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Mass transport and solidification phenomenon in dissimilar metals arc welding
International Journal of Heat and Mass Transfer 144 (2019) 118703
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Mass transport and solidification phenomenon in dissimilar metals arc welding Fatemeh Hejripour ⇑, Brian T. Helenbrook, Daniel T. Valentine, Daryush K. Aidun Mechanical and Aeronautical Engineering Department, Clarkson University, 8 Clarkson Ave., Potsdam, NY 13699-5725, United States
a r t i c l e
i n f o
Article history: Received 29 March 2019 Received in revised form 31 July 2019 Accepted 5 September 2019 Available online 12 September 2019 Keywords: Arc welding Dissimilar metals welding Mass transport Solidification characteristics
a b s t r a c t A 3D transient numerical simulation is developed to study the arc welding of dissimilar metals for three sets of processing parameters. The model is used to investigate the fluid flow impacts on mass transport during the process. The predicted mass distribution agrees well with experimental composition measurements obtained from electron dispersive spectroscopy (EDS) analysis. The temperature distribution and the top surface shapes also match well with the experimental data. The morphology of the weld metal has a crucial impact on the weldment’s mechanical properties, and the prediction of solidification structure is key to improving weld quality. To this end, thermal results are applied to analyze the solidification behavior of the weld pool. The solidification parameters are calculated at the weld pool interface and the results are compared with the observed morphology from the experiments. The experimental observations confirm the presence of asymmetric solidification as demonstrated by the proposed model. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The use of different alloys in a weld provides the flexibility to design a product with both technical and economic advantages. The arc welding of dissimilar metals is a joining method which is widely used in the nuclear and chemical industries. Arc welding produces a uniform mixed weld zone (WZ) between the two different alloys, which improves the mechanical properties. However, the process is challenging due to the differences in thermophysical properties and chemistry of the alloys. In dissimilar alloy welds, it is important to understand the mixing process to achieve a high-quality weld. Modeling can be used to optimize the welding parameters with no need for costly experiments. Therefore, numerical modeling of the welding of dissimilar metals has been developed in recent years. Many researchers used linear laser welding of dissimilar alloys. In the numerical models, the top surface of the weld pool could be considered as a free surface or a flat surface. The weld penetration can be predicted more accurately considering a free surface [1]. Esfahani et al. [2] investigated fluid flow and alloy composition in a three-dimensional weld between carbon steel and stainless steel. The surface topology was tracked using an adaptive mesh refinement on the free surface of the melt pool. Their model predicted the dilution and homogeneity of the weld bead. Lian and Luo studied a transient model of a dis⇑ Corresponding author. E-mail address: [email protected] (F. Hejripour). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118703 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
similar weld under a pulsed laser [3]. They used a dynamic mesh method to obtain the free surface deformation and predicted surface ripple formation due to the periodical laser and molten pool solidification. Besides affecting the mass distribution inside the fusion zone, the solidification process can also cause defects during laser welding of dissimilar metals. Li et al. [4] developed a transient three-dimensional model of laser welding between 304SS and Ni considering the free surface deformation of the melt pool. They used thermal solidification data (temperature gradient and solidification rate) to predict the microstructural morphology of the weld zone. In several reported works, the top surface of the weld pool is assumed to be flat. Mukherjee et al. performed a 3D numerical simulation using the finite volume formulation [5] of the transport phenomena in laser welding of Fe–Al dissimilar metallic couple with a Ta sheet placed between. Marangoni forces were included in the modeling. It was concluded that the Fe-side melted further resulting in asymmetric thermal and velocity fields. Métais et al. [6] modeled a 3D simulation of the welding of dissimilar steels. A quasi-stationary state was assumed to develop turbulent flow, heat transfer, and mass transfer physics. The predicted weld zone profile and chemical element distribution in the weld achieved an accurate agreement with the experiment. The fluid flow and mass transport are different in Gas Metal Arc Welding (GMAW) because of the arc electromagnetic field. The electromagnetic forces affect the mass distribution and final quality of the fusion zone. A number of Multiphysics simulations of the GMAW process have been performed ([7–9]). However, there is
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little literature on the simulation of linear arc welding of dissimilar alloys. Daha et al. [10] developed a numerical heat transfer and fluid flow model of the welding of dissimilar steels using plasma arc welding (PAW). Using the transient model, they optimized the Keyhole PAW processes to gain sufficient energy and penetration. Bahrami et al. [11] used COMSOL Multiphysics to model the heat, fluid flow, and mass transfer for linear GTA welding of alloy 304 to 1018 steel assuming a flat top surface. The model predicted the distribution of the alloying elements in the weld zone as verified by comparison with experimental results. Their models of the welding linear dissimilar metals assumed the process to be quasisteady. However, the model using steady state assumptions are not able to predict mixing phenomena right after arc initiation and the moment the arc is shut off. In addition, the steady state study might not provide accurate results in cases of having a large weld pool (WP). A time dependent study could track the mixing in the WP and the solidification behavior after the arc passes. It also provides a better understanding of the unmixed zone (UMZ) formation. This region which is known as ‘‘partially melted zone” (PMZ) as well [12], is mostly formed along the fusion boundary of a ferritic/martensitic base metal with an austenitic weld zone [13]. The composition varies continuously from the Heat Affected Zone (HAZ) to the weld metal across this narrow martensitic band [14]. The UMZ affects the mechanical property across the weldment and causes failure of dissimilar metal welds during the post weld heat treatment [15]. In this study, two dissimilar alloys of Inconel 718 (austenitic alloy) and 410 stainless steel (martensitic alloy) are chosen. The final microstructure in the weld zone of these alloys is austenite. These two alloys have vast applications in the nuclear and aerospace industries [16]. In the current study, Inconel 718, which is a non-magnetic alloy, is autogenously welded to the martensitic 410SS. The fully coupled electromagnetic, heat transfer, fluid flow, and mass transfer equations are solved numerically using COMSOL Multiphysics [17]. The predicted distributions of chemical elements are compared with the experimental results. Also, the correlation of the fluid convection with the UMZ formation is studied numerically and experimentally. The solidification behavior is calculated using the transient simulation. Finally, the model is validated against experimentally solidified microstructures from the WZ for various welding parameters.
The welded coupons were sectioned across the weld and mounted. The samples were polished using silicon carbide papers. They were etched with Glyceria (30 ml HNO3 + 30 ml HCl + 15 ml glycerin) to reveal the microstructure. Finally, optical microscopy (OM) and energy dispersive spectroscopy (EDS) were carried out to investigate the WZs’ characteristics. 3. Physical model In this section, a 3D model is developed to track the convective force effects on the fluid flow and mass transport using COMSOL Multiphysics version 5.2a. Fig. 1 shows the geometry of the 3D model with the same dimensions of the plates used in the experiment. The arc initiates at the origin and passes along the contact surfaces of two dissimilar plates with a constant travel speed. The origin is considered at 3 mm distance from the domains’ wall to avoid the melt pool passing through the wall. After 15 s, the welding process was finished at about the end of the domains for cases 1 and 3 and partially through the domains for case 2. The following assumptions are made: The fluid flow is incompressible and laminar. The vaporization and solidification shrinkages are not considered. The thermal physical properties of the solution in the WP are assumed to be constant but different from the solid base metals. The top surface of the WP was assumed to be flat. The reason is discussed in Section 4.3. 3.1. Governing equations A Boussinesq type flow is assumed to govern the fluid motion in the WP. Mass continuity can be written as:
@ ql þ r ðql uÞ ¼ 0 @t
@ b @ b @ b k, and ql is the density of the pool. u is the i þ @y j þ @z where r ¼ @x
velocity field and t is time. The fluid flow is driven by a combination of forces in the molten pool that includes electromagnetic, Marangoni and buoyancy forces as well as frictional forces in the mushy zone. The forces and inhomogeneous heat flux are illustrated in Fig. 2. Conservation of linear momentum is described as follows:
2. Experimental procedure Inconel 718 plates were welded to the 410 stainless steel plates autogenously with the three sets of the welding parameters shown in Table 1. Coupon dimensions were 55 15 3.2 mm. To monitor the temperature variations of the plates during the welding process, two thermocouples were attached to the top surfaces of the plates. The chemical compositions of the alloys are listed in Table 2.
ð1Þ
ql
h i @u þ u r u ¼ r pI þ l ru þ ruT þ F b þ F L þ F d @t
ð2Þ
where l is the averaged liquid viscosity of the molten metals and p is the pressure field. F b is buoyancy force in the z-direction described as
F b ¼ ql ðbT ðT T r Þ þ bc ðc cr ÞÞg b k
ð3Þ
Table 1 The welding parameters used in the simulation. Case
Travel speed (mm/s)
Arc current (A)
Arc voltage (v)
Shielding gas
Heat input (J/mm)
1 2 3
3.5 3 3.5
100 100 120
13 13 15
Pure Argon Pure Argon Pure Argon
371 433 514
Table 2 The material composition of the alloys (wt%). Plate
Ni
Cr
Mo
Nb
Si
Ti
S
P
Cu
Mn
C
Al
Co
B
N
Sn
Fe
Stainless steel type 410 Inconel 718
0.24 55
12.01 21
0.04 3.3
– 5.16
0.33 0.35
– 1.15
0.001 <0.001
0.025 0.015
0.13 0.3
0.46 0.35
0.14 0.08
0.01 0.8
– 1.0
– 0.006
0.03 –
0.01 –
Bal Bal.
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F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703 Table 3 The thermal material properties of the dissimilar alloys [22].
Fig. 1. The geometry of the plates used in the simulation.
