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Three-dimensional transient thermoelectric currents in deep penetration laser welding of austenite stainless steel
Optics and Lasers in Engineering 91 (2017) 196–205
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Three-dimensional transient thermoelectric currents in deep penetration laser welding of austenite stainless steel
MARK
⁎
Xin Chena, Shengyong Panga, , Xinyu Shaob, Chunming Wanga, Jianzhong Xiaoa, Ping Jiangb a b
State Key Laboratory of Material Processing and Die & Mould Technology, Huazhong University of Science and Technology (HUST), Luoyu Rd, 1037 Wuhan, PR China State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology (HUST), Luoyu Rd, 1037 Wuhan, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Deep penetration laser welding Thermoelectric currents Self-induced magnetic field Time-dependent Three-dimensional circulations
The existence of thermoelectric currents (TECs) in workpieces during the laser welding of metals has been common knowledge for more than 15 years. However, the time-dependent evolutions of TECs in laser welding remain unclear. The present study developed a novel three-dimensional theoretical model of thermoelectric phenomena in the fiber laser welding of austenite stainless steel and used it to observe the time-dependent evolutions of TECs for the first time. Our model includes the complex physical effects of thermal, electromagnetic, fluid and phase transformation dynamics occurring at the millimeter laser ablated zone, which allowed us to simulate the TEC, self-induced magnetic field, Lorentz force, keyhole and weld pool behaviors varying with the welding time for different parameters. We found that TECs are truly three-dimensional, timedependent, and uneven with a maximum current density of around 107 A/m2 located at the liquid-solid (L/S) interface near the front or bottom part of the keyhole at a laser power of 1.5 kW and a welding speed of 3 m/min. The TEC formed three-dimensional circulations moving from the melting front to solidification front in the solid part of workpiece, after which the contrary direction was followed in the liquid part. High frequency oscillation characteristics (2.2–8.5 kHz) were demonstrated in the TEC, which coincides with that of the keyhole instability (2.0–5.0 kHz). The magnitude of the self-induced magnetic field and Lorentz force can reach 0.1 mT and 1 kN/ m3, respectively, which are both consistent with literature data. The predicted results of the weld dimensions by the proposed model agree well with the experimental results. Our findings could enhance the fundamental understanding of thermoelectric phenomena in laser welding.
1. Introduction Thermoelectric currents (TECs) caused by the Seebeck effect are generated when two junctions of a closed loop made by two dissimilar conducting materials are placed in different temperatures. TECs have long been known to play important roles in many industrial processes, such as in nuclear reactor boiling [1], electron beam welding [2–5], and directional solidification [6–8]. TECs are also found near the interaction zone during the laser welding process of metals [9]. Nevertheless, to the best of the authors’ knowledge, there is currently a lack of reported research on the time-dependent evolutions of TECs in the high energy beam welding process. TECs in high-energy beam welding process have been discussed and explored in previous research. Paulini et al. [3] proposed a simple analytical model for TECs in the electron beam (EB) and laser welding of two dissimilar metals. They numerically showed that a TEC at more than 100 A may occur in plates with a 20- or 30 mm thickness and a 0.1- to 1 mT magnetic field may be induced at the surface of the ⁎
workpiece during the electron beam welding process. Wei et al. [4,10,11] experimentally and analytically investigated the thermoelectric magnetism (TEM) in the electron beam (EB) welding of dissimilar metals. They found that the TEC could reach around 104 A and the magnetic field could reach around 10 Gauss during the welding process. Moreover, Wei et al. were the first to derive possible influence factors for the TEM and EB deflection angles by scale analysis. Kern et al. [9] first detected the net current of 8–14 A in the interaction zone during the magnet-assisted CO2 laser welding of an aluminum alloy, which they proposed to be the TEC, and later argued the possibility for a two-dimensional (2D) TEC distribution. Ambrosy et al. [12] also tested currents in the CO2 laser welding process, although these were very weak currents in the Nd: YAG welding process. They thought that the main currents in the weld pool during CO2 laser welding were not TEC but were caused by a laser-induced plasma jet. Lange et al. [13] analytically demonstrated and proved that the currents present during Nd:YAG laser conduction welding were indeed TECs. Furthermore, Lange et al. also predicted the 2D distributions of TEC, thereby
Corresponding author. E-mail address: [email protected] (S. Pang).
http://dx.doi.org/10.1016/j.optlaseng.2016.12.001 Received 18 September 2016; Received in revised form 1 December 2016; Accepted 2 December 2016 0143-8166/ © 2016 Elsevier Ltd. All rights reserved.
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maintain consistent simulation conditions. The weld was subsequently cut, ground, polished, and etched. The weld dimensions were then measured under an optical microscope (OM) to compare with the simulation results. The complex dynamic behaviors of the thermal, electromagnetic, fluid, and phase transformations in the specimens were observed during laser welding [Fig. 1(b) and (c)]. The production principle of TECs is shown in Fig. 1(c) for the laser welding process. Different Seebeck coefficients between the solid and liquid metals [9] at different temperature gradients may have influenced the production of TECs. Maxwell electromagnetic theory may be equipped to solve for the induced TEC, magnetic field, Lorentz force and Joule heating. The boundary conditions (time-dependent L/S and L/V interfaces) and temperature gradients for the TECs can be calculated by solving the comprehensive computational fluid dynamics (CFD) model for laser welding. Currently, many researches have been made on the keyhole, weld pool and vapor plume behaviors and weld joints integrity during fiber laser welding [14–16]. Besides, the numerical simulation method has been an efficient way to be used to investigate the complex dynamic behaviors in laser welding, since proposed laser welding models display similar results to those derived from the experiments. There are many comprehensive laser welding CFD models, all of which could be used to reasonably predict the transient evolutions of the self-consistent keyhole, weld pool, and vapor plume [17–24]. Based on our previous welltested CFD model of the keyhole and weld pool dynamics [18,25–30] and the Maxwell electromagnetic theory, the present study developed a novel three-dimensional theoretical model of the thermoelectric phenomena to solve the evolutions of TECs, self-induced magnetic field, and Lorentz force in the deep penetration laser welding process. Fiber laser welding was considered the main process for aforementioned model. The welding processes used in the simulations were the same as
confirming the original assumption suggested by Kern et al. However, the calculated directions between the two 2D distributions lay on opposite orientations. These research discoveries successfully found and explained some feathers of the TEC in the high-energy beam welding process. Unfortunately, the time-dependent evolutions of TECs are still not well understood. In this paper, we propose a novel three-dimensional transient model of the thermoelectric phenomena in the fiber laser welding of austenite stainless steel and use it to investigate the characteristics of TECs. Our model includes the complex physical effects of thermal, electromagnetic, fluid and phase transformation dynamics occurring at the millimeter-scale laser ablated zone. The proposed model can simultaneously simulate characteristics of TECs as well as its keyhole and weld pool dynamics. The time-dependent evolutions, three-dimensional flow patterns of TECs, self-induced magnetic field, and Lorentz force during laser welding are predicted and analyzed. The magnitude and oscillation behaviors of TECs are theoretically studied and discussed. The predicted results are compared with the experimental and literature data. 2. Materials and methods The present study used typical 304 stainless steels with a 3 mm plate thickness for the deep penetration laser welding experiments. The composition is shown in Table 1. A continuous wave (CW) fiber laser (IPG YLR-4000, maximum power: 4 kW) with a wavelength of 1.07 µm was used for bead-on-plate welding. The laser beam, which is delivered by a fiber system and focused on the specimen surface, has a spot radius around 0.2 mm at the focal position. The experimental setup for laser welding is shown in Fig. 1(a). The welding process parameters are shown in Table 2. Before welding the specimen was carefully cleaned with acetone to eliminate the possibility of the producing oil stains and oxide films. A shielding gas was not used during the welding process to
Table 2 Process parameters for deep penetration fiber laser welding of 304 stainless steel.
Table 1 Chemical composition of 304 stainless steel. Element
C
Si
Mn
P
S
Ni
Cr
Fe
%
0.07
0.46
0.78
0.032
0.06
8.10
18.32
Balance
Process No.
Laser power (kW)
Welding speed (m/min)
Beam radius (mm)
1 2 3
1.5 1.5 1.8
4.0 3.0 3.0
0.2 0.2 0.2
Fig. 1. Experimental setup and physical phenomena for fiber laser welding: (a) welding equipment; (b) dynamic behaviors of keyhole, weld pool and vapor plume in the keyhole; (c) the principle of the production of thermoelectric magnetic phenomena in weld pool; the coupling behaviors including the production of TEC and their effects on welding process is also shown between (b) and (c).
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the transient keyhole is always full of hot vapor plume, for simplicity, the keyhole free surface and outside of the workpiece are both assumed insulated. The boundary condition for the TEC and magnetic field can be expressed as follows:
that in the experiments. The shielding gas was not used to reduce computation costs, although this can be easily incorporated with the developed model. A Gaussian beam intensity distribution with a beam radius of 0.2 mm was used in the simulations. The electric currents in laser welding can be described using the Ohm's law, which is shown as follows:
→→ j ⋅ n = 0,
→ j = −σe (∇ϕe + S∇T ),
⎯→ ⎯ (→ n ⋅∇) A = 0,
(1)
(10) → where n is the unit normal vector of boundary surface, which can be obtained by Eq. (11) at the keyhole free surface [33]:
where σe is electrical conductivity; ϕe is the electrical scalar potential; S is the absolute thermoelectric power, also called Seebeck coefficient; and T is the temperature, where ∇T denotes the thermal gradient. ⎯→ ⎯ Noting that if a magnetic field B0 is applied in the laser welding ⎯→ ⎯ u × B0 (here neglected), should process, the induced electric currents, → be incorporated into the Eq. (1) in the weld pool due to the motion of the molten metal, which moves at a velocity of → u in the magnetic field. There are no sources of electrons, therefore the continuity equation of the electric current is shown as follows:
→ ∇⋅ j = 0.
