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Numerical simulation of heat transfer and fluid flow during vacuum electron beam welding of 2219 aluminium girth joints
Journal Pre-proof Numerical simulation of heat transfer and fluid flow during vacuum electron beam welding of 2219 aluminium girth joints Ziyou Yang, Yuchao Fang, Jingshan He PII:
S0042-207X(20)30093-2
DOI:
https://doi.org/10.1016/j.vacuum.2020.109256
Reference:
VAC 109256
To appear in:
Vacuum
Received Date: 7 November 2019 Revised Date:
6 February 2020
Accepted Date: 8 February 2020
Please cite this article as: Yang Z, Fang Y, He J, Numerical simulation of heat transfer and fluid flow during vacuum electron beam welding of 2219 aluminium girth joints, Vacuum, https://doi.org/10.1016/ j.vacuum.2020.109256. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Elsevier Ltd. All rights reserved.
Numerical simulation of heat transfer and fluid flow during vacuum electron beam welding of 2219 aluminium girth joints Ziyou Yang a, Yuchao Fang a, Jingshan He a,* a
State Key Laboratory of Advanced Welding and Joining, Harbin
Institute of Technology, Harbin 150001, China * Corresponding author E-mail address:
[email protected] (Jingshan He)
ABSTRACT In this paper, a three-dimensional model, which is combined with the volume of fluid (VOF) model, is established to study the dynamic behaviour and keyhole stability of circumferential weld pools in vacuum electron beam welding (EBW). The influences of gravity, the Marangoni effect and recoil pressure are taken into account during the simulation process. For partial penetration welding, the humps on the keyhole wall cause a redistribution of the surface tension; furthermore, there is little difference in the keyhole evolution during flat welding and girth welding due to the supporting effect of the base metal. After entering the full penetration stage, a tail forms at the circumferential weld pool surface under the action of the Marangoni effect and the recoil pressure. Remarkably, the fluctuations in the temperature and flow velocity are
1
more intense at the lower weld pool surface than that at the upper surface due to the interaction between the electron beam and the keyhole wall. In addition, the flow field on a three-dimensional scale is analysed. Moreover, corresponding experiments are carried out to verify the accuracy of the models adopted in this study. The simulation results are consistent with the experimental data.
Keywords: Vacuum electron beam welding, Circumferential molten pool, Flow field, Supporting effect, Gravity
1. Introduction Electron beam welding (EBW), which is a processing method used in a vacuum environment with a high energy density, a high welding speed and a narrow heat-affected zone, has become a new technique to guarantee high-quality welded joints [1,2]. Due to the characteristics of EBW technology, this approach is particularly suitable for welding dissimilar metals and materials with high thermal conductivity, such as aluminium alloys, to create different welding structures [3]. Due to these excellent features and the corresponding production of high-quality, lightweight parts, EBW has been frequently applied in the series production of modern aircraft [4]. In previous works, many experimental studies and theoretical analyses have been conducted to predict the welded joint quality and process stability during EBW of aluminium alloys. Many studies have indicated that the welding structure has a great
2
influence on the quality of the welded joints with the same processing parameters [5,6]. Wu and Kim [7] noted that the properties of pipe welded joints are different from those of plate joints. Schumacher [8] considered that the incident beam position relative to the workpiece was a significant factor that affected the weld seam quality. Moreover, a substantial number of findings suggested that the heat transfer and flow field during the welding process are closely related to the quality of welded joints [9]. Therefore, the investigation of the dynamic weld pool behaviour not only has theoretical and practical meaning but also deepens our understanding of the EBW process. With the development and application of computer technology, numerical simulations can be used to visualize the dynamic welding process to study the molten pool behaviour and predict the stress field to control the welding formation. In recent years, a series of numerical studies on the flow field in high-energy beam welding have been carried out by Na’s group, involving the welding heat source model [10,11], keyhole stability [12], molten pool fluctuations [13] and welding defects [14]. Sohail et al [15] developed a model to study the flow field of fibre laser welding at eight different positions from 0 to 360°. Wu et al [16] adopted a coordinate rotation of arc models to discuss the molten pool pattern of gas metal arc (GMA) welding of horizontal fillets. Yang et al [17] proposed a three-dimensional technique to investigate the thermal-fluid coupled field during double-sided laser beam welding of T-joints. Although the molten pool behaviour in different welding structures has been studied by many researchers, these studies essentially investigated flat plate welding, not girth welding. Lacki and
3
Adamus [18] presented a numerical analysis on EBW of tubes and analysed the heat-affected zones and residual stress in the joints. Rong et al. [19] established a finite element method (FEM) model to calculate the welding deformation and residual stress in hybrid laser-arc girth welds. Many studies have contributed greatly to the numerical simulation of girth welds. However, to date, the corresponding conclusions are only for thermal and stress fields, without considering the effect of the molten pool free surface on welded joints. In conclusion, in order to optimize the EBW process of girth joints, the circumferential molten pool behaviour is worth studying. In this paper, a three-dimensional mathematical model considering heat transfer and flow fields is developed to analyse the weld pool behaviour in EBW of girth joints. The functions of gravity, the Marangoni effect and recoil pressure are added into this model. The volume of fluid (VOF) model is adopted to track the molten pool surface. A heat source described as a Gaussian distribution is employed to represent the electron beam energy. The temperature field, fluid flow field and molten pool characteristics during EBW of the girth weld joint are discussed using the established model in Fluent 15.0. The corresponding experiment is carried out to determine the validity of the simulation data.
2. Mathematical model 2.1. Modelling assumptions A schematic of the electron beam girth welding in this work is shown in Fig. 1. The y-axis is in the length direction of the circular structure. Section A-A represents the xoz
4
plane, as shown in Fig. 1(b). In the welding process, the position of the electron beam remains unchanged, and the workpiece rotates anti-clockwise. EBW involves a complex multi-field coupling phenomenon that simultaneously contains fluid flow and conduction (solid), convection (liquid) and radiation heat transfer mechanisms. Therefore, many researchers have attempted to simplify the numerical models of the welding process by making various assumptions. In the present simulation, the following assumptions and simplifications have been employed without compromising the accuracy of the solutions. (1) The melt is supposed to be a laminar, incompressible fluid with Newtonian viscosity. (2) The electron beam profile is assumed to be Gaussian before entering the keyhole. (3) The material properties are constant, and the Boussinesq approximation is adopted. (4) The environmental temperature of the workpiece is 300 K.
(a) Girth weld seam of EBW
(b) Molten pool on section A-A (xoz plane)
Fig. 1. Schematic diagram of electron beam girth welding.
5
2.2. Governing equations and heat source model Based on the above assumptions, three conservation equations of computational fluid dynamics (CFD) are used to describe the fluid flow of the melt and heat transfer in the molten pool [20]. Continuity equation: +
+
+
=0
(1)
X-momentum equation: +
+
+
=−
+
+
+
=−
+
+
+
+
(2)
Y-momentum equation: +
+
+
+
(3)
Z-momentum equation: +
+
+
=−
+
=
+
+
+
+
(4)
Energy equation: +
+
+
+
+
(5)
where u, v and w represent the velocity components in the x, y and z directions, respectively; ,
, p, k, Cp and H represent the density, dynamic viscosity, pressure,
thermal conductivity, specific heat capacity at constant pressure and mixed enthalpy, respectively; Su, Sv, and Sw are the momentum source terms in the x, y and z directions, which are composed of the surface tension ( , and
), buoyancy force
and gravity
6
,
, and
), recoil pressure (
,
[14]; SE is the energy source term,
which is composed of the energy input !" vaporization heat dissipation !" =
+
=
+
=
in the welding process [15]. (6) (7)
+
= !"