Alloy property
Unit
Inconel 718
410 SS
Solidus temperature (T s ) Liquidus temperature (T l ) Solidus density (qs ) Liquidus density (ql ) Dynamic viscosity (l) Solid thermal conductivity (ks ) Liquid thermal conductivity (kl ) Coefficient of thermal expansion (bT ) Solid specific heat (C ps ) Liquid specific heat (C pl ) Latent heat (DH) Surface emissivity () Electrical conductivity (r)
°K °K kg m3 kg m3 kg m1 s1 W m1 °K1 W m1 °K1 °K1
1528 1610 8200 7580 7.5 103 25 27 16.0 106
1753 1803 7640 7483 5.1 103 24.9 29.3 11.7 106
J kg1 °K1 J kg1 °K1 J kg1 – S m1
625 778 292 103 0.8 7 105
460 847 250 103 0.2 17.5 105
Table 4 The diffusion coefficients of the solutes used in the simulation [19,20]. Material
Chemical element
Ds (m2 =sÞ
Dl (m2 =sÞ
Inconel 718
Fe Ni Cr Fe Ni Cr
3 1014 5 1014 5 1014 6 1013 – 2 1012
8 1010 5.5 109 3.5 109 – – –
410 Stainless steel
Fig. 2. A schematic illustration of the fluid volume forces acting in the WP.
where Tr is the reference temperature which is taken as the liquidus temperature of the molten pool and cr is the concentration of solute at T r . bT and bc denote thermal and solute volumetric expansion coefficients, respectively. g is gravitational acceleration. Since the arc produces a magnetic field, Lorentz forces affect the fluid flow significantly. F L represents the Lorentz force due to arc current density J and magnetic flux B,
FL ¼ J B
Table 5 Alloying element concentrations used in the simulation (wt%). Ci
Inconel 718
410 SS
Fe Ni Cr
20 60 20
87 0 13
ð4Þ
The other effective force on the flow motion is a source term, F d , which is the frictional resistance to flow in the solid-liquid mushy zone. This force vanishes in the liquid phase. According to the Carman-Kozeny equation for flow through a porous media ([18]), F d is obtained as follows,
Fd ¼
ð1 f l Þ fl þ e 3
in which
2
Amush u
ð5Þ
e and Amush are small and large numbers, respectively. In
this study, e is assumed to be 103, and Amush is 6 104 mkg3 s (COMSOL library). f l is a smooth function which represents the liquid fraction,
fl ¼
8 > <0 > :
T < Ts
TT s T l T s
Ts < T < Tl
1
T > Tl
ð6Þ
where T s and T l are solidus and liquidus temperatures, respectively. The temperature field was determined by solving the energy equation which is defined as
qC p
@T þ u rT ¼ r krT @t
ð7Þ
Fig. 3. The transition of Iron concentration with the Heaviside step function with a scale of 0.3 mm.
where q, C p and k denote the density, heat capacity and thermal conductivity which have different values in the solids and liquid domains. Since there are no measured thermal material properties in the mushy zone in the literature, in this study, it is assumed to
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F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703 Table 7 The comparison of numerical velocity magnitude and temperature with different meshes. m
Point coordinate (mm)
Mesh
juj
36, 0.5, 0.2 (Inconel side)
1 2 3 1 2 3
0.0095 0.0160 0.0143 0.0101 0.0128 0.0143
36, 0.5, 0.2 (410 SS side)
s
at t = 12 s
T (°K) at t = 12 s 1891.73 1915.53 1915.55 1940.67 1963.99 1964.58
BCC crystal structure and the diffusion coefficients for the Fe-Cr stainless steel solid [21], are also given in Table 4. 3.2. Computational domains and boundary conditions The model includes four computational domains (see Fig. 1). Two larger domains are defined as solid domains of two dissimilar alloys. Heat transfer and electromagnetic equations are solved for all domains. The smaller domains where the molten pool occurs, are governed by the fluid flow and mass transfer equations in addition to the heat transfer and electromagnetic field. The boundary conditions of the computational domain are described below:
Fig. 4. Computational mesh of the model in (a) 3D view, (b) 2D view; (c) The side view of the liquid domain.
1. Electromagnetic field: vary from the solid state to the liquid state using the following equation
M ¼ Ms þ ðMl Ms Þf l
Gaussian distribution of the normal current density is applied to model the arc distribution on the top side of the entire domains as
1 0 3 ðx V t t Þ2 þ y2 3I A J n ¼ 2 exp@ pr i r2i
ð8Þ
where Ms and Ml are the thermal material property at solidus and liquidus temperatures which are given in Table 3. The apparent heat capacity is the summation of an equivalent specific heat and latent heat (COMSOL Library) while the phase of material changes which is written as
C p ¼ f l C pl þ ð1 f l ÞC ps þ Lf
d f l ql þ ð1 f l Þqs dT 2q
where I and r i are arc current and arc radius with the value of 4 mm on which the arc power is focused, respectively. V t denotes the arc travel speed. The bottom side is assumed to be ground (Voltage = 0). Other sides are assigned as insulated boundaries. Regarding the magnetic field, all faces are assumed to be insulated.
ð9Þ
where C ps and C pl are specific heat in solid and liquid phases, respectively. Lf is latent heat due to phase transition. The species conservation equation is
@C i þ u rC i ¼ r Di rC i @t
ð11Þ
2. Temperature field: The top surface of the model is subjected to inward heat flux, convective heat flux, and radiation to ambient temperature (T amb Þ. A Gaussian distribution is specified for the distribution of the heat flux. The boundary condition at the top surface is written as 1 0 3 ðx V t t Þ2 þ y2 3gVI A hðT T amb Þ r T 4 T 4 qn¼ exp@ amb 2 2 pri ri
ð10Þ
where C i is the ith alloying element concentration and Di is the mass diffusion coefficient of the element. In this study, the mass transport equation was solved for three major elements in the alloys which are Iron (Fe), Nickle (Ni) and Chromium (Cr). The WZ is predicted to be fully austenitic according to the Shaeffler diagram [19] with the dilution of 55% from Inconel 718 and 45% from the 410 SS in the fusion zone. Consequently, the WZ has an FCC crystal structure. Table 4 provides the diffusion coefficients of these elements in the Inconel 718 solid and liquid based on Fe-Ni-Cr alloys with the FCC lattice crystal structure [20]. The 410 SS solid has
ð12Þ where g is the arc efficiency assumed to be 0.7 in this model and V is arc voltage. In this study, the arc power distribution of 3 is chosen to achieve a higher focus. In the convection term, h denotes the heat transfer coefficient. In the radiation part of the equation, r and are
Table 6 The mesh properties of the model for case 2. Mesh
1 2 3
Maximum element size (mm) Top boundary of Xl
Xl
Xs
0.2 0.1 0.08
0.5 0.25 0.2
10.5 5.5 4.4
Number of elements
Number of grid points
159,747 935,322 1,691,393
234,215 1,320,993 2,367,910
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
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Fig. 5. A comparison of the welds’ geometries for the three cases at (a) the top view of the weldments, (b) the top view of the numerical model and (c) the weld cross section.
Fig. 6. Computed temperature field for the three cases at t = 12 s.
the Stefan-Boltzman constant and surface emissivity, respectively. Other sides of the model have heat loss due to both convection and radiation. 3. Velocity field: The top side of the melted part is considered as a slip wall. The thermocapillary force is balanced by viscous stress along the top surface ([23]). In COMSOL Multiphysics, the Marangoni equation is solved by coupling heat transfer and fluid flow studies as
l
@u dc dc ¼ fl rs T þ rs C s @z dT dC
ð13Þ
4. Species field: A uniform initial value of the concentration shown in Table 5, is assumed for the domain of each alloy. All faces are assumed to be impermeable to the diffusion of the elements [11]. 3.3. Numerical implementation A time dependent study is performed to model the 3D welding process using COMSOL Multiphysics version 5.3a. The material properties used in the model are given in Table 3. The dilution (volume fraction) of the alloys in the WZ is considered to calculate the thermal properties of the WP (Ml) as follows [26]:
A410 Ml Aw
Ml ¼
4.3 104 N m1 K1 in the range of temperatures in the molten zone according to Sahoo equations [25].
Ml_410 and Ml_718 are liquidus material properties of the base metals. The dilution of each base metal was calculated and averaged based on an area measurement of the experimental weld zones (Aw Þ for three cases. A410 and A718 are the melted cross section area of the base metals. The average dilutions were obtained as 0.55 for the Inconel and 0.45 for the 410SS. For initial conditions, a smooth Heaviside step function with continuous second derivative and a scale of 0.3 mm was used to
zone. rs is the surface tangential gradient. c and C s are the surface tension and the surfactant element concentration, respectively. Based on the compositions of the alloys provided by vendors, the amount of sulfur is less than 0.001 wt% in both alloys (see Table 2). Therefore, the gradient of C s is essentially zero [24]. The surface ten dc sion derivative with respect to temperature dT is calculated to be
410
þ
A718 Ml Aw
where l @u denotes the shear stress on the top surface of the melted @z
718
ð14Þ
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transition the material concentrations from the Inconel domain to the stainless steel one smoothly. For example, Fig. 3 shows the transition of iron (Fe) concentration from 20 wt% within the Inconel to 87 wt% in the stainless steel. The fluid flow computation needs to be solved using a fine mesh to reach convergence. So, the computational domains are divided into two domains of solid (Xs ) and liquid (Xl ) for each material as illustrated in Fig. 4. A coarser mesh was applied in the dis-
cretization of the solid domains. The unstructured tetrahedral mesh was used to discretize the domains. To test the mesh resolution, three sets of mesh densities were adopted for the model of case 2. The mesh size was decreased with the same proportion in all domains. The mesh properties are listed in Table 6. It should be noted that mesh 3 is not a factor of too refinement because the maximum number of nodes was restricted because of limited computational resources.
Fig. 7. The validation of the temperature profile for the three cases in the middle of 410SS plate and Inconel 718 plate.
Fig. 8. Computed velocity field and mass transport (Nickel distribution) at location of x = 36 mm for Case 2 at (a) t = 12 s, (b) t = 12.3 s and (c) t = 12.6 s.
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
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Fig. 9. Alloying elements (Fe, Ni and Cr) distributions within the cross section for the three cases.
Fig. 10. (a) The locations of EDS measurements across the WZ along a horizontal line (z = 0.2 mm) for case 2, and (b–d) the verification of the calculated mass distribution with the experimental measurements.