∇ϕ → n = . ∇ϕ
The TEC in the deep penetration laser welding can be solved by Eqs. (1) and (2). The self-induced magnetic field in the workpiece (assuming an isotropic material) can be solved using the Ampere's law:
⎯→ ⎯ → ∇⋅(∇ A ) = −μ0 j ,
(3) ⎯→ ⎯ where μ0 is the permeability of the vacuum, and A is the magnetic ⎯→ ⎯ ⎯→ ⎯ vector potential, which is expressed by the formulation, B = ∇ × A . ⎯→ ⎯ ⎯→ ⎯ Here A also satisfies Lorentz gauge, ∇⋅ A = 0 . The induced Lorentz ⎯→ ⎯ force F can be calculated using the following equation: (4)
The temperature gradient and transient solid-liquid-vapor interfaces for TECs must be solved using the proposed model to solve the threedimensional transient TEC. The heat transfer and fluid flow in the laser welding process are solved by the three conservation equations in hydrodynamics [26]:
∇⋅→ u = 0,
(5)
⎯ ⎛ ∂ ⎯→ μ ⎯→ ⎯→ ⎯ ⎯→ ⎯ ⎞ ⎯→ ⎯ ⎯ ⎯ ⎯→ ⎯ Cρ ⎯→ u + ( u ⋅∇) u ⎟⎟ = ∇⋅(μl ∇ u ) − ∇p − l u − |u |u ρ ⎜⎜ K K ⎝ ∂t ⎠ ⎯→ ⎯
→→ ⎞ ⎛ ∂T j ⋅j ρCp ⎜ + (→ u ⋅∇) T ⎟ = ∇⋅(k ∇T ) + , ⎠ ⎝ ∂t σe
3. Results and discussion
⎯⎯⎯→
+ ρg β (T − Tref ) + FL ,
3.1. Evolutions of TEC with three-dimensional transient keyhole
(6)
Fig. 2 shows the evolutions of the thermoelectric currents (TECs) with a self-consistent keyhole during laser welding (process No. 2). The distributions of the TECs are far from uniform and are highly timedependent. At the very beginning of the welding, a large part of the TEC ( > 1.0×107 A/m2) was regularly generated around a small concave [Fig. 2(a)]. The TECs are able to reach a maximum value of 7.0×107 A/ m2. Away from the small concave, the TEC rapidly decreases. As the welding process proceeds, the large part of the TEC moves to the place near the front and bottom keyholes [Figs. 2(b) and (d)] and the maximum value of the TEC decreases. When the welding process enters a quasi-steady state (at around 20 ms), the maximum value of the TEC decreases to about 3.0×107 A/m2. Furthermore, the distributions of TEC change as the keyhole surface becomes more irregular or many
(7)
g , T , Tref , β , Cp , k respectively represent the three u , ρ , p , μl , → where → dimensional velocity vector, density, pressure, viscosity, gravitational vector, temperature, reference temperature, thermal expansion coefficient, thermal capacity and thermal conductivity. C is an inertial parameter related to the liquid fraction fl , such that C = 0.13f l−3/2 [31,32]. K is the Carman-Kozeny coefficient of the mixture model. The last term of Eq. (7) is the Joule heating generated by electrical currents. The keyhole free surface is tracked by the Level Set method [30], which can be expressed as follows: ∂ϕ → + u ⋅∇ϕ = 0, ∂t
(11)
The developed three-dimensional transient model for the thermoelectric phenomena was solved using high-order finite difference methods with an in-house parallelized code. The numerical method for the dynamics of the keyhole and weld pool was presented in previous research [18,26,29]. The thermoelectric magnetic governing equation and boundary conditions [Eqs. (1)–(3), (9), and (10)] followed a fifth-order weighted essentially non-oscillatory (WENO) scheme and a second-order center difference scheme for the discretization of the convective term and diffusion term, respectively. A parallel incomplete Cholesky-conjugate gradient (ICCG) method was used to solve Poisson's equation for the electric scalar potential ϕe and magnetic vector ⎯→ ⎯ potential A . A uniform mesh space of 0.025 mm and a small time step (typically around 10−7 s) are used in the simulations of the deep penetration fiber laser welding. The physical parameters used in the calculations of thermoelectric magnetic parameters are shown in Table 3. It is difficult to accurately measure the Seebeck coefficient, therefore an average value of this parameter was used in the calculations [13]. The values for the other physical parameters, such as heat conductivity, viscosity, density, specific heat capacity, melting and vaporization temperature, latent heat of melting and evaporation, etc. were gathered from previous reports [26]. A small part of the specimens, specifically 3 mm×1.5 mm ×3 mm in the welding, cross-section and penetration directions respectively, were used in the simulations to allow easier monitoring of the welding values used for calculations.
(2)
⎯→ ⎯ → ⎯→ ⎯ FL = j × B .
(9)
(8) Table 3 Thermoelectric magnetic parameters used in the simulations.
where ϕ is the time-varying signed distance function. The liquid-solid interface is tracked using the mixture method. The absorbed laser energy of keyhole wall, following multiple reflections, is calculated using a robust ray tracing method [27]. The detailed governing equations, boundary conditions, and numerical methods for dynamics of the self-consistent keyhole and weld pool have been systematically presented in previous research [18,26] and are not repeated here. Since 198
Property
Symbol
Value
Liquid Seebeck efficient (V K−1) Solid Seebeck efficient (V K−1) Electrical conductivity (Ω m)−1 Permeability of vacuum (T m A−1)
Sl Ss σe μ0
−4.0×10−6 (Lange et al., [13]) −0.9×10−6 (Lange et al., [13]) 7.7×105 (Liu et al., [34]) 4π×10−7
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Fig. 2. Evolution of TEC with self-consistent keyhole during laser welding (process No. 2): (a-d) the top and longitudinal section view of TEC at the welding of 0.164 ms, 10.713 ms, 17.882 ms, 29.328 ms, respectively, the longitudinal section view can be obtained by rotating 90 degrees clockwise along with x-axis and then rotating 90° clockwise along with y-axis; (e) curves of TEC over welding time at point A, B, and C (0.025 mm, 0.175 mm, 0.325 mm in y-axis direction, and 1.0 mm in x-axis direction from the zero point) of the workpiece surface shown in (d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
directly absorbed the effective laser energy, which are then transferred into the entire welding zone to create a large temperature gradient near the front and bottom keyholes. As a result, the TEC will be larger at the liquid-solid interface than any other place. The maximum TEC value also decreased as the welding time goes on due to the decrease of the temperature gradient, because the large temperature gradient is a key factor and influences the three-dimensional TECs in the deep penetration laser welding process. The time-dependent L/V and L/S interfaces also have important effects on the three-dimensional transient TEC. The vapor plume inside the time-dependent keyhole during fiber laser welding is weakly ionized [35,36] and has been previously considered an insulator [37], such that the boundary of the TEC will always change during laser welding and no TEC flow will exist inside the keyhole. The occurrence of a Seebeck effect relies on the gradient of Seebeck coefficient, thus TECs may not exist in any single solid or liquid phase far from the liquid-solid interface. Fig. 3 shows the TEC distributions at a welding time of 23.605 ms during laser welding in two different welding processes (Nos. 1 and 3). The TEC distribution values remain constant, while the characteristics differ as compared to the results of process No. 2. Welding direction (xaxis) TEC values at the middle and bottom of the keyhole, which are shown in Figs. 3(a) and (b), are also presented in Fig. 3(c). The TEC is largest near the front (B and E) or bottom (C and F) of the keyhole. The TEC is larger at the L/S interface and nearly all the TEC remains at this location. These demonstrate that the aforementioned characteristics of
humps occur on the keyhole wall [Figs. 2(b) and (d)]. Fig. 2 also shows a larger TEC value ( > 1.0×106 A/m2) near the melting and solidification fronts (liquid-solid interface) than other places on the workpiece during the whole laser welding process (Fig. 2). Locations farther away from the liquid-solid interface experiences minimal current, which is consistent with previous literature data [8]. Fig. 2(e) shows the curves of the TEC over welding time at points A, B, and C with different distances (0.025 mm, 0.175 mm, 0.325 mm in y-axis direction) from the center of the weld pool (1.0 mm in x-axis direction from the zero point), respectively [Fig. 2(d)]. The TEC values are always changing, and the largest one occurs when the point (point C) is in the closest distance from the L/S interface, specifically at the welding time of about 10.5 ms. According to the definitions of the TEC and Ohm's law [Eq. (3)], the value and distribution of TECs depend on the temperature gradient used in laser welding without considering the changes of Seebeck coefficient over time. At the very beginning of the welding process, the temperature of the welding zone is an approximate Gaussian distribution and the temperature gradient is regulated around the keyhole [18,30]. The strong effective laser energy is majorly focused on the small concave and creates a very high temperature gradient. Therefore, the large part of the TEC, which can reach 7.0×107 A/m2, also locates itself around the small concave. As the welding time proceeds, the weld pool is stretched and deepened because of the welding speed during the continuous laser welding process. The front and bottom keyhole walls 199
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Fig. 3. Distributions of TEC with self-consistent keyhole at the welding time of 23.605 ms during laser welding (longitudinal section view): (a) process No. 1; (b) process No. 2; (c) curves of TEC values at the middle and bottom lines of keyhole in (a) and (b) in the welding direction (x-axis), the TEC values at points of A, B, C, D, E, and F in (a) and (b) are given in the corresponding points in (c).
argument can be stated for vertical orientation circulations near the lower parts of the weld pool. The aforementioned indicates that the two-dimensional model [13] may not be used to describe and further investigate the three-dimensional transient TEC phenomena in the laser keyhole welding process. The three-dimensional TEC streamlines at a welding time of 23.605 ms in different welding processes (processes Nos. 1 and 3) are shown in Fig. 5. The characteristics of the flow pattern are nearly identical to that in process No. 2. This further demonstrates that the welding process, including the laser power and welding speed (in a certain range), do not influence the characteristics of the threedimensional transient TEC in deep penetration fiber laser welding process.
