welding speeds is a good option to improve the GMA welding process. Thereby, a new hybrid welding process consisting of an oscillating single mode laser and a conventional pulsed gas metal arc can be a useful prospect for welding ultra-high strength steel structures with lap joint and gap-bridging configuration in automobile manufacturing. Due to the lap joint configuration and the high welding speed and welding current, this oscillating single mode laser-GMA hybrid welding process displays distinct features, such as high velocity droplet impingement, complex fluid flow in weld pool and varied arc heat distribution. However, the current experimental and simulation research on this hybrid welding process is too limited to formulate a knowledge base. Numerical simulation, in general, is a powerful tool to obtain complete understanding of the physical phenomena and the underlying mechanisms of welding processes, as emphasized by Murphy (2015). Therefore, development of mathematical models focusing on the characteristics of the heat distribution, temperature field and fluid flow behavior in the weld pool of oscillating single mode laser-GMA hybrid lap
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Fig. 1. Sketch of combined heat source of oscillating laser-GMA hybrid welding.
welding process would be an ideal approach to achieve the process optimization. For general laser-GMA hybrid welding process, several mathematical models have been developed. Piekarska and Kubiak (2011) described the arc heat and laser heat by ‘double ellipsoidal’ heat model and CIN model respectively to estimate the temperature field and fluid velocity field in the weld pool. Zhang and Wu (2015) investigated the influence of molten fluid flow on temperature field, thermal cycles and weld geometry by a three dimensional quasisteady state laser-GMA hybrid welding model, but used a keyhole model presumably set in the computational domain. Cho et al. (2010) suggested a complicated laser heat source model based on summation of laser radiation by ray tracing technique combined with a Gaussian plane arc heat distribution model. Nonetheless, all these models are concerned with general laser-GMA hybrid welding process in bead-on-plate configuration. Regarding complex joint types, Kim et al. (2003) developed a three dimensional heat conduction model for the GMA welding of fillet joints. In their model, the arc heat was described by a classic Gaussian plane heat source model using a boundary fitted coordinate system. Kumar and DebRoy (2007) developed a numerical model to investigate the effects of the fillet joint tilt angle and weld positions on the temperature profiles and fluid flow field in GMA fillet welding process. To the authors’ knowledge, the number of numerical models of lap weld joints are relatively much lower than those for fillet weld joints. A possible reason for scarcity of investigations is the irregular arc characteristics resulted from the intrinsic asymmetry of lap joint which makes it difficult to model the welding process. Meng et al. (2015) considered the effects of lap joint on the arc heat distribution and calculated the temperature field of large spot laser-MIG arc brazing-fusion welding of Al alloy to galvanized steel in lap joint. The model dealt with temperature field caused by heat conduction, but did not include the influence of fluid flow which in fact plays a critical role in determining the weld pool geometry and thermal history, as suggested by Zhou and Tsai (2008). In this study, a three dimensional transient heat transfer and fluid flow model was developed to conduct numerical analysis of the oscillating single mode laser-GMA hybrid welding of lap joint. Experiments were carried out to validate the results of numerical simulation.
2. Characteristic of oscillating laser-GMA hybrid welding The oscillating single mode laser-GMA hybrid welding process where the gas metal arc plays the major role is different from the general laser-GMA hybrid welding process where the laser produces deep penetration in thick plates. The single mode laser is used as an assistant approach to stabilize arc. Thiel et al. (2012) have found that the single mode laser requires oscillation movements to redistribute the locally constricted energy so that a more continuous and stable hybrid welding process can be realized. In our hybrid welding experiments, the weld cross-sections with and without laser oscillations are almost similar. However, the weld without laser oscillation shows a deep-penetration channel along the laser path when the welding speed reaches 6 m/min. This penetration channel is due to the localization of extremely high heat of the single mode laser. Moreover, the penetration channel has propensity to decrease weld mechanical properties by expanding the heat affected zone. On the other hand, the weld cross-section with laser oscillation is free from this penetration channel. Therefore, oscillation of laser is extremely important to normalize the laser heat deposition area and improve its efficiency. Keeping in view the wide use of lap welded sheet joints in automobile industries, a lap configuration with a welding speed as high as 6 m/min is considered in this study. As suggested by Möller et al. (2014), the lap welding is conducted by employing a fillet weld angle of 30 ◦ to melt off more of the upper sheet edge and transfer less heat to the bottom sheet. Fig. 1 shows the schematic of combined heat source of oscillating single mode laser–GMA hybrid welding for lap joint. It conveys the following characteristics of this hybrid welding: (a) the GMA process and an oscillating laser beam transfer heat to weldment, (b) the lap joint and arc inclination configuration make the experimental process and mathematical modelling more complicated, and (c) droplets carrying heat, mass and momentum impinge on the weld pool at a specific angle. Oscillation is perpendicular to welding direction in line pattern at an optimum amplitude and frequency, and changes laser heat distribution. For the lap joint, the heat flux and pressure from the arc are distributed in ways different from that for a bead-on-plate or a butt joint. Therefore, the hybrid heat source distribution should be established by taking the lap joint into consideration, and the droplet transfer should be accurately
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Fig. 2. Asymmetric distribution of arc heat on the workpiece.
Fig. 3. Sketch of heat distribution of inclined arc on lap joint.
estimated in terms of the amount of mass, heat and momentum as well as the direction of momentum. In the current simulation model of oscillating single mode laserGMA hybrid process for lap configuration, it is necessary to address some coordinate systems defined to deal with welding speed, lap joint and arc inclination configuration. To simplify the definitions, the laser beam is considered to move along the welding centerline without oscillation. As shown in Fig. 1(a), the original coordinate Co.0 (Oxyz) defined by the software is still with the workpiece where all the solution work, i.e., equation discretization and numerical iteration, is done. The coordinate Co.1 (O x y z ) is introduced to describe the moving combined heat source of arc and laser in the lap joint. The origin of Co.1, O , is the intersection between the axis of laser beam and the welding centerline, and the point Oarc is the intersection between the axis of arc and the welding centerline, denoting the arc leading configuration. On one hand, the x axis of Co.1 is collinear with x axis of Co.0, and the speed of Co.1 equals to the welding speed. On the other hand, the z axis of Co.1 has an angle of 30 ◦ against the vertical direction to the workpiece, as shown in Fig. 1(b). In order to describe the heat and force dis-
tribution on the weld pool surface, a coordinate Co.2 (O"x"y"z") is defined, and the origin of Co.2, O", is the intersection between the axis of laser beam and the weld pool surface. The transformation between these coordinates will be explained in a later section. In addition, following assumptions are made to simplify the whole process: (i) the molten metal is assumed as incompressible Newtonian fluid; (ii) the deposition of laser heat is in conduction mode due to high welding speed as well as high oscillating frequency of laser beam; (iii) the small gap between the two sheets in lap joint to help the aluminium vapour to escape is ignored in the simulation since the gap has insignificant effects on the weld geometry and fluid flow in weld pool; (iv) average current and voltage are used to calculate the arc power, and the pulse effect is neglected.
3. Mathematical formulations In the oscillating laser-GMA hybrid welding process of steel sheets in lap joint, the workpieces are heated, melted, even evaporated. When a weld pool is formed, the molten metal flow occurs, which determines the heat transfer in the weld pool.
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Fig. 4. Schematic representation of coordinate transformation.
Fig. 5. Schematic representation of droplet transfer.
3.1. Governing equations
fraction set as 0.68. The liquid fraction fl is assumed as a linear function of temperature:
The governing equations describing the heat and mass transfer phenomena and fluid dynamics in laser-GMA hybrid welding process include mass, momentum and energy conservation equations. Continuity equation
∇ ·V =0
fl =
∂V + V · ∇V ∂t
= −∇ P + ∇ 2 V − Cmushy
(1 − fl ) fl3
+A
(2)
where is the fluid density, t is the time, P is the hydrostatic pressure, Cmushy is the mushy zone constant, A is a small positive constant. The third term on the right-hand side of Eq. (2) is the momentum sink due to the reduced porosity in the mushy zone. G is the gravitational acceleration due to body force. fl is the liquid fraction. is the dynamic viscosity which is set as a large number in solid zone, a relatively small constant in liquid zone and a function of liquid fraction in the mushy zone (Cho et al., 2009) expressed as follows:
=
⎧ 100 ⎪ ⎨ ⎪ ⎩
min l
l 1 − (1 − fl ) /fscr
−1.55
T < Ts
, 100
T − Ts
Ts ≤ T ≤ Tl
T − Ts ⎪ ⎪ ⎩ l
(4)
T > Tl
Energy equation
2
V + G
T < Ts
1
(1)
where V is the velocity vector of fluid flow in weld pool. Momentum equation
⎧ 0 ⎪ ⎪ ⎨
∂h + V · ∇h ∂t
= ∇ · (∇ T )
(5)
The energy is formulated by enthalpy continuum model in the solid-liquid phase transition:
h=
⎧ C T ⎪ ⎨ ps ⎪ ⎩
T ≤ Ts
h (Ts ) + fl × Lf
Ts ≤ T ≤ Tl
h (Tl ) + Cpl (T − Tl )
T > Tl
(6)
where h is the enthalpy of material, is the thermal conductivity, Cps is the specific heat of solid phase and Cpl is the specific heat of liquid phase, Lf is the latent heat of fusion, fl is the liquid fraction as described by Eq. (4).
(3)
Ts ≤ T < Tl Tl ≤ T
where l is the molten metal viscosity, Ts is the solidus temperature, Tl is the liquidus temperature, fscr is the characteristic solid
3.2. VOF method VOF method is used to track the free surface between two or more fluid phases which are not interpenetrating. The fluid phase
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Fig. 6. Solution domain and boundary types for calculation.
