## 3 Results and Discussion
### Weld Zone Grain Morphology  
Representative grain morphology maps at various welding speeds were determined by EBSD and shown in Figure 4. All weld cross-sections show both equiaxed grains in the centre and columnar grains near fusion lines. The growth of columnar grains is mainly along two directions due to the directional heat conduction during cooling stage: first, it is along the vertical direction from the bottom part to the fusion zone and secondly it develops horizontally from the upper part towards the weld centre. The formation of equiaxed grains in the weld centre is attributed to two phenomena:  
1. [label=()]
2. the energy flux distribution of an oscillated laser beam (Figure 5), \(E(x,y)\), computed by Equation (2) [34] shows a 'M' shape in the transverse direction, with the peak energy deposition at two turning points of the oscillation path. \[E(x,\ y)=\int_{0}^{T}P(t)exp\Big{\{}-2*[(x-x(t))^{2}+(y-y(t))^{2}]/r^{2}\Big{\}} \ dt,\ []\] (2) where \(P(t)\) is the time-dependent instant power of laser beam expressed in Figure 1, \(r\) (\(r\) = 0.16 mm) is the radius of laser beam at \(A_{z}\) = 2 mm. \(x(t)\) and \(y(t)\) are the moving track of oscillating beam and can be expressed by Equations (3) and (4), respectively. \[x(t)=S_{x}*t,\ [\text{mm}]\] (3) \[y(t)=A_{y}*\cos(2\pi ft)/2,\ [\text{mm}]\] (4)  
As confirmed by [PERSON] et al. [35], transverse oscillating welding introduces a wider molten pool and more uniform temperature gradient (G) in the fusion zone compared to rectilinear welding, which is favourable for the formation of equiaxed grains based on the solidification theory proposed by [PERSON] and [PERSON] [36].  
Figure 3: Evaluation of weld shape as function of welding parameters. (**a**) Weld depth of fusion and (**b**) effective weld width at interface.  
2. the turbulence of molten material in the rear of the molten pool which is induced by the beam oscillation, disturbs the growth of columnar grains in the mushy zone and promote the formation of equiaxed grains. However, this stirring effect induced by transverse beam oscillation is relatively weak as compared to longitudinal and circular oscillations because the oscillations occur only in front of the molten pool [34].  
Distribution of the size of columnar grain expressed by the length of major axis from elliptical fitting and total area of equiaxed grains are plotted in Figure 6. It is interesting to see that a lower welding speed facilitates the growth of equiaxed grains while suppresses the formation of columnar grains. Regarding the energy flux distribution (Figure 5), it is reasonable to infer that the evolution of grain morphology with reduced welding speeds is attributed to the higher energy deposition at the two edges of fusion zone (Figure 5b), which works as a stronger thermal barrier near the boundary of fusion and leads to a lower temperature gradient (G) within the fusion zone during subsequent solidification process [4]. Modelling work in [4, 34, 35] also confirmed the presence of a reduced G within the fusion zone as the energy deposition at two edges of fusion zone increases, which results in a larger constitutive undercooling region of the molten material and promotes the formation of equiaxed grains.  
Figure 4: Representative EBSD Euler maps showing the grain structures of equiaxed and columnar grains in the weld zone of joint produced in processing windows (**a**) S2-F50; (**b**) S4-F100; and, (**c**) S6-F150.  
Figure 5: (**a**) Computed energy flux distribution on material surface in each processing window and (**b**) distribution of averaged energy flux intensity along transverse position. Note that energy flux intensity was calculated with Equation (2) normalised by the maximum E(x, y) among three processing windows.