2.1 Opening gap experiments
A multi-mode fibre laser (IPG, maximum power output 15 kW) was used for the experiments. The laser beam was used in focal position and slightly inclined (7°) to avoid back-reflections into the fibre. A power of 3 kW at a welding speed of 3 m/min and Argon shielding through a side-gas nozzle at 18 L/min was applied for all experiments.
In order to evaluate the gap bridgability, an opening gap experiment was set up (Fig. 1). The laser beam was moved from the practical zero-gap along the 100 mm long sheets that showed a gap of 0.6 mm at the end of the welding process. The gap width at failure was extracted as a measure of gap bridgability [13].
During the welding, a high-speed camera (Photron) was used to visualize the processing zone at a recording frame rate of 4000 fps in combination with an illumination system (Cavitar). From the videos, the melt pool lengths and widths were measured.
2.2 Beam shapes
Refractive beam shaping optics were used to form various multi-spot beam shapes. The quattroXX optic (Adloptica, Berlin, Germany) gives up to four separate laser spots in a square of is 0.68x0.68 mm using a 150 mm collimator and 250 mm focusing lens. The peaXXus optic (Adloptica, Berlin, Germany) gives a square of 0.45x0.45 mm with up to nine spots. The analyzed beam profiles and related high-speed images are shown in Fig. 2.
2.3 Melt pool appearance calculations
In order to model the circumstances that can lead to a break-up of the melt bridge between the joining partners during welding, a simplified analytical model was developed. The model considers the melt pool dimensions (extracted from high-speed images) and predicts the keyhole height based on surface tension effects in the melt pool.
The available material \({A}_{melt}\) and volume \({V}_{melt}\) for creating the melt pool was calculated as the cross-sectional area and along the melt pool length \(l\), respectively (Fig. 3a) to
\({A}_{melt}=\left(s-g\right)\bullet t\) \({V}_{melt}={A}_{melt}\bullet l\) (1)
with the melt pool width \(s\), the gap width \(g\) and the sheet thickness \(t\).
The melt pool surface height \(h\) (yellow line in Fig. 3) was assumed to follow a logarithmic curve from behind the keyhole to the rear of the melt pool along the melt pool length \(l\) as a fit from high-speed imaging observations of the melt pool surface.
$$h\left(l\right)=0.1\bullet ln\left(l\right)+0.4$$
2
Since the main acting force on the melt pool surface behind the keyhole is the surface tension, the local curvature of the melt pool surface along the melt pool length and width must be equal in value with different curvature to form a stable system (Young-Laplace equation):
$$\frac{\gamma }{{R}_{1}}=-\frac{\gamma }{{R}_{2}}$$
3
with the surface tension \(\gamma\) of the material and the radii of the two curvatures \({R}_{1}\) and \({R}_{2}\) both denoted to \(R\) (Fig. 3b).
The area \(A\) (Fig. 3b) was calculated along the melt pool length with the circle length \(b\) to
$$A=\frac{R\bullet b}{2}-\frac{s\bullet \left(R-h\right)}{2}$$
4
The total area was derived by integrating along the melt pool length \(dl\) and