Fig. 7. 3-D perspective views of temperature field at moment t = 0.325 s.
configuration is defined by volume fraction function F. The function F is governed by the following conservation equation:
∂F + ∇ · (V F) = 0 ∂t
(7)
The material properties in the transport equations are determined by the presence of the component phases in each control volume in VOF method. Some specific material property of the computing cell involving iron phase and gas phase is defined as follows: Pc = FFe PFe + (1 − FFe )Pair
(8)
where Pc is the volume fraction weighted average material property, Pi is the ith phase’s material property, Fi is the ith phase’s volume fraction. 3.3. Arc heat source 3.3.1. An asymmetric distribution of arc heat in lap joint In this high speed welding process with lap configuration and arc inclination, the arc heat distribution on the workpiece is asymmetric not only in the welding direction but also in the transverse direction. Defining heat distribution between the two sheets is
always a critical problem in lap joint welding, as investigated by Ebert-Spiegel et al. (2015). The arc heat distribution is defined in coordinate Co.1, where four distribution parameters, af ,ar ,bp and bn are introduced to represent the heat distribution features for lap joint and arc inclination configuration, as shown in Fig. 2. When an inclined arc deposits on the weldments of lap joint, the heat density at local points on the receiving surface differs depending on the distance from those points to the wire tip. As shown in Fig. 3, since the distance from point B to the wire tip is shorter than that from point A to the wire tip, the heat flux density at point B is larger than that at point A, according to the principle of minimum voltage in theory of arc physics. Thus, the distance between the points on the weld pool surface to the wire tip should be taken into account in modeling the arc heat distribution for inclined arc in lap joint. The heat flux at a point on the weld pool surface is inversely proportional to the square of the distance between the point and the wire tip. Therefore, a dimensionless factor d is introduced into the arc heat model:
d=
2 Lpa 2 Larc
(9)
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where Lpa is the distance between the computing cell and wire tip, Larc is the arc length which is assumed to be the distance between the wire tip and the intersection point of the extension line of wire tip and welding centerline as shown in Fig. 3. To keep the arc power conserved, a calculation adjustment parameter, Kd is used, which is defined by comparison between the theoretical arc power and the actually loaded power in the computation domain. The arc heat distribution is expressed as follows: qa (x , y ) =
qa (x , y ) =
qa (x , y ) =
qa (x , y ) =
Kd · 12UI
Kd · 12UI
Kd · 12UI
Kd · 12UI
af + ar
af + ar
af + ar
af + ar
(bp + bn ) d
(bp + bn ) d
(bp + bn ) d
(bp + bn ) d
exp −
exp −
exp −
exp −
3(x − dla )
2
−
a2f 3(x − dla )
2
a2f 3(x − dla )
2
−
a2r 3(x − dla ) a2r
−
2
−
3y 2 b2p 3y 2 b2n 3y 2 b2p 3y 2 b2n
UI
qa
where [F] stands for the volume fraction change of iron phase across the thickness of the free surface and obviously equals to zero here. and Cp are the mean density and mean specific heat of iron phase and gas phase, respectively. The term, (xi ) Cp (xi ) / Cp is used to avoid change of free surface thickness caused by energy source term. 3.4. Laser heat source
, x − dla ≥ 0, y < 0
, x − dla < 0, y ≥ 0
, x − dla < 0, y < 0
(11)
(x , y )dx dy
S
where U is the average voltage, I is the average welding current, Uw is the welding speed, dla is the distance between laser and arc, is the heat transfer efficiency of the electric arc and 0.52 was used in this study with reference to the experimental measurement results given by Siewert et al. (2013). 3.3.2. Asymmetric volumetric distribution of arc heat In FLUENT, the heat flux on the weld pool surface has to be transformed into a volumetric term when it is added into the energy conservation equation as a source term. In order to keep energy conserved, the CSF (continuum surface force) model proposed by Brackbill et al. (1992) was used to transform the plane heat flux into volumetric heat flux. As shown in Fig. 3, the heat flux vector on the weld pool surface, qS , is defined as follows: qS = qP n
(16)
, x − dla ≥ 0, y ≥ 0
(10)
Kd =
qV = qVx (x ) + qVy (y ) + qVz (z )
(12)
To develop a laser distribution, it’s worth noting the physical mechanisms of the interaction of the arc with the oscillating beam. In fact, the interactions may be broken down to two phenomena: the arc stabilization and the net heat generation. In the first, the oscillating laser is the most beneficial when the welding speed is high. In single GMA welding process, the arc becomes unstable and its attachment spot undergoes frequent fluctuations at welding speeds as high as 6 m/min. However, in oscillating laser-GMA hybrid welding process, the single mode laser produces considerable amounts of metal vapor, providing conductive channel for arc plasma, such that the arc becomes stable and deposits heat successively. In the second, the oscillation provides chance for homogenization of laser power which has been explained in more detail in Section 2. The heat, producing an undesirable deeppenetration channel without oscillation now contributes to form a more effective joint. Together with a stable arc heat deposition, the total net heat generation has been improved. In summary, the laser oscillations affect the laser heat distribution by homogenizing the laser power and the arc stabilization by controlling the metal vapor behavior in wavering zone. In fact, the generated metal vapor and its subsequent contribution to arc stabilization change a little, owing to the small oscillation amplitude as well as high welding speed. As an initial state of this study, the oscillating laser heat distribution is considered in a simplified way by neglecting the oscillation effects on metal vapor. Laser heat is supposed to be dispersed on the region along the weaving locus and its density is treated with a spatial averaging method. Therefore, the laser power is assumed as a cylindrical volumetric heat source characterized by power density uniform in the radial direction and exponentially decaying down the penetration depth. It is defined in coordinate Co.2 and described by the following formula:
ln
where qP is the heat flux value at the projection point B’, and n is the normal vector of local surface. qP is calculated by Eq. (10), qS has three components, qSx , qSy and qSz in Cartesian coordinates:
ql (x"e; , y"e; , z"e; ) =
qSx = qS cos ˛
where rL and H are the effective radius and height of laser heat source, respectively and is the attenuation coefficient determined by empirical value.
qSy = qS cos ˇ
(13)
qSz = qS cos
Hr 2L
( − 1)
exp
( ) z"e; H
(17)
3.5. Arc pressure
where ˛,ˇ, are the direction angles of normal vector n with respect to x, y, z axis, respectively. n is defined by gradient of volume fraction as follows: n = ∇F
It is assumed that the distribution of welding current density is in the same mode as the heat flux distribution, and then the arc pressure distribution, defined in coordinate Co.1, is written as:
(14)
Following the mathematical method proposed by Brackbill et al. (1992), the volumetric components of heat flux, derived from the plane heat flux, are given as:
PA = Cj
PA = Cj
∇ F (x ) (x ) Cp (x )
qVx (x ) = qSx (x )
[F]
qVy (y ) = qSy (y ) qVz (z ) = qSz (z )
l Ql ln ( )
Cp
∇ F(y ) (y )Cp (y ) [F]
Cp
∇ F (z ) (z ) Cp (z ) [F]
Cp
(15)
2
2
2
2
(x − dla ) y 2 30 I 2 exp −3 −3 2 2 (ar + af ) (bn + bp ) d af 2 bp
2 (ar
(x − dla ) y 2 30 I 2 exp −3 −3 2 + af ) (bn + bp ) d af 2 bn
PA = Cj
(x − dla ) y 2 30 I 2 exp −3 −3 2 2 (ar + af ) (bn + bp ) d ar 2 bp
PA = Cj
(x − dla ) y 2 30 I 2 exp −3 −3 2 2 (ar + af ) (bn + bp ) d ar 2 bn
x − dla ≥ 0, y ≥ 0
x − dla ≥ 0, y < 0
(18) x − dla < 0, y ≥ 0
x − dla < 0, y < 0
where Cj is the adjustment factor for arc pressure and 0 is the permeability of vacuum.
X.S. Gao et al. / Journal of Materials Processing Technology 242 (2017) 147–159
153
Fig. 8. Temperature field on the transverse cross-section (x = 20 mm).
3.6. Electromagnetic force A simplified expression suggested by Tsao and Wu (1988) is employed to calculate the electromagnetic force inside the weld pool, and it is defined in coordinateCo.2, Fex = −
Fey = −
Fez =
m I 2 42 j2 r m I 2 42 j2 r
I2
−
exp
−
exp
r2 2 j2 r2
1 − exp
m 1 − exp 42 r 2 L
−
−
1 − exp
2 j2
r2 2 j2
−
2
r2 2 j2 r2
z 1− L
1−
2 j2
2
1−
z"e; L
z"e; L
(x − dla ) r
2
y"e; r
(19)
(20)
(21)
r=
2
(x"e; −dla ) + y"e;2
(22)
where m is the material permeability, r is the distance to arc heat source center, L is the effective sheet thickness, and j is the electromagnetic force distribution parameter. j is determined by asymmetric heat distribution parameters as follows:
j =
af + ar
bp + bn
24
(23)
3.7. Coordinate transformation As demonstrated in Section 2, this simulation model involves several coordinates due to the complex hybrid welding process. All the governing equations are solved in the original coordinate Co.0(Oxyz) by the software packages, while the heat and force distribution of laser and arc are established in the coordinates Co.1(O x y z ) and Co.2(O x y z ) moving with the hybrid head. In order to apply the heat and force analytical formula in the com-
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Table 1 Chemical composition of used material in experiments. Material
C
Si
Mn
P
S
Al
Nb
Ti
Cr + Mo
B
22MnB5 G3Si1
0.25 0.08
0.40 0.9
1.40 1.5
0.025 0.015
0.010 0.012
0.015 –
0.10 –
0.05 –
0.50 –
0.005 –
Table 2 Process parameters.
Table 3 Material properties used in the simulation.
