*2.1. Material Properties and Methods*

Sheets of aluminum alloy 5456 with a thickness of 5 mm were used as the base metal in this investigation. The length and the width of these aluminum alloy sheets were 100 mm and 50 mm, respectively. Table 1 illustrates the chemical composition of this alloy. In order for the dendritic growth of grains within the fusion zone to be investigated, the scanning electron microscopy (SEM) was utilized.


**Table 1.** Chemical composition of samples (in wt.%).

To weld AA5456 sheets in the bead-on-plate condition, a pulsed Nd:YAG laser with the model of IQL-10 was used. This laser apparatus was able to produce a maximum power of 80 W, a wavelength of 1064 nm, a focal length of 100 mm, and a spot diameter of 0.5 mm on the substrate. In the current study, the laser beam was collided with the substrate through the top surface. To protect the welding pool and its surroundings, argon gas at a flow rate of 30 l/min was applied linearly in the welding direction. Table 2 depicts the specific parameters which have been performed in the laser welding process.



Thermophysical properties of the material such as density, specific heat, and thermal conductivity vary with temperature such that they should be calculated via polynomial coefficients method which is described below. These coefficients are depicted in Table 3 [16–18].

**Table 3.** Polynomial coefficients vary with temperature *T* for calculation of Density *D*, Specific Heat at constant pressure *C*p, and Thermal Conductivity λ of Aluminum alloy 5456 [16–18].


As was mentioned above, thermophysical characteristics of the material are computed via polynomial coefficient. The value of each parameter was calculated as function of temperature using COMSOL Multiphysics; these diagrams are shown in Figure 1. In addition, in order for the phase change in the mushy zone to be considered, the heat capacity method is solved by encompassing the latent heat (*<sup>L</sup>* = <sup>290</sup> kJ·kg<sup>−</sup>1) of the base metal [19]. By doing so, the modified specific heat can be calculated in the mushy zone between the solidus and liquidus temperatures of the material Δ*Tm*, which is about 67 K; in this region, average melting temperature is defined to be 877.5 K approximately [20] (Equation (1)).

$$\mathbf{C}\_{p} = \begin{cases} \begin{array}{c} \mathbb{C}\_{p,\text{sensible}} \text{ for } T < T\_{\text{m}} - 0.5\Delta T\_{\text{m}} \text{ or } T > T\_{\text{m}} + 0.5\Delta T\_{\text{m}}\\ \end{array} \\\end{cases} \\ \begin{array}{c} \text{for } T < T\_{\text{m}} - 0.5\Delta T\_{\text{m}} \text{ or } T > T\_{\text{m}} + 0.5\Delta T\_{\text{m}} < T < T\_{\text{m}} + 0.5\Delta T\_{\text{m}} \end{array} \tag{1}$$

in this equation, *cp* and *T* illustrate the specific heat and temperature, respectively.

**Figure 1.** Variation of thermophysical properties for 5456 aluminum alloy (AA5456 with temperature: (**a**) specific heat; (**b**) density; and (**c**) thermal conductivity.