In this model, the arc, the Eq. (12), was initiated at the time of zero and ended after 14 s. The model duration was 15 s to capture the WP solidification after the arc shut off. After that, the thermal simulation was solved for another 15 s for the solidified domains using the previous temperature results as initial values for the new calculation. The computations were performed on a desktop computer with two microprocessors (2.93 GHz) and 24 GB RAM. To save the computation time, the electromagnetic equation was solved in a separate time dependent study. The time step of this study was picked by the software with the maximum value of 0.008 s. The other
physics including fluid flow, heat transfer and mass transfer were solved in another study using the interpolated results of the electromagnetic field’s solution at each time step. The segregated approach was applied to solve these coupled physics. The maximum time step of 0.004 s was set by the solvers.
4. Results and discussion Three mesh densities (described in Table 6) were adapted for case 2 to analyze the mesh sensitivity. The velocity magnitude
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and temperature at two points, located in the liquid domain of two base metals, were calculated and given in Table 7. The numerical values for the flow dynamics, heat transfer and mass transport (see Fig. 10) indicate negligible changes in the solutions of mesh 2 and mesh 3. As a result, mesh 2 was picked to compute all of the cases to save the computation time. 4.1. Weld geometry To compare the numerical results with the experiments, Fig. 5 shows both the top view and the cross-sectional view of the welds. The calculated mixed region based on the mass transport equation (Fe wt%) is shown in Fig. 5b. By comparing Fig. 5a and b, it is obvious that although the arc oscillated between the two alloys during the welding process at some points, the simulations have predicted
the weld width accurately. In addition, the calculated welds’ profiles at the initial and ending stages of the welding process were in fair agreement with the corresponding experiment. Fig. 5b also indicates that the WP reaches to steady state in case 3 in a shorter time in compared to two other cases. A comparison between the experimental and calculated welds profiles at welds cross sections are presented in Fig. 5c. The weldments have been sectioned at the position of 20 mm before the ending points to perform the metallography. The numerical welds profiles (shown as a solid line) have been selected at corresponding locations in the simulations. Fig. 5c shows that the penetrations of the welds have been well predicted at the Inconel 718 side for all three cases, however there is a maximum deviation of 23% present at the 410SS side. This discrepancy may be due to a difference between the 410SS thermal properties used in the simulations and the experiments.
Fig. 11. The locations of EDS measurements across the WZ along a vertical line (y = 0) for case 2, and (b) the corresponding microstructure of the butt joint area.
Table 8 The chemical composition of the points shown in Fig. 10.
Point 1 Point 2 Point 3 Point 4 Point 5
Method
Cr
Fe
Ni
EDS measurement Numerical prediction EDS measurement Numerical prediction EDS measurement Numerical prediction EDS measurement Numerical prediction EDS measurement Numerical prediction
18.300.48 17.0 17.750.46 17.7 20.280.48 19.0 12.210.38 13 12.620.39 13
33.380.87 48.2 44.600.93 43.7 21.130.73 28.2 86.951.16 87 86.841.15 87
48.331.40 34.7 37.651.31 38.7 58.591.43 51.6 0.840.35 0 0.540.33 0
d Errors () are obtained by the EDS analysis.
Fig. 12. A comparison of the velocity magnitude for the three cases at t = 12.6 s.
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
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Fig. 13. The fusion boundary on the 410SS side of the three cases.
Table 9 Shielding gas and liquid weld properties. Property
Unit
Argon gas density (qAr ) Weld pool density (ql ) Argon flow rate (Q ) Gas velocity (v Ar ¼ Q =A) Torch cap diameter (d)
Value 3
Area of torch outlet (A ¼ pd =4) Surface tension coefficient (c) Length of the weld pool (L) Maximum velocity at the top surface (jujmax ) 2
kg m kg m3 cfh m s1 m m2
1.784 7510 27 0.596 0.012 1.13 104
N m1 m m s1
1.88 0.007 in case 3 0.16
ferent thermal properties of the alloys. It shows that the temperature increases in the 410SS more rapidly compared to the Inconel 718. This phenomenon is confirmed by temperature measurements using two thermocouples during as shown in Fig. 7. The thermocouples were attached in the middle of the base plates’ top surfaces and 10 mm from the butt joint as shown in Fig. 6. The experimental measurements were compared with the calculated temperature in Fig. 7. The deviation between the results might be due to mesh coarsening at the solid domains, losing the calculation accuracy in these domains. Nevertheless, the trends were found in good agreement. 4.3. Dynamic and mass transport phenomenon
4.2. Temperature field and model validation Fig. 6 shows the calculated temperature field at top surfaces for the cases at t = 12 s. The fusion boundary of the WP is illustrated as a black solid line showing the boundary between the liquidus and solidus temperatures for each alloy. The WP becomes larger as the heat input increases from 370 J/mm in case 1 to 433 J/mm and 514 J/mm in cases 2 and 3, respectively. The maximum temperature increases from 2240 K in case 1 to 2860 K in case 3 by raising the heat input. The isotherms are also plotted to illustrate the temperature distribution during the welding process. The isotherms are asymmetric with respect to the weld centerline due to the dif-
The velocity field in dissimilar metals arc welding becomes complicated when one of the alloys is magnetic and the other one is not. The difference of Lorentz force magnitude between the magnetic side (410SS) and the non-magnetic one (Inconel 718) enhances the flow circulation around the WP. This flow affects the mass transport and mixing phenomenon during the welding process. Fig. 8 shows the flow field at three different moments with an increment of 0.3 s at the cross-sectional plane of x = 36 mm in case 2. The solid black line illustrates the fusion boundary at the corresponding instant. The streamlines and arrows indicate the flow direction. It should be noted that the maximum
Fig. 14. Computed heating/cooling rate at the solid/liquid interface.
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velocity occurs at the Inconel 718 side and the magnitude is 0.088 m/s. Fig. 8a shows the fluid flow in the front part of the molten pool and the corresponding Ni distribution. This plane is centered under the arc at t = 12 s resulting in the highest magnitude of the Lorentz force in the 410SS side. This volume force pushes the fluid from the 410SS side (shown by arrows) toward the Inconel 718 side. The Marangoni force interacts with other volume forces causing the generation of one strong vortex at each side of the WP. These vortices produce a vorticial flow motion in addition to the flow circulation inside the WP. In the initial stage of mixing in the front part of the WP, the flow transfers the material of 410SS toward the Inconel 718 side. However, a mixed region is induced by Marangoni effects near the top surface of the WP at 410SS side. In the middle of the WP (see Fig. 8b, t = 12.3 s), the flow starts changing direction from Inconel 718 side toward the 410SS side. The fluid flow injects the Inconel 718 material into the WP, especially toward the 410SS side. Consequently, higher amounts of Inconel alloying elements grow in the WP on the 410SS side. The Inconel injection continues at the rear side of the WP as shown in Fig. 8c (t = 12.6 s) and becomes mixed with the liquid material inside the WP. However, there is insufficient time to mix the entire liquid Inconel 718 with the WP material. As shown in Fig. 9, a small amount of liquid Inconel 718 gets solidified on top of the joint in the WZ. This region is an UMZ formed inside the fusion zone of all three cases according to the numerical predictions. It should be noted that heat input enhancement induces a more uniform mixed WZ as a result of higher dilution from each alloy. More dilution provides further liquid materials inside the WP to get mixed. To validate the mass transport predictions, EDS analysis has been carried out along a horizontal line across the WZ of case 2 with a 0.2 mm distance under the weld top surface as presented in Fig. 10a. Fig. 10b–d show the comparison of the Fe, Ni and Cr distributions, respectively, in the experimental WZ with the numerical model using different meshes. The calculated compositional results for meshes 1 and 2 matched well with the EDS composition measurements. The composition has also been evaluated along a vertical line at the weld joint from the top surface to the bottom as shown in Fig. 11a. The measured compositions at the picked points are listed in Table 8. The chemical composition of Point 3 (Fig. 11a) has been found very similar to the composition of Inconel 718, which shows the existence of Inconel 718 material inside the WZ right above the weld joint. This is consistent with the mass transport predictions (see the UMZ in Fig. 9). The optical microscopy image of this region (point 3) is shown in Fig. 11b to investigate the solidification morphology. It should be noted that the morphology is dependent on the solute redistribution during solidification [27]. As shown in Fig. 11b, the elongated cells are stretched from the Inconel 718 side toward the 410SS side above the joint where point 3 is located. It is noticed that Point 1 is located 0.3 mm below the top surface. The composition of Point 1 was expected to be close to the results shown in Fig. 10. However, it contains lower Fe content and a higher amount of Ni which was in conflict with the EDS results shown in Fig. 10. According to the literature, laves phase and Nb-rich intermetallics exist in the WZ of Inconel 718 [28]. Therefore, the composition of these points has been remeasured by adding Nb and Mo elements to the three other alloying elements. The obtained composition of this point showed the amounts of 6.9 wt% and 3.1 wt% for Nb and Mo, respectively, which confirms that Point 1 is located in a Nb-rich region. It depends on the type of Nb-rich precipitate, the Fe and Ni content vary in this region. The maximum velocity (jujmax ) which occurs on the top surface of the WP on the Inconel side. In cases 1, 2 and 3 the maximum velocity is 0.078, 0.088 and 0.16 m/s, respectively. The Reynolds
number can be employed to determine the stability of the flow. The Reynolds number is defined as follows.
Re ¼
LR ql jujmax
l
ð15Þ
where LR is the width of the WP. The calculated Reynolds numbers are below 1000 and no temporal instability occurred during the calculation indicating that turbulent flow is nonsignificant in any of the three cases [24,25]. The magnitude of the velocity at the rear side of the WP where the maximum penetration occurs, at the time of 12 s is illustrated in Fig. 12. The stronger convection in case 3 due to larger volume forces within the fluid, results in a higher velocity compared to two other cases. The enhanced convection could assist in mixing the bulk of the WP well. The fact that the fluid flow in case 3 removed the melted base material completely and mixed the liquid materials inside the WP. Therefore, the unmixed zone (UMZ) formed along the fusion boundaries has been eliminated. The UMZ has detrimental effects in dissimilar metals weld in the case of existing a ferritic/martensitic base metal and an austenitic WZ [29]. This UMZ has been observed in cases 1 and 2 but removed in case 3 as shown in Fig. 13. Thus, the growth of the convection
Fig. 15. Calculated (a) solidification parameter, (b) cooling rate, (c) solidification rate and (d) temperature gradient at the cross section of the weld at t = 12.5 s for case 1.