Laser power, Ql (kW) Laser beam oscillation frequency, fo (Hz) Laser beam oscillation amplitude, 2As (mm) Average welding current, I(A) Average arc voltage, U(V) Pulse frequency, f (Hz) Laser-arc-distance, dla (mm) Fillet weld angle, (degree) Welding speed, Uw (m/min) Wire feeding rate, WFS(m/min)
1 200 0.7 320 36 250 1 30 6 20
putation domain, the original coordinate needs translation and rotation transformations. As shown in Fig. 4(a), the original
coordinate Co.0(Oxyz) should be transformed to Co.0 O x with a translation by a distance equal to the product of welding speed and time (Uw t) to represent the
moving combined heat source. Then, the coordinate Co.0 O x should be transformed to Co.1(O x y z ) with a counterclockwise rotation by an angle to calculate the arc heat and arc pressure distributions, as shown in Fig. 4(b). In order to deal with the electromagnetic force and volumetric laser heat terms, choice of reference plane in the lap configuration is puzzling, while the top weld surface is the reference plane in butt joint. In this case, weld pool free surface is assumed as the reference plane, and a tracking algorithm is conducted at every time step to obtain the intersection point, O between the laser beam axis and the free surface of weld pool. Then, the coordinate Co.1(O x y z ) is translated to that intersection point to get the coordinate Co.2(O x y z ). The forward and backward transformations between coordinateCo.0, Co.1 and Co.2 are expressed as follows:
⎡ ⎤ x
⎡
1
0
0
⎤⎡
x − Uw t
⎣ y ⎦ = ⎣ 0 cos − sin ⎦ ⎣ z
0
⎡ ⎤ x
⎡
1
⎣y⎦ = ⎣0 z
⎡
x
0
⎤
⎡
1
sin 0 cos − sin
0
cos 0
⎤⎡
x + Uw t
sin ⎦ ⎣
y
cos
z
0
0
⎡ ⎤ x
⎡
1
⎣y⎦ = ⎣0 z
0
sin
0
⎤⎡
cos − sin
cos
0
x − Uw t y
⎤⎡
x + Uw t y
(24)
⎤ ⎦
⎤ ⎡ ⎤ 0
7200 1800 1760 3100 temperature dependent, Eq. (44) 754 temperature dependent, Eq. (45) temperature dependent 1.5 × 10−6 temperature dependent 0.4 1.26 × 10−6 3.13 × 105 7.34 × 106
3.8. Droplet transfer In GMA welding, the wire melts continuously. Droplets form at the wire tip and then transfer into the weld pool. The droplets are treated as iron phase fluid which flows into the computation domain periodically from the velocity inlet boundary. For the study case, the arc is inclined to the vertical line by 30 ◦ , and the droplets are assumed to flow into the molten pool along the arc axis. Since the fluid flow in weld pool is affected by droplet impingement during high current GMA welding process, the inclination feature of droplets should be taken into consideration. The droplet temperature, droplet velocity, droplet detachment frequency, radius of velocity inlet and flow duration in one cycle should be defined. The schematic representation of droplet transfer is shown in Fig. 5. The droplet velocity in the velocity inlet boundary has two components in y and z direction, vdy and vdz , respectively, which are expressed as follows:
vdy = vd sin
(26)
vdz = vd cos
(27)
a
⎤
value
Density, (kg/m−3 ) Liquid temperature, Tl (K) Solidus temperature, Ts (K) boiling temperature, TLV (K) Thermal conductivity, (W m−1 K−1 ) Specific heat of liquid phase, Cpl (J kg−1 K−1 ) Specific heat of solid phase, Cps (J kg−1 K−1 ) Viscosity, (kg m−1 s −1 ) Coefficient of thermal expansion, ˇ (K−1 ) Surface tension coefficient, (N m−1 ) Emissivity, ε Magnetic permeability, m (H m−1 ) Latent heat of fusion, Lf (J kg−1 ) Latent heat of vaporization, HLV (J kg−1 )
where vd is the droplet velocity calculated by the method suggested by Kim et al. (2003),
⎦+⎣0⎦
z
⎢ sin ⎦ ⎣ cos
⎦
z
⎢ ⎥ ⎣ ⎣ y ⎦ = 0 cos − sin ⎦ ⎣ z
y
⎤
Physical properties
(25)
⎥ ⎦
z − a
v20 + 2ad Larc
vd =
where v0 is initial droplet velocity, ad is the droplet acceleration. The initial droplet velocity is derived following the experimental results of Lin et al. (2001) and is expressed as:
v0 = where x, y, z, x , y , z andx , y , z are the axis components of original coordinate Co.0, rotation coordinate Co.1and translation coordinate Co.2,respectively, Uw is the welding speed, t is the time, a is the length between intersection point O and origin of coordinate Co.1, is the tilt angle of arc.
(28)
−0.33692 + 0.00854 I/2rd
(29)
where rd is the droplet radius and expressed as follows:
rd =
3
3vw rw 2 4fd
(30)
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155
where vg and g are the velocity and density of shielding gas, respectively, m is the density of droplet, Cd is the drag coefficient. The velocity of the shielding gas is calculated using the following equation:
vg = k1 × I
(32)
where k1 is a constant and it is equal to 0.25 in this study. The droplet temperature is set to 2500 K according to experimental results given by Siewert et al. (2013). The droplet detachment frequency is equal to the arc pulse frequency because the metal transfer mode is one droplet per pulse, in this study. The radius of velocity inlet boundary is set as the radius of wire. The flow duration in one cycle, td , is determined according to mass conservation and is expressed as: td =
vw rw2 vd rd2 fd
(33)
With defined droplet velocity, radius of velocity inlet and flow duration in one cycle, the droplet volume is then determined which is closely related to the weld geometry. When the iron phase fluid flows into the computation domain, the droplet is transformed into sphere shape with the help of surface tension. 3.9. Boundary conditions As shown in Fig. 6, the simulation model apparently has two phases, i.e., gas phase plotted by blank domain and iron phase plotted by solid domain. In the gas phase domain, plane EFGH is the velocity inlet boundary for droplets generation, plane ABCD is the pressure outlet and other planes are set as wall boundaries. In the iron phase domain, the bottom and lateral planes are set as wall boundaries with heat loss by convection and radiation. The top surface of weldments is treated as free surface tracked by VOF method, and the arc heat and pressure act on that surface as source terms. At top surface, the thermal boundary condition is given as: −
∂T = qa + ql + qd − qcov − qrad − qevp ∂n
(34)
where is thermal conductivity, n is the magnitude of normal vecter of local surface, qa is the arc heat input, ql is the laser heat input, qd is the droplet heat input, qcov , qrad and qevp are heat loss by convection, radiation and evaporation, respectively. qcov = hc (T − T∞ )
4 qrad = SB ε T 4 − T∞
H ∗
qevp = 0.82 !
2MRgu T
H ∗ = HLV +
Fig. 9. Fluid flow field on the transverse cross-section (x = 20 mm).
where vw is the wire feeding speed, rw is the wire radius, fd is the droplet detachment frequency. The droplet acceleration because of the plasma drag force and gravity is given as: ad =
2 3 vg g C +G 8 rd m d
(31)
(35)
P0 exp
c (c + 1) Rgu T 2 (c − 1)
H ∗
T − TLV Rgu TTLV
(36) (37)
(38)
where hc is the convective heat transfer coefficient, T∞ is the ambient temperature, SB is the Stephan-Boltzmann constant, εis the material emissivity, H ∗ is the enthalpy of vapor flowing at sonic velocity, M is the atomic mass, Rgu is the universal gas constant, TLV is the equilibrium temperature between gas phase and liquid phase, HLV is the latent heat of evaporation, and c is a proportionality factor. The velocity boundary condition in the normal direction of surface is given as: −P + 2
∂v n = −PA − PD + s ∂n
(39)
where vn is the normal component of velocity, PA is the arc pressure, PD is the droplet impingement force, and s is surface tension force, and the local surface curvature.
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Fig. 10. Fluid flow field on the transverse cross-section (x = 33 mm).
The velocity boundary condition in the tangential direction of surface is given as:
Surface tension is calculated by the following equation proposed by Sahoo et al. (1988),
∂ ∂T ∂ s =− s ∂n ∂T ∂s
0
(40)
where vs is the tangential component of velocity, s is the tangential vector of local surface.
s = s − A (T − Ts ) − Rg Ts ln
1 + k1 as exp
−H 0 Rg T
(41)
where s 0 is surface tension of pure iron at the melting point, A is the negative of d/dT for pure iron, Rg is the gas constant, s is the surface excess at saturation, k1 is a constant related to the entropy
X.S. Gao et al. / Journal of Materials Processing Technology 242 (2017) 147–159
157
of segregation, as is the activity of sulfur, and H 0 is the standard heat of adsorption. On the wall boundary, there is no heat input but heat loss by convection and radiation, −
∂T = −qcov − qrad ∂n
(42)
The velocity boundary condition is given as: u = 0, v = 0, w = 0
(43)
4. Results and discussion The base metal was 22MnB5 boron alloy steel sheets of thickness 1.5 mm, and the filler material was wire (G3Si1) with a diameter of 1.0 mm. The chemical compositions of these materials are listed in Table 1. The experiments of single mode laser-GMA hybrid welding with oscillation were conducted. The process parameters used in the experiments are listed in Table 2. The material properties used in the simulation are given in Table 3. The solution domain and boundary types for calculation are shown in Fig. 6. The solution domain was set as 60 mm in length, 18 mm in width, and 6 mm in depth with 3 mm height of gas domain to track the free surface of molten pool. Due to a small area of calculation domain compared to the whole workpiece, a forced convective heat transfer coefficient obtained through trial and error was employed. The fine cells with size of 0.25 mm were used in the center domain with 8 mm width marked by blue line, while coarse cells with gradually increasing size were used in other domains. The simulation was conducted by commercial FLUENT package and the Pressure-Implicit with Splitting of Operators (PISOs) pressure-velocity coupling method was employed to solve the governing equations with boundary conditions. All the heat and force source terms were added into the governing equations at every iteration step by user-definedfunctions.