the three-dimensional transient TEC, where it is absent in welding processes, such as laser power and welding speed (at a certain range), during deep penetration fiber laser welding. 3.2. Characteristics of three-dimensional TEC flow pattern Fig. 4 shows the TEC streamline at a welding time of 23.605 ms in the top, longitudinal section, and its three-dimensional (3D) view during laser welding (process No. 2). The TEC flows from the melting front to the solidification front while it is in solid phase. Conversely, TEC flows opposite of its solid phase flow while it is in weld pool. As it passes the keyhole, the TEC flows along the keyhole wall [Figs. 4(a) and (c)]. These characteristics suggest that the TEC in the laser keyhole welding process is composed of many annular flows (Fig. 4), which is consistent literature data [3,11]. Two big horizontal orientation vortexes in the front welding zone are typically found near the keyhole wall [Fig. 4(a)], and a large vertical orientation vortex near the bottom keyhole wall [Fig. 4(b)]. The annual flow of TECs in a 3D view can be divided into two main types, horizontal and vertical, respectively [Fig. 4(b)]. The flow pattern of TECs in the deep penetration laser welding process is three-dimensional but does not follow plane circulations. During deep penetration laser welding, the liquid-solid interface and the distribution of temperature gradient both follow three-dimensional geometry. Therefore, the distribution of TECs can be assumed to be truly three-dimensional. Specific circulations directions (horizontal or vertical) rely strongly on the direction of temperature gradient. The horizontal temperature gradient is larger near the surface weld pool, resulting in the horizontal orientation TEC circulations. The same
3.3. Characteristics of self-induced magnetic field and Lorentz force The self-induced TEC magnetic field distributions at a welding time of 23.605 ms during laser welding are shown in Fig. 6 (process No. 2). The distribution of magnetic field is three-dimensional and far from uniform. Large magnetic fields generated at the solid-liquid interface near the front and bottom keyholes. The maximum value of the magnetic flux density (MFD) can reach 0.3 mT or an even larger value. The MFD rapidly decreases at places father from the two aforementioned location. This non-uniform distribution can also be clearly found at slices with a distance of 0.65 mm and 1.4 mm below the top of workpiece, respectively [Figs. 6(b) and (c)]. The MFD near the front keyhole [Fig. 6(b)] and bottom keyhole [Fig. 6(c)] reaches about 0.05 mT and 0.12 mT, respectively. Conversely, other locations only have an MFD less than 0.01 mT. A typical clockwise vortex of magnetic field is 200
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Fig. 4. TEC streamline at the welding time of 23.605 ms during laser welding (process No. 2): (a) top view; (b) longitudinal section view; (c) and (d) 3D view.
Fig. 5. 3D view of TEC streamline at the welding time of 23.605 ms during laser welding: (a) process No. 1; (b) process No. 3.
Lorentz force in places away from the front and bottom keyholes is small enough to be neglected (less than 1 N/m3). Fig. 7(c) shows the variation curves of the Lorentz force over welding time at points A and B [Figs. 7(a) and (b)]. The Lorentz force of points A and B can reach top values (1 kN/m3 for point A and 0.45 kN/m3 for point B) when those points are placed closest near the melting front interface. At the other welding times, the Lorentz force is small. Therefore, the Lorentz force is time-dependent in the laser welding process. This demonstrates close relationship of the distribution and evolution of the Lorentz force to the three-dimensional transient TEC.
shown in slice 3 [Fig. 6(c)], which is produced by a beam of downward TEC flows near the bottom keyhole [Fig. 4(b)]. The horizontal slice and longitudinal section views of the induced Lorentz force at a welding time of 23.605 ms during laser welding (process No. 2) are shown in Figs. 7(a) and (b), respectively. Large Lorentz force is also produced at the liquid-solid interface near the front and bottom keyholes. The maximum value can reach about 2 kN/m3, or an even larger value. The direction of the Lorentz force at this location mainly follows the tangential direction of the liquid-solid interface, which may have a shear effect on the interface. Furthermore, the 201
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Fig. 6. Distributions of self-induced magnetic field at the welding time of 23.605 ms during laser welding (process No. 2): (a) 3D view; (b) and (c) horizontal slice at a distance of 0.65 mm and 1.4 mm below the top of workpiece, respectively.
Fig. 7. Distributions of induced Lorentz force at the welding time of 23.605 ms during laser welding (process No. 2): (a) longitudinal section view; (b) horizontal slice (slice at a distance of 0.7 mm below the top of workpiece); (c) variation curves of Lorentz force at points A (at a distance of 1.925 mm in x-axis from zero point and center of workpiece in y-axis) and B (at a distance of 1.65 mm in x-axis and 1.05 mm in y-axis from zero point) shown in (a) and (b) during laser welding process.
Given that the magnetic field assumed to be induced only by TEC in laser welding [Eq. (3)], the value and distribution of the magnetic field is determined by the time-dependent and three-dimensional TEC. The magnitude of the MFD is around 0.1 mT, which is reasonably consistent to the theoretical result (0.1–1 mT) submitted by Paulini et al. [3] and the experimental results (around 10 Gauss) of Wei et al. [10] for EB welding of dissimilar metals. The present MFD is less than that of the literature data and may be a result of the Seebeck coefficient difference used in this research (3.1×10−6 V/K) and that used in the EB welding of dissimilar metals (around 1.0×10−5 V/K). The Lorentz force, produced by the transient, three-dimensional TEC cuts the self-induced magnetic field line [Eq. (5)]. Similarly, the Lorentz force is also threedimensional, uneven, and varies with time. Therefore, the TEC and the self-induced magnetic field and Lorentz force in deep penetration laser welding could not be well described and understood by the twodimensional or steady-state theoretical models.
3.4. Theoretical analysis 3.4.1. The magnitude of TEC in laser welding process In order to study the magnitude of TEC, a scale analysis is used in the following discussion. According to Ohm's law, integrating Eq. (1) along the closed curves across the liquid-solid interface gives [4,10,11]:
∂T ∼ ∼ jlx − jsx = σe (Ss − Sl ) ∼ , ∂x
(12)
∂T ∼ ∼ jly − jsy = σe (Ss − Sl ) ∼ , ∂y
(13)
∂T ∼ ∼ jlz − jsz = σe (Ss − Sl ) ∼ , ∂z
(14)
where subscript l and s respectively donate the liquid and solid phase. Eqs. (12)–(14) indicate that the thermoelectric currents are contributed
202
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Fig. 8. Variation curves in three different welding processes during laser welding: (a) the maximum TEC curves; (b) the keyhole depth curves.
gradient. Therefore, the keyhole instability may be used to characterize the violent degree of the TEC oscillations in the laser keyhole welding process. Fig. 8 shows the evolutions of the maximum TEC and the keyhole depth within 28 ms for the different welding processes, respectively, during laser welding. Fig. 8(a) shows the rapid increase of the TEC to its tip value at the very beginning of welding and decrease to a relatively small and stable value, with frequency oscillation after the welding of around 12 ms given that the keyhole depth reached a quasi-steady state shown in Fig. 8(b). Fig. 9 illustrates the oscillation frequency of the maximum TEC measured to be around 2.2–8.5 kHz, which is consistent with that of the keyhole depth (around 2.0– 5.0 kHz). The amplitude of the TEC oscillations increases with that value of the heat input [Fig. 8(b)], which is consistent with that of keyhole depth oscillations [Fig. 8(a)]. These agreements confirm the relationship between the TEC oscillations and of the keyhole instability. The average amplitudes of the maximum TEC and keyhole depth in the three welding process are shown in Fig. 9. A simple but practical linear formula of the amplitudes between the maximum TEC and keyhole depth (called keyhole depth-TEC relationship, the blue line in Fig. 9), can be expressed as follows:
by the gradient of the Seebeck coefficients between the molten liquid and solid metal. Scaling Eqs. (12)–(14) leads to [10,11]:
T − T∞ ∼ j ∝ σe (Ss − Sl ) m , δT
(15)
where Tm and T∞ are melting and ambient temperature, respectively, and δT donates the thermal diffusion thickness. The magnitude of TEC is inversely proportional to the thermal diffusion thickness in deep penetration laser welding process. The present research defined σe , Ss − Sl , Tm , and T∞ are 7.7×105 Ω−1 m−1, 3.1×10−6 V/K, 1727 K, and 300 K, respectively. The melting width is around 1.0 mm, and the width of weld pool is around 0.5 mm. Therefore, the thermal diffusion thickness δT is around 0.25 mm. As a result, the magnitude of the TEC estimated by Eq. (15) can reach 1.4×107 A/m2, which is consistent with the simulation results. 3.4.2. Violent degree of TEC oscillation We have learned that the TEC is uneven and time-dependent during the deep penetration laser welding process because of temperature distribution oscillation and boundary geometry. Temperature distribution oscillations are closely related to the keyhole instability. The large temperature gradient produced near the keyhole wall directly illuminated by the laser beam and the TEC is linear with the temperature
A ∼j = k 0⋅Ak
(16)
where A ∼j and Ak respectively donate the amplitudes of the maximum TEC and keyhole depth and k 0 is a constant coefficient in a certain range (8.63×1010 A/m3). Therefore, the violent degree of oscillations of the maximum TEC can be related back to the keyhole instability, specifically with to the keyhole depth-TEC relationship. By using this relationship, the violent degree of TEC oscillations may be estimated by observing the keyhole depth oscillation.
