3.2.1 Experimental procedure

The base material was 2024 aluminum alloy in initial T6 condition with a thickness of 6 mm. The material was cut into several pieces with 300 ˜ <sup>60</sup>˜ 6 mm<sup>3</sup> dimensions. The nominal chemical composition of the base metal is shown in Table 3. Pure argon (99%) was employed as shielding gas with flow rates of 15–18 L/min for VP-GTAW.

Heat and Mass Transfer of Additive Manufacturing Processes for Metals DOI: http://dx.doi.org/10.5772/intechopen.84889


Table 3.

Chemical composition of the deposited 2024 aluminum alloy/wt%.

In VP-GTAW welding system, Fronius MagicWave 3000 welding power source was adopted. The VP-GTA welding process was used square wave AC mode. Before deposition, oil and other impurities were removed using acetone. The arc welding parameters applied in the experiments are presented in Table 4. Among them, the magnitude of DCEN welding current is Ien, the magnitude of DCEP welding current is Iep, the welding speed is u, the pulse frequency is f. The DCEP duty ratio of VP arc was fixed at 50%.

After the experiments, the samples for metallographic observations were prepared by sectioning the deposits along the vertical direction using an electrical discharge wire cutting machine (Suzhou Simos CNC Technology Co., Ltd., Suzhou, China). Then, the samples were etched with modified Keller solution (50 ml H2O, 1 ml HCL, 1.5 ml HF, and 2.5 ml HNO3) after the processes of rough grinding, fine grinding, and polishing. The microstructure of the treated specimen was observed by Eclipse MA200 light microscope (OM) (Nikon Instruments (Shanghai) Co., Ltd., Shanghai, China).

#### 3.2.2 Numerical modeling of MFCAM process

#### 3.2.2.1 Physical model assumptions

A numerical model coupling electromagnetism force, heat transfer, and fluid flow in melt is derived in this section. The electric arc is modeled by an equivalent heat source applied to the upper surface of a workpiece. Gaussian distribution function can be used to describe the modeled electric arc quantities. It was assumed that the welding torch moves at a constant welding speed. The electromagnetic, continuity, momentum, and energy equations can be solved in the weld pool. The considered problem possesses symmetry with respect to the longitudinal vertical median plane, can therefore be calculated as one-half plate.

Up to now, there is no direct literature addressing the quantitative relation of shielding gas flow rate and weld bead dimensions during the VP-GTAW process. There is an optimum flow rate for weld shielding gases, but this is often decided by preference or experience. In this study, the thermocapillary-driven flow region is protected from atmosphere by pure argon (Ar) gas, and the flowing rate of the shielding gas was 15–18 L/min.


Table 4. Parameters for VP-GTA welding of aluminum.

#### 3.2.2.2 Governing equations

The numerical simulation of heat and mass transfer processes are governed by a set of equations in Flow3D model. In the present study, the liquid metal is assumed to be incompressible Newtonian fluid, and the flow should be laminar. The electric arc was assumed as an internal boundary condition can be described as Eq. (13).

$$k\frac{\partial T}{\partial \overline{n}} = \dot{q}\_{\text{ov}} - \dot{q}\_{\text{conv}} - \dot{q}\_{\text{rad}} \tag{13}$$

where , , are the arc heat input, convective and radiative heat loss, respectively, is the surface normal.

In this study, according to the actual processing conditions that the welding current in case of DCEP and DCEN (Ien/Iep = 240/120 A) is high enough, arc stiffness and impact force exerted onto the weld pool surface is larger, and the arc column is perpendicular to the surface of the weldment. So, the Goldak's double-ellipsoidal heat source model was adopted [25], which can provide relatively accurate results, especially for the low penetration surface melting process. In the moving volumetric heat source model, the power density distributions of the front and rear quadrants can be described by Eqs. (14) and (15), respectively,

$$q\_r = \frac{6\sqrt{3}q\_{ov}f\_r}{\pi a\_r b c \sqrt{\pi}} \exp\left(-3[\frac{\chi^2}{a\_r^2} + \frac{\chi^2}{b^2} + \frac{\varpi^2}{c^2}]\right) \tag{14}$$

$$q\_{f} = \frac{6\sqrt{3}q\_{ow}f\_{f}}{\pi a\_{f}bc\sqrt{\pi}}\exp\left(-3[\frac{\mathbf{x}^{2}}{a\_{f}^{2}} + \frac{\mathbf{y}^{2}}{b^{2}} + \frac{\mathbf{z}^{2}}{c^{2}}]\right) \tag{15}$$

where ff and fr are the front and rear fraction of the heat flux; af, ar, b and c are the parametric values obtained from the metallographic data and the weld bead profile; qarc is the welding arc heat input.

The heat loss and can be calculated as follow:

$$
\dot{q}\_{\rm conv} \equiv h\_{\rm conv} (T - T\_0) \tag{16}
$$

$$\dot{q}\_{rad} = \varepsilon \sigma\_{sb} \left( T^4 - T\_0^4 \right) \tag{17}$$

According to the Vinokurov's empirical model [26], combined convectionradiation heat transfer coefficient was utilized as:

$$h\_{vino} = 2.41 \times 10^{-3} \varepsilon T^{1.61} \tag{18}$$

The pressure boundary conditions on the weld pool surface can be described as Eq. (19).

$$P = P\_{\rm av} + \frac{\mathcal{Y}}{R\_c} \tag{19}$$

where Parc is the arc pressure, Rc is the curvature radius of the weld pool surface. The surface tension γ can be calculated as follow:

Heat and Mass Transfer of Additive Manufacturing Processes for Metals DOI: http://dx.doi.org/10.5772/intechopen.84889

$$\gamma = \gamma\_o \text{-} \gamma\_T (T - T\_l) \tag{20}$$

The arc pressure distribution was assumed to follow the distribution of current density. It can be modeled by a Gaussian model with the same radius of arc drag force, as blow [27].

$$P\_{\rm avr}(\mathbf{x}, \mathbf{y}) = \frac{\mu\_0 I^2}{4\pi^2 \sigma\_r^2} \exp\left(-(\frac{r^2}{2\sigma\_r^2})\right) \tag{21}$$

where μ0 is the magnetic permeability of free space, σ<sup>r</sup> is the arc pressure parameter (DCEN phase: σ<sup>r</sup> = σp, EN; DCEP phase: σ<sup>r</sup> = σp, EP).

The arc drag force on the weld pool is greatly dependent on the current, the composition of shielding gas, and the tip angle of electrode. Here, the effect of arc drag force is considered as a spatial boundary distribution, which can be represented as follows [28].

$$P\_{Days}(r) = P\_{\text{Aav}} \sqrt{\frac{r}{r\_{\text{Shour}}}} \exp - (\frac{r}{r\_{\text{Shour}}})^2 \tag{22}$$

where rShear is the distribution parameter of arc drag force.

The body force mainly includes electromagnetic force (EMF), gravity, and buoyancy. The gravity acceleration is 9.81 m/s2 . The temperature-dependent properties were used for the density. The electromagnetic force, as an important body force, was considered by adopting the elliptically symmetric welding current density [29, 30]. The equations relating EMF are listed as below.

$$F\_x = -J\_x \times B\_\theta \frac{X}{r\_a} \tag{23}$$

$$F\_x = -J\_r \times B\_\vartheta \tag{24}$$

$$J\_z = \frac{I}{2\pi} \int\_0^\sigma \lambda J\_0(\lambda r\_s) \exp(-\frac{\lambda^2 \sigma\_x}{2}) \frac{\sinh[\lambda(c-z)]}{\sinh(\lambda c)} d\lambda \tag{25}$$

$$J\_r = \frac{I}{2\pi} \int\_0^\pi \lambda J\_1(\lambda r\_s) \exp(-\frac{\lambda^2 \sigma\_s}{2}) \frac{\cosh[\lambda(c-z)]}{\sinh(\lambda c)} d\lambda \tag{26}$$

$$B\_{\theta} = \frac{\mu\_{n}I}{2\pi} \int\_{0}^{\infty} J\_{1}(\mathcal{A}r\_{a}) \exp(-\frac{\mathcal{\lambda}^{2}\sigma\_{\pi}}{2}) \frac{\sinh[\mathcal{\lambda}(c-z)]}{\sinh(\mathcal{\lambda}c)} d\mathcal{\lambda} \tag{27}$$

$$\sigma\_o = \sqrt{(\varkappa - \varkappa\_0)^2 + [\frac{\sigma\_x}{\sigma\_y}(\wp - \wp\_0)]^2} \tag{28}$$

where I is the arc current (DCEN phase: I = Ien, σ<sup>j</sup> = σj, EN; DCEP phase: I = Iep, σ<sup>j</sup> = σj, EP), Fi are the components of the EMF force in the i-direction (i = x, y, z), B<sup>θ</sup> is the angular component of the magnetic field, Jz and Jr are the axial and radial

current density in the cylindrical coordinate system, J0 and J1 are the zero order and one order Bessel function, respectively, z indicates the vertical depth from top surface of workpiece, and c is the workpiece thickness.