⎧ 36.5 T ≤ 573K ⎪ ⎪ ⎨ −0.040T + 59.630 573K < T ≤ 673K = 673K < T ≤ 1173K 0.013T + 23.901 ⎪ ⎪ ⎩ 39.5
T > 1173K
⎧ 0.409T + 325.727 T ≤ 553K ⎪ ⎪ ⎨ −0.626T + 907.205 553K < T ≤ 673K Cps = 0.211T + 351.615 673K < T ≤ 1173K ⎪ ⎪ ⎩ 600
(44)
(45)
1173K < T ≤ 1760K
4.1. Temperature field evolution and weld geometry Fig. 7 shows three dimensional perspective view of the calculated temperature field. In order to directly show the weld pool profile, the highest temperature in the temperature scale is set as 1760 K which is the solidus temperature of 22MnB5. The red part represents the weld pool and droplets. Fig. 8 shows the calculated temperature field evolution on the transverse cross-section. As shown in Fig. 8(a), the base metal at this cross-section (x = 20 mm) begins to melt at moment t = 0.17 s. At this instant, the arc is 2 mm behind the observing plane (x = 20 mm). At moment t = 0.19 s, the arc just arrives at this plane (x = 20 mm), and one droplet transfers into the weld pool, as shown in Fig. 8(b). As time goes by, the overheated droplet impinges on the side wall of the upper sheet, and the heat carried by droplets promotes the melting of the upper sheet, so that a weld pool boundary profile different from the former moment appears, especially in the upper sheet, as displayed in Fig. 8(c). The temperature gradient in the upper sheet is larger than that in the lower sheet due to more heat dissipation in the two sheets. As the heat source passes away
Fig. 11. Fluid flow field on the longitudinal cross-section (y = 0 mm).
from the plane (x = 20 mm), the cooling stages begins. Fig. 8(d)–(f) show the cooling process of molten metal. The weld pool’s width shrinks before its depth as the temperature gradient on both sides of weld pool are larger, as shown in Fig. 8(d). At moment t = 0.62s, the solidified region gradually elevates owing to the filler metal addition and finally forms the weld reinforcement. At this instant,
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Fig. 12. Comparison of the predicted and measured weld prolife geometry.
the temperature gradient is almost parallel to the sheet surface, which means that the heat transfers only in horizontal direction as shown in Fig. 8(f). 4.2. Molten pool dynamics The calculated flow field evolution on the transverse crosssection at x = 20 mm are displayed in Fig. 9. The melting isotherms and weld pool free surface are portrayed as blue lines. At moment t = 0.17 s, the arc does not arrive at the observation plane (x = 20 mm), and there is no droplet transfer. As demonstrated in Fig. 9(a), the fluid flows outward at the top surface of upper sheet while the fluid flows downward at the side surface of upper sheet. The fluid flow is driven by Marangoni force due to surface tension spatial gradient and gravity at this instant. At moment t = 0.19 s, one droplet impinges on the molten pool on this plane, and the resulting fluid flow becomes the dominant flow pattern in the weld pool. The momentum carried by the droplet forms two flows. One is upward to the upper part of the motel pool, another is downward to the lower part of the molten pool, and the two flows transfer the heat and mass carried by the droplet to the other parts of the weld pool, as shown in Fig. 9(b). When the observing plane is just behind the droplet impinging position, the molten metal flows upward due to backward flow caused by droplet impingement force, as shown in Fig. 9(c) and (d). With increasing distance between droplet impinging position and the observing plane, the effect of droplet impingement on fluid flow at this plane decreases. As shown in Fig. 9(e), there is a counterclockwise vortex in the molten pool, which is distinct from the flow mode in bead-on-plate welding process where there are two symmetric vortexes corresponding to the weld center line, as agreed upon by DebRoy and David (1995). The molten metal flows from the upper part to the lower part near the surface and flows backward with a reduced velocity after it strikes the weld pool bottom. The downward flow in the molten pool surface is driven by Marangoni shear stress and gravity, and the upward flow loses its velocity due to the friction dissipation in the fluid. The heat and momentum delivered by droplets have significant influence on the weld pool geometry and temperature field. In order to investigate the droplet effects directly, the transverse cross-section at x = 33 mm is chosen to observe the variation of the flow velocity field during one droplet impingement process.
In Fig. 10, a different temperature scale is used. The regions with temperature 1760 K and above (yellow and those on the right of yellow in the temperature legend) represent the weld pool. Before the droplet impingement (t = 0.325 s), the molten metal is distributed on both sides of the molten pool, and the molten layer is thin at the middle part of weld pool. When the droplet impinges on the middle part of the molten pool, the molten metal layer at this location is too thin to dampen the flow momentum. The droplet with relatively high momentum strikes the bottom of molten pool and splits into two flows which transfer the heat and mass of the droplet to the upper and lower parts of the weld pool, respectively. As shown in Fig. 10(b), the upper sheet melts pronouncedly after the droplet impingement. The flow pattern in Fig. 10(c) is similar with that in Fig. 9(e). Since the fluid flow in the weld pool is three dimensional, the flow pattern on the transverse cross-section alone is not adequate to present a full description. Fig. 11 shows the fluid flow field on the longitudinal cross-section at y = 0 mm. The flow patterns accessed from the transverse cross-section can be confirmed by those from the longitudinal cross-section. As shown in Fig. 11(a), the molten metal flows forward and backward due to the droplet impingement, and the forward flow corresponds to the extra molten metal when the material begins to melt in Fig. 8(a). The fluid flow velocity decreases as the distance from the impingement point increases. The two flows reunite on the weld pool surface at a position behind the weld pool where the temperature is about 2000 K. This indicates that the driving force has been changed from droplet impingement force to Marangoni shear stress, because the temperature corresponding to the highest surface tension is 1966 K. The interior molten metal flows upward in the rear part of weld pool, corresponding to the reverse flow pattern in Fig. 9(e). 4.3. Validation of the model It is the common way to validate the simulation results by experimentally measured transverse cross-section geometry of weld. The weld transverse cross-section consists of fusion line and reinforcement profile. Fig. 12 presents that the calculated fusion line is in fair agreement with the corresponding experimental result, while the reinforcement profile exhibits marginal difference. The calculated height of reinforcement is slightly lower, while the calculated bead width is slightly higher. This minor discrepancy may be due to
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the small viscosity value and the assumption that the fluid in weld pool is incompressible. The underestimated viscosity may make the droplet impingement force driven outward flow spread easier across a larger area, and the molten metal conserves its volume during solidification process, resulting in insufficient shrinkage of weld pool. On the other hand, the minor surface tension differences between applied model and the real welding process may also contribute to the small discrepancy in the final weld profile. 5. Conclusions A three dimensional transient numerical model is developed to understand the temperature field and fluid flow in oscillating single mode laser-GMA hybrid lap welding process. This model is one of the very few that dealt with the intricacies associated with lap joint simulation. Validity of the model is examined by comparison of calculated results with experimental results. The conclusions are as follows. (1) The distinct temperature fields were related to the lap joint and arc inclination configuration. The temperature gradient and the heat conduction speed in the upper sheet are higher than those in the lower sheet during welding. During solidification process, the weld pool’s width shrinks before its depth. In the end, heat transfer occurs exclusively in the horizontal direction. (2) Two characteristic flow patterns appear after droplet impingement with an inclination angle, one flowing upward towards the upper sheet and the other flowing downward towards the lower sheet. Both the flows transfer droplet-induced-heat and momentum from the impingement position to the other parts of weld pool. Appropriate velocity and impingement position of droplet produces reasonable weld geometry. (3) The fluid flow near the droplet impingement position is outward and driven by droplet impingement force while that in the rear of weld pool exhibits a counterclockwise vortex and is governed by Marangoni force and gravity. (4) Good precision between the weld cross-section profiles obtained from the experiment and proposed model confirms that the model fairly represents the heat distribution of arc and laser. The spatially averaged oscillating laser heat distribution prevents a deep-penetration through workpiece along laser path and a stable arc heat distribution due to metal vapor produces continuous and effective weld joint. In addition, flow characteristics of oscillating laser-GMA hybrid welding in lap configuration also can be proved reliable. Acknowledgements The authors wish to thank the financial support for this research from Shandong Province Natural Science Foundation in China (Grant No. ZR2014EEM002). They are also grateful to the PPP Program, i.e., Project based Personnel Exchange Program with China Scholarship Council and German Academic Exchange Service (DAAD).
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References Brackbill, J.U., Kothe, D.B., Zemach, C., 1992. A continuum method for modeling surface tension. J. Comput. Phys. 100 (2), 335–354. Cho, J., Farson, D.F., Milewski, J.O., Hollis, K.J., 2009. Weld pool flows during initial stages of keyhole formation in laser welding. J. Phys. D: Appl. Phys. 42, 175502. Cho, W., Na, S., Cho, M., Lee, J., 2010. Numerical study of alloying element distribution in CO2 laser–GMA hybrid welding. Comp. Mater. Sci. 49 (4), 792–800. Chsel, J., Loeschner, U., Schwind, S., Hartwig, L., Schille, J., Exner, H., Huebner, P., Eysert, A., 2013. Highspeed laser welding of steel using a high-power single-mode continuous-wave fiber laser. SPIE LASE (86030L-86030L-11). DebRoy, T., David, S.A., 1995. Physical processes in fusion welding. Rev. Mod. Phys. 67 (1), 85. Ebert-Spiegel, M., Goecke, S.F., Rethmeier, M., 2015. Possibilities for compensating a higher heat input, in particular by the torch offset relative to the top sheet at the fillet weld on a lap joint. Weld. World 59 (3), 443–453. Kim, C.H., Zhang, W., DebRoy, T., 2003. Modeling of temperature field and solidified surface profile during gas–metal arc fillet welding. J. Appl. Phys. 94 (4), 2667. Kumar, A., DebRoy, T., 2007. Heat transfer and fluid flow during gas-metal-arc fillet welding for various joint configurations and welding positions. Metall. Mater. Trans. A. 38 (3), 506–519. Lin, Q., Li, X., Simpson, S.W., 2001. Metal transfer measurements in gas metal arc welding. J. Phys. D: Appl. Phys. 34 (3), 347–353. Möller, F., Kügler, H., Kötschau, S., Geier, A., Goecke, S.F., 2014. Gap bridging ability in laser GMA hybrid welding of thin 22MnB5 sheets. Phys. Procedia 56, 620–629. Meng, X.M., Qin, G.L., Su, Y.H., Fu, B.L., Ji, Y., 2015. Numerical simulation of large spot laser + MIG arc brazing–fusion welding of Al alloy to galvanized steel. J. Mater. Process. Technol. 222, 307–314. Murphy, A.B., 2015. A perspective on arc welding research: the importance of the arc, unresolved questions and future directions. Plasma Chem. Plasma Process. 35 (3), 471–489. Piekarska, W., Kubiak, M., 2011. Three-dimensional model for numerical analysis of thermal phenomena in laser–arc hybrid welding process. Int. J. Heat Mass Transfer 54 (23–24), 4966–4974. Rossini, M., Spena, P.R., Cortese, L., Matteis, P., Firrao, D., 2015. Investigation on dissimilar laser welding of advanced high strength steel sheets for the automotive industry. Mater. Sci. Eng. A. 628, 288–296. Sahoo, P., Debroy, T., McNallan, M.J., 1988. Surface tension of binary metal—surface active solute systems under conditions relevant to welding metallurgy. Metall. Trans. B. 19 (3), 483–491. Siewert, E., Schein, J., Forster, G., 2013. Determination of enthalpy, temperature, surface tension and geometry of the material transfer in PGMAW for the system argon–iron. J. Phys. D: Appl. Phys. 46 (22), 224008. Thiel, C., Hess, A., Weber, R., Graf, T., 2012. Stabilization of Laser Welding Processes by Means of Beam Oscillation. SPIE Photonics Europe International Society for Optics and Photonics. Tsao, K.C., Wu, C.S., 1988. Fluid flow and heat transfer in GMA weld pools. Weld. J. 67 (3), 70s–75s. Zhang, Z.Z., Wu, C.S., 2015. Effect of fluid flow in the weld pool on the numerical simulation accuracy of the thermal field in hybrid welding. J. Mater. Process. Technol. 20, 215–223. Zhou, J., Tsai, H.L., 2008. Modeling of transport phenomena in hybrid laser-MIG keyhole welding. Int. J. Heat Mass Transfer. 51 (17–18), 4353–4366.
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Numerical simulation of temperature field, fluid flow and weld bead formation in oscillating single mode laser-GMA hybrid welding X.S. Gao a , C.S. Wu a,∗ , S.F. Goecke b , H. Kügler c a b c
MOE Key Lab for Liquid-Solid Structure Evolution and Materials Processing, Institute of Materials Joining, Shandong University, Jinan 250061, China Technische Hochschule Brandenburg, Brandenburg an der Havel, D-14770, Germany BIAS- Bremer Institut fuer Angewandte Strahltechnik, Bremen, D-28359, Germany
a r t i c l e
i n f o
Article history: Received 25 October 2016 Received in revised form 22 November 2016 Accepted 23 November 2016 Available online 24 November 2016 Keywords: Oscillating laser-GMA hybrid welding Lap joint Three dimensional numerical model Droplet impingement Weld pool behavior
a b s t r a c t A three dimensional numerical model of oscillating single mode laser-GMA hybrid welding process with lap joint and arc inclination configuration has been developed for the first time. The model is used to investigate the temperature field and fluid flow corresponding to the aforesaid welding process and weld configuration. An asymmetric distribution of arc heat and a cylindrical volumetric distribution of laser heat are established to describe the heat transfer from the combined heat source to the workpieces. The droplet with predefined temperature and velocity is impinged on the weld pool at a given fillet weld angle. Arc pressure, electromagnetic force, Marangoni force and buoyancy are also considered in the model with some modifications with respect to the lap joint and arc inclination configuration. Results show that the droplet impingement process has a significant influence on the weld geometry, temperature field and fluid flow pattern due to the transfer of mass, energy and momentum into the weld pool. These unique temperature fields and flow patterns are characteristic to the lap joint and arc inclination configuration. The proposed model exhibits close correspondence with the experimental results with respect to weld geometry. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Press-hardened steels are candidate materials for crashresistance applications in automobile industry. However, their efficient welding is an issue. Rossini et al. (2015) have found that laser butt welding successfully joins dissimilar advanced high strength steels such as TRIP steel, DP steel and 22MnB5 steel combinations and this process is an effective solution to assemble car body parts. Oscillating single mode laser welding has the advantages of high welding speed and excellent concentrated heat density. In the oscillating single mode laser welding of 22MnB5 steels, Chsel et al. (2013) have reported a 10% loss in tensile strength of weld joint as compared to the parent metal. In addition, the above process is involved with strict demands for workpiece alignment and no feeding wire, which limit application of the process in the automobile industry where welding of various joint types with inevitable gaps is essential. On the other hand, the gas metal arc (GMA) welding process is widely used in the current automobile industry because of its excellent gap-bridge ability, meeting the
∗ Corresponding author. E-mail address: [email protected] (C.S. Wu). http://dx.doi.org/10.1016/j.jmatprotec.2016.11.028 0924-0136/© 2016 Elsevier B.V. All rights reserved.
demands of most weld joint types and welding positions. However, high welding speeds make the GMA welding process unstable, so relatively low welding speeds are recommended. It appears that introduction of laser to stabilize the arc process at higher welding speeds is a good option to improve the GMA welding process. Thereby, a new hybrid welding process consisting of an oscillating single mode laser and a conventional pulsed gas metal arc can be a useful prospect for welding ultra-high strength steel structures with lap joint and gap-bridging configuration in automobile manufacturing. Due to the lap joint configuration and the high welding speed and welding current, this oscillating single mode laser-GMA hybrid welding process displays distinct features, such as high velocity droplet impingement, complex fluid flow in weld pool and varied arc heat distribution. However, the current experimental and simulation research on this hybrid welding process is too limited to formulate a knowledge base. Numerical simulation, in general, is a powerful tool to obtain complete understanding of the physical phenomena and the underlying mechanisms of welding processes, as emphasized by Murphy (2015). Therefore, development of mathematical models focusing on the characteristics of the heat distribution, temperature field and fluid flow behavior in the weld pool of oscillating single mode laser-GMA hybrid lap
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Fig. 1. Sketch of combined heat source of oscillating laser-GMA hybrid welding.
welding process would be an ideal approach to achieve the process optimization. For general laser-GMA hybrid welding process, several mathematical models have been developed. Piekarska and Kubiak (2011) described the arc heat and laser heat by ‘double ellipsoidal’ heat model and CIN model respectively to estimate the temperature field and fluid velocity field in the weld pool. Zhang and Wu (2015) investigated the influence of molten fluid flow on temperature field, thermal cycles and weld geometry by a three dimensional quasisteady state laser-GMA hybrid welding model, but used a keyhole model presumably set in the computational domain. Cho et al. (2010) suggested a complicated laser heat source model based on summation of laser radiation by ray tracing technique combined with a Gaussian plane arc heat distribution model. Nonetheless, all these models are concerned with general laser-GMA hybrid welding process in bead-on-plate configuration. Regarding complex joint types, Kim et al. (2003) developed a three dimensional heat conduction model for the GMA welding of fillet joints. In their model, the arc heat was described by a classic Gaussian plane heat source model using a boundary fitted coordinate system. Kumar and DebRoy (2007) developed a numerical model to investigate the effects of the fillet joint tilt angle and weld positions on the temperature profiles and fluid flow field in GMA fillet welding process. To the authors’ knowledge, the number of numerical models of lap weld joints are relatively much lower than those for fillet weld joints. A possible reason for scarcity of investigations is the irregular arc characteristics resulted from the intrinsic asymmetry of lap joint which makes it difficult to model the welding process. Meng et al. (2015) considered the effects of lap joint on the arc heat distribution and calculated the temperature field of large spot laser-MIG arc brazing-fusion welding of Al alloy to galvanized steel in lap joint. The model dealt with temperature field caused by heat conduction, but did not include the influence of fluid flow which in fact plays a critical role in determining the weld pool geometry and thermal history, as suggested by Zhou and Tsai (2008). In this study, a three dimensional transient heat transfer and fluid flow model was developed to conduct numerical analysis of the oscillating single mode laser-GMA hybrid welding of lap joint. Experiments were carried out to validate the results of numerical simulation.
2. Characteristic of oscillating laser-GMA hybrid welding The oscillating single mode laser-GMA hybrid welding process where the gas metal arc plays the major role is different from the general laser-GMA hybrid welding process where the laser produces deep penetration in thick plates. The single mode laser is used as an assistant approach to stabilize arc. Thiel et al. (2012) have found that the single mode laser requires oscillation movements to redistribute the locally constricted energy so that a more continuous and stable hybrid welding process can be realized. In our hybrid welding experiments, the weld cross-sections with and without laser oscillations are almost similar. However, the weld without laser oscillation shows a deep-penetration channel along the laser path when the welding speed reaches 6 m/min. This penetration channel is due to the localization of extremely high heat of the single mode laser. Moreover, the penetration channel has propensity to decrease weld mechanical properties by expanding the heat affected zone. On the other hand, the weld cross-section with laser oscillation is free from this penetration channel. Therefore, oscillation of laser is extremely important to normalize the laser heat deposition area and improve its efficiency. Keeping in view the wide use of lap welded sheet joints in automobile industries, a lap configuration with a welding speed as high as 6 m/min is considered in this study. As suggested by Möller et al. (2014), the lap welding is conducted by employing a fillet weld angle of 30 ◦ to melt off more of the upper sheet edge and transfer less heat to the bottom sheet. Fig. 1 shows the schematic of combined heat source of oscillating single mode laser–GMA hybrid welding for lap joint. It conveys the following characteristics of this hybrid welding: (a) the GMA process and an oscillating laser beam transfer heat to weldment, (b) the lap joint and arc inclination configuration make the experimental process and mathematical modelling more complicated, and (c) droplets carrying heat, mass and momentum impinge on the weld pool at a specific angle. Oscillation is perpendicular to welding direction in line pattern at an optimum amplitude and frequency, and changes laser heat distribution. For the lap joint, the heat flux and pressure from the arc are distributed in ways different from that for a bead-on-plate or a butt joint. Therefore, the hybrid heat source distribution should be established by taking the lap joint into consideration, and the droplet transfer should be accurately
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Fig. 2. Asymmetric distribution of arc heat on the workpiece.
Fig. 3. Sketch of heat distribution of inclined arc on lap joint.
estimated in terms of the amount of mass, heat and momentum as well as the direction of momentum. In the current simulation model of oscillating single mode laserGMA hybrid process for lap configuration, it is necessary to address some coordinate systems defined to deal with welding speed, lap joint and arc inclination configuration. To simplify the definitions, the laser beam is considered to move along the welding centerline without oscillation. As shown in Fig. 1(a), the original coordinate Co.0 (Oxyz) defined by the software is still with the workpiece where all the solution work, i.e., equation discretization and numerical iteration, is done. The coordinate Co.1 (O x y z ) is introduced to describe the moving combined heat source of arc and laser in the lap joint. The origin of Co.1, O , is the intersection between the axis of laser beam and the welding centerline, and the point Oarc is the intersection between the axis of arc and the welding centerline, denoting the arc leading configuration. On one hand, the x axis of Co.1 is collinear with x axis of Co.0, and the speed of Co.1 equals to the welding speed. On the other hand, the z axis of Co.1 has an angle of 30 ◦ against the vertical direction to the workpiece, as shown in Fig. 1(b). In order to describe the heat and force dis-
tribution on the weld pool surface, a coordinate Co.2 (O"x"y"z") is defined, and the origin of Co.2, O", is the intersection between the axis of laser beam and the weld pool surface. The transformation between these coordinates will be explained in a later section. In addition, following assumptions are made to simplify the whole process: (i) the molten metal is assumed as incompressible Newtonian fluid; (ii) the deposition of laser heat is in conduction mode due to high welding speed as well as high oscillating frequency of laser beam; (iii) the small gap between the two sheets in lap joint to help the aluminium vapour to escape is ignored in the simulation since the gap has insignificant effects on the weld geometry and fluid flow in weld pool; (iv) average current and voltage are used to calculate the arc power, and the pulse effect is neglected.
3. Mathematical formulations In the oscillating laser-GMA hybrid welding process of steel sheets in lap joint, the workpieces are heated, melted, even evaporated. When a weld pool is formed, the molten metal flow occurs, which determines the heat transfer in the weld pool.
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Fig. 4. Schematic representation of coordinate transformation.
Fig. 5. Schematic representation of droplet transfer.
3.1. Governing equations
fraction set as 0.68. The liquid fraction fl is assumed as a linear function of temperature:
The governing equations describing the heat and mass transfer phenomena and fluid dynamics in laser-GMA hybrid welding process include mass, momentum and energy conservation equations. Continuity equation
∇ ·V =0
fl =
∂V + V · ∇V ∂t
= −∇ P + ∇ 2 V − Cmushy
(1 − fl ) fl3
+A
(2)
where is the fluid density, t is the time, P is the hydrostatic pressure, Cmushy is the mushy zone constant, A is a small positive constant. The third term on the right-hand side of Eq. (2) is the momentum sink due to the reduced porosity in the mushy zone. G is the gravitational acceleration due to body force. fl is the liquid fraction. is the dynamic viscosity which is set as a large number in solid zone, a relatively small constant in liquid zone and a function of liquid fraction in the mushy zone (Cho et al., 2009) expressed as follows:
=
⎧ 100 ⎪ ⎨ ⎪ ⎩
min l
l 1 − (1 − fl ) /fscr
−1.55
T < Ts
, 100
T − Ts
Ts ≤ T ≤ Tl
T − Ts ⎪ ⎪ ⎩ l
(4)
T > Tl
Energy equation
2
V + G
T < Ts
1
(1)
where V is the velocity vector of fluid flow in weld pool. Momentum equation
⎧ 0 ⎪ ⎪ ⎨
∂h + V · ∇h ∂t
= ∇ · (∇ T )
(5)
The energy is formulated by enthalpy continuum model in the solid-liquid phase transition:
h=
⎧ C T ⎪ ⎨ ps ⎪ ⎩
T ≤ Ts
h (Ts ) + fl × Lf
Ts ≤ T ≤ Tl
h (Tl ) + Cpl (T − Tl )
T > Tl
(6)
where h is the enthalpy of material, is the thermal conductivity, Cps is the specific heat of solid phase and Cpl is the specific heat of liquid phase, Lf is the latent heat of fusion, fl is the liquid fraction as described by Eq. (4).
(3)
Ts ≤ T < Tl Tl ≤ T
where l is the molten metal viscosity, Ts is the solidus temperature, Tl is the liquidus temperature, fscr is the characteristic solid
3.2. VOF method VOF method is used to track the free surface between two or more fluid phases which are not interpenetrating. The fluid phase
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Fig. 6. Solution domain and boundary types for calculation.
Fig. 7. 3-D perspective views of temperature field at moment t = 0.325 s.
configuration is defined by volume fraction function F. The function F is governed by the following conservation equation:
∂F + ∇ · (V F) = 0 ∂t
(7)
The material properties in the transport equations are determined by the presence of the component phases in each control volume in VOF method. Some specific material property of the computing cell involving iron phase and gas phase is defined as follows: Pc = FFe PFe + (1 − FFe )Pair
(8)
where Pc is the volume fraction weighted average material property, Pi is the ith phase’s material property, Fi is the ith phase’s volume fraction. 3.3. Arc heat source 3.3.1. An asymmetric distribution of arc heat in lap joint In this high speed welding process with lap configuration and arc inclination, the arc heat distribution on the workpiece is asymmetric not only in the welding direction but also in the transverse direction. Defining heat distribution between the two sheets is
always a critical problem in lap joint welding, as investigated by Ebert-Spiegel et al. (2015). The arc heat distribution is defined in coordinate Co.1, where four distribution parameters, af ,ar ,bp and bn are introduced to represent the heat distribution features for lap joint and arc inclination configuration, as shown in Fig. 2. When an inclined arc deposits on the weldments of lap joint, the heat density at local points on the receiving surface differs depending on the distance from those points to the wire tip. As shown in Fig. 3, since the distance from point B to the wire tip is shorter than that from point A to the wire tip, the heat flux density at point B is larger than that at point A, according to the principle of minimum voltage in theory of arc physics. Thus, the distance between the points on the weld pool surface to the wire tip should be taken into account in modeling the arc heat distribution for inclined arc in lap joint. The heat flux at a point on the weld pool surface is inversely proportional to the square of the distance between the point and the wire tip. Therefore, a dimensionless factor d is introduced into the arc heat model:
d=
2 Lpa 2 Larc
(9)
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where Lpa is the distance between the computing cell and wire tip, Larc is the arc length which is assumed to be the distance between the wire tip and the intersection point of the extension line of wire tip and welding centerline as shown in Fig. 3. To keep the arc power conserved, a calculation adjustment parameter, Kd is used, which is defined by comparison between the theoretical arc power and the actually loaded power in the computation domain. The arc heat distribution is expressed as follows: qa (x , y ) =
qa (x , y ) =
qa (x , y ) =
qa (x , y ) =
Kd · 12UI
Kd · 12UI
Kd · 12UI
Kd · 12UI
af + ar
af + ar
af + ar
af + ar
(bp + bn ) d
(bp + bn ) d
(bp + bn ) d
(bp + bn ) d
exp −
exp −
exp −
exp −
3(x − dla )
2
−
a2f 3(x − dla )
2
a2f 3(x − dla )
2
−
a2r 3(x − dla ) a2r
−
2
−
3y 2 b2p 3y 2 b2n 3y 2 b2p 3y 2 b2n
UI
qa
where [F] stands for the volume fraction change of iron phase across the thickness of the free surface and obviously equals to zero here. and Cp are the mean density and mean specific heat of iron phase and gas phase, respectively. The term, (xi ) Cp (xi ) / Cp is used to avoid change of free surface thickness caused by energy source term. 3.4. Laser heat source
, x − dla ≥ 0, y < 0
, x − dla < 0, y ≥ 0
, x − dla < 0, y < 0
(11)
(x , y )dx dy
S
where U is the average voltage, I is the average welding current, Uw is the welding speed, dla is the distance between laser and arc, is the heat transfer efficiency of the electric arc and 0.52 was used in this study with reference to the experimental measurement results given by Siewert et al. (2013). 3.3.2. Asymmetric volumetric distribution of arc heat In FLUENT, the heat flux on the weld pool surface has to be transformed into a volumetric term when it is added into the energy conservation equation as a source term. In order to keep energy conserved, the CSF (continuum surface force) model proposed by Brackbill et al. (1992) was used to transform the plane heat flux into volumetric heat flux. As shown in Fig. 3, the heat flux vector on the weld pool surface, qS , is defined as follows: qS = qP n
(16)
, x − dla ≥ 0, y ≥ 0
(10)
Kd =
qV = qVx (x ) + qVy (y ) + qVz (z )
(12)
To develop a laser distribution, it’s worth noting the physical mechanisms of the interaction of the arc with the oscillating beam. In fact, the interactions may be broken down to two phenomena: the arc stabilization and the net heat generation. In the first, the oscillating laser is the most beneficial when the welding speed is high. In single GMA welding process, the arc becomes unstable and its attachment spot undergoes frequent fluctuations at welding speeds as high as 6 m/min. However, in oscillating laser-GMA hybrid welding process, the single mode laser produces considerable amounts of metal vapor, providing conductive channel for arc plasma, such that the arc becomes stable and deposits heat successively. In the second, the oscillation provides chance for homogenization of laser power which has been explained in more detail in Section 2. The heat, producing an undesirable deeppenetration channel without oscillation now contributes to form a more effective joint. Together with a stable arc heat deposition, the total net heat generation has been improved. In summary, the laser oscillations affect the laser heat distribution by homogenizing the laser power and the arc stabilization by controlling the metal vapor behavior in wavering zone. In fact, the generated metal vapor and its subsequent contribution to arc stabilization change a little, owing to the small oscillation amplitude as well as high welding speed. As an initial state of this study, the oscillating laser heat distribution is considered in a simplified way by neglecting the oscillation effects on metal vapor. Laser heat is supposed to be dispersed on the region along the weaving locus and its density is treated with a spatial averaging method. Therefore, the laser power is assumed as a cylindrical volumetric heat source characterized by power density uniform in the radial direction and exponentially decaying down the penetration depth. It is defined in coordinate Co.2 and described by the following formula:
ln
where qP is the heat flux value at the projection point B’, and n is the normal vector of local surface. qP is calculated by Eq. (10), qS has three components, qSx , qSy and qSz in Cartesian coordinates:
ql (x"e; , y"e; , z"e; ) =
qSx = qS cos ˛
where rL and H are the effective radius and height of laser heat source, respectively and is the attenuation coefficient determined by empirical value.
qSy = qS cos ˇ
(13)
qSz = qS cos
Hr 2L
( − 1)
exp
( ) z"e; H
(17)
3.5. Arc pressure
where ˛,ˇ, are the direction angles of normal vector n with respect to x, y, z axis, respectively. n is defined by gradient of volume fraction as follows: n = ∇F
It is assumed that the distribution of welding current density is in the same mode as the heat flux distribution, and then the arc pressure distribution, defined in coordinate Co.1, is written as:
(14)
Following the mathematical method proposed by Brackbill et al. (1992), the volumetric components of heat flux, derived from the plane heat flux, are given as:
PA = Cj
PA = Cj
∇ F (x ) (x ) Cp (x )
qVx (x ) = qSx (x )
[F]
qVy (y ) = qSy (y ) qVz (z ) = qSz (z )
l Ql ln ( )
Cp
∇ F(y ) (y )Cp (y ) [F]
Cp
∇ F (z ) (z ) Cp (z ) [F]
Cp
(15)
2
2
2
2
(x − dla ) y 2 30 I 2 exp −3 −3 2 2 (ar + af ) (bn + bp ) d af 2 bp
2 (ar
(x − dla ) y 2 30 I 2 exp −3 −3 2 + af ) (bn + bp ) d af 2 bn
PA = Cj
(x − dla ) y 2 30 I 2 exp −3 −3 2 2 (ar + af ) (bn + bp ) d ar 2 bp
PA = Cj
(x − dla ) y 2 30 I 2 exp −3 −3 2 2 (ar + af ) (bn + bp ) d ar 2 bn
x − dla ≥ 0, y ≥ 0
x − dla ≥ 0, y < 0
(18) x − dla < 0, y ≥ 0
x − dla < 0, y < 0
where Cj is the adjustment factor for arc pressure and 0 is the permeability of vacuum.
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153
Fig. 8. Temperature field on the transverse cross-section (x = 20 mm).
3.6. Electromagnetic force A simplified expression suggested by Tsao and Wu (1988) is employed to calculate the electromagnetic force inside the weld pool, and it is defined in coordinateCo.2, Fex = −
Fey = −
Fez =
m I 2 42 j2 r m I 2 42 j2 r
I2
−
exp
−
exp
r2 2 j2 r2
1 − exp
m 1 − exp 42 r 2 L
−
−
1 − exp
2 j2
r2 2 j2
−
2
r2 2 j2 r2
z 1− L
1−
2 j2
2
1−
z"e; L
z"e; L
(x − dla ) r
2
y"e; r
(19)
(20)
(21)
r=
2
(x"e; −dla ) + y"e;2
(22)
where m is the material permeability, r is the distance to arc heat source center, L is the effective sheet thickness, and j is the electromagnetic force distribution parameter. j is determined by asymmetric heat distribution parameters as follows:
j =
af + ar
bp + bn
24
(23)
3.7. Coordinate transformation As demonstrated in Section 2, this simulation model involves several coordinates due to the complex hybrid welding process. All the governing equations are solved in the original coordinate Co.0(Oxyz) by the software packages, while the heat and force distribution of laser and arc are established in the coordinates Co.1(O x y z ) and Co.2(O x y z ) moving with the hybrid head. In order to apply the heat and force analytical formula in the com-
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Table 1 Chemical composition of used material in experiments. Material
C
Si
Mn
P
S
Al
Nb
Ti
Cr + Mo
B
22MnB5 G3Si1
0.25 0.08
0.40 0.9
1.40 1.5
0.025 0.015
0.010 0.012
0.015 –
0.10 –
0.05 –
0.50 –
0.005 –
Table 2 Process parameters.
Table 3 Material properties used in the simulation.
Laser power, Ql (kW) Laser beam oscillation frequency, fo (Hz) Laser beam oscillation amplitude, 2As (mm) Average welding current, I(A) Average arc voltage, U(V) Pulse frequency, f (Hz) Laser-arc-distance, dla (mm) Fillet weld angle, (degree) Welding speed, Uw (m/min) Wire feeding rate, WFS(m/min)
1 200 0.7 320 36 250 1 30 6 20
putation domain, the original coordinate needs translation and rotation transformations. As shown in Fig. 4(a), the original
coordinate Co.0(Oxyz) should be transformed to Co.0 O x with a translation by a distance equal to the product of welding speed and time (Uw t) to represent the
moving combined heat source. Then, the coordinate Co.0 O x should be transformed to Co.1(O x y z ) with a counterclockwise rotation by an angle to calculate the arc heat and arc pressure distributions, as shown in Fig. 4(b). In order to deal with the electromagnetic force and volumetric laser heat terms, choice of reference plane in the lap configuration is puzzling, while the top weld surface is the reference plane in butt joint. In this case, weld pool free surface is assumed as the reference plane, and a tracking algorithm is conducted at every time step to obtain the intersection point, O between the laser beam axis and the free surface of weld pool. Then, the coordinate Co.1(O x y z ) is translated to that intersection point to get the coordinate Co.2(O x y z ). The forward and backward transformations between coordinateCo.0, Co.1 and Co.2 are expressed as follows:
⎡ ⎤ x
⎡
1
0
0
⎤⎡
x − Uw t
⎣ y ⎦ = ⎣ 0 cos − sin ⎦ ⎣ z
0
⎡ ⎤ x
⎡
1
⎣y⎦ = ⎣0 z
⎡
x
0
⎤
⎡
1
sin 0 cos − sin
0
cos 0
⎤⎡
x + Uw t
sin ⎦ ⎣
y
cos
z
0
0
⎡ ⎤ x
⎡
1
⎣y⎦ = ⎣0 z
0
sin
0
⎤⎡
cos − sin
cos
0
x − Uw t y
⎤⎡
x + Uw t y
(24)
⎤ ⎦
⎤ ⎡ ⎤ 0
7200 1800 1760 3100 temperature dependent, Eq. (44) 754 temperature dependent, Eq. (45) temperature dependent 1.5 × 10−6 temperature dependent 0.4 1.26 × 10−6 3.13 × 105 7.34 × 106
3.8. Droplet transfer In GMA welding, the wire melts continuously. Droplets form at the wire tip and then transfer into the weld pool. The droplets are treated as iron phase fluid which flows into the computation domain periodically from the velocity inlet boundary. For the study case, the arc is inclined to the vertical line by 30 ◦ , and the droplets are assumed to flow into the molten pool along the arc axis. Since the fluid flow in weld pool is affected by droplet impingement during high current GMA welding process, the inclination feature of droplets should be taken into consideration. The droplet temperature, droplet velocity, droplet detachment frequency, radius of velocity inlet and flow duration in one cycle should be defined. The schematic representation of droplet transfer is shown in Fig. 5. The droplet velocity in the velocity inlet boundary has two components in y and z direction, vdy and vdz , respectively, which are expressed as follows:
vdy = vd sin
(26)
vdz = vd cos
(27)
a
⎤
value
Density, (kg/m−3 ) Liquid temperature, Tl (K) Solidus temperature, Ts (K) boiling temperature, TLV (K) Thermal conductivity, (W m−1 K−1 ) Specific heat of liquid phase, Cpl (J kg−1 K−1 ) Specific heat of solid phase, Cps (J kg−1 K−1 ) Viscosity, (kg m−1 s −1 ) Coefficient of thermal expansion, ˇ (K−1 ) Surface tension coefficient, (N m−1 ) Emissivity, ε Magnetic permeability, m (H m−1 ) Latent heat of fusion, Lf (J kg−1 ) Latent heat of vaporization, HLV (J kg−1 )
where vd is the droplet velocity calculated by the method suggested by Kim et al. (2003),
⎦+⎣0⎦
z
⎢ sin ⎦ ⎣ cos
⎦
z
⎢ ⎥ ⎣ ⎣ y ⎦ = 0 cos − sin ⎦ ⎣ z
y
⎤
Physical properties
(25)
⎥ ⎦
z − a
v20 + 2ad Larc
vd =
where v0 is initial droplet velocity, ad is the droplet acceleration. The initial droplet velocity is derived following the experimental results of Lin et al. (2001) and is expressed as:
v0 = where x, y, z, x , y , z andx , y , z are the axis components of original coordinate Co.0, rotation coordinate Co.1and translation coordinate Co.2,respectively, Uw is the welding speed, t is the time, a is the length between intersection point O and origin of coordinate Co.1, is the tilt angle of arc.
(28)
−0.33692 + 0.00854 I/2rd
(29)
where rd is the droplet radius and expressed as follows:
rd =
3
3vw rw 2 4fd
(30)
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where vg and g are the velocity and density of shielding gas, respectively, m is the density of droplet, Cd is the drag coefficient. The velocity of the shielding gas is calculated using the following equation:
vg = k1 × I
(32)
where k1 is a constant and it is equal to 0.25 in this study. The droplet temperature is set to 2500 K according to experimental results given by Siewert et al. (2013). The droplet detachment frequency is equal to the arc pulse frequency because the metal transfer mode is one droplet per pulse, in this study. The radius of velocity inlet boundary is set as the radius of wire. The flow duration in one cycle, td , is determined according to mass conservation and is expressed as: td =
vw rw2 vd rd2 fd
(33)
With defined droplet velocity, radius of velocity inlet and flow duration in one cycle, the droplet volume is then determined which is closely related to the weld geometry. When the iron phase fluid flows into the computation domain, the droplet is transformed into sphere shape with the help of surface tension. 3.9. Boundary conditions As shown in Fig. 6, the simulation model apparently has two phases, i.e., gas phase plotted by blank domain and iron phase plotted by solid domain. In the gas phase domain, plane EFGH is the velocity inlet boundary for droplets generation, plane ABCD is the pressure outlet and other planes are set as wall boundaries. In the iron phase domain, the bottom and lateral planes are set as wall boundaries with heat loss by convection and radiation. The top surface of weldments is treated as free surface tracked by VOF method, and the arc heat and pressure act on that surface as source terms. At top surface, the thermal boundary condition is given as: −
∂T = qa + ql + qd − qcov − qrad − qevp ∂n
(34)
where is thermal conductivity, n is the magnitude of normal vecter of local surface, qa is the arc heat input, ql is the laser heat input, qd is the droplet heat input, qcov , qrad and qevp are heat loss by convection, radiation and evaporation, respectively. qcov = hc (T − T∞ )
4 qrad = SB ε T 4 − T∞
H ∗
qevp = 0.82 !
2MRgu T
H ∗ = HLV +
Fig. 9. Fluid flow field on the transverse cross-section (x = 20 mm).
where vw is the wire feeding speed, rw is the wire radius, fd is the droplet detachment frequency. The droplet acceleration because of the plasma drag force and gravity is given as: ad =
2 3 vg g C +G 8 rd m d
(31)
(35)
P0 exp
c (c + 1) Rgu T 2 (c − 1)
H ∗
T − TLV Rgu TTLV
(36) (37)
(38)
where hc is the convective heat transfer coefficient, T∞ is the ambient temperature, SB is the Stephan-Boltzmann constant, εis the material emissivity, H ∗ is the enthalpy of vapor flowing at sonic velocity, M is the atomic mass, Rgu is the universal gas constant, TLV is the equilibrium temperature between gas phase and liquid phase, HLV is the latent heat of evaporation, and c is a proportionality factor. The velocity boundary condition in the normal direction of surface is given as: −P + 2
∂v n = −PA − PD + s ∂n
(39)
where vn is the normal component of velocity, PA is the arc pressure, PD is the droplet impingement force, and s is surface tension force, and the local surface curvature.
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Fig. 10. Fluid flow field on the transverse cross-section (x = 33 mm).
The velocity boundary condition in the tangential direction of surface is given as:
Surface tension is calculated by the following equation proposed by Sahoo et al. (1988),
∂ ∂T ∂ s =− s ∂n ∂T ∂s
0
(40)
where vs is the tangential component of velocity, s is the tangential vector of local surface.
s = s − A (T − Ts ) − Rg Ts ln
1 + k1 as exp
−H 0 Rg T
(41)
where s 0 is surface tension of pure iron at the melting point, A is the negative of d/dT for pure iron, Rg is the gas constant, s is the surface excess at saturation, k1 is a constant related to the entropy
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157
of segregation, as is the activity of sulfur, and H 0 is the standard heat of adsorption. On the wall boundary, there is no heat input but heat loss by convection and radiation, −
∂T = −qcov − qrad ∂n
(42)
The velocity boundary condition is given as: u = 0, v = 0, w = 0
(43)
4. Results and discussion The base metal was 22MnB5 boron alloy steel sheets of thickness 1.5 mm, and the filler material was wire (G3Si1) with a diameter of 1.0 mm. The chemical compositions of these materials are listed in Table 1. The experiments of single mode laser-GMA hybrid welding with oscillation were conducted. The process parameters used in the experiments are listed in Table 2. The material properties used in the simulation are given in Table 3. The solution domain and boundary types for calculation are shown in Fig. 6. The solution domain was set as 60 mm in length, 18 mm in width, and 6 mm in depth with 3 mm height of gas domain to track the free surface of molten pool. Due to a small area of calculation domain compared to the whole workpiece, a forced convective heat transfer coefficient obtained through trial and error was employed. The fine cells with size of 0.25 mm were used in the center domain with 8 mm width marked by blue line, while coarse cells with gradually increasing size were used in other domains. The simulation was conducted by commercial FLUENT package and the Pressure-Implicit with Splitting of Operators (PISOs) pressure-velocity coupling method was employed to solve the governing equations with boundary conditions. All the heat and force source terms were added into the governing equations at every iteration step by user-definedfunctions.
⎧ 36.5 T ≤ 573K ⎪ ⎪ ⎨ −0.040T + 59.630 573K < T ≤ 673K = 673K < T ≤ 1173K 0.013T + 23.901 ⎪ ⎪ ⎩ 39.5
T > 1173K
⎧ 0.409T + 325.727 T ≤ 553K ⎪ ⎪ ⎨ −0.626T + 907.205 553K < T ≤ 673K Cps = 0.211T + 351.615 673K < T ≤ 1173K ⎪ ⎪ ⎩ 600
(44)
(45)
1173K < T ≤ 1760K
4.1. Temperature field evolution and weld geometry Fig. 7 shows three dimensional perspective view of the calculated temperature field. In order to directly show the weld pool profile, the highest temperature in the temperature scale is set as 1760 K which is the solidus temperature of 22MnB5. The red part represents the weld pool and droplets. Fig. 8 shows the calculated temperature field evolution on the transverse cross-section. As shown in Fig. 8(a), the base metal at this cross-section (x = 20 mm) begins to melt at moment t = 0.17 s. At this instant, the arc is 2 mm behind the observing plane (x = 20 mm). At moment t = 0.19 s, the arc just arrives at this plane (x = 20 mm), and one droplet transfers into the weld pool, as shown in Fig. 8(b). As time goes by, the overheated droplet impinges on the side wall of the upper sheet, and the heat carried by droplets promotes the melting of the upper sheet, so that a weld pool boundary profile different from the former moment appears, especially in the upper sheet, as displayed in Fig. 8(c). The temperature gradient in the upper sheet is larger than that in the lower sheet due to more heat dissipation in the two sheets. As the heat source passes away
Fig. 11. Fluid flow field on the longitudinal cross-section (y = 0 mm).
from the plane (x = 20 mm), the cooling stages begins. Fig. 8(d)–(f) show the cooling process of molten metal. The weld pool’s width shrinks before its depth as the temperature gradient on both sides of weld pool are larger, as shown in Fig. 8(d). At moment t = 0.62s, the solidified region gradually elevates owing to the filler metal addition and finally forms the weld reinforcement. At this instant,
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Fig. 12. Comparison of the predicted and measured weld prolife geometry.
the temperature gradient is almost parallel to the sheet surface, which means that the heat transfers only in horizontal direction as shown in Fig. 8(f). 4.2. Molten pool dynamics The calculated flow field evolution on the transverse crosssection at x = 20 mm are displayed in Fig. 9. The melting isotherms and weld pool free surface are portrayed as blue lines. At moment t = 0.17 s, the arc does not arrive at the observation plane (x = 20 mm), and there is no droplet transfer. As demonstrated in Fig. 9(a), the fluid flows outward at the top surface of upper sheet while the fluid flows downward at the side surface of upper sheet. The fluid flow is driven by Marangoni force due to surface tension spatial gradient and gravity at this instant. At moment t = 0.19 s, one droplet impinges on the molten pool on this plane, and the resulting fluid flow becomes the dominant flow pattern in the weld pool. The momentum carried by the droplet forms two flows. One is upward to the upper part of the motel pool, another is downward to the lower part of the molten pool, and the two flows transfer the heat and mass carried by the droplet to the other parts of the weld pool, as shown in Fig. 9(b). When the observing plane is just behind the droplet impinging position, the molten metal flows upward due to backward flow caused by droplet impingement force, as shown in Fig. 9(c) and (d). With increasing distance between droplet impinging position and the observing plane, the effect of droplet impingement on fluid flow at this plane decreases. As shown in Fig. 9(e), there is a counterclockwise vortex in the molten pool, which is distinct from the flow mode in bead-on-plate welding process where there are two symmetric vortexes corresponding to the weld center line, as agreed upon by DebRoy and David (1995). The molten metal flows from the upper part to the lower part near the surface and flows backward with a reduced velocity after it strikes the weld pool bottom. The downward flow in the molten pool surface is driven by Marangoni shear stress and gravity, and the upward flow loses its velocity due to the friction dissipation in the fluid. The heat and momentum delivered by droplets have significant influence on the weld pool geometry and temperature field. In order to investigate the droplet effects directly, the transverse cross-section at x = 33 mm is chosen to observe the variation of the flow velocity field during one droplet impingement process.
In Fig. 10, a different temperature scale is used. The regions with temperature 1760 K and above (yellow and those on the right of yellow in the temperature legend) represent the weld pool. Before the droplet impingement (t = 0.325 s), the molten metal is distributed on both sides of the molten pool, and the molten layer is thin at the middle part of weld pool. When the droplet impinges on the middle part of the molten pool, the molten metal layer at this location is too thin to dampen the flow momentum. The droplet with relatively high momentum strikes the bottom of molten pool and splits into two flows which transfer the heat and mass of the droplet to the upper and lower parts of the weld pool, respectively. As shown in Fig. 10(b), the upper sheet melts pronouncedly after the droplet impingement. The flow pattern in Fig. 10(c) is similar with that in Fig. 9(e). Since the fluid flow in the weld pool is three dimensional, the flow pattern on the transverse cross-section alone is not adequate to present a full description. Fig. 11 shows the fluid flow field on the longitudinal cross-section at y = 0 mm. The flow patterns accessed from the transverse cross-section can be confirmed by those from the longitudinal cross-section. As shown in Fig. 11(a), the molten metal flows forward and backward due to the droplet impingement, and the forward flow corresponds to the extra molten metal when the material begins to melt in Fig. 8(a). The fluid flow velocity decreases as the distance from the impingement point increases. The two flows reunite on the weld pool surface at a position behind the weld pool where the temperature is about 2000 K. This indicates that the driving force has been changed from droplet impingement force to Marangoni shear stress, because the temperature corresponding to the highest surface tension is 1966 K. The interior molten metal flows upward in the rear part of weld pool, corresponding to the reverse flow pattern in Fig. 9(e). 4.3. Validation of the model It is the common way to validate the simulation results by experimentally measured transverse cross-section geometry of weld. The weld transverse cross-section consists of fusion line and reinforcement profile. Fig. 12 presents that the calculated fusion line is in fair agreement with the corresponding experimental result, while the reinforcement profile exhibits marginal difference. The calculated height of reinforcement is slightly lower, while the calculated bead width is slightly higher. This minor discrepancy may be due to
X.S. Gao et al. / Journal of Materials Processing Technology 242 (2017) 147–159
the small viscosity value and the assumption that the fluid in weld pool is incompressible. The underestimated viscosity may make the droplet impingement force driven outward flow spread easier across a larger area, and the molten metal conserves its volume during solidification process, resulting in insufficient shrinkage of weld pool. On the other hand, the minor surface tension differences between applied model and the real welding process may also contribute to the small discrepancy in the final weld profile. 5. Conclusions A three dimensional transient numerical model is developed to understand the temperature field and fluid flow in oscillating single mode laser-GMA hybrid lap welding process. This model is one of the very few that dealt with the intricacies associated with lap joint simulation. Validity of the model is examined by comparison of calculated results with experimental results. The conclusions are as follows. (1) The distinct temperature fields were related to the lap joint and arc inclination configuration. The temperature gradient and the heat conduction speed in the upper sheet are higher than those in the lower sheet during welding. During solidification process, the weld pool’s width shrinks before its depth. In the end, heat transfer occurs exclusively in the horizontal direction. (2) Two characteristic flow patterns appear after droplet impingement with an inclination angle, one flowing upward towards the upper sheet and the other flowing downward towards the lower sheet. Both the flows transfer droplet-induced-heat and momentum from the impingement position to the other parts of weld pool. Appropriate velocity and impingement position of droplet produces reasonable weld geometry. (3) The fluid flow near the droplet impingement position is outward and driven by droplet impingement force while that in the rear of weld pool exhibits a counterclockwise vortex and is governed by Marangoni force and gravity. (4) Good precision between the weld cross-section profiles obtained from the experiment and proposed model confirms that the model fairly represents the heat distribution of arc and laser. The spatially averaged oscillating laser heat distribution prevents a deep-penetration through workpiece along laser path and a stable arc heat distribution due to metal vapor produces continuous and effective weld joint. In addition, flow characteristics of oscillating laser-GMA hybrid welding in lap configuration also can be proved reliable. Acknowledgements The authors wish to thank the financial support for this research from Shandong Province Natural Science Foundation in China (Grant No. ZR2014EEM002). They are also grateful to the PPP Program, i.e., Project based Personnel Exchange Program with China Scholarship Council and German Academic Exchange Service (DAAD).
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