3.5. On validation The predicted magnitude of the induced magnetic field follows the literature data very consistently. The dynamics of the self-consistent keyhole and weld pool following our previous computational fluid dynamics (CFD) laser welding models were also deemed reliable [18,25–30]. However, it is very difficult to directly experimentally verify the time-dependent evolutions and three-dimensional TEC distributions in laser welding. The predicted weld dimensions suggested by the proposed model were used to compare the experimental results (Fig. 10). The predicted size and shape of the weld (blue dotted line) was in close agreement with the experimental results (black full line) in the three different welding processes. In summary, the predicted results of the TEC are reasonable and can serve as the basis for the thermoelectric phenomena in the high-energy beam welding process.
Fig. 9. The keyhole depth-TEC relationship during deep penetration laser welding of austenite stainless steel. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 10. Comparisons of predicted the weld profile and experimental data in different welding processes during laser welding process of 304 stainless steel: (a) process No. 1; (b) process No. 2; (c) process No. 3.
Trans 1990;112(3):714–20. [5] Dragunov VK, Chepurin MV. Electron beam welding of dissimilar alloys under conditions of the generation of thermoelectric current. Weld J 2002;1990(16):466–74. [6] Li X, Gagnoud A, Fautrelle Y, Ren Z, Moreau R, Zhang Y, Esling C. Dendrite fragmentation and columnar-to-equiaxed transition during directional solidification at lower growth speed under a strong magnetic field. Acta Mater 2012;60:3321–32. [7] Li X, Wang J, Du D, Zhang Y, Fautrelle Y, Nguyen-Thi H, Gagnoud A, Ren Z, Moreau R. Effect of a transverse magnetic field on the growth of equiaxed grains during directional solidification. Mater Lett 2015;161:595–600. [8] Wang J, Fautrelle Y, Nguyen-Thi H, Reinhart G, Liao H, Li X, Zhong Y, Ren Z. Thermoelectric magnetohydrodynamic flows and their induced change of solid– liquid interface shape in static magnetic field-assisted directional solidification. Metall Mater Trans A 2016;4A:1169–79. [9] Kern M, Berger P, Hügel H. Magneto-fluid dynamic control of seam quality in CO2 laser beam welding. Weld J 2000;79:72-s–78-s. [10] Wei PS, Chung FK. Three-dimensional electron-beam deflection and missed joint in welding and dissimilar metals. J Heat Transf 1997;119:832–9. [11] Wei PS, Wen C. Missed joint induced by thermoelectric magnetic field in electronbeam welding dissimilar metals experiment and scale analysis. Metall Mater Trans B 2002;33B:765–73. [12] Ambrosy G, Avilov V, Berger P, Hügel H. Laser induced plasma as a source for an intensive current to produce electromagnetic forces in the weld pool. In: Proceedings of the XVI International Symposium on Gas Flow, Chemical Lasers, and High-Power Lasers. SPIE, Gmunden, Austria. Vol. 6346, 63461Q1–8; 2007. [13] Lange A, Cramer A, Beyer E. Thermoelectric currents in laser induced melts pools. J Laser Appl 2009;21:82–7. [14] Tenner F, Brock C, Klämpfl F, Schmidt M. Analysis of the correlation between plasma plume and keyhole behavior in laser metal welding for the modeling of the keyhole geometry. Opt Lasers Eng 2015;64:32–41. [15] Luo M, Shin YC. Vision-based weld pool boundary extraction and width measurement during keyhole fiber laser welding. Opt Lasers Eng 2015;64:59–70. [16] Ai Y, Shao X, Jiang P, Li P, Liu Y, Liu W. Welded joints integrity analysis and optimization for fiber laser welding of dissimilar materials. Opt Lasers Eng 2016;86:62–74. [17] Ki H, Mazumder J, Mohanty PS. Modeling of laser keyhole welding: part I. Mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free surface evolution. Metall Mater Trans A 2002;33:1817–30. [18] Pang S, Chen L, Zhou J, Yin Y, Chen T. A three-dimensional sharp interface model for self-consistent keyhole and weld pool dynamics in deep penetration laser welding. J Phys D: Appl Phys 2011;44:025301. [19] Zhao H, Niu W, Zhang B, Lei Y, Kodama M, Ishide T. Modelling of keyhole dynamics and porosity formation considering the adaptive keyhole shape and three-phase coupling during deep-penetration laser welding. J Phys D: Appl Phys 2011;44:485302. [20] Cho WI, Na SJ, Thomy C, Vollertsen F. Numerical simulation of molten pool dynamics in high power disk laser welding. J Mater Process Technol 2012;212:262–75. [21] Courtois M, Carin M, Le Masson P, Gaied S, Balabane M. A complete model of keyhole and melt pool dynamics to analyze instabilities and collapse during laser welding. J Laser Appl 2014;26:042001. [22] Zhang L, Zhang J, Gumenyuk A, Rethmeier M, Na SJ. Numerical simulation of full penetration laser welding of thick steel plate with high power high brightness laser. J Mater Process Technol 2014;214:1710–20. [23] Meng W, Li Z, Lu F, Wu Y, Chen J, Katayama S. Porosity formation mechanism and its prevention in laser lap welding for T-joints. J Mater Process Technol 2014;214:1658–64. [24] Tan W, Shin Y. Analysis of multi-phase interaction and its effects on keyhole dynamics with a multi-physics numerical model. J Phys D: Appl Phys 2014;47:345501.
4. Conclusions The present study first developed a three-dimensional theoretical model for the thermoelectric phenomena to investigate the timedependent evolutions of TEC, induced magnetic field, and Lorentz force in the deep penetration fiber laser welding of 304 stainless steel. The predicted results are well consistent with the available experimental and literature data. The main conclusions are shown as follows: 1) The TEC, induced magnetic field and Lorentz force are timedependent, three dimensional and uneven. The large TECs are located at the liquid-solid interface near the front and bottom keyholes, and the value can reach 107 A/m2, or an even larger value. The magnitude of the self-induced magnetic flux density and Lorentz force can reach around 0.1 mT and 1 kN/m3, respectively. 2) The TECs are three-dimensional circulations moving from the melting front to the solidification front in solid part of the workpiece, contrary to the direction of the liquid part. It will produce three typical vortexes of the TEC in the welding process (two horizon orientation vortexes near the upper and front keyholes and a vertical orientation vortex near the bottom keyhole). 3) In a certain range, the welding process parameters including the laser power and welding speed will change the magnitude but not the dynamic characteristics of the TEC, such as the TEC flow patterns, in the deep penetration laser welding process. 4) The TEC oscillations are closely related to keyhole instability. The oscillation frequency (around 2.2–8.5 kHz) and average amplitude of the maximum TEC are consistent with those of the keyhole depth (oscillation frequency, around 2.0–5.0 kHz). Acknowledgement The authors would like to acknowledge the National Natural Science Foundation of China (No. 51675202), the National Basic Research Program of Chinese (973 Program, No. 2014CB046703) and the National Natural Science Foundation of China (No. 51105153) for financial support. References [1] Shercliff JA. Thermoelectric magnetohydrodynamics. J Fluid Mech 1979;91:231–51. [2] Anatychuk LI, Luste OY. Thermoelectric eddy currents and transverse thermal emf in zonally inhomogeneous plates. Sov Phys J 1969;12:801–3. [3] Paulini J, Simon G, Decker I. Beam deflection in electron beam welding by thermoelectric eddy currents. J Phys D: Appl Phys 1990;23:486–95. [4] Wei PS, Lii TW. Electron beam deflection when welding dissimilar metals. J Heat
204
Optics and Lasers in Engineering 91 (2017) 196–205
X. Chen et al.
2006;39:1257–66. [32] Zhou J, Tsai HL, Lehnhoff T. Investigation of transport phenomena and defect formation in pulsed laser keyhole welding of zinc-coated steels. J Phys D: Appl Phys 2006;39:5338–55. [33] Oscher S, Fedkiw RP. Level set methods and dynamic implicit surfaces. Berlin: Springer press; 2002. [34] Liu J, Rao Z, Liao S, Tsai H. Numerical investigation of weld pool behaviors and ripple formation for a moving GTA welding under pulsed currents. Int J Heat Mass Transf 2015;91:990–1000. [35] Zhang M, Chen G, Zhou Y, Li S. Direct observation of keyhole characteristics in deep penetration laser welding with a 10 kW fiber laser. Opt Express 2013;21:19997–20004. [36] Kawahito Y, Matsumoto N, Mizutani M, Katayama S. Characterisation of plasma induced during high power fibre laser welding of stainless steel. Sci Technol Weld Join 2008;13:744–8. [37] Bachmann M, Avilov V, Gumenyuk A, Rethmeier M. Experimental and numerical investigation of an electromagnetic weld pool support system for high power laser beam welding of austenitic stainless steel. J Mater Process Technol 2014;214:578–91.