$&
, radiation heat dissipation !#$% and
+
−
− !#$% − !"
(8) $&
(9)
The material enthalpy H is also handled by the enthalpy-porosity technique to help account for the solid-liquid phase transition [14]. This method treats the deformable region (partially solidified region) as a porous medium. The porosity in each cell is set equal to the liquid fraction in that cell. In fully solidified regions, the porosity is equal to zero, which extinguishes the velocities in these regions [17]. ' = ℎ#") + * 1=3
./0
+& ,- + 1∆'
(10)
0 - < -5 6 7 -5 86 7
< - < -9
(11)
1 - > -9
where ℎ#") and -#") are the reference enthalpy and reference temperature; ∆' is
the latent heat of fusion; 1 is the liquid fraction, which is defined by the
enthalpy-porosity method; and -5 and -9 are the solidus temperature and liquidus temperature.
The VOF model is adopted to calculate the keyhole free surface and transient evolution of the molten pool [21]. <
+=
<
+>
<
+?
<
=0
(12)
where F is the fluid volume fraction function. If F=0, then the cell contains only
7
vacuum. If F=1, then the cell is filled with liquid metal. If 0
DEF G#HI
exp −3
O = OP + Q|CP − C|
IN I
#HI
(13) (14)
where Q is the heat input; S is the welding energy efficiency related to KL110 EBW machine, and its value is 0.95 [23]; and r0 is the focal radius of the electron beam at the upper surface of the dynamic keyhole. In this study, the defocused distance is 0 mm, so at z0= 20 mm, the beam radius r0 is 0.25 mm. Q is an attenuation coefficient (0.0135), which represents the degree of beam divergence.
2.3. Driving forces In the numerical calculation process, the driving forces in the molten pool play a critical role in the flow pattern. Fig. 2 is a schematic diagram of the force analysis for the keyhole wall, which consists of the tangential and normal forces at any point on the keyhole wall. The normal forces consist of the recoil pressure evaporation, the hydrostatic pressure of the curved interface Marangoni shear force 5
U
T
induced by
caused by gravity and the additional pressure
affected by surface tension. The tangential forces include the induced by the surface tension gradient and the shear force
caused by liquid metal flow [24].
8
Fig. 2. Schematic diagram of the force analysis on the keyhole wall. In the EBW process, the recoil pressure generated by the rapid evaporation of the liquid metal surface promotes the formation of a keyhole, while the surface tension and hydrostatic pressure promote the closure of the keyhole. The keyhole fluctuates rapidly due to the competition between the recoil pressure and surface tension [25]. The force on the keyhole wall is always in dynamic equilibrium. The balance on the keyhole wall can be described by the following two formulas. The resultant force in the direction normal to the keyhole wall at any time and location is [24]: =
+
T
+
U
(15)
The resultant force in the tangential direction of the keyhole wall at any time and location is [24]: = where
−
5
=
⋅
5W
−
X
ZW Y
+
[
5W
(16)
is the viscosity coefficient; > and >Y are the tangential velocity component
and the normal velocity component of the viscous fluid, respectively; tension temperature gradient;
5W
is the surface
is the tangential temperature gradient of the keyhole
wall; and \ZW and ]W are normal and tangential unit vectors, respectively. The surface tension is described as follows: 9
U
= ^_ = ^ `_P +
- − -T b
aU
a
(17)
where k represents the free surface curvature and _ represents the surface tension
coefficient, which can be determined as a linear function of temperature [26]. _P represents the surface tension at the melting point,
aU
a
represents the temperature
coefficient for the surface tension, and Tm represents the melting point of the aluminium alloy. The recoil pressure caused by the evaporation process can be expressed by the Clausius-Clapeyron equation [27]: = 0.54 P exp f
6 g
h
(18)
g
where P0 is the ambient pressure, Tb represents the boiling point of the metal, T represents the temperature of the keyhole wall, and R represents the universal gas constant. The hydrostatic and hydrodynamic pressures can be described by the following formulas [28]: T j
= gℎ
=
(19)
k[I lm
where
(20) represents the density, g represents gravitational acceleration, h represents the
height of the liquid metal in the molten pool and nY represents the velocity of the liquid metal. The buoyancy force derived from the density gradient can be described according to the Boussinesq approximation as follows: = o1 - − -P
(21) 10
where
, o, 1 and T0 represent the density, gravity, thermal expansion rate and
ambient temperature, respectively.
2.4. Boundary conditions To solve the conservation equations described in Eqs. (1)-(5), the detailed boundary conditions were set as shown hereafter. For the keyhole and molten pool free surface, the thermal boundary conditions consisting of the electron beam energy, radiation and evaporation can be described as follows: K
Zq Y
= !"
− !#$% − !"
$&
= !"
− rs - t − -Pt −
where qebw is the absorbed electron beam energy,
9
9 n" $& f
(22)
is the density of the liquid metal,
Vevap represents the evaporation-induced keyhole surface recession speed, and Lv represents the evaporation latent heat. For other surfaces, the thermal boundary, which mainly involves radiation rather than convection in vacuum EBW, is described as follows: ^
Zq Y
= −rs - t − -Pt
(23)
where T and T0 represent the workpiece temperature and ambient temperature, respectively; r represents the surface radiation emissivity; and s represents the Stefan-Boltzmann constant.
2.5. Thermo-physical properties and mesh generation This paper uses 2219 aluminium alloy with a thickness of 2 mm. The chemical composition is shown in Table 1. Considering the chemical composition, the thermo-physical properties of the base metal and relevant coefficients examined in the simulations are summarized in Table 2 [23]. 11
Table 1 Chemical composition of the base metal (wt.%) Component
Cu
Si
Fe
Mn
Mg
V
Zr
Zn
Ti
Mass fraction
5.8-6.8
≤0.2
≤0.3
0.2-0.4
≤1.8
0.05-0.15
0.10-0.25
≤0.1
0.02-0.10
Table 2 Material properties of 2219 aluminium alloy [23]. Physical property
Symbol
Density of solid
s
Density of liquid
l
Unit
Value
kg∙m-3
2700
kg∙m-3
2400
Specific heat of solid
Cs
J∙kg-1∙K-1
871
Specific heat of liquid
Cl
J∙kg-1 K-1
1060
Thermal conductivity of solid
Ks
W∙m-1∙K-1
238
Thermal conductivity of liquid
Kl
W∙m-1∙K-1
100
Boiling point
Tb
K
2730
Latent heat of fusion
Hm
J∙kg-1
3.87×105
Latent heat of evaporation
Hv
J∙kg-1
1.08×107
Surface tension at 930 K
σ
N∙m-1
0.914
Temperature coefficient of surface tension
,s ,-
N∙m-1∙K-1
-0.35×10-3
Solidus temperature
Ts
K
820
Liquidus temperature
Tl
K
930
12
Impurity elements ≤0.15
Al rest
Ambient temperature
Tref
K
300
Gravitational acceleration
g
m∙s-2
9.81
In this simulation, O-mesh is used in the geometric model of the girth welding. The void regions at both the upper and lower sides for free surface tracking are all set to 1 mm, as shown in Fig. 1(b). The total number of elements in the simulations is 2,104,032. The minimum cell size is 0.125 mm, as shown in Fig. 3.
Fig. 3. Mesh generation in the numerical calculation. The commercial CFD software ANSYS Fluent Release 15.0 based on the finite volume method was employed to solve the conservation equations of the fluid field and temperature field during the EBW process. The user-defined function (UDF) was compiled in the C language to introduce additional momentum and energy sources.
3. Experiment The EBW experiment for verification of the simulation results was performed on a circular framework with a large vacuum EBW machine (KL-110 with a maximum accelerating voltage of 60 kV). The welded structures consisted of 2 mm thick 2219 aluminium alloys, which were specifically applied for lower shell fuselage applications in the aircraft industry. In this paper, the aluminium plates were clamped and welded in a vacuum chamber after cleaning the plates under a vacuum of 5×10−2 Pa. The aluminium alloy butt joints were welded at an accelerating voltage of 60 kV and a beam 13
current of 12 mA. The welding speed was set to 10 mm/s. The characteristic parameters of the electron beam are listed in Table 3. Table 3 EBW parameters used in the experiment. Accelerating voltage
Beam current
Focal radius
Focal plane z0
Welding speed
(kV)
(mA)
(µm)
(mm)
(mm/s)
60
12
250
0
10
Test name
Cylinder welding
After welding, the specimens were cut and polished using a series of SiC emery papers with grit sizes from 200 to 1000, for which water was used as a coolant. To reveal the microstructure, 1% HF+1.5% HCl+2.5% HNO3 was adopted as an etchant. The etched samples were studied under an optical microscope.
4. Results and discussion 4.1 Validation of the simulation models Fig. 4 presents the temperature distribution of the weld pool during the whole welding process. Note that the white arrow represents the rotation direction of the workpiece, whereas the heat source of the electron beam is fixed. Within approximately 1.5 s from the beginning of the process, the molten pool spreads in an unsteady way. During the quasi-steady state, the weld pool merely changes its shapes and position.
14
(a) t=0.5 s
(b) t=1.0 s
(c) t=1.5 s
(d) t=2.0 s
(e) t=2.5 s
Fig. 4. Development of temperature field in the numerical model of the girth welding process. Fig. 5 represents the variation in the weld pool dimensions during the whole welding process. The molten pool length at the girth welding position becomes relatively stable after approximately 1.5 s. During the quasi-steady stage, the simulated dimensions of the weld pool are approximately 6.5 mm at the upper surface and 6.1 mm at the lower surface.
Fig. 5. Simulation results of the molten pool dimensions. To verify the accuracy of the models adopted in this research, the weld profiles obtained from the calculations were compared with those from the EBW experiments, as shown 15
in Fig. 6. The dimensions of the welding profiles obtained from the calculations and experiments are also summed up in this picture. Fig. 6 shows that the simulated girth weld profiles agree well with the experiments. These results indicate that the adopted models in this study are effective and reasonable.
Fig. 6. Comparisons of the experimental results and predicted results. According to the solidification theory, the temperature gradient G, solidification velocity R, and their combined parameters GR and G/R in the molten pool affect the scale of the microstructure and morphology in the weld seam. Generally, the grain size increases with the decrease in GR, while the morphology changes from columnar dendrites to equiaxed dendrites with the decrease in G/R [30-33]. GR and G/R can be calculated by the G and R obtained directly from the simulation results. Fig. 7 displays the microstructure obtained by scanning electron microscopy (SEM) around points A, B and C, which are located at the top, the centre and the bottom of the weld seam, as shown in Fig. 6. In addition, the calculated GR and G/R are also marked. As depicted in the figure, a higher GR and lower G/R are observed at the upper region, while a lower GR and higher G/R are found at the lower region. Consequently, 16
according to the solidification mechanisms, it can be reasonably inferred that the equiaxed crystal and finer microstructure are prone to occur at the upper region of the weld seam, while the columnar crystal and coarser solidified structure may be found at the lower region. In addition, equiaxed dendrites are clearly observed around point A, and fine columnar dendrites and coarse columnar dendrites are observed around point B and point C, respectively. In conclusion, the simulation trend is in good agreement with the experimentally observed results.
Fig. 7. Solidified microstructure obtained by SEM at points A, B and C. Elemental mappings, obtained from scanning across the interface via energy dispersive spectroscopy (EDS), are shown in Fig. 8. The base metal region and weld seam region bounded by dotted lines represent the regions before and after welding, respectively. The main elements Al, Cu and Mg in the alloy were detected, and the corresponding EDS results of the marked regions in Fig. 8(a) are listed in Table 4. Decreases in the content of the main alloying elements due to evaporation can be found in the EDS results. Moreover, Fig. 8 shows that the elements are uniformly distributed due to sufficient mixing of the melt [34] and the content of elemental Mg in the weld seam is significantly lower than that in the base metal. To judge whether the loss rate is the same
17
at different positions, the content of Mg is measured with an electron probe, as shown in Fig. 9.
(a)
Mapping
scan
(b) Al
(c) Cu
(d) Mg
region Fig. 8. EDS mappings of different elements in the weld cross section. Table 4 EDS results of the regions before and after welding. Element (wt %)
Al
Cu
Mg
Before welding
90.52
6.13
1.82
After welding
90.17
5.92
1.27
Fig. 9(a) shows that the closer the position is to the weld seam centre, the lower the content of elemental Mg. Because the boiling point of Mg (1363 K) is much lower than that of Al (2730 K) and Cu (2835 K), Mg vaporizes more easily when the keyhole surface evaporates considerably. This phenomenon may be the reason for the change in element content along the width direction of the weld seam. Fig. 9(b) shows that the content of Mg decreases along the depth direction of the weld. This phenomenon may be caused by the high energy at the keyhole bottom, which causes more intense evaporation of Mg.
18
(a) Width direction of the weld seam
(b) Depth direction of the weld seam
Fig. 9. Elemental Mg content in different positions of the weld seam.
4.2 Keyhole evolution The transient keyhole fluctuation in EBW of 2219 aluminium alloy at the girth welding position is presented in Fig. 10. In the initial stage of the EBW process, the keyhole and molten pool profiles are regular and shallow, as shown in Fig. 10(a) and (b). With the process of EBW, the keyhole depth becomes larger due to the recoil pressure, and its profile tends to be irregular. As the keyhole depth increases, the recoil pressure, surface tension and hydrostatic pressure of the melt rebuild a new balance of pressure on the keyhole surface. At this time, humps emerge and lead to the redistribution of the surface tension. As a result, these humps move along the keyhole surface under the effect of the Marangoni effect, which causes free surface fluctuations, as shown in Fig. 10(c)-(e). After approximately 0.175 s, the aluminium sheet is completely penetrated, and a through-keyhole is formed, as shown in Fig. 10(f). For the partial penetration welding, the keyhole fluctuation process obtained from the simulations is similar to the experimental observation of Li et al. [29].
19
Fig. 10. Formation of a keyhole profile during EBW.
4.3 Melt flow patterns Fig. 11 represents the expansion of the molten pool in terms of the temperature field and flow field. During the initial period of the full penetration welding, it can also be seen that a through-keyhole does not always exist but keeps opening and closing alternately. In addition, it is observed that there is a growing volume of liquid metal from the upper and lower parts of the molten pool in the initial stage of full penetration welding. In theory, this phenomenon may be associated with the action of the Marangoni effect and the influence of gravity between the top surface and bottom surface. For the penetration welding, the conclusion that the tail of the molten pool surface forms easily under the appropriate process conditions was also confirmed by Zhang’ s study [35].
20
Fig. 11. Evolution of the flow pattern and the temperature field in a longitudinal section side view. As the keyhole size increases, the melt ejected from the keyhole by the recoil pressure flows towards the rear-top part of the weld pool under the action of the Marangoni effect. When the base metal has just been penetrated completely at 0.170 s, the melt at the weld pool bottom is subjected to the recoil pressure and then moves to the rear-bottom part of the molten pool. Moreover, the electron beam is lost from the through-keyhole, causing variation in energy absorption along the keyhole depth. Fig. 21
11(b) shows that an uneven distribution of the electron beam on the keyhole surface causes the keyhole to collapse at approximately 0.200 s. Then, a rather steady stream of the overheated melt under the keyhole is transported to the tail of the weld pool by surface tension. The lower surface of the weld pool far from the keyhole centre is equivalent to being reheated. Therefore, the weld pool is extended and becomes longer in the lower part, as presented in Fig. 11(c). At the rear parts of the weld pool, the liquid metal flowing backward is hindered by the solid-liquid interface and then flows towards the centre of the molten pool. The movement of the melt in these directions is gradually weakened and accompanied by the stretching of the weld pool in both upper and lower sides, as demonstrated by the arrowed curves in Fig. 11(d). Therefore, the weld pool dimensions in the middle of the workpiece thickness decrease gradually. The corresponding calculated streamlines reflecting the development of the weld pool are presented in Fig. 12.
(a) t=0.170 s
(b) t=0.200 s
(c) t=0.300 s
(d) t=0.400 s
Fig. 12. Simulated streamlines in a longitudinal section side view. Fig. 13 shows points 1-7, which represent seven typical positions in the weld pool. Fig. 14(a)-(c) shows the simulation results of the flow velocity in the x-axis direction during EBW. In the upper and lower parts of the molten pool, the liquid metal is discharged by
22
the recoil pressure in the keyhole and then flows to the rear part of the weld pool (P1 and P5). The melt in this direction changes the flow direction at the edge of the weld pool (P2 and P6). In the middle part of the weld pool, the melt on the upper and lower sides converges and then flows towards the keyhole wall (P3 and P4). It is remarkable that the melt flow has an obvious cyclical characteristic. In Zhang's numerical analysis, a similar law of periodic fluctuation in the velocity of the molten pool was also obtained [35].
Fig. 13. Schematic of points 1-6 in the molten pool.
(a) X-velocity of points 1 and 2
(b) X-velocity of points 3 and 4
23
(c) X-velocity of points 5 and 6 Fig. 14. Calculated x-velocity evolution curves. A comparison of the flow velocity in different positions at the same moment shows that the flow in the lower part of the molten pool is more intense than that in the upper part. This phenomenon may be due to the deep penetration effect of EBW [35]. The energy heat source is concentrated at the keyhole bottom, leading to the melt in the lower part of the weld pool being directly subjected to the recoil pressure, thereby obtaining greater kinetic energy. In addition, the flow direction of these points along the x-axis can indirectly verify the correctness of the flow field analysis in Fig. 11. Fig. 15 shows the temperature curve of different positions on the molten pool surface with respect to time. A comparison of the temperature variation in different positions at the same time shows that the temperature of the melt is lower farther away from the keyhole centre. This finding also explains why the Marangoni effect is the cause of the formation of the tail of the molten pool in Fig. 11(d). In addition, at the same distance from the keyhole centre, more intense temperature fluctuations occur at the lower molten pool surface than at the upper molten pool surface, which may be 24
caused by periodic fluctuations of the keyhole. When keyhole collapse occurs, the electron beam energy is hindered by the liquid metal due to the keyhole bridge, which prevents the electron beam from reaching the back of the workpiece. At this point, the temperature at the lower molten pool surface decreases. When the through-keyhole is formed, the electron beam can more easily reach the molten pool backside, thereby increasing the temperature at the lower molten pool surface. The more intense temperature fluctuation in the lower part of the molten pool leads to more intense evaporation, which is the reason why the content of Mg in Fig. 9(b) changes along the depth direction of the weld seam.
(a) Temperature of points 7-10
(b) Temperature of points 11-13
Fig. 15. Calculated temperature evolution curves. In fact, the molten pool flow is extremely complicated. The flow direction of the liquid metal is not a simple superposition of cross section and longitudinal section vortexes. Fig. 16(a) represents the position of the horizontal section of the molten pool at different depths. Fig. 16(b) and (c) show the flow field during the welding process, in which the arrow direction is the melt flow direction in the weld pool. Fig. 16(b) shows 25
that the melt flows in the three-dimensional space instead of flowing in the two-dimensional scale. At the R=19.6 cross section, the melt flows from the centre of the keyhole wall to the boundary of the molten pool. The R=19.2 section is located in the middle part of the weld pool where shrinkage occurs, resulting in a reduction in the molten pool area. The response of the liquid meal around the keyhole is the same as that in the previous section. The melt flows to the keyhole wall from the molten pool tail. At the R=18.8 and R=18.4 cross sections, the upward flow tendency is formed at the axis of the molten pool.
Fig. 16. Flow of the molten pool with different depth sections. On a three-dimensional scale, the flow direction of the liquid metal is represented in Fig. 17. This figure shows that the flow pattern of the melt is roughly the same as longitudinal section analysis of the molten pool in Fig. 11. Remarkably, there are many vortexes that flow around a central pillar around the bottom of the keyhole wall. This phenomenon may be caused by the opposite effect of recoil pressure and the Marangoni
26
effect on the keyhole wall.
(a) Visual angle 1
(b) Visual angle 2 Fig. 17. Three-dimensional flow field in the weld pool.
4.4 Molten pool characteristics of girth welding There is little difference between flat welding and girth welding in terms of the keyhole evolution in different positions. A possible reason for this limited distinction can be explained by the relationship between the molten pool and the workpiece. For partial penetration EBW, the base metal plays a key role in supporting the molten pool from all sides, thereby cancelling or reducing the influence of the workpiece shape on the molten pool behaviour. Fig. 18 sketches the mechanism of this influence.
27
Fig. 18. Sketch of supporting effect before full penetration welding. There is no doubt that gravity, vapour recoil pressure, surface tension, hydrostatic pressure and hydrodynamic pressure are the main driving forces in the molten pool of flat welding. However, the effect of gravity on the circumferential molten pool is different from that of the flat welding. Fig. 19 shows the diagrams of the role of gravity in the molten pool. Fig. 19(a) shows that the extension direction of the weld pool is perpendicular to the gravitational direction in flat welding, whereas this direction makes an acute angle in girth welding, as shown in Fig. 19(b). In the circumferential weld pool, force generated by gravity can perform positive work on the melt in the direction of the circumferential molten pool expansion. The role of gravity in the molten pool is also one of the critical differences between flat welding and girth welding.
(a) Gravity in the flat welding pool
(b) Gravity in the girth welding pool
Fig. 19. Diagram of the effect of gravity on the molten pool.
28
5. Conclusion (1) The comparison between the experimental data and the simulation results verifies that the three-dimensional mathematical model adopted in this study is an appropriate representation of electron beam girth welding. (2) In partial penetration EBW, there is no obvious difference in keyhole evolution between flat welding and girth welding due to the supporting effect of the unfused base metal on the molten pool. (3) After entering the full penetration stage, the tail of the molten pool extends rapidly under the influence of the Marangoni effect and recoil pressure. The fluctuations in the temperature and the flow velocity of the melt are more intense at the lower weld pool surface than that at the upper surface. This phenomenon is caused by the continuous collapse and opening of the keyhole bottom, resulting in the intermittent energy of the electron beam energy reaching the bottom of the molten pool. (4) During electron beam girth welding, the force generated by gravity can perform positive work on the expansion of the upper surface of the weld pool, which results in the upper surface being longer and more stable than the lower surface. The role of gravity in the molten pool is also one of the critical differences between flat welding and girth welding. (5) The flow pattern in the weld pool is complicated, and it is not a simple superposition of the vortexes in different sections. In the circumferential molten pool, there are many vortexes that flow around a central pillar around the bottom of the keyhole wall, which
29
may be caused by the opposite effect of the recoil pressure and Marangoni effect on the keyhole wall.
Acknowledgements This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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35
HIGHLIGHTS A model for studying the heat transfer and fluid flow during EBW of the girth joints is developed. The keyhole fluctuation and molten pool shape with the corresponding temperature and velocity field are simulated. The flow field in the circumferential molten pool is revealed on a three-dimensional scale. The influence of gravity on the circumferential molten pool is discussed.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0042-207X(20)30093-2
DOI:
https://doi.org/10.1016/j.vacuum.2020.109256
Reference:
VAC 109256
To appear in:
Vacuum
Received Date: 7 November 2019 Revised Date:
6 February 2020
Accepted Date: 8 February 2020
Please cite this article as: Yang Z, Fang Y, He J, Numerical simulation of heat transfer and fluid flow during vacuum electron beam welding of 2219 aluminium girth joints, Vacuum, https://doi.org/10.1016/ j.vacuum.2020.109256. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Elsevier Ltd. All rights reserved.
Numerical simulation of heat transfer and fluid flow during vacuum electron beam welding of 2219 aluminium girth joints Ziyou Yang a, Yuchao Fang a, Jingshan He a,* a
State Key Laboratory of Advanced Welding and Joining, Harbin
Institute of Technology, Harbin 150001, China * Corresponding author E-mail address:
[email protected] (Jingshan He)
ABSTRACT In this paper, a three-dimensional model, which is combined with the volume of fluid (VOF) model, is established to study the dynamic behaviour and keyhole stability of circumferential weld pools in vacuum electron beam welding (EBW). The influences of gravity, the Marangoni effect and recoil pressure are taken into account during the simulation process. For partial penetration welding, the humps on the keyhole wall cause a redistribution of the surface tension; furthermore, there is little difference in the keyhole evolution during flat welding and girth welding due to the supporting effect of the base metal. After entering the full penetration stage, a tail forms at the circumferential weld pool surface under the action of the Marangoni effect and the recoil pressure. Remarkably, the fluctuations in the temperature and flow velocity are
1
more intense at the lower weld pool surface than that at the upper surface due to the interaction between the electron beam and the keyhole wall. In addition, the flow field on a three-dimensional scale is analysed. Moreover, corresponding experiments are carried out to verify the accuracy of the models adopted in this study. The simulation results are consistent with the experimental data.
Keywords: Vacuum electron beam welding, Circumferential molten pool, Flow field, Supporting effect, Gravity
1. Introduction Electron beam welding (EBW), which is a processing method used in a vacuum environment with a high energy density, a high welding speed and a narrow heat-affected zone, has become a new technique to guarantee high-quality welded joints [1,2]. Due to the characteristics of EBW technology, this approach is particularly suitable for welding dissimilar metals and materials with high thermal conductivity, such as aluminium alloys, to create different welding structures [3]. Due to these excellent features and the corresponding production of high-quality, lightweight parts, EBW has been frequently applied in the series production of modern aircraft [4]. In previous works, many experimental studies and theoretical analyses have been conducted to predict the welded joint quality and process stability during EBW of aluminium alloys. Many studies have indicated that the welding structure has a great
2
influence on the quality of the welded joints with the same processing parameters [5,6]. Wu and Kim [7] noted that the properties of pipe welded joints are different from those of plate joints. Schumacher [8] considered that the incident beam position relative to the workpiece was a significant factor that affected the weld seam quality. Moreover, a substantial number of findings suggested that the heat transfer and flow field during the welding process are closely related to the quality of welded joints [9]. Therefore, the investigation of the dynamic weld pool behaviour not only has theoretical and practical meaning but also deepens our understanding of the EBW process. With the development and application of computer technology, numerical simulations can be used to visualize the dynamic welding process to study the molten pool behaviour and predict the stress field to control the welding formation. In recent years, a series of numerical studies on the flow field in high-energy beam welding have been carried out by Na’s group, involving the welding heat source model [10,11], keyhole stability [12], molten pool fluctuations [13] and welding defects [14]. Sohail et al [15] developed a model to study the flow field of fibre laser welding at eight different positions from 0 to 360°. Wu et al [16] adopted a coordinate rotation of arc models to discuss the molten pool pattern of gas metal arc (GMA) welding of horizontal fillets. Yang et al [17] proposed a three-dimensional technique to investigate the thermal-fluid coupled field during double-sided laser beam welding of T-joints. Although the molten pool behaviour in different welding structures has been studied by many researchers, these studies essentially investigated flat plate welding, not girth welding. Lacki and
3
Adamus [18] presented a numerical analysis on EBW of tubes and analysed the heat-affected zones and residual stress in the joints. Rong et al. [19] established a finite element method (FEM) model to calculate the welding deformation and residual stress in hybrid laser-arc girth welds. Many studies have contributed greatly to the numerical simulation of girth welds. However, to date, the corresponding conclusions are only for thermal and stress fields, without considering the effect of the molten pool free surface on welded joints. In conclusion, in order to optimize the EBW process of girth joints, the circumferential molten pool behaviour is worth studying. In this paper, a three-dimensional mathematical model considering heat transfer and flow fields is developed to analyse the weld pool behaviour in EBW of girth joints. The functions of gravity, the Marangoni effect and recoil pressure are added into this model. The volume of fluid (VOF) model is adopted to track the molten pool surface. A heat source described as a Gaussian distribution is employed to represent the electron beam energy. The temperature field, fluid flow field and molten pool characteristics during EBW of the girth weld joint are discussed using the established model in Fluent 15.0. The corresponding experiment is carried out to determine the validity of the simulation data.
2. Mathematical model 2.1. Modelling assumptions A schematic of the electron beam girth welding in this work is shown in Fig. 1. The y-axis is in the length direction of the circular structure. Section A-A represents the xoz
4
plane, as shown in Fig. 1(b). In the welding process, the position of the electron beam remains unchanged, and the workpiece rotates anti-clockwise. EBW involves a complex multi-field coupling phenomenon that simultaneously contains fluid flow and conduction (solid), convection (liquid) and radiation heat transfer mechanisms. Therefore, many researchers have attempted to simplify the numerical models of the welding process by making various assumptions. In the present simulation, the following assumptions and simplifications have been employed without compromising the accuracy of the solutions. (1) The melt is supposed to be a laminar, incompressible fluid with Newtonian viscosity. (2) The electron beam profile is assumed to be Gaussian before entering the keyhole. (3) The material properties are constant, and the Boussinesq approximation is adopted. (4) The environmental temperature of the workpiece is 300 K.
(a) Girth weld seam of EBW
(b) Molten pool on section A-A (xoz plane)
Fig. 1. Schematic diagram of electron beam girth welding.
5
2.2. Governing equations and heat source model Based on the above assumptions, three conservation equations of computational fluid dynamics (CFD) are used to describe the fluid flow of the melt and heat transfer in the molten pool [20]. Continuity equation: +
+
+
=0
(1)
X-momentum equation: +
+
+
=−
+
+
+
=−
+
+
+
+
(2)
Y-momentum equation: +
+
+
+
(3)
Z-momentum equation: +
+
+
=−
+
=
+
+
+
+
(4)
Energy equation: +
+
+
+
+
(5)
where u, v and w represent the velocity components in the x, y and z directions, respectively; ,
, p, k, Cp and H represent the density, dynamic viscosity, pressure,
thermal conductivity, specific heat capacity at constant pressure and mixed enthalpy, respectively; Su, Sv, and Sw are the momentum source terms in the x, y and z directions, which are composed of the surface tension ( , and
), buoyancy force
and gravity
6
,
, and
), recoil pressure (
,
[14]; SE is the energy source term,
which is composed of the energy input !" vaporization heat dissipation !" =
+
=
+
=
in the welding process [15]. (6) (7)
+
= !"
$&
, radiation heat dissipation !#$% and
+
−
− !#$% − !"
(8) $&
(9)
The material enthalpy H is also handled by the enthalpy-porosity technique to help account for the solid-liquid phase transition [14]. This method treats the deformable region (partially solidified region) as a porous medium. The porosity in each cell is set equal to the liquid fraction in that cell. In fully solidified regions, the porosity is equal to zero, which extinguishes the velocities in these regions [17]. ' = ℎ#") + * 1=3
./0
+& ,- + 1∆'
(10)
0 - < -5 6 7 -5 86 7
< - < -9
(11)
1 - > -9
where ℎ#") and -#") are the reference enthalpy and reference temperature; ∆' is
the latent heat of fusion; 1 is the liquid fraction, which is defined by the
enthalpy-porosity method; and -5 and -9 are the solidus temperature and liquidus temperature.
The VOF model is adopted to calculate the keyhole free surface and transient evolution of the molten pool [21]. <
+=
<
+>
<
+?
<
=0
(12)
where F is the fluid volume fraction function. If F=0, then the cell contains only
7
vacuum. If F=1, then the cell is filled with liquid metal. If 0
DEF G#HI
exp −3
O = OP + Q|CP − C|
IN I
#HI
(13) (14)
where Q is the heat input; S is the welding energy efficiency related to KL110 EBW machine, and its value is 0.95 [23]; and r0 is the focal radius of the electron beam at the upper surface of the dynamic keyhole. In this study, the defocused distance is 0 mm, so at z0= 20 mm, the beam radius r0 is 0.25 mm. Q is an attenuation coefficient (0.0135), which represents the degree of beam divergence.
2.3. Driving forces In the numerical calculation process, the driving forces in the molten pool play a critical role in the flow pattern. Fig. 2 is a schematic diagram of the force analysis for the keyhole wall, which consists of the tangential and normal forces at any point on the keyhole wall. The normal forces consist of the recoil pressure evaporation, the hydrostatic pressure of the curved interface Marangoni shear force 5
U
T
induced by
caused by gravity and the additional pressure
affected by surface tension. The tangential forces include the induced by the surface tension gradient and the shear force
caused by liquid metal flow [24].
8
Fig. 2. Schematic diagram of the force analysis on the keyhole wall. In the EBW process, the recoil pressure generated by the rapid evaporation of the liquid metal surface promotes the formation of a keyhole, while the surface tension and hydrostatic pressure promote the closure of the keyhole. The keyhole fluctuates rapidly due to the competition between the recoil pressure and surface tension [25]. The force on the keyhole wall is always in dynamic equilibrium. The balance on the keyhole wall can be described by the following two formulas. The resultant force in the direction normal to the keyhole wall at any time and location is [24]: =
+
T
+
U
(15)
The resultant force in the tangential direction of the keyhole wall at any time and location is [24]: = where
−
5
=
⋅
5W
−
X
ZW Y
+
[
5W
(16)
is the viscosity coefficient; > and >Y are the tangential velocity component
and the normal velocity component of the viscous fluid, respectively; tension temperature gradient;
5W
is the surface
is the tangential temperature gradient of the keyhole
wall; and \ZW and ]W are normal and tangential unit vectors, respectively. The surface tension is described as follows: 9
U
= ^_ = ^ `_P +
- − -T b
aU
a
(17)
where k represents the free surface curvature and _ represents the surface tension
coefficient, which can be determined as a linear function of temperature [26]. _P represents the surface tension at the melting point,
aU
a
represents the temperature
coefficient for the surface tension, and Tm represents the melting point of the aluminium alloy. The recoil pressure caused by the evaporation process can be expressed by the Clausius-Clapeyron equation [27]: = 0.54 P exp f
6 g
h
(18)
g
where P0 is the ambient pressure, Tb represents the boiling point of the metal, T represents the temperature of the keyhole wall, and R represents the universal gas constant. The hydrostatic and hydrodynamic pressures can be described by the following formulas [28]: T j
= gℎ
=
(19)
k[I lm
where
(20) represents the density, g represents gravitational acceleration, h represents the
height of the liquid metal in the molten pool and nY represents the velocity of the liquid metal. The buoyancy force derived from the density gradient can be described according to the Boussinesq approximation as follows: = o1 - − -P
(21) 10
where
, o, 1 and T0 represent the density, gravity, thermal expansion rate and
ambient temperature, respectively.
2.4. Boundary conditions To solve the conservation equations described in Eqs. (1)-(5), the detailed boundary conditions were set as shown hereafter. For the keyhole and molten pool free surface, the thermal boundary conditions consisting of the electron beam energy, radiation and evaporation can be described as follows: K
Zq Y
= !"
− !#$% − !"
$&
= !"
− rs - t − -Pt −
where qebw is the absorbed electron beam energy,
9
9 n" $& f
(22)
is the density of the liquid metal,
Vevap represents the evaporation-induced keyhole surface recession speed, and Lv represents the evaporation latent heat. For other surfaces, the thermal boundary, which mainly involves radiation rather than convection in vacuum EBW, is described as follows: ^
Zq Y
= −rs - t − -Pt
(23)
where T and T0 represent the workpiece temperature and ambient temperature, respectively; r represents the surface radiation emissivity; and s represents the Stefan-Boltzmann constant.
2.5. Thermo-physical properties and mesh generation This paper uses 2219 aluminium alloy with a thickness of 2 mm. The chemical composition is shown in Table 1. Considering the chemical composition, the thermo-physical properties of the base metal and relevant coefficients examined in the simulations are summarized in Table 2 [23]. 11
Table 1 Chemical composition of the base metal (wt.%) Component
Cu
Si
Fe
Mn
Mg
V
Zr
Zn
Ti
Mass fraction
5.8-6.8
≤0.2
≤0.3
0.2-0.4
≤1.8
0.05-0.15
0.10-0.25
≤0.1
0.02-0.10
Table 2 Material properties of 2219 aluminium alloy [23]. Physical property
Symbol
Density of solid
s
Density of liquid
l
Unit
Value
kg∙m-3
2700
kg∙m-3
2400
Specific heat of solid
Cs
J∙kg-1∙K-1
871
Specific heat of liquid
Cl
J∙kg-1 K-1
1060
Thermal conductivity of solid
Ks
W∙m-1∙K-1
238
Thermal conductivity of liquid
Kl
W∙m-1∙K-1
100
Boiling point
Tb
K
2730
Latent heat of fusion
Hm
J∙kg-1
3.87×105
Latent heat of evaporation
Hv
J∙kg-1
1.08×107
Surface tension at 930 K
σ
N∙m-1
0.914
Temperature coefficient of surface tension
,s ,-
N∙m-1∙K-1
-0.35×10-3
Solidus temperature
Ts
K
820
Liquidus temperature
Tl
K
930
12
Impurity elements ≤0.15
Al rest
Ambient temperature
Tref
K
300
Gravitational acceleration
g
m∙s-2
9.81
In this simulation, O-mesh is used in the geometric model of the girth welding. The void regions at both the upper and lower sides for free surface tracking are all set to 1 mm, as shown in Fig. 1(b). The total number of elements in the simulations is 2,104,032. The minimum cell size is 0.125 mm, as shown in Fig. 3.
Fig. 3. Mesh generation in the numerical calculation. The commercial CFD software ANSYS Fluent Release 15.0 based on the finite volume method was employed to solve the conservation equations of the fluid field and temperature field during the EBW process. The user-defined function (UDF) was compiled in the C language to introduce additional momentum and energy sources.
3. Experiment The EBW experiment for verification of the simulation results was performed on a circular framework with a large vacuum EBW machine (KL-110 with a maximum accelerating voltage of 60 kV). The welded structures consisted of 2 mm thick 2219 aluminium alloys, which were specifically applied for lower shell fuselage applications in the aircraft industry. In this paper, the aluminium plates were clamped and welded in a vacuum chamber after cleaning the plates under a vacuum of 5×10−2 Pa. The aluminium alloy butt joints were welded at an accelerating voltage of 60 kV and a beam 13
current of 12 mA. The welding speed was set to 10 mm/s. The characteristic parameters of the electron beam are listed in Table 3. Table 3 EBW parameters used in the experiment. Accelerating voltage
Beam current
Focal radius
Focal plane z0
Welding speed
(kV)
(mA)
(µm)
(mm)
(mm/s)
60
12
250
0
10
Test name
Cylinder welding
After welding, the specimens were cut and polished using a series of SiC emery papers with grit sizes from 200 to 1000, for which water was used as a coolant. To reveal the microstructure, 1% HF+1.5% HCl+2.5% HNO3 was adopted as an etchant. The etched samples were studied under an optical microscope.
4. Results and discussion 4.1 Validation of the simulation models Fig. 4 presents the temperature distribution of the weld pool during the whole welding process. Note that the white arrow represents the rotation direction of the workpiece, whereas the heat source of the electron beam is fixed. Within approximately 1.5 s from the beginning of the process, the molten pool spreads in an unsteady way. During the quasi-steady state, the weld pool merely changes its shapes and position.
14
(a) t=0.5 s
(b) t=1.0 s
(c) t=1.5 s
(d) t=2.0 s
(e) t=2.5 s
Fig. 4. Development of temperature field in the numerical model of the girth welding process. Fig. 5 represents the variation in the weld pool dimensions during the whole welding process. The molten pool length at the girth welding position becomes relatively stable after approximately 1.5 s. During the quasi-steady stage, the simulated dimensions of the weld pool are approximately 6.5 mm at the upper surface and 6.1 mm at the lower surface.
Fig. 5. Simulation results of the molten pool dimensions. To verify the accuracy of the models adopted in this research, the weld profiles obtained from the calculations were compared with those from the EBW experiments, as shown 15
in Fig. 6. The dimensions of the welding profiles obtained from the calculations and experiments are also summed up in this picture. Fig. 6 shows that the simulated girth weld profiles agree well with the experiments. These results indicate that the adopted models in this study are effective and reasonable.
Fig. 6. Comparisons of the experimental results and predicted results. According to the solidification theory, the temperature gradient G, solidification velocity R, and their combined parameters GR and G/R in the molten pool affect the scale of the microstructure and morphology in the weld seam. Generally, the grain size increases with the decrease in GR, while the morphology changes from columnar dendrites to equiaxed dendrites with the decrease in G/R [30-33]. GR and G/R can be calculated by the G and R obtained directly from the simulation results. Fig. 7 displays the microstructure obtained by scanning electron microscopy (SEM) around points A, B and C, which are located at the top, the centre and the bottom of the weld seam, as shown in Fig. 6. In addition, the calculated GR and G/R are also marked. As depicted in the figure, a higher GR and lower G/R are observed at the upper region, while a lower GR and higher G/R are found at the lower region. Consequently, 16
according to the solidification mechanisms, it can be reasonably inferred that the equiaxed crystal and finer microstructure are prone to occur at the upper region of the weld seam, while the columnar crystal and coarser solidified structure may be found at the lower region. In addition, equiaxed dendrites are clearly observed around point A, and fine columnar dendrites and coarse columnar dendrites are observed around point B and point C, respectively. In conclusion, the simulation trend is in good agreement with the experimentally observed results.
Fig. 7. Solidified microstructure obtained by SEM at points A, B and C. Elemental mappings, obtained from scanning across the interface via energy dispersive spectroscopy (EDS), are shown in Fig. 8. The base metal region and weld seam region bounded by dotted lines represent the regions before and after welding, respectively. The main elements Al, Cu and Mg in the alloy were detected, and the corresponding EDS results of the marked regions in Fig. 8(a) are listed in Table 4. Decreases in the content of the main alloying elements due to evaporation can be found in the EDS results. Moreover, Fig. 8 shows that the elements are uniformly distributed due to sufficient mixing of the melt [34] and the content of elemental Mg in the weld seam is significantly lower than that in the base metal. To judge whether the loss rate is the same
17
at different positions, the content of Mg is measured with an electron probe, as shown in Fig. 9.
(a)
Mapping
scan
(b) Al
(c) Cu
(d) Mg
region Fig. 8. EDS mappings of different elements in the weld cross section. Table 4 EDS results of the regions before and after welding. Element (wt %)
Al
Cu
Mg
Before welding
90.52
6.13
1.82
After welding
90.17
5.92
1.27
Fig. 9(a) shows that the closer the position is to the weld seam centre, the lower the content of elemental Mg. Because the boiling point of Mg (1363 K) is much lower than that of Al (2730 K) and Cu (2835 K), Mg vaporizes more easily when the keyhole surface evaporates considerably. This phenomenon may be the reason for the change in element content along the width direction of the weld seam. Fig. 9(b) shows that the content of Mg decreases along the depth direction of the weld. This phenomenon may be caused by the high energy at the keyhole bottom, which causes more intense evaporation of Mg.
18
(a) Width direction of the weld seam
(b) Depth direction of the weld seam
Fig. 9. Elemental Mg content in different positions of the weld seam.
4.2 Keyhole evolution The transient keyhole fluctuation in EBW of 2219 aluminium alloy at the girth welding position is presented in Fig. 10. In the initial stage of the EBW process, the keyhole and molten pool profiles are regular and shallow, as shown in Fig. 10(a) and (b). With the process of EBW, the keyhole depth becomes larger due to the recoil pressure, and its profile tends to be irregular. As the keyhole depth increases, the recoil pressure, surface tension and hydrostatic pressure of the melt rebuild a new balance of pressure on the keyhole surface. At this time, humps emerge and lead to the redistribution of the surface tension. As a result, these humps move along the keyhole surface under the effect of the Marangoni effect, which causes free surface fluctuations, as shown in Fig. 10(c)-(e). After approximately 0.175 s, the aluminium sheet is completely penetrated, and a through-keyhole is formed, as shown in Fig. 10(f). For the partial penetration welding, the keyhole fluctuation process obtained from the simulations is similar to the experimental observation of Li et al. [29].
19
Fig. 10. Formation of a keyhole profile during EBW.
4.3 Melt flow patterns Fig. 11 represents the expansion of the molten pool in terms of the temperature field and flow field. During the initial period of the full penetration welding, it can also be seen that a through-keyhole does not always exist but keeps opening and closing alternately. In addition, it is observed that there is a growing volume of liquid metal from the upper and lower parts of the molten pool in the initial stage of full penetration welding. In theory, this phenomenon may be associated with the action of the Marangoni effect and the influence of gravity between the top surface and bottom surface. For the penetration welding, the conclusion that the tail of the molten pool surface forms easily under the appropriate process conditions was also confirmed by Zhang’ s study [35].
20
Fig. 11. Evolution of the flow pattern and the temperature field in a longitudinal section side view. As the keyhole size increases, the melt ejected from the keyhole by the recoil pressure flows towards the rear-top part of the weld pool under the action of the Marangoni effect. When the base metal has just been penetrated completely at 0.170 s, the melt at the weld pool bottom is subjected to the recoil pressure and then moves to the rear-bottom part of the molten pool. Moreover, the electron beam is lost from the through-keyhole, causing variation in energy absorption along the keyhole depth. Fig. 21
11(b) shows that an uneven distribution of the electron beam on the keyhole surface causes the keyhole to collapse at approximately 0.200 s. Then, a rather steady stream of the overheated melt under the keyhole is transported to the tail of the weld pool by surface tension. The lower surface of the weld pool far from the keyhole centre is equivalent to being reheated. Therefore, the weld pool is extended and becomes longer in the lower part, as presented in Fig. 11(c). At the rear parts of the weld pool, the liquid metal flowing backward is hindered by the solid-liquid interface and then flows towards the centre of the molten pool. The movement of the melt in these directions is gradually weakened and accompanied by the stretching of the weld pool in both upper and lower sides, as demonstrated by the arrowed curves in Fig. 11(d). Therefore, the weld pool dimensions in the middle of the workpiece thickness decrease gradually. The corresponding calculated streamlines reflecting the development of the weld pool are presented in Fig. 12.
(a) t=0.170 s
(b) t=0.200 s
(c) t=0.300 s
(d) t=0.400 s
Fig. 12. Simulated streamlines in a longitudinal section side view. Fig. 13 shows points 1-7, which represent seven typical positions in the weld pool. Fig. 14(a)-(c) shows the simulation results of the flow velocity in the x-axis direction during EBW. In the upper and lower parts of the molten pool, the liquid metal is discharged by
22
the recoil pressure in the keyhole and then flows to the rear part of the weld pool (P1 and P5). The melt in this direction changes the flow direction at the edge of the weld pool (P2 and P6). In the middle part of the weld pool, the melt on the upper and lower sides converges and then flows towards the keyhole wall (P3 and P4). It is remarkable that the melt flow has an obvious cyclical characteristic. In Zhang's numerical analysis, a similar law of periodic fluctuation in the velocity of the molten pool was also obtained [35].
Fig. 13. Schematic of points 1-6 in the molten pool.
(a) X-velocity of points 1 and 2
(b) X-velocity of points 3 and 4
23
(c) X-velocity of points 5 and 6 Fig. 14. Calculated x-velocity evolution curves. A comparison of the flow velocity in different positions at the same moment shows that the flow in the lower part of the molten pool is more intense than that in the upper part. This phenomenon may be due to the deep penetration effect of EBW [35]. The energy heat source is concentrated at the keyhole bottom, leading to the melt in the lower part of the weld pool being directly subjected to the recoil pressure, thereby obtaining greater kinetic energy. In addition, the flow direction of these points along the x-axis can indirectly verify the correctness of the flow field analysis in Fig. 11. Fig. 15 shows the temperature curve of different positions on the molten pool surface with respect to time. A comparison of the temperature variation in different positions at the same time shows that the temperature of the melt is lower farther away from the keyhole centre. This finding also explains why the Marangoni effect is the cause of the formation of the tail of the molten pool in Fig. 11(d). In addition, at the same distance from the keyhole centre, more intense temperature fluctuations occur at the lower molten pool surface than at the upper molten pool surface, which may be 24
caused by periodic fluctuations of the keyhole. When keyhole collapse occurs, the electron beam energy is hindered by the liquid metal due to the keyhole bridge, which prevents the electron beam from reaching the back of the workpiece. At this point, the temperature at the lower molten pool surface decreases. When the through-keyhole is formed, the electron beam can more easily reach the molten pool backside, thereby increasing the temperature at the lower molten pool surface. The more intense temperature fluctuation in the lower part of the molten pool leads to more intense evaporation, which is the reason why the content of Mg in Fig. 9(b) changes along the depth direction of the weld seam.
(a) Temperature of points 7-10
(b) Temperature of points 11-13
Fig. 15. Calculated temperature evolution curves. In fact, the molten pool flow is extremely complicated. The flow direction of the liquid metal is not a simple superposition of cross section and longitudinal section vortexes. Fig. 16(a) represents the position of the horizontal section of the molten pool at different depths. Fig. 16(b) and (c) show the flow field during the welding process, in which the arrow direction is the melt flow direction in the weld pool. Fig. 16(b) shows 25
that the melt flows in the three-dimensional space instead of flowing in the two-dimensional scale. At the R=19.6 cross section, the melt flows from the centre of the keyhole wall to the boundary of the molten pool. The R=19.2 section is located in the middle part of the weld pool where shrinkage occurs, resulting in a reduction in the molten pool area. The response of the liquid meal around the keyhole is the same as that in the previous section. The melt flows to the keyhole wall from the molten pool tail. At the R=18.8 and R=18.4 cross sections, the upward flow tendency is formed at the axis of the molten pool.
Fig. 16. Flow of the molten pool with different depth sections. On a three-dimensional scale, the flow direction of the liquid metal is represented in Fig. 17. This figure shows that the flow pattern of the melt is roughly the same as longitudinal section analysis of the molten pool in Fig. 11. Remarkably, there are many vortexes that flow around a central pillar around the bottom of the keyhole wall. This phenomenon may be caused by the opposite effect of recoil pressure and the Marangoni
26
effect on the keyhole wall.
(a) Visual angle 1
(b) Visual angle 2 Fig. 17. Three-dimensional flow field in the weld pool.
4.4 Molten pool characteristics of girth welding There is little difference between flat welding and girth welding in terms of the keyhole evolution in different positions. A possible reason for this limited distinction can be explained by the relationship between the molten pool and the workpiece. For partial penetration EBW, the base metal plays a key role in supporting the molten pool from all sides, thereby cancelling or reducing the influence of the workpiece shape on the molten pool behaviour. Fig. 18 sketches the mechanism of this influence.
27
Fig. 18. Sketch of supporting effect before full penetration welding. There is no doubt that gravity, vapour recoil pressure, surface tension, hydrostatic pressure and hydrodynamic pressure are the main driving forces in the molten pool of flat welding. However, the effect of gravity on the circumferential molten pool is different from that of the flat welding. Fig. 19 shows the diagrams of the role of gravity in the molten pool. Fig. 19(a) shows that the extension direction of the weld pool is perpendicular to the gravitational direction in flat welding, whereas this direction makes an acute angle in girth welding, as shown in Fig. 19(b). In the circumferential weld pool, force generated by gravity can perform positive work on the melt in the direction of the circumferential molten pool expansion. The role of gravity in the molten pool is also one of the critical differences between flat welding and girth welding.
(a) Gravity in the flat welding pool
(b) Gravity in the girth welding pool
Fig. 19. Diagram of the effect of gravity on the molten pool.
28
5. Conclusion (1) The comparison between the experimental data and the simulation results verifies that the three-dimensional mathematical model adopted in this study is an appropriate representation of electron beam girth welding. (2) In partial penetration EBW, there is no obvious difference in keyhole evolution between flat welding and girth welding due to the supporting effect of the unfused base metal on the molten pool. (3) After entering the full penetration stage, the tail of the molten pool extends rapidly under the influence of the Marangoni effect and recoil pressure. The fluctuations in the temperature and the flow velocity of the melt are more intense at the lower weld pool surface than that at the upper surface. This phenomenon is caused by the continuous collapse and opening of the keyhole bottom, resulting in the intermittent energy of the electron beam energy reaching the bottom of the molten pool. (4) During electron beam girth welding, the force generated by gravity can perform positive work on the expansion of the upper surface of the weld pool, which results in the upper surface being longer and more stable than the lower surface. The role of gravity in the molten pool is also one of the critical differences between flat welding and girth welding. (5) The flow pattern in the weld pool is complicated, and it is not a simple superposition of the vortexes in different sections. In the circumferential molten pool, there are many vortexes that flow around a central pillar around the bottom of the keyhole wall, which
29
may be caused by the opposite effect of the recoil pressure and Marangoni effect on the keyhole wall.
Acknowledgements This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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HIGHLIGHTS A model for studying the heat transfer and fluid flow during EBW of the girth joints is developed. The keyhole fluctuation and molten pool shape with the corresponding temperature and velocity field are simulated. The flow field in the circumferential molten pool is revealed on a three-dimensional scale. The influence of gravity on the circumferential molten pool is discussed.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: