*2.3. Calculation of Cooling Rate, Growth Rate and Thermal Gradient*

The cooling rate of weld can be evaluated by the two equations shown below [6]. For thick plate:

$$C\_R = 2 \times \pi \times k \times (T\_C - T\_0) / H\_{\text{net}} \tag{4}$$

For thin plate:

$$\mathcal{C}\_R = 2 \times \pi \times k \times \rho \times c \times t^2 \times \left(T\_\odot - T\_0\right)^3 / H\_{\rm net} \tag{5}$$

where *CR* <sup>=</sup> cooling rate (K·s<sup>−</sup>1), *<sup>k</sup>* <sup>=</sup> thermal conductivity <sup>=</sup> 15 W·m−1·K<sup>−</sup>1, <sup>ρ</sup> <sup>=</sup> density <sup>=</sup> 7850 Kg·m<sup>−</sup>3, *c* = specific heat = 500 J·Kg−1·K−1, *t* = plate thickness(mm), *TC* = peak temperature = 1534.15 K, *<sup>T</sup>*<sup>0</sup> <sup>=</sup> final temperature <sup>=</sup> 300.15 K and *Hnet* <sup>=</sup> heat input rate(J·m<sup>−</sup>1). The relative plate thickness factor was derived to select the proper cooling rate Equation [6]:

$$\tau = t \times \sqrt{\rho \times c \times (T\_{\odot} - T\_0) / H\_{\text{net}}} \tag{6}$$

Equation (4) is applicable when τ ≥ 0.75, else Equation (5) is appropriate. In this study, 3 mm thin base plate was used, τ of all the studied conditions was lower than 0.75. Therefore, Equation (5) was selected to calculate the cooling rate. The dendrite growth rate in the solidification zone at the end of the weld is calculated as follows [6]:

$$R = v \cos \theta \tag{7}$$

where *R* = growth rate (mm/s), *v* = welding speed (mm/s) = 3.5 mm/s, θ = the angle between the normal to solidification front and the welding direction. The calculation equation of the thermal gradient of weld pool (G, K <sup>×</sup> mm<sup>−</sup>1) without considering the convection of the weld pool is as follows [6]:

$$G = \mathbb{C}\_{\mathbb{R}} / \mathbb{R} \tag{8}$$