[25] Pang S, Chen W, Wang W. A quantitative model of keyhole instability induced porosity in laser welding of titanium alloy. Metall Mater Trans A 2014;45:2808–18. [26] Pang S, Chen X, Zhou J, Shao X, Wang C. 3D transient multiphase model for keyhole, vapor plume, and weld pool dynamics in laser welding including the ambient pressure effect. Opt Lasers Eng 2015;74:47–58. [27] Pang S, Chen W, Zhou J, Liao D. Self-consistent modelling of keyhole and weld pool dynamics in tandem dual beam laser welding of aluminum alloy. J Mater Process Technol 2015;217:131–43. [28] Pang S, Hirano K, Fabbro R, Jiang T. Explanation of penetration depth variation during laser welding under variable ambient pressure. J Laser Appl 2015;27:022007. [29] Pang S, Chen X, Li W, Shao X, Gong S. Efficient multiple time scale method for modeling compressible vapor plume dynamics inside transient keyhole during fiber laser welding. Opt Laser Technol 2016;77:203–14. [30] Pang S, Chen X, Zhou J, Shao X, Gong S, Xiao J. Dynamics of vapor plume in transient keyhole during laser welding of stainless steel: local evaporation, plume swing and gas entrapment into porosity. Opt Lasers Eng 2016;82:28–40. [31] Rai R, DebRoy T. Tailoring weld geometry during keyhole mode laser welding using a genetic algorithm and a heat transfer model. J Phys D: Appl Phys
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Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Three-dimensional transient thermoelectric currents in deep penetration laser welding of austenite stainless steel
MARK
⁎
Xin Chena, Shengyong Panga, , Xinyu Shaob, Chunming Wanga, Jianzhong Xiaoa, Ping Jiangb a b
State Key Laboratory of Material Processing and Die & Mould Technology, Huazhong University of Science and Technology (HUST), Luoyu Rd, 1037 Wuhan, PR China State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology (HUST), Luoyu Rd, 1037 Wuhan, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: Deep penetration laser welding Thermoelectric currents Self-induced magnetic field Time-dependent Three-dimensional circulations
The existence of thermoelectric currents (TECs) in workpieces during the laser welding of metals has been common knowledge for more than 15 years. However, the time-dependent evolutions of TECs in laser welding remain unclear. The present study developed a novel three-dimensional theoretical model of thermoelectric phenomena in the fiber laser welding of austenite stainless steel and used it to observe the time-dependent evolutions of TECs for the first time. Our model includes the complex physical effects of thermal, electromagnetic, fluid and phase transformation dynamics occurring at the millimeter laser ablated zone, which allowed us to simulate the TEC, self-induced magnetic field, Lorentz force, keyhole and weld pool behaviors varying with the welding time for different parameters. We found that TECs are truly three-dimensional, timedependent, and uneven with a maximum current density of around 107 A/m2 located at the liquid-solid (L/S) interface near the front or bottom part of the keyhole at a laser power of 1.5 kW and a welding speed of 3 m/min. The TEC formed three-dimensional circulations moving from the melting front to solidification front in the solid part of workpiece, after which the contrary direction was followed in the liquid part. High frequency oscillation characteristics (2.2–8.5 kHz) were demonstrated in the TEC, which coincides with that of the keyhole instability (2.0–5.0 kHz). The magnitude of the self-induced magnetic field and Lorentz force can reach 0.1 mT and 1 kN/ m3, respectively, which are both consistent with literature data. The predicted results of the weld dimensions by the proposed model agree well with the experimental results. Our findings could enhance the fundamental understanding of thermoelectric phenomena in laser welding.
1. Introduction Thermoelectric currents (TECs) caused by the Seebeck effect are generated when two junctions of a closed loop made by two dissimilar conducting materials are placed in different temperatures. TECs have long been known to play important roles in many industrial processes, such as in nuclear reactor boiling [1], electron beam welding [2–5], and directional solidification [6–8]. TECs are also found near the interaction zone during the laser welding process of metals [9]. Nevertheless, to the best of the authors’ knowledge, there is currently a lack of reported research on the time-dependent evolutions of TECs in the high energy beam welding process. TECs in high-energy beam welding process have been discussed and explored in previous research. Paulini et al. [3] proposed a simple analytical model for TECs in the electron beam (EB) and laser welding of two dissimilar metals. They numerically showed that a TEC at more than 100 A may occur in plates with a 20- or 30 mm thickness and a 0.1- to 1 mT magnetic field may be induced at the surface of the ⁎
workpiece during the electron beam welding process. Wei et al. [4,10,11] experimentally and analytically investigated the thermoelectric magnetism (TEM) in the electron beam (EB) welding of dissimilar metals. They found that the TEC could reach around 104 A and the magnetic field could reach around 10 Gauss during the welding process. Moreover, Wei et al. were the first to derive possible influence factors for the TEM and EB deflection angles by scale analysis. Kern et al. [9] first detected the net current of 8–14 A in the interaction zone during the magnet-assisted CO2 laser welding of an aluminum alloy, which they proposed to be the TEC, and later argued the possibility for a two-dimensional (2D) TEC distribution. Ambrosy et al. [12] also tested currents in the CO2 laser welding process, although these were very weak currents in the Nd: YAG welding process. They thought that the main currents in the weld pool during CO2 laser welding were not TEC but were caused by a laser-induced plasma jet. Lange et al. [13] analytically demonstrated and proved that the currents present during Nd:YAG laser conduction welding were indeed TECs. Furthermore, Lange et al. also predicted the 2D distributions of TEC, thereby
Corresponding author. E-mail address: [email protected] (S. Pang).
http://dx.doi.org/10.1016/j.optlaseng.2016.12.001 Received 18 September 2016; Received in revised form 1 December 2016; Accepted 2 December 2016 0143-8166/ © 2016 Elsevier Ltd. All rights reserved.
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maintain consistent simulation conditions. The weld was subsequently cut, ground, polished, and etched. The weld dimensions were then measured under an optical microscope (OM) to compare with the simulation results. The complex dynamic behaviors of the thermal, electromagnetic, fluid, and phase transformations in the specimens were observed during laser welding [Fig. 1(b) and (c)]. The production principle of TECs is shown in Fig. 1(c) for the laser welding process. Different Seebeck coefficients between the solid and liquid metals [9] at different temperature gradients may have influenced the production of TECs. Maxwell electromagnetic theory may be equipped to solve for the induced TEC, magnetic field, Lorentz force and Joule heating. The boundary conditions (time-dependent L/S and L/V interfaces) and temperature gradients for the TECs can be calculated by solving the comprehensive computational fluid dynamics (CFD) model for laser welding. Currently, many researches have been made on the keyhole, weld pool and vapor plume behaviors and weld joints integrity during fiber laser welding [14–16]. Besides, the numerical simulation method has been an efficient way to be used to investigate the complex dynamic behaviors in laser welding, since proposed laser welding models display similar results to those derived from the experiments. There are many comprehensive laser welding CFD models, all of which could be used to reasonably predict the transient evolutions of the self-consistent keyhole, weld pool, and vapor plume [17–24]. Based on our previous welltested CFD model of the keyhole and weld pool dynamics [18,25–30] and the Maxwell electromagnetic theory, the present study developed a novel three-dimensional theoretical model of the thermoelectric phenomena to solve the evolutions of TECs, self-induced magnetic field, and Lorentz force in the deep penetration laser welding process. Fiber laser welding was considered the main process for aforementioned model. The welding processes used in the simulations were the same as
confirming the original assumption suggested by Kern et al. However, the calculated directions between the two 2D distributions lay on opposite orientations. These research discoveries successfully found and explained some feathers of the TEC in the high-energy beam welding process. Unfortunately, the time-dependent evolutions of TECs are still not well understood. In this paper, we propose a novel three-dimensional transient model of the thermoelectric phenomena in the fiber laser welding of austenite stainless steel and use it to investigate the characteristics of TECs. Our model includes the complex physical effects of thermal, electromagnetic, fluid and phase transformation dynamics occurring at the millimeter-scale laser ablated zone. The proposed model can simultaneously simulate characteristics of TECs as well as its keyhole and weld pool dynamics. The time-dependent evolutions, three-dimensional flow patterns of TECs, self-induced magnetic field, and Lorentz force during laser welding are predicted and analyzed. The magnitude and oscillation behaviors of TECs are theoretically studied and discussed. The predicted results are compared with the experimental and literature data. 2. Materials and methods The present study used typical 304 stainless steels with a 3 mm plate thickness for the deep penetration laser welding experiments. The composition is shown in Table 1. A continuous wave (CW) fiber laser (IPG YLR-4000, maximum power: 4 kW) with a wavelength of 1.07 µm was used for bead-on-plate welding. The laser beam, which is delivered by a fiber system and focused on the specimen surface, has a spot radius around 0.2 mm at the focal position. The experimental setup for laser welding is shown in Fig. 1(a). The welding process parameters are shown in Table 2. Before welding the specimen was carefully cleaned with acetone to eliminate the possibility of the producing oil stains and oxide films. A shielding gas was not used during the welding process to
Table 2 Process parameters for deep penetration fiber laser welding of 304 stainless steel.
Table 1 Chemical composition of 304 stainless steel. Element
C
Si
Mn
P
S
Ni
Cr
Fe
%
0.07
0.46
0.78
0.032
0.06
8.10
18.32
Balance
Process No.
Laser power (kW)
Welding speed (m/min)
Beam radius (mm)
1 2 3
1.5 1.5 1.8
4.0 3.0 3.0
0.2 0.2 0.2
Fig. 1. Experimental setup and physical phenomena for fiber laser welding: (a) welding equipment; (b) dynamic behaviors of keyhole, weld pool and vapor plume in the keyhole; (c) the principle of the production of thermoelectric magnetic phenomena in weld pool; the coupling behaviors including the production of TEC and their effects on welding process is also shown between (b) and (c).
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the transient keyhole is always full of hot vapor plume, for simplicity, the keyhole free surface and outside of the workpiece are both assumed insulated. The boundary condition for the TEC and magnetic field can be expressed as follows:
that in the experiments. The shielding gas was not used to reduce computation costs, although this can be easily incorporated with the developed model. A Gaussian beam intensity distribution with a beam radius of 0.2 mm was used in the simulations. The electric currents in laser welding can be described using the Ohm's law, which is shown as follows:
→→ j ⋅ n = 0,
→ j = −σe (∇ϕe + S∇T ),
⎯→ ⎯ (→ n ⋅∇) A = 0,
(1)
(10) → where n is the unit normal vector of boundary surface, which can be obtained by Eq. (11) at the keyhole free surface [33]:
where σe is electrical conductivity; ϕe is the electrical scalar potential; S is the absolute thermoelectric power, also called Seebeck coefficient; and T is the temperature, where ∇T denotes the thermal gradient. ⎯→ ⎯ Noting that if a magnetic field B0 is applied in the laser welding ⎯→ ⎯ u × B0 (here neglected), should process, the induced electric currents, → be incorporated into the Eq. (1) in the weld pool due to the motion of the molten metal, which moves at a velocity of → u in the magnetic field. There are no sources of electrons, therefore the continuity equation of the electric current is shown as follows:
→ ∇⋅ j = 0.
∇ϕ → n = . ∇ϕ
The TEC in the deep penetration laser welding can be solved by Eqs. (1) and (2). The self-induced magnetic field in the workpiece (assuming an isotropic material) can be solved using the Ampere's law:
⎯→ ⎯ → ∇⋅(∇ A ) = −μ0 j ,
(3) ⎯→ ⎯ where μ0 is the permeability of the vacuum, and A is the magnetic ⎯→ ⎯ ⎯→ ⎯ vector potential, which is expressed by the formulation, B = ∇ × A . ⎯→ ⎯ ⎯→ ⎯ Here A also satisfies Lorentz gauge, ∇⋅ A = 0 . The induced Lorentz ⎯→ ⎯ force F can be calculated using the following equation: (4)
The temperature gradient and transient solid-liquid-vapor interfaces for TECs must be solved using the proposed model to solve the threedimensional transient TEC. The heat transfer and fluid flow in the laser welding process are solved by the three conservation equations in hydrodynamics [26]:
∇⋅→ u = 0,
(5)
⎯ ⎛ ∂ ⎯→ μ ⎯→ ⎯→ ⎯ ⎯→ ⎯ ⎞ ⎯→ ⎯ ⎯ ⎯ ⎯→ ⎯ Cρ ⎯→ u + ( u ⋅∇) u ⎟⎟ = ∇⋅(μl ∇ u ) − ∇p − l u − |u |u ρ ⎜⎜ K K ⎝ ∂t ⎠ ⎯→ ⎯
→→ ⎞ ⎛ ∂T j ⋅j ρCp ⎜ + (→ u ⋅∇) T ⎟ = ∇⋅(k ∇T ) + , ⎠ ⎝ ∂t σe
3. Results and discussion
⎯⎯⎯→
+ ρg β (T − Tref ) + FL ,
3.1. Evolutions of TEC with three-dimensional transient keyhole
(6)
Fig. 2 shows the evolutions of the thermoelectric currents (TECs) with a self-consistent keyhole during laser welding (process No. 2). The distributions of the TECs are far from uniform and are highly timedependent. At the very beginning of the welding, a large part of the TEC ( > 1.0×107 A/m2) was regularly generated around a small concave [Fig. 2(a)]. The TECs are able to reach a maximum value of 7.0×107 A/ m2. Away from the small concave, the TEC rapidly decreases. As the welding process proceeds, the large part of the TEC moves to the place near the front and bottom keyholes [Figs. 2(b) and (d)] and the maximum value of the TEC decreases. When the welding process enters a quasi-steady state (at around 20 ms), the maximum value of the TEC decreases to about 3.0×107 A/m2. Furthermore, the distributions of TEC change as the keyhole surface becomes more irregular or many
(7)
g , T , Tref , β , Cp , k respectively represent the three u , ρ , p , μl , → where → dimensional velocity vector, density, pressure, viscosity, gravitational vector, temperature, reference temperature, thermal expansion coefficient, thermal capacity and thermal conductivity. C is an inertial parameter related to the liquid fraction fl , such that C = 0.13f l−3/2 [31,32]. K is the Carman-Kozeny coefficient of the mixture model. The last term of Eq. (7) is the Joule heating generated by electrical currents. The keyhole free surface is tracked by the Level Set method [30], which can be expressed as follows: ∂ϕ → + u ⋅∇ϕ = 0, ∂t
(11)
The developed three-dimensional transient model for the thermoelectric phenomena was solved using high-order finite difference methods with an in-house parallelized code. The numerical method for the dynamics of the keyhole and weld pool was presented in previous research [18,26,29]. The thermoelectric magnetic governing equation and boundary conditions [Eqs. (1)–(3), (9), and (10)] followed a fifth-order weighted essentially non-oscillatory (WENO) scheme and a second-order center difference scheme for the discretization of the convective term and diffusion term, respectively. A parallel incomplete Cholesky-conjugate gradient (ICCG) method was used to solve Poisson's equation for the electric scalar potential ϕe and magnetic vector ⎯→ ⎯ potential A . A uniform mesh space of 0.025 mm and a small time step (typically around 10−7 s) are used in the simulations of the deep penetration fiber laser welding. The physical parameters used in the calculations of thermoelectric magnetic parameters are shown in Table 3. It is difficult to accurately measure the Seebeck coefficient, therefore an average value of this parameter was used in the calculations [13]. The values for the other physical parameters, such as heat conductivity, viscosity, density, specific heat capacity, melting and vaporization temperature, latent heat of melting and evaporation, etc. were gathered from previous reports [26]. A small part of the specimens, specifically 3 mm×1.5 mm ×3 mm in the welding, cross-section and penetration directions respectively, were used in the simulations to allow easier monitoring of the welding values used for calculations.
(2)
⎯→ ⎯ → ⎯→ ⎯ FL = j × B .
(9)
(8) Table 3 Thermoelectric magnetic parameters used in the simulations.
where ϕ is the time-varying signed distance function. The liquid-solid interface is tracked using the mixture method. The absorbed laser energy of keyhole wall, following multiple reflections, is calculated using a robust ray tracing method [27]. The detailed governing equations, boundary conditions, and numerical methods for dynamics of the self-consistent keyhole and weld pool have been systematically presented in previous research [18,26] and are not repeated here. Since 198
Property
Symbol
Value
Liquid Seebeck efficient (V K−1) Solid Seebeck efficient (V K−1) Electrical conductivity (Ω m)−1 Permeability of vacuum (T m A−1)
Sl Ss σe μ0
−4.0×10−6 (Lange et al., [13]) −0.9×10−6 (Lange et al., [13]) 7.7×105 (Liu et al., [34]) 4π×10−7
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Fig. 2. Evolution of TEC with self-consistent keyhole during laser welding (process No. 2): (a-d) the top and longitudinal section view of TEC at the welding of 0.164 ms, 10.713 ms, 17.882 ms, 29.328 ms, respectively, the longitudinal section view can be obtained by rotating 90 degrees clockwise along with x-axis and then rotating 90° clockwise along with y-axis; (e) curves of TEC over welding time at point A, B, and C (0.025 mm, 0.175 mm, 0.325 mm in y-axis direction, and 1.0 mm in x-axis direction from the zero point) of the workpiece surface shown in (d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
directly absorbed the effective laser energy, which are then transferred into the entire welding zone to create a large temperature gradient near the front and bottom keyholes. As a result, the TEC will be larger at the liquid-solid interface than any other place. The maximum TEC value also decreased as the welding time goes on due to the decrease of the temperature gradient, because the large temperature gradient is a key factor and influences the three-dimensional TECs in the deep penetration laser welding process. The time-dependent L/V and L/S interfaces also have important effects on the three-dimensional transient TEC. The vapor plume inside the time-dependent keyhole during fiber laser welding is weakly ionized [35,36] and has been previously considered an insulator [37], such that the boundary of the TEC will always change during laser welding and no TEC flow will exist inside the keyhole. The occurrence of a Seebeck effect relies on the gradient of Seebeck coefficient, thus TECs may not exist in any single solid or liquid phase far from the liquid-solid interface. Fig. 3 shows the TEC distributions at a welding time of 23.605 ms during laser welding in two different welding processes (Nos. 1 and 3). The TEC distribution values remain constant, while the characteristics differ as compared to the results of process No. 2. Welding direction (xaxis) TEC values at the middle and bottom of the keyhole, which are shown in Figs. 3(a) and (b), are also presented in Fig. 3(c). The TEC is largest near the front (B and E) or bottom (C and F) of the keyhole. The TEC is larger at the L/S interface and nearly all the TEC remains at this location. These demonstrate that the aforementioned characteristics of
humps occur on the keyhole wall [Figs. 2(b) and (d)]. Fig. 2 also shows a larger TEC value ( > 1.0×106 A/m2) near the melting and solidification fronts (liquid-solid interface) than other places on the workpiece during the whole laser welding process (Fig. 2). Locations farther away from the liquid-solid interface experiences minimal current, which is consistent with previous literature data [8]. Fig. 2(e) shows the curves of the TEC over welding time at points A, B, and C with different distances (0.025 mm, 0.175 mm, 0.325 mm in y-axis direction) from the center of the weld pool (1.0 mm in x-axis direction from the zero point), respectively [Fig. 2(d)]. The TEC values are always changing, and the largest one occurs when the point (point C) is in the closest distance from the L/S interface, specifically at the welding time of about 10.5 ms. According to the definitions of the TEC and Ohm's law [Eq. (3)], the value and distribution of TECs depend on the temperature gradient used in laser welding without considering the changes of Seebeck coefficient over time. At the very beginning of the welding process, the temperature of the welding zone is an approximate Gaussian distribution and the temperature gradient is regulated around the keyhole [18,30]. The strong effective laser energy is majorly focused on the small concave and creates a very high temperature gradient. Therefore, the large part of the TEC, which can reach 7.0×107 A/m2, also locates itself around the small concave. As the welding time proceeds, the weld pool is stretched and deepened because of the welding speed during the continuous laser welding process. The front and bottom keyhole walls 199
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Fig. 3. Distributions of TEC with self-consistent keyhole at the welding time of 23.605 ms during laser welding (longitudinal section view): (a) process No. 1; (b) process No. 2; (c) curves of TEC values at the middle and bottom lines of keyhole in (a) and (b) in the welding direction (x-axis), the TEC values at points of A, B, C, D, E, and F in (a) and (b) are given in the corresponding points in (c).
argument can be stated for vertical orientation circulations near the lower parts of the weld pool. The aforementioned indicates that the two-dimensional model [13] may not be used to describe and further investigate the three-dimensional transient TEC phenomena in the laser keyhole welding process. The three-dimensional TEC streamlines at a welding time of 23.605 ms in different welding processes (processes Nos. 1 and 3) are shown in Fig. 5. The characteristics of the flow pattern are nearly identical to that in process No. 2. This further demonstrates that the welding process, including the laser power and welding speed (in a certain range), do not influence the characteristics of the threedimensional transient TEC in deep penetration fiber laser welding process.