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
11
Fig. 16. Color range of data points with respect to the weld center at the top surface, (b) the G-R scatter plot for case 1, (c) a comparison of G-R values between cases 1 and 2, (d) a comparison of G-R values between cases 1 and 3 and (e) the schematic illustration of G-R diagram containing various substructural regions.
due to the Lorentz forces increase will improve the mechanical properties. The effects of the gas flow and weld pool dynamic on the top surface, respectively, were estimated using the Weber numbers as follows
WeAr ¼
qAr v Ar 2 d c
ð16Þ
where qAr is the density of Argon in the gas state. v Ar is the gas velocity at the torch cap outlet and d is the torch cap diameter. c is the surface tension coefficient of the weld pool which is assumed to be equal to the surface tension coefficient of Inconel 718. The values are listed in Table 9. The Weber number of the gas is obtained as 0.0076. On the other hand, the Weber number of the weld pool is calculated as follows:
12
Weweld ¼
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
ql jujmax 2 L c
ð17Þ
where L is the length of the weld pool. The maximum Weweld occurs in case 3 with a value of 0.715. According to the very low value of the Weber number (W1) for the shielding gas, the gas dynamic impact on the free surface is negligible. The Weber number of the liquid pool is less than unity. It means that the free surface affects the weld pool dynamic only moderately and thus is not considered in this study. 4.4. Solidification and morphology The mechanical properties of the welds depend on the grain structure formed during the solidification. To predict the solidification morphology in the WZ, the solidification parameters are required to be obtained. To this end, the current simulation has been used to determine these parameters including the solidification rate (R), temperature gradient (G), solidification parameter (G=R) and cooling rate (G:R). Fig. 14 shows the heating/cooling rate variation at the solid/liquid interface where the liquid fraction is 0.9. The dashed line illustrates the interface between the heated and cooled sides of the WP. The cooling process occurs at the rear side of the WP called the solidification front. The solidification takes place normal to the solid/liquid interface at any point such as Point A shown in Fig. 14, in the same direction as the heat flow ! ( G ). Thus, the local solidification rate can be obtained as follows [30]:
R ¼ Vt
rT jjrTjj
ð18Þ
where jjrTjj is the magnitude of the temperature gradient (G) in the liquid at the solidification front. The solidification is a 3D phenomenon occurring at the solid/ liquid interface of the molten pool. Therefore, the solidification parameters have been calculated on the interface at the solidification front on the iso-surface shown in Fig. 14. Fig. 15 projects the solidification parameters calculated on the solidification surface shown in Fig. 14 onto a y-z plane for case 1. The plots show noisy results due to the numerical oscillation around the Mushy zone in the simulation. It is seen that the solidification parameter (G=R) increases, and the cooling rate (G R) decreases continuously from the weld center to the fusion boundaries. Moreover, the cooling rate is higher on the 410 SS side. The solidification rate (R) gets to the maximum value at the weld center near the top surface. The temperature gradient (G) is lower at the middle of the WZ on the Inconel 718 side due to differences in the thermo-physical properties of the dissimilar alloys. The calculated G-R diagrams for the three cases with the comparisons between the cases are shown in Fig. 16. Fig. 16a shows the scatter data points on the solid/liquid interface with the liquid fraction of 0.9. The points are colored by the distance from the point to the weld centerline on the top surface. The magnitude of the temperature gradient is plotted versus the solidification rate of the data points for case 1 in Fig. 16b using the same point coloring scheme. The data points of the 410 SS and Inconel 718 sides are distinguished in the diagram. It is evident that the temperature
Fig. 17. The solidification morphology at different regions for case 1 (subfigures A-C are at the same magnification).
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
gradient on the 410 SS side is higher than the Inconel 718 side. According to the G-R diagram shown in Fig. 16e, the 410 SS side is predicted to have a finer solidification structure in the WZ. Figs. 16c and 15d display the colored data points for case 2 and case 3, respectively, and gray points for case 1. The lower arc travel speed in case 2 resulted in an insignificant rise in the temperature gradient at the weld center. However, the cooling rate (G R) decreases because of the reduction in the solidification rate. Fig. 16d shows that the temperature gradient is dramatically dropped in case 3 with the arc current increase and the cooling rate is reduced. Nevertheless, the range of the cooling rate reduction in the middle of WZs is not noticeable to impact the solidification structure as will be observed in the experimental micrographs. It is worth mentioning that the solidification parameters are asymmetric with respect to the weld center in dissimilar metals welding (see Fig. 15). Thus, the morphology of the WZ is expected to be different on each side. Figs. 17–19 show the solidification structure of three regions including the fusion boundaries (subfigures A and C) and middle of the WZs (subfigure B) for cases 1, 2 and 3, respectively. According to the constitutional supercooling crite DT ria GR < DLeq , the cellular substructure is formed under this condition and other substructural zones will be formed by increasing the cooling rate [27]. DT eq is the equilibrium solidification range and DL is the solute diffusivity assumed to be averaged as 5 1089
m2 s
in this study (Table 4). Thus,
DT eq DL
is 16 109
Ks m2
for
Inconel 718 side. The computational results indicate that the constitutional supercooling criterion is satisfied in the three cases. Based on the observations in Figs. 17A, 18A and 19A, the morphology of the WZs in three cases interestingly show the cells are formed along both fusion boundaries on the Inconel 718 side.
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However, the mechanism of epitaxial growth made the formation of the dendritic cells due to similar crystallographic orientation of the HAZ grains (FCC) and the WZ. On the 410SS side, the crystal structure of the HAZ (BCC) was different from the WZ (FCC). Consequently, the epitaxial growth did not occur as shown in Figs. 17C, 18C, and 19C. On the 410SS side, the UMZ along the fusion boundaries has a planar structure [12] as shown in Figs. 17C and 18C. However, this zone was removed due to liquid convection in case 3 as observed in Fig. 19C. As shown in Fig. 15, the 410SS side has a higher temperature gradient which as the solidification rate further increases, the transition from plane front to cells occurs. The cellular dendritic structures became finer in the weld center as shown in Fig. 17B, 18B, and 19B, where cooling rate increases (see Fig. 15b). These dendrites have been transformed to fine equiaxed near the top surface due to the supercooling. Overall, the morphology of the WZ does not follow a certain pattern showing that it is dependent on the solute redistribution and segregation in the WZ which is not taken into account in this study. Fig. 17A represents an incomplete mixing in the fusion zone of case 1 forming several islands of cellular substructure on the Inconel 718 side. In addition, the different types of solidification structures elongated in different directions are observed on the 410 SS side as shown in Fig. 17C. In cases 2 and 3, the morphology of the WZ with a fully mixed region demonstrates a mixture of dendritic solidification structures elongated toward the weld center as shown in Fig. 18(A, C) and 19(A, C). The calculated solidification parameters show the high solidification parameter and the low cooling rate at the regions of A and C unlike region B (weld center). These regions are shown in the G-R diagram in Fig. 16e. The 410SS sides of the WZs (see Figs. 18C and
Fig. 18. The solidification morphology at different regions for case 2 (subfigures A-C are at the same magnification).
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Fig. 19. The solidification morphology at different regions for case 3 (subfigures A-C are at the same magnification).
19C) contain a combination of finer cellular, dendritic cellular and columnar structures in compared to the Inconel 718 sides (see Figs. 18A and 19A), which confirms the numerical predictions as described previously (see Fig. 16b). In addition, the calculated cooling rate and solidification parameter predicted the formation of fine equiaxed structure in the region B matched well with the experimental observations (see Fig. 16e). The 3D transient model can be used for the prediction of the mass distribution and solidification during the welding process. The solidification texture impacts the mechanical properties of the WZ. Therefore, the prediction of the weld texture with different process parameters could avoid costly experiments. In the future, the current model could be coupled with a computational thermo-kinetic simulation of temperature and time-dependent aging precipitation in the solid-state phase transformation. Such a coupled model will be able to predict the nucleation, growth and coarsening of the precipitates during the welding process. The precipitate phase distributions will determine the weld’s mechanical properties. 5. Conclusion In this study, the transient fluid flow and mass transport of dissimilar metals welding were simulated, and corresponding experiments were performed. Three sets of process parameters were used to study the influence of the arc travel speed and arc current on the quality of the weld. Some important conclusions are summarized as follows:
The numerical weld configuration in the arc travel direction was well matched with the experimental results. The dimensions of the weld geometry at the cross section obtained accurately for the Inconel side, but with a discrepancy for the stainless steel side due to differences in the alloy’s thermophysical properties with used ones in the simulation. The fluid flow dynamic has a remarkable impact on the redistribution of the mass concentrations in the WP. Good precision between the mass distribution obtained from the simulation and experiment confirms that the model is capable of mass transport prediction during the welding process. The numerical results showed that the intensity of the velocity due to increasing electromagnetic forces caused the removal of the UMZ. This does not occur with lower arc travel speed. The computed solidification parameters could describe the morphology characteristics of the real weld zone. The cooling rate decreases with the increase of the heat input and enhances along a distance away from the fusion boundaries toward the region close to the top surface where the finest morphology was observed. In addition, the heat input enhancement resulted a reduction in G/R value led to the growth of dendrites formation in the weld zone. The numerical prediction represented asymmetric G/R and cooling rate GR with respect to the joint due to the dissimilarity of the alloys’ thermophysical properties. The 410 SS side was predicted to have a finer solidification structure than the Inconel 718 matched well with the experimental observation.
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Declaration of Competing Interest None.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Mass transport and solidification phenomenon in dissimilar metals arc welding Fatemeh Hejripour ⇑, Brian T. Helenbrook, Daniel T. Valentine, Daryush K. Aidun Mechanical and Aeronautical Engineering Department, Clarkson University, 8 Clarkson Ave., Potsdam, NY 13699-5725, United States
a r t i c l e
i n f o
Article history: Received 29 March 2019 Received in revised form 31 July 2019 Accepted 5 September 2019 Available online 12 September 2019 Keywords: Arc welding Dissimilar metals welding Mass transport Solidification characteristics
a b s t r a c t A 3D transient numerical simulation is developed to study the arc welding of dissimilar metals for three sets of processing parameters. The model is used to investigate the fluid flow impacts on mass transport during the process. The predicted mass distribution agrees well with experimental composition measurements obtained from electron dispersive spectroscopy (EDS) analysis. The temperature distribution and the top surface shapes also match well with the experimental data. The morphology of the weld metal has a crucial impact on the weldment’s mechanical properties, and the prediction of solidification structure is key to improving weld quality. To this end, thermal results are applied to analyze the solidification behavior of the weld pool. The solidification parameters are calculated at the weld pool interface and the results are compared with the observed morphology from the experiments. The experimental observations confirm the presence of asymmetric solidification as demonstrated by the proposed model. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The use of different alloys in a weld provides the flexibility to design a product with both technical and economic advantages. The arc welding of dissimilar metals is a joining method which is widely used in the nuclear and chemical industries. Arc welding produces a uniform mixed weld zone (WZ) between the two different alloys, which improves the mechanical properties. However, the process is challenging due to the differences in thermophysical properties and chemistry of the alloys. In dissimilar alloy welds, it is important to understand the mixing process to achieve a high-quality weld. Modeling can be used to optimize the welding parameters with no need for costly experiments. Therefore, numerical modeling of the welding of dissimilar metals has been developed in recent years. Many researchers used linear laser welding of dissimilar alloys. In the numerical models, the top surface of the weld pool could be considered as a free surface or a flat surface. The weld penetration can be predicted more accurately considering a free surface [1]. Esfahani et al. [2] investigated fluid flow and alloy composition in a three-dimensional weld between carbon steel and stainless steel. The surface topology was tracked using an adaptive mesh refinement on the free surface of the melt pool. Their model predicted the dilution and homogeneity of the weld bead. Lian and Luo studied a transient model of a dis⇑ Corresponding author. E-mail address: [email protected] (F. Hejripour). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118703 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
similar weld under a pulsed laser [3]. They used a dynamic mesh method to obtain the free surface deformation and predicted surface ripple formation due to the periodical laser and molten pool solidification. Besides affecting the mass distribution inside the fusion zone, the solidification process can also cause defects during laser welding of dissimilar metals. Li et al. [4] developed a transient three-dimensional model of laser welding between 304SS and Ni considering the free surface deformation of the melt pool. They used thermal solidification data (temperature gradient and solidification rate) to predict the microstructural morphology of the weld zone. In several reported works, the top surface of the weld pool is assumed to be flat. Mukherjee et al. performed a 3D numerical simulation using the finite volume formulation [5] of the transport phenomena in laser welding of Fe–Al dissimilar metallic couple with a Ta sheet placed between. Marangoni forces were included in the modeling. It was concluded that the Fe-side melted further resulting in asymmetric thermal and velocity fields. Métais et al. [6] modeled a 3D simulation of the welding of dissimilar steels. A quasi-stationary state was assumed to develop turbulent flow, heat transfer, and mass transfer physics. The predicted weld zone profile and chemical element distribution in the weld achieved an accurate agreement with the experiment. The fluid flow and mass transport are different in Gas Metal Arc Welding (GMAW) because of the arc electromagnetic field. The electromagnetic forces affect the mass distribution and final quality of the fusion zone. A number of Multiphysics simulations of the GMAW process have been performed ([7–9]). However, there is
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little literature on the simulation of linear arc welding of dissimilar alloys. Daha et al. [10] developed a numerical heat transfer and fluid flow model of the welding of dissimilar steels using plasma arc welding (PAW). Using the transient model, they optimized the Keyhole PAW processes to gain sufficient energy and penetration. Bahrami et al. [11] used COMSOL Multiphysics to model the heat, fluid flow, and mass transfer for linear GTA welding of alloy 304 to 1018 steel assuming a flat top surface. The model predicted the distribution of the alloying elements in the weld zone as verified by comparison with experimental results. Their models of the welding linear dissimilar metals assumed the process to be quasisteady. However, the model using steady state assumptions are not able to predict mixing phenomena right after arc initiation and the moment the arc is shut off. In addition, the steady state study might not provide accurate results in cases of having a large weld pool (WP). A time dependent study could track the mixing in the WP and the solidification behavior after the arc passes. It also provides a better understanding of the unmixed zone (UMZ) formation. This region which is known as ‘‘partially melted zone” (PMZ) as well [12], is mostly formed along the fusion boundary of a ferritic/martensitic base metal with an austenitic weld zone [13]. The composition varies continuously from the Heat Affected Zone (HAZ) to the weld metal across this narrow martensitic band [14]. The UMZ affects the mechanical property across the weldment and causes failure of dissimilar metal welds during the post weld heat treatment [15]. In this study, two dissimilar alloys of Inconel 718 (austenitic alloy) and 410 stainless steel (martensitic alloy) are chosen. The final microstructure in the weld zone of these alloys is austenite. These two alloys have vast applications in the nuclear and aerospace industries [16]. In the current study, Inconel 718, which is a non-magnetic alloy, is autogenously welded to the martensitic 410SS. The fully coupled electromagnetic, heat transfer, fluid flow, and mass transfer equations are solved numerically using COMSOL Multiphysics [17]. The predicted distributions of chemical elements are compared with the experimental results. Also, the correlation of the fluid convection with the UMZ formation is studied numerically and experimentally. The solidification behavior is calculated using the transient simulation. Finally, the model is validated against experimentally solidified microstructures from the WZ for various welding parameters.
The welded coupons were sectioned across the weld and mounted. The samples were polished using silicon carbide papers. They were etched with Glyceria (30 ml HNO3 + 30 ml HCl + 15 ml glycerin) to reveal the microstructure. Finally, optical microscopy (OM) and energy dispersive spectroscopy (EDS) were carried out to investigate the WZs’ characteristics. 3. Physical model In this section, a 3D model is developed to track the convective force effects on the fluid flow and mass transport using COMSOL Multiphysics version 5.2a. Fig. 1 shows the geometry of the 3D model with the same dimensions of the plates used in the experiment. The arc initiates at the origin and passes along the contact surfaces of two dissimilar plates with a constant travel speed. The origin is considered at 3 mm distance from the domains’ wall to avoid the melt pool passing through the wall. After 15 s, the welding process was finished at about the end of the domains for cases 1 and 3 and partially through the domains for case 2. The following assumptions are made: The fluid flow is incompressible and laminar. The vaporization and solidification shrinkages are not considered. The thermal physical properties of the solution in the WP are assumed to be constant but different from the solid base metals. The top surface of the WP was assumed to be flat. The reason is discussed in Section 4.3. 3.1. Governing equations A Boussinesq type flow is assumed to govern the fluid motion in the WP. Mass continuity can be written as:
@ ql þ r ðql uÞ ¼ 0 @t
@ b @ b @ b k, and ql is the density of the pool. u is the i þ @y j þ @z where r ¼ @x
velocity field and t is time. The fluid flow is driven by a combination of forces in the molten pool that includes electromagnetic, Marangoni and buoyancy forces as well as frictional forces in the mushy zone. The forces and inhomogeneous heat flux are illustrated in Fig. 2. Conservation of linear momentum is described as follows:
2. Experimental procedure Inconel 718 plates were welded to the 410 stainless steel plates autogenously with the three sets of the welding parameters shown in Table 1. Coupon dimensions were 55 15 3.2 mm. To monitor the temperature variations of the plates during the welding process, two thermocouples were attached to the top surfaces of the plates. The chemical compositions of the alloys are listed in Table 2.
ð1Þ
ql
h i @u þ u r u ¼ r pI þ l ru þ ruT þ F b þ F L þ F d @t
ð2Þ
where l is the averaged liquid viscosity of the molten metals and p is the pressure field. F b is buoyancy force in the z-direction described as
F b ¼ ql ðbT ðT T r Þ þ bc ðc cr ÞÞg b k
ð3Þ
Table 1 The welding parameters used in the simulation. Case
Travel speed (mm/s)
Arc current (A)
Arc voltage (v)
Shielding gas
Heat input (J/mm)
1 2 3
3.5 3 3.5
100 100 120
13 13 15
Pure Argon Pure Argon Pure Argon
371 433 514
Table 2 The material composition of the alloys (wt%). Plate
Ni
Cr
Mo
Nb
Si
Ti
S
P
Cu
Mn
C
Al
Co
B
N
Sn
Fe
Stainless steel type 410 Inconel 718
0.24 55
12.01 21
0.04 3.3
– 5.16
0.33 0.35
– 1.15
0.001 <0.001
0.025 0.015
0.13 0.3
0.46 0.35
0.14 0.08
0.01 0.8
– 1.0
– 0.006
0.03 –
0.01 –
Bal Bal.
3
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703 Table 3 The thermal material properties of the dissimilar alloys [22].
Fig. 1. The geometry of the plates used in the simulation.
Alloy property
Unit
Inconel 718
410 SS
Solidus temperature (T s ) Liquidus temperature (T l ) Solidus density (qs ) Liquidus density (ql ) Dynamic viscosity (l) Solid thermal conductivity (ks ) Liquid thermal conductivity (kl ) Coefficient of thermal expansion (bT ) Solid specific heat (C ps ) Liquid specific heat (C pl ) Latent heat (DH) Surface emissivity () Electrical conductivity (r)
°K °K kg m3 kg m3 kg m1 s1 W m1 °K1 W m1 °K1 °K1
1528 1610 8200 7580 7.5 103 25 27 16.0 106
1753 1803 7640 7483 5.1 103 24.9 29.3 11.7 106
J kg1 °K1 J kg1 °K1 J kg1 – S m1
625 778 292 103 0.8 7 105
460 847 250 103 0.2 17.5 105
Table 4 The diffusion coefficients of the solutes used in the simulation [19,20]. Material
Chemical element
Ds (m2 =sÞ
Dl (m2 =sÞ
Inconel 718
Fe Ni Cr Fe Ni Cr
3 1014 5 1014 5 1014 6 1013 – 2 1012
8 1010 5.5 109 3.5 109 – – –
410 Stainless steel
Fig. 2. A schematic illustration of the fluid volume forces acting in the WP.
where Tr is the reference temperature which is taken as the liquidus temperature of the molten pool and cr is the concentration of solute at T r . bT and bc denote thermal and solute volumetric expansion coefficients, respectively. g is gravitational acceleration. Since the arc produces a magnetic field, Lorentz forces affect the fluid flow significantly. F L represents the Lorentz force due to arc current density J and magnetic flux B,
FL ¼ J B
Table 5 Alloying element concentrations used in the simulation (wt%). Ci
Inconel 718
410 SS
Fe Ni Cr
20 60 20
87 0 13
ð4Þ
The other effective force on the flow motion is a source term, F d , which is the frictional resistance to flow in the solid-liquid mushy zone. This force vanishes in the liquid phase. According to the Carman-Kozeny equation for flow through a porous media ([18]), F d is obtained as follows,
Fd ¼
ð1 f l Þ fl þ e 3
in which
2
Amush u
ð5Þ
e and Amush are small and large numbers, respectively. In
this study, e is assumed to be 103, and Amush is 6 104 mkg3 s (COMSOL library). f l is a smooth function which represents the liquid fraction,
fl ¼
8 > <0 > :
T < Ts
TT s T l T s
Ts < T < Tl
1
T > Tl
ð6Þ
where T s and T l are solidus and liquidus temperatures, respectively. The temperature field was determined by solving the energy equation which is defined as
qC p
@T þ u rT ¼ r krT @t
ð7Þ
Fig. 3. The transition of Iron concentration with the Heaviside step function with a scale of 0.3 mm.
where q, C p and k denote the density, heat capacity and thermal conductivity which have different values in the solids and liquid domains. Since there are no measured thermal material properties in the mushy zone in the literature, in this study, it is assumed to
4
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703 Table 7 The comparison of numerical velocity magnitude and temperature with different meshes. m
Point coordinate (mm)
Mesh
juj
36, 0.5, 0.2 (Inconel side)
1 2 3 1 2 3
0.0095 0.0160 0.0143 0.0101 0.0128 0.0143
36, 0.5, 0.2 (410 SS side)
s
at t = 12 s
T (°K) at t = 12 s 1891.73 1915.53 1915.55 1940.67 1963.99 1964.58
BCC crystal structure and the diffusion coefficients for the Fe-Cr stainless steel solid [21], are also given in Table 4. 3.2. Computational domains and boundary conditions The model includes four computational domains (see Fig. 1). Two larger domains are defined as solid domains of two dissimilar alloys. Heat transfer and electromagnetic equations are solved for all domains. The smaller domains where the molten pool occurs, are governed by the fluid flow and mass transfer equations in addition to the heat transfer and electromagnetic field. The boundary conditions of the computational domain are described below:
Fig. 4. Computational mesh of the model in (a) 3D view, (b) 2D view; (c) The side view of the liquid domain.
1. Electromagnetic field: vary from the solid state to the liquid state using the following equation
M ¼ Ms þ ðMl Ms Þf l
Gaussian distribution of the normal current density is applied to model the arc distribution on the top side of the entire domains as
1 0 3 ðx V t t Þ2 þ y2 3I A J n ¼ 2 exp@ pr i r2i
ð8Þ
where Ms and Ml are the thermal material property at solidus and liquidus temperatures which are given in Table 3. The apparent heat capacity is the summation of an equivalent specific heat and latent heat (COMSOL Library) while the phase of material changes which is written as
C p ¼ f l C pl þ ð1 f l ÞC ps þ Lf
d f l ql þ ð1 f l Þqs dT 2q
where I and r i are arc current and arc radius with the value of 4 mm on which the arc power is focused, respectively. V t denotes the arc travel speed. The bottom side is assumed to be ground (Voltage = 0). Other sides are assigned as insulated boundaries. Regarding the magnetic field, all faces are assumed to be insulated.
ð9Þ
where C ps and C pl are specific heat in solid and liquid phases, respectively. Lf is latent heat due to phase transition. The species conservation equation is
@C i þ u rC i ¼ r Di rC i @t
ð11Þ
2. Temperature field: The top surface of the model is subjected to inward heat flux, convective heat flux, and radiation to ambient temperature (T amb Þ. A Gaussian distribution is specified for the distribution of the heat flux. The boundary condition at the top surface is written as 1 0 3 ðx V t t Þ2 þ y2 3gVI A hðT T amb Þ r T 4 T 4 qn¼ exp@ amb 2 2 pri ri
ð10Þ
where C i is the ith alloying element concentration and Di is the mass diffusion coefficient of the element. In this study, the mass transport equation was solved for three major elements in the alloys which are Iron (Fe), Nickle (Ni) and Chromium (Cr). The WZ is predicted to be fully austenitic according to the Shaeffler diagram [19] with the dilution of 55% from Inconel 718 and 45% from the 410 SS in the fusion zone. Consequently, the WZ has an FCC crystal structure. Table 4 provides the diffusion coefficients of these elements in the Inconel 718 solid and liquid based on Fe-Ni-Cr alloys with the FCC lattice crystal structure [20]. The 410 SS solid has
ð12Þ where g is the arc efficiency assumed to be 0.7 in this model and V is arc voltage. In this study, the arc power distribution of 3 is chosen to achieve a higher focus. In the convection term, h denotes the heat transfer coefficient. In the radiation part of the equation, r and are
Table 6 The mesh properties of the model for case 2. Mesh
1 2 3
Maximum element size (mm) Top boundary of Xl
Xl
Xs
0.2 0.1 0.08
0.5 0.25 0.2
10.5 5.5 4.4
Number of elements
Number of grid points
159,747 935,322 1,691,393
234,215 1,320,993 2,367,910
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
5
Fig. 5. A comparison of the welds’ geometries for the three cases at (a) the top view of the weldments, (b) the top view of the numerical model and (c) the weld cross section.
Fig. 6. Computed temperature field for the three cases at t = 12 s.
the Stefan-Boltzman constant and surface emissivity, respectively. Other sides of the model have heat loss due to both convection and radiation. 3. Velocity field: The top side of the melted part is considered as a slip wall. The thermocapillary force is balanced by viscous stress along the top surface ([23]). In COMSOL Multiphysics, the Marangoni equation is solved by coupling heat transfer and fluid flow studies as
l
@u dc dc ¼ fl rs T þ rs C s @z dT dC
ð13Þ
4. Species field: A uniform initial value of the concentration shown in Table 5, is assumed for the domain of each alloy. All faces are assumed to be impermeable to the diffusion of the elements [11]. 3.3. Numerical implementation A time dependent study is performed to model the 3D welding process using COMSOL Multiphysics version 5.3a. The material properties used in the model are given in Table 3. The dilution (volume fraction) of the alloys in the WZ is considered to calculate the thermal properties of the WP (Ml) as follows [26]:
A410 Ml Aw
Ml ¼
4.3 104 N m1 K1 in the range of temperatures in the molten zone according to Sahoo equations [25].
Ml_410 and Ml_718 are liquidus material properties of the base metals. The dilution of each base metal was calculated and averaged based on an area measurement of the experimental weld zones (Aw Þ for three cases. A410 and A718 are the melted cross section area of the base metals. The average dilutions were obtained as 0.55 for the Inconel and 0.45 for the 410SS. For initial conditions, a smooth Heaviside step function with continuous second derivative and a scale of 0.3 mm was used to
zone. rs is the surface tangential gradient. c and C s are the surface tension and the surfactant element concentration, respectively. Based on the compositions of the alloys provided by vendors, the amount of sulfur is less than 0.001 wt% in both alloys (see Table 2). Therefore, the gradient of C s is essentially zero [24]. The surface ten dc sion derivative with respect to temperature dT is calculated to be
410
þ
A718 Ml Aw
where l @u denotes the shear stress on the top surface of the melted @z
718
ð14Þ
6
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
transition the material concentrations from the Inconel domain to the stainless steel one smoothly. For example, Fig. 3 shows the transition of iron (Fe) concentration from 20 wt% within the Inconel to 87 wt% in the stainless steel. The fluid flow computation needs to be solved using a fine mesh to reach convergence. So, the computational domains are divided into two domains of solid (Xs ) and liquid (Xl ) for each material as illustrated in Fig. 4. A coarser mesh was applied in the dis-
cretization of the solid domains. The unstructured tetrahedral mesh was used to discretize the domains. To test the mesh resolution, three sets of mesh densities were adopted for the model of case 2. The mesh size was decreased with the same proportion in all domains. The mesh properties are listed in Table 6. It should be noted that mesh 3 is not a factor of too refinement because the maximum number of nodes was restricted because of limited computational resources.
Fig. 7. The validation of the temperature profile for the three cases in the middle of 410SS plate and Inconel 718 plate.
Fig. 8. Computed velocity field and mass transport (Nickel distribution) at location of x = 36 mm for Case 2 at (a) t = 12 s, (b) t = 12.3 s and (c) t = 12.6 s.
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
7
Fig. 9. Alloying elements (Fe, Ni and Cr) distributions within the cross section for the three cases.
Fig. 10. (a) The locations of EDS measurements across the WZ along a horizontal line (z = 0.2 mm) for case 2, and (b–d) the verification of the calculated mass distribution with the experimental measurements.
In this model, the arc, the Eq. (12), was initiated at the time of zero and ended after 14 s. The model duration was 15 s to capture the WP solidification after the arc shut off. After that, the thermal simulation was solved for another 15 s for the solidified domains using the previous temperature results as initial values for the new calculation. The computations were performed on a desktop computer with two microprocessors (2.93 GHz) and 24 GB RAM. To save the computation time, the electromagnetic equation was solved in a separate time dependent study. The time step of this study was picked by the software with the maximum value of 0.008 s. The other
physics including fluid flow, heat transfer and mass transfer were solved in another study using the interpolated results of the electromagnetic field’s solution at each time step. The segregated approach was applied to solve these coupled physics. The maximum time step of 0.004 s was set by the solvers.
4. Results and discussion Three mesh densities (described in Table 6) were adapted for case 2 to analyze the mesh sensitivity. The velocity magnitude
8
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and temperature at two points, located in the liquid domain of two base metals, were calculated and given in Table 7. The numerical values for the flow dynamics, heat transfer and mass transport (see Fig. 10) indicate negligible changes in the solutions of mesh 2 and mesh 3. As a result, mesh 2 was picked to compute all of the cases to save the computation time. 4.1. Weld geometry To compare the numerical results with the experiments, Fig. 5 shows both the top view and the cross-sectional view of the welds. The calculated mixed region based on the mass transport equation (Fe wt%) is shown in Fig. 5b. By comparing Fig. 5a and b, it is obvious that although the arc oscillated between the two alloys during the welding process at some points, the simulations have predicted
the weld width accurately. In addition, the calculated welds’ profiles at the initial and ending stages of the welding process were in fair agreement with the corresponding experiment. Fig. 5b also indicates that the WP reaches to steady state in case 3 in a shorter time in compared to two other cases. A comparison between the experimental and calculated welds profiles at welds cross sections are presented in Fig. 5c. The weldments have been sectioned at the position of 20 mm before the ending points to perform the metallography. The numerical welds profiles (shown as a solid line) have been selected at corresponding locations in the simulations. Fig. 5c shows that the penetrations of the welds have been well predicted at the Inconel 718 side for all three cases, however there is a maximum deviation of 23% present at the 410SS side. This discrepancy may be due to a difference between the 410SS thermal properties used in the simulations and the experiments.
Fig. 11. The locations of EDS measurements across the WZ along a vertical line (y = 0) for case 2, and (b) the corresponding microstructure of the butt joint area.
Table 8 The chemical composition of the points shown in Fig. 10.
Point 1 Point 2 Point 3 Point 4 Point 5
Method
Cr
Fe
Ni
EDS measurement Numerical prediction EDS measurement Numerical prediction EDS measurement Numerical prediction EDS measurement Numerical prediction EDS measurement Numerical prediction
18.300.48 17.0 17.750.46 17.7 20.280.48 19.0 12.210.38 13 12.620.39 13
33.380.87 48.2 44.600.93 43.7 21.130.73 28.2 86.951.16 87 86.841.15 87
48.331.40 34.7 37.651.31 38.7 58.591.43 51.6 0.840.35 0 0.540.33 0
d Errors () are obtained by the EDS analysis.
Fig. 12. A comparison of the velocity magnitude for the three cases at t = 12.6 s.
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
9
Fig. 13. The fusion boundary on the 410SS side of the three cases.
Table 9 Shielding gas and liquid weld properties. Property
Unit
Argon gas density (qAr ) Weld pool density (ql ) Argon flow rate (Q ) Gas velocity (v Ar ¼ Q =A) Torch cap diameter (d)
Value 3
Area of torch outlet (A ¼ pd =4) Surface tension coefficient (c) Length of the weld pool (L) Maximum velocity at the top surface (jujmax ) 2
kg m kg m3 cfh m s1 m m2
1.784 7510 27 0.596 0.012 1.13 104
N m1 m m s1
1.88 0.007 in case 3 0.16
ferent thermal properties of the alloys. It shows that the temperature increases in the 410SS more rapidly compared to the Inconel 718. This phenomenon is confirmed by temperature measurements using two thermocouples during as shown in Fig. 7. The thermocouples were attached in the middle of the base plates’ top surfaces and 10 mm from the butt joint as shown in Fig. 6. The experimental measurements were compared with the calculated temperature in Fig. 7. The deviation between the results might be due to mesh coarsening at the solid domains, losing the calculation accuracy in these domains. Nevertheless, the trends were found in good agreement. 4.3. Dynamic and mass transport phenomenon
4.2. Temperature field and model validation Fig. 6 shows the calculated temperature field at top surfaces for the cases at t = 12 s. The fusion boundary of the WP is illustrated as a black solid line showing the boundary between the liquidus and solidus temperatures for each alloy. The WP becomes larger as the heat input increases from 370 J/mm in case 1 to 433 J/mm and 514 J/mm in cases 2 and 3, respectively. The maximum temperature increases from 2240 K in case 1 to 2860 K in case 3 by raising the heat input. The isotherms are also plotted to illustrate the temperature distribution during the welding process. The isotherms are asymmetric with respect to the weld centerline due to the dif-
The velocity field in dissimilar metals arc welding becomes complicated when one of the alloys is magnetic and the other one is not. The difference of Lorentz force magnitude between the magnetic side (410SS) and the non-magnetic one (Inconel 718) enhances the flow circulation around the WP. This flow affects the mass transport and mixing phenomenon during the welding process. Fig. 8 shows the flow field at three different moments with an increment of 0.3 s at the cross-sectional plane of x = 36 mm in case 2. The solid black line illustrates the fusion boundary at the corresponding instant. The streamlines and arrows indicate the flow direction. It should be noted that the maximum
Fig. 14. Computed heating/cooling rate at the solid/liquid interface.
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F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
velocity occurs at the Inconel 718 side and the magnitude is 0.088 m/s. Fig. 8a shows the fluid flow in the front part of the molten pool and the corresponding Ni distribution. This plane is centered under the arc at t = 12 s resulting in the highest magnitude of the Lorentz force in the 410SS side. This volume force pushes the fluid from the 410SS side (shown by arrows) toward the Inconel 718 side. The Marangoni force interacts with other volume forces causing the generation of one strong vortex at each side of the WP. These vortices produce a vorticial flow motion in addition to the flow circulation inside the WP. In the initial stage of mixing in the front part of the WP, the flow transfers the material of 410SS toward the Inconel 718 side. However, a mixed region is induced by Marangoni effects near the top surface of the WP at 410SS side. In the middle of the WP (see Fig. 8b, t = 12.3 s), the flow starts changing direction from Inconel 718 side toward the 410SS side. The fluid flow injects the Inconel 718 material into the WP, especially toward the 410SS side. Consequently, higher amounts of Inconel alloying elements grow in the WP on the 410SS side. The Inconel injection continues at the rear side of the WP as shown in Fig. 8c (t = 12.6 s) and becomes mixed with the liquid material inside the WP. However, there is insufficient time to mix the entire liquid Inconel 718 with the WP material. As shown in Fig. 9, a small amount of liquid Inconel 718 gets solidified on top of the joint in the WZ. This region is an UMZ formed inside the fusion zone of all three cases according to the numerical predictions. It should be noted that heat input enhancement induces a more uniform mixed WZ as a result of higher dilution from each alloy. More dilution provides further liquid materials inside the WP to get mixed. To validate the mass transport predictions, EDS analysis has been carried out along a horizontal line across the WZ of case 2 with a 0.2 mm distance under the weld top surface as presented in Fig. 10a. Fig. 10b–d show the comparison of the Fe, Ni and Cr distributions, respectively, in the experimental WZ with the numerical model using different meshes. The calculated compositional results for meshes 1 and 2 matched well with the EDS composition measurements. The composition has also been evaluated along a vertical line at the weld joint from the top surface to the bottom as shown in Fig. 11a. The measured compositions at the picked points are listed in Table 8. The chemical composition of Point 3 (Fig. 11a) has been found very similar to the composition of Inconel 718, which shows the existence of Inconel 718 material inside the WZ right above the weld joint. This is consistent with the mass transport predictions (see the UMZ in Fig. 9). The optical microscopy image of this region (point 3) is shown in Fig. 11b to investigate the solidification morphology. It should be noted that the morphology is dependent on the solute redistribution during solidification [27]. As shown in Fig. 11b, the elongated cells are stretched from the Inconel 718 side toward the 410SS side above the joint where point 3 is located. It is noticed that Point 1 is located 0.3 mm below the top surface. The composition of Point 1 was expected to be close to the results shown in Fig. 10. However, it contains lower Fe content and a higher amount of Ni which was in conflict with the EDS results shown in Fig. 10. According to the literature, laves phase and Nb-rich intermetallics exist in the WZ of Inconel 718 [28]. Therefore, the composition of these points has been remeasured by adding Nb and Mo elements to the three other alloying elements. The obtained composition of this point showed the amounts of 6.9 wt% and 3.1 wt% for Nb and Mo, respectively, which confirms that Point 1 is located in a Nb-rich region. It depends on the type of Nb-rich precipitate, the Fe and Ni content vary in this region. The maximum velocity (jujmax ) which occurs on the top surface of the WP on the Inconel side. In cases 1, 2 and 3 the maximum velocity is 0.078, 0.088 and 0.16 m/s, respectively. The Reynolds
number can be employed to determine the stability of the flow. The Reynolds number is defined as follows.
Re ¼
LR ql jujmax
l
ð15Þ
where LR is the width of the WP. The calculated Reynolds numbers are below 1000 and no temporal instability occurred during the calculation indicating that turbulent flow is nonsignificant in any of the three cases [24,25]. The magnitude of the velocity at the rear side of the WP where the maximum penetration occurs, at the time of 12 s is illustrated in Fig. 12. The stronger convection in case 3 due to larger volume forces within the fluid, results in a higher velocity compared to two other cases. The enhanced convection could assist in mixing the bulk of the WP well. The fact that the fluid flow in case 3 removed the melted base material completely and mixed the liquid materials inside the WP. Therefore, the unmixed zone (UMZ) formed along the fusion boundaries has been eliminated. The UMZ has detrimental effects in dissimilar metals weld in the case of existing a ferritic/martensitic base metal and an austenitic WZ [29]. This UMZ has been observed in cases 1 and 2 but removed in case 3 as shown in Fig. 13. Thus, the growth of the convection
Fig. 15. Calculated (a) solidification parameter, (b) cooling rate, (c) solidification rate and (d) temperature gradient at the cross section of the weld at t = 12.5 s for case 1.