the three-dimensional transient TEC, where it is absent in welding processes, such as laser power and welding speed (at a certain range), during deep penetration fiber laser welding. 3.2. Characteristics of three-dimensional TEC flow pattern Fig. 4 shows the TEC streamline at a welding time of 23.605 ms in the top, longitudinal section, and its three-dimensional (3D) view during laser welding (process No. 2). The TEC flows from the melting front to the solidification front while it is in solid phase. Conversely, TEC flows opposite of its solid phase flow while it is in weld pool. As it passes the keyhole, the TEC flows along the keyhole wall [Figs. 4(a) and (c)]. These characteristics suggest that the TEC in the laser keyhole welding process is composed of many annular flows (Fig. 4), which is consistent literature data [3,11]. Two big horizontal orientation vortexes in the front welding zone are typically found near the keyhole wall [Fig. 4(a)], and a large vertical orientation vortex near the bottom keyhole wall [Fig. 4(b)]. The annual flow of TECs in a 3D view can be divided into two main types, horizontal and vertical, respectively [Fig. 4(b)]. The flow pattern of TECs in the deep penetration laser welding process is three-dimensional but does not follow plane circulations. During deep penetration laser welding, the liquid-solid interface and the distribution of temperature gradient both follow three-dimensional geometry. Therefore, the distribution of TECs can be assumed to be truly three-dimensional. Specific circulations directions (horizontal or vertical) rely strongly on the direction of temperature gradient. The horizontal temperature gradient is larger near the surface weld pool, resulting in the horizontal orientation TEC circulations. The same
3.3. Characteristics of self-induced magnetic field and Lorentz force The self-induced TEC magnetic field distributions at a welding time of 23.605 ms during laser welding are shown in Fig. 6 (process No. 2). The distribution of magnetic field is three-dimensional and far from uniform. Large magnetic fields generated at the solid-liquid interface near the front and bottom keyholes. The maximum value of the magnetic flux density (MFD) can reach 0.3 mT or an even larger value. The MFD rapidly decreases at places father from the two aforementioned location. This non-uniform distribution can also be clearly found at slices with a distance of 0.65 mm and 1.4 mm below the top of workpiece, respectively [Figs. 6(b) and (c)]. The MFD near the front keyhole [Fig. 6(b)] and bottom keyhole [Fig. 6(c)] reaches about 0.05 mT and 0.12 mT, respectively. Conversely, other locations only have an MFD less than 0.01 mT. A typical clockwise vortex of magnetic field is 200
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Fig. 4. TEC streamline at the welding time of 23.605 ms during laser welding (process No. 2): (a) top view; (b) longitudinal section view; (c) and (d) 3D view.
Fig. 5. 3D view of TEC streamline at the welding time of 23.605 ms during laser welding: (a) process No. 1; (b) process No. 3.
Lorentz force in places away from the front and bottom keyholes is small enough to be neglected (less than 1 N/m3). Fig. 7(c) shows the variation curves of the Lorentz force over welding time at points A and B [Figs. 7(a) and (b)]. The Lorentz force of points A and B can reach top values (1 kN/m3 for point A and 0.45 kN/m3 for point B) when those points are placed closest near the melting front interface. At the other welding times, the Lorentz force is small. Therefore, the Lorentz force is time-dependent in the laser welding process. This demonstrates close relationship of the distribution and evolution of the Lorentz force to the three-dimensional transient TEC.
shown in slice 3 [Fig. 6(c)], which is produced by a beam of downward TEC flows near the bottom keyhole [Fig. 4(b)]. The horizontal slice and longitudinal section views of the induced Lorentz force at a welding time of 23.605 ms during laser welding (process No. 2) are shown in Figs. 7(a) and (b), respectively. Large Lorentz force is also produced at the liquid-solid interface near the front and bottom keyholes. The maximum value can reach about 2 kN/m3, or an even larger value. The direction of the Lorentz force at this location mainly follows the tangential direction of the liquid-solid interface, which may have a shear effect on the interface. Furthermore, the 201
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Fig. 6. Distributions of self-induced magnetic field at the welding time of 23.605 ms during laser welding (process No. 2): (a) 3D view; (b) and (c) horizontal slice at a distance of 0.65 mm and 1.4 mm below the top of workpiece, respectively.
Fig. 7. Distributions of induced Lorentz force at the welding time of 23.605 ms during laser welding (process No. 2): (a) longitudinal section view; (b) horizontal slice (slice at a distance of 0.7 mm below the top of workpiece); (c) variation curves of Lorentz force at points A (at a distance of 1.925 mm in x-axis from zero point and center of workpiece in y-axis) and B (at a distance of 1.65 mm in x-axis and 1.05 mm in y-axis from zero point) shown in (a) and (b) during laser welding process.
Given that the magnetic field assumed to be induced only by TEC in laser welding [Eq. (3)], the value and distribution of the magnetic field is determined by the time-dependent and three-dimensional TEC. The magnitude of the MFD is around 0.1 mT, which is reasonably consistent to the theoretical result (0.1–1 mT) submitted by Paulini et al. [3] and the experimental results (around 10 Gauss) of Wei et al. [10] for EB welding of dissimilar metals. The present MFD is less than that of the literature data and may be a result of the Seebeck coefficient difference used in this research (3.1×10−6 V/K) and that used in the EB welding of dissimilar metals (around 1.0×10−5 V/K). The Lorentz force, produced by the transient, three-dimensional TEC cuts the self-induced magnetic field line [Eq. (5)]. Similarly, the Lorentz force is also threedimensional, uneven, and varies with time. Therefore, the TEC and the self-induced magnetic field and Lorentz force in deep penetration laser welding could not be well described and understood by the twodimensional or steady-state theoretical models.
3.4. Theoretical analysis 3.4.1. The magnitude of TEC in laser welding process In order to study the magnitude of TEC, a scale analysis is used in the following discussion. According to Ohm's law, integrating Eq. (1) along the closed curves across the liquid-solid interface gives [4,10,11]:
∂T ∼ ∼ jlx − jsx = σe (Ss − Sl ) ∼ , ∂x
(12)
∂T ∼ ∼ jly − jsy = σe (Ss − Sl ) ∼ , ∂y
(13)
∂T ∼ ∼ jlz − jsz = σe (Ss − Sl ) ∼ , ∂z
(14)
where subscript l and s respectively donate the liquid and solid phase. Eqs. (12)–(14) indicate that the thermoelectric currents are contributed
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Fig. 8. Variation curves in three different welding processes during laser welding: (a) the maximum TEC curves; (b) the keyhole depth curves.
gradient. Therefore, the keyhole instability may be used to characterize the violent degree of the TEC oscillations in the laser keyhole welding process. Fig. 8 shows the evolutions of the maximum TEC and the keyhole depth within 28 ms for the different welding processes, respectively, during laser welding. Fig. 8(a) shows the rapid increase of the TEC to its tip value at the very beginning of welding and decrease to a relatively small and stable value, with frequency oscillation after the welding of around 12 ms given that the keyhole depth reached a quasi-steady state shown in Fig. 8(b). Fig. 9 illustrates the oscillation frequency of the maximum TEC measured to be around 2.2–8.5 kHz, which is consistent with that of the keyhole depth (around 2.0– 5.0 kHz). The amplitude of the TEC oscillations increases with that value of the heat input [Fig. 8(b)], which is consistent with that of keyhole depth oscillations [Fig. 8(a)]. These agreements confirm the relationship between the TEC oscillations and of the keyhole instability. The average amplitudes of the maximum TEC and keyhole depth in the three welding process are shown in Fig. 9. A simple but practical linear formula of the amplitudes between the maximum TEC and keyhole depth (called keyhole depth-TEC relationship, the blue line in Fig. 9), can be expressed as follows:
by the gradient of the Seebeck coefficients between the molten liquid and solid metal. Scaling Eqs. (12)–(14) leads to [10,11]:
T − T∞ ∼ j ∝ σe (Ss − Sl ) m , δT
(15)
where Tm and T∞ are melting and ambient temperature, respectively, and δT donates the thermal diffusion thickness. The magnitude of TEC is inversely proportional to the thermal diffusion thickness in deep penetration laser welding process. The present research defined σe , Ss − Sl , Tm , and T∞ are 7.7×105 Ω−1 m−1, 3.1×10−6 V/K, 1727 K, and 300 K, respectively. The melting width is around 1.0 mm, and the width of weld pool is around 0.5 mm. Therefore, the thermal diffusion thickness δT is around 0.25 mm. As a result, the magnitude of the TEC estimated by Eq. (15) can reach 1.4×107 A/m2, which is consistent with the simulation results. 3.4.2. Violent degree of TEC oscillation We have learned that the TEC is uneven and time-dependent during the deep penetration laser welding process because of temperature distribution oscillation and boundary geometry. Temperature distribution oscillations are closely related to the keyhole instability. The large temperature gradient produced near the keyhole wall directly illuminated by the laser beam and the TEC is linear with the temperature
A ∼j = k 0⋅Ak
(16)
where A ∼j and Ak respectively donate the amplitudes of the maximum TEC and keyhole depth and k 0 is a constant coefficient in a certain range (8.63×1010 A/m3). Therefore, the violent degree of oscillations of the maximum TEC can be related back to the keyhole instability, specifically with to the keyhole depth-TEC relationship. By using this relationship, the violent degree of TEC oscillations may be estimated by observing the keyhole depth oscillation.
3.5. On validation The predicted magnitude of the induced magnetic field follows the literature data very consistently. The dynamics of the self-consistent keyhole and weld pool following our previous computational fluid dynamics (CFD) laser welding models were also deemed reliable [18,25–30]. However, it is very difficult to directly experimentally verify the time-dependent evolutions and three-dimensional TEC distributions in laser welding. The predicted weld dimensions suggested by the proposed model were used to compare the experimental results (Fig. 10). The predicted size and shape of the weld (blue dotted line) was in close agreement with the experimental results (black full line) in the three different welding processes. In summary, the predicted results of the TEC are reasonable and can serve as the basis for the thermoelectric phenomena in the high-energy beam welding process.
Fig. 9. The keyhole depth-TEC relationship during deep penetration laser welding of austenite stainless steel. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 10. Comparisons of predicted the weld profile and experimental data in different welding processes during laser welding process of 304 stainless steel: (a) process No. 1; (b) process No. 2; (c) process No. 3.
Trans 1990;112(3):714–20. [5] Dragunov VK, Chepurin MV. Electron beam welding of dissimilar alloys under conditions of the generation of thermoelectric current. Weld J 2002;1990(16):466–74. [6] Li X, Gagnoud A, Fautrelle Y, Ren Z, Moreau R, Zhang Y, Esling C. Dendrite fragmentation and columnar-to-equiaxed transition during directional solidification at lower growth speed under a strong magnetic field. Acta Mater 2012;60:3321–32. [7] Li X, Wang J, Du D, Zhang Y, Fautrelle Y, Nguyen-Thi H, Gagnoud A, Ren Z, Moreau R. Effect of a transverse magnetic field on the growth of equiaxed grains during directional solidification. Mater Lett 2015;161:595–600. [8] Wang J, Fautrelle Y, Nguyen-Thi H, Reinhart G, Liao H, Li X, Zhong Y, Ren Z. Thermoelectric magnetohydrodynamic flows and their induced change of solid– liquid interface shape in static magnetic field-assisted directional solidification. Metall Mater Trans A 2016;4A:1169–79. [9] Kern M, Berger P, Hügel H. Magneto-fluid dynamic control of seam quality in CO2 laser beam welding. Weld J 2000;79:72-s–78-s. [10] Wei PS, Chung FK. Three-dimensional electron-beam deflection and missed joint in welding and dissimilar metals. J Heat Transf 1997;119:832–9. [11] Wei PS, Wen C. Missed joint induced by thermoelectric magnetic field in electronbeam welding dissimilar metals experiment and scale analysis. Metall Mater Trans B 2002;33B:765–73. [12] Ambrosy G, Avilov V, Berger P, Hügel H. Laser induced plasma as a source for an intensive current to produce electromagnetic forces in the weld pool. In: Proceedings of the XVI International Symposium on Gas Flow, Chemical Lasers, and High-Power Lasers. SPIE, Gmunden, Austria. Vol. 6346, 63461Q1–8; 2007. [13] Lange A, Cramer A, Beyer E. Thermoelectric currents in laser induced melts pools. J Laser Appl 2009;21:82–7. [14] Tenner F, Brock C, Klämpfl F, Schmidt M. Analysis of the correlation between plasma plume and keyhole behavior in laser metal welding for the modeling of the keyhole geometry. Opt Lasers Eng 2015;64:32–41. [15] Luo M, Shin YC. Vision-based weld pool boundary extraction and width measurement during keyhole fiber laser welding. Opt Lasers Eng 2015;64:59–70. [16] Ai Y, Shao X, Jiang P, Li P, Liu Y, Liu W. Welded joints integrity analysis and optimization for fiber laser welding of dissimilar materials. Opt Lasers Eng 2016;86:62–74. [17] Ki H, Mazumder J, Mohanty PS. Modeling of laser keyhole welding: part I. Mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free surface evolution. Metall Mater Trans A 2002;33:1817–30. [18] Pang S, Chen L, Zhou J, Yin Y, Chen T. A three-dimensional sharp interface model for self-consistent keyhole and weld pool dynamics in deep penetration laser welding. J Phys D: Appl Phys 2011;44:025301. [19] Zhao H, Niu W, Zhang B, Lei Y, Kodama M, Ishide T. Modelling of keyhole dynamics and porosity formation considering the adaptive keyhole shape and three-phase coupling during deep-penetration laser welding. J Phys D: Appl Phys 2011;44:485302. [20] Cho WI, Na SJ, Thomy C, Vollertsen F. Numerical simulation of molten pool dynamics in high power disk laser welding. J Mater Process Technol 2012;212:262–75. [21] Courtois M, Carin M, Le Masson P, Gaied S, Balabane M. A complete model of keyhole and melt pool dynamics to analyze instabilities and collapse during laser welding. J Laser Appl 2014;26:042001. [22] Zhang L, Zhang J, Gumenyuk A, Rethmeier M, Na SJ. Numerical simulation of full penetration laser welding of thick steel plate with high power high brightness laser. J Mater Process Technol 2014;214:1710–20. [23] Meng W, Li Z, Lu F, Wu Y, Chen J, Katayama S. Porosity formation mechanism and its prevention in laser lap welding for T-joints. J Mater Process Technol 2014;214:1658–64. [24] Tan W, Shin Y. Analysis of multi-phase interaction and its effects on keyhole dynamics with a multi-physics numerical model. J Phys D: Appl Phys 2014;47:345501.
4. Conclusions The present study first developed a three-dimensional theoretical model for the thermoelectric phenomena to investigate the timedependent evolutions of TEC, induced magnetic field, and Lorentz force in the deep penetration fiber laser welding of 304 stainless steel. The predicted results are well consistent with the available experimental and literature data. The main conclusions are shown as follows: 1) The TEC, induced magnetic field and Lorentz force are timedependent, three dimensional and uneven. The large TECs are located at the liquid-solid interface near the front and bottom keyholes, and the value can reach 107 A/m2, or an even larger value. The magnitude of the self-induced magnetic flux density and Lorentz force can reach around 0.1 mT and 1 kN/m3, respectively. 2) The TECs are three-dimensional circulations moving from the melting front to the solidification front in solid part of the workpiece, contrary to the direction of the liquid part. It will produce three typical vortexes of the TEC in the welding process (two horizon orientation vortexes near the upper and front keyholes and a vertical orientation vortex near the bottom keyhole). 3) In a certain range, the welding process parameters including the laser power and welding speed will change the magnitude but not the dynamic characteristics of the TEC, such as the TEC flow patterns, in the deep penetration laser welding process. 4) The TEC oscillations are closely related to keyhole instability. The oscillation frequency (around 2.2–8.5 kHz) and average amplitude of the maximum TEC are consistent with those of the keyhole depth (oscillation frequency, around 2.0–5.0 kHz). Acknowledgement The authors would like to acknowledge the National Natural Science Foundation of China (No. 51675202), the National Basic Research Program of Chinese (973 Program, No. 2014CB046703) and the National Natural Science Foundation of China (No. 51105153) for financial support. References [1] Shercliff JA. Thermoelectric magnetohydrodynamics. J Fluid Mech 1979;91:231–51. [2] Anatychuk LI, Luste OY. Thermoelectric eddy currents and transverse thermal emf in zonally inhomogeneous plates. Sov Phys J 1969;12:801–3. [3] Paulini J, Simon G, Decker I. Beam deflection in electron beam welding by thermoelectric eddy currents. J Phys D: Appl Phys 1990;23:486–95. [4] Wei PS, Lii TW. Electron beam deflection when welding dissimilar metals. J Heat
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Optics and Lasers in Engineering 91 (2017) 196–205
X. Chen et al.
2006;39:1257–66. [32] Zhou J, Tsai HL, Lehnhoff T. Investigation of transport phenomena and defect formation in pulsed laser keyhole welding of zinc-coated steels. J Phys D: Appl Phys 2006;39:5338–55. [33] Oscher S, Fedkiw RP. Level set methods and dynamic implicit surfaces. Berlin: Springer press; 2002. [34] Liu J, Rao Z, Liao S, Tsai H. Numerical investigation of weld pool behaviors and ripple formation for a moving GTA welding under pulsed currents. Int J Heat Mass Transf 2015;91:990–1000. [35] Zhang M, Chen G, Zhou Y, Li S. Direct observation of keyhole characteristics in deep penetration laser welding with a 10 kW fiber laser. Opt Express 2013;21:19997–20004. [36] Kawahito Y, Matsumoto N, Mizutani M, Katayama S. Characterisation of plasma induced during high power fibre laser welding of stainless steel. Sci Technol Weld Join 2008;13:744–8. [37] Bachmann M, Avilov V, Gumenyuk A, Rethmeier M. Experimental and numerical investigation of an electromagnetic weld pool support system for high power laser beam welding of austenitic stainless steel. J Mater Process Technol 2014;214:578–91.
[25] Pang S, Chen W, Wang W. A quantitative model of keyhole instability induced porosity in laser welding of titanium alloy. Metall Mater Trans A 2014;45:2808–18. [26] Pang S, Chen X, Zhou J, Shao X, Wang C. 3D transient multiphase model for keyhole, vapor plume, and weld pool dynamics in laser welding including the ambient pressure effect. Opt Lasers Eng 2015;74:47–58. [27] Pang S, Chen W, Zhou J, Liao D. Self-consistent modelling of keyhole and weld pool dynamics in tandem dual beam laser welding of aluminum alloy. J Mater Process Technol 2015;217:131–43. [28] Pang S, Hirano K, Fabbro R, Jiang T. Explanation of penetration depth variation during laser welding under variable ambient pressure. J Laser Appl 2015;27:022007. [29] Pang S, Chen X, Li W, Shao X, Gong S. Efficient multiple time scale method for modeling compressible vapor plume dynamics inside transient keyhole during fiber laser welding. Opt Laser Technol 2016;77:203–14. [30] Pang S, Chen X, Zhou J, Shao X, Gong S, Xiao J. Dynamics of vapor plume in transient keyhole during laser welding of stainless steel: local evaporation, plume swing and gas entrapment into porosity. Opt Lasers Eng 2016;82:28–40. [31] Rai R, DebRoy T. Tailoring weld geometry during keyhole mode laser welding using a genetic algorithm and a heat transfer model. J Phys D: Appl Phys
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