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
11
Fig. 16. Color range of data points with respect to the weld center at the top surface, (b) the G-R scatter plot for case 1, (c) a comparison of G-R values between cases 1 and 2, (d) a comparison of G-R values between cases 1 and 3 and (e) the schematic illustration of G-R diagram containing various substructural regions.
due to the Lorentz forces increase will improve the mechanical properties. The effects of the gas flow and weld pool dynamic on the top surface, respectively, were estimated using the Weber numbers as follows
WeAr ¼
qAr v Ar 2 d c
ð16Þ
where qAr is the density of Argon in the gas state. v Ar is the gas velocity at the torch cap outlet and d is the torch cap diameter. c is the surface tension coefficient of the weld pool which is assumed to be equal to the surface tension coefficient of Inconel 718. The values are listed in Table 9. The Weber number of the gas is obtained as 0.0076. On the other hand, the Weber number of the weld pool is calculated as follows:
12
Weweld ¼
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
ql jujmax 2 L c
ð17Þ
where L is the length of the weld pool. The maximum Weweld occurs in case 3 with a value of 0.715. According to the very low value of the Weber number (W1) for the shielding gas, the gas dynamic impact on the free surface is negligible. The Weber number of the liquid pool is less than unity. It means that the free surface affects the weld pool dynamic only moderately and thus is not considered in this study. 4.4. Solidification and morphology The mechanical properties of the welds depend on the grain structure formed during the solidification. To predict the solidification morphology in the WZ, the solidification parameters are required to be obtained. To this end, the current simulation has been used to determine these parameters including the solidification rate (R), temperature gradient (G), solidification parameter (G=R) and cooling rate (G:R). Fig. 14 shows the heating/cooling rate variation at the solid/liquid interface where the liquid fraction is 0.9. The dashed line illustrates the interface between the heated and cooled sides of the WP. The cooling process occurs at the rear side of the WP called the solidification front. The solidification takes place normal to the solid/liquid interface at any point such as Point A shown in Fig. 14, in the same direction as the heat flow ! ( G ). Thus, the local solidification rate can be obtained as follows [30]:
R ¼ Vt
rT jjrTjj
ð18Þ
where jjrTjj is the magnitude of the temperature gradient (G) in the liquid at the solidification front. The solidification is a 3D phenomenon occurring at the solid/ liquid interface of the molten pool. Therefore, the solidification parameters have been calculated on the interface at the solidification front on the iso-surface shown in Fig. 14. Fig. 15 projects the solidification parameters calculated on the solidification surface shown in Fig. 14 onto a y-z plane for case 1. The plots show noisy results due to the numerical oscillation around the Mushy zone in the simulation. It is seen that the solidification parameter (G=R) increases, and the cooling rate (G R) decreases continuously from the weld center to the fusion boundaries. Moreover, the cooling rate is higher on the 410 SS side. The solidification rate (R) gets to the maximum value at the weld center near the top surface. The temperature gradient (G) is lower at the middle of the WZ on the Inconel 718 side due to differences in the thermo-physical properties of the dissimilar alloys. The calculated G-R diagrams for the three cases with the comparisons between the cases are shown in Fig. 16. Fig. 16a shows the scatter data points on the solid/liquid interface with the liquid fraction of 0.9. The points are colored by the distance from the point to the weld centerline on the top surface. The magnitude of the temperature gradient is plotted versus the solidification rate of the data points for case 1 in Fig. 16b using the same point coloring scheme. The data points of the 410 SS and Inconel 718 sides are distinguished in the diagram. It is evident that the temperature
Fig. 17. The solidification morphology at different regions for case 1 (subfigures A-C are at the same magnification).
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
gradient on the 410 SS side is higher than the Inconel 718 side. According to the G-R diagram shown in Fig. 16e, the 410 SS side is predicted to have a finer solidification structure in the WZ. Figs. 16c and 15d display the colored data points for case 2 and case 3, respectively, and gray points for case 1. The lower arc travel speed in case 2 resulted in an insignificant rise in the temperature gradient at the weld center. However, the cooling rate (G R) decreases because of the reduction in the solidification rate. Fig. 16d shows that the temperature gradient is dramatically dropped in case 3 with the arc current increase and the cooling rate is reduced. Nevertheless, the range of the cooling rate reduction in the middle of WZs is not noticeable to impact the solidification structure as will be observed in the experimental micrographs. It is worth mentioning that the solidification parameters are asymmetric with respect to the weld center in dissimilar metals welding (see Fig. 15). Thus, the morphology of the WZ is expected to be different on each side. Figs. 17–19 show the solidification structure of three regions including the fusion boundaries (subfigures A and C) and middle of the WZs (subfigure B) for cases 1, 2 and 3, respectively. According to the constitutional supercooling crite DT ria GR < DLeq , the cellular substructure is formed under this condition and other substructural zones will be formed by increasing the cooling rate [27]. DT eq is the equilibrium solidification range and DL is the solute diffusivity assumed to be averaged as 5 1089
m2 s
in this study (Table 4). Thus,
DT eq DL
is 16 109
Ks m2
for
Inconel 718 side. The computational results indicate that the constitutional supercooling criterion is satisfied in the three cases. Based on the observations in Figs. 17A, 18A and 19A, the morphology of the WZs in three cases interestingly show the cells are formed along both fusion boundaries on the Inconel 718 side.
13
However, the mechanism of epitaxial growth made the formation of the dendritic cells due to similar crystallographic orientation of the HAZ grains (FCC) and the WZ. On the 410SS side, the crystal structure of the HAZ (BCC) was different from the WZ (FCC). Consequently, the epitaxial growth did not occur as shown in Figs. 17C, 18C, and 19C. On the 410SS side, the UMZ along the fusion boundaries has a planar structure [12] as shown in Figs. 17C and 18C. However, this zone was removed due to liquid convection in case 3 as observed in Fig. 19C. As shown in Fig. 15, the 410SS side has a higher temperature gradient which as the solidification rate further increases, the transition from plane front to cells occurs. The cellular dendritic structures became finer in the weld center as shown in Fig. 17B, 18B, and 19B, where cooling rate increases (see Fig. 15b). These dendrites have been transformed to fine equiaxed near the top surface due to the supercooling. Overall, the morphology of the WZ does not follow a certain pattern showing that it is dependent on the solute redistribution and segregation in the WZ which is not taken into account in this study. Fig. 17A represents an incomplete mixing in the fusion zone of case 1 forming several islands of cellular substructure on the Inconel 718 side. In addition, the different types of solidification structures elongated in different directions are observed on the 410 SS side as shown in Fig. 17C. In cases 2 and 3, the morphology of the WZ with a fully mixed region demonstrates a mixture of dendritic solidification structures elongated toward the weld center as shown in Fig. 18(A, C) and 19(A, C). The calculated solidification parameters show the high solidification parameter and the low cooling rate at the regions of A and C unlike region B (weld center). These regions are shown in the G-R diagram in Fig. 16e. The 410SS sides of the WZs (see Figs. 18C and
Fig. 18. The solidification morphology at different regions for case 2 (subfigures A-C are at the same magnification).
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F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
Fig. 19. The solidification morphology at different regions for case 3 (subfigures A-C are at the same magnification).
19C) contain a combination of finer cellular, dendritic cellular and columnar structures in compared to the Inconel 718 sides (see Figs. 18A and 19A), which confirms the numerical predictions as described previously (see Fig. 16b). In addition, the calculated cooling rate and solidification parameter predicted the formation of fine equiaxed structure in the region B matched well with the experimental observations (see Fig. 16e). The 3D transient model can be used for the prediction of the mass distribution and solidification during the welding process. The solidification texture impacts the mechanical properties of the WZ. Therefore, the prediction of the weld texture with different process parameters could avoid costly experiments. In the future, the current model could be coupled with a computational thermo-kinetic simulation of temperature and time-dependent aging precipitation in the solid-state phase transformation. Such a coupled model will be able to predict the nucleation, growth and coarsening of the precipitates during the welding process. The precipitate phase distributions will determine the weld’s mechanical properties. 5. Conclusion In this study, the transient fluid flow and mass transport of dissimilar metals welding were simulated, and corresponding experiments were performed. Three sets of process parameters were used to study the influence of the arc travel speed and arc current on the quality of the weld. Some important conclusions are summarized as follows:
The numerical weld configuration in the arc travel direction was well matched with the experimental results. The dimensions of the weld geometry at the cross section obtained accurately for the Inconel side, but with a discrepancy for the stainless steel side due to differences in the alloy’s thermophysical properties with used ones in the simulation. The fluid flow dynamic has a remarkable impact on the redistribution of the mass concentrations in the WP. Good precision between the mass distribution obtained from the simulation and experiment confirms that the model is capable of mass transport prediction during the welding process. The numerical results showed that the intensity of the velocity due to increasing electromagnetic forces caused the removal of the UMZ. This does not occur with lower arc travel speed. The computed solidification parameters could describe the morphology characteristics of the real weld zone. The cooling rate decreases with the increase of the heat input and enhances along a distance away from the fusion boundaries toward the region close to the top surface where the finest morphology was observed. In addition, the heat input enhancement resulted a reduction in G/R value led to the growth of dendrites formation in the weld zone. The numerical prediction represented asymmetric G/R and cooling rate GR with respect to the joint due to the dissimilarity of the alloys’ thermophysical properties. The 410 SS side was predicted to have a finer solidification structure than the Inconel 718 matched well with the experimental observation.
F. Hejripour et al. / International Journal of Heat and Mass Transfer 144 (2019) 118703
Declaration of Competing Interest None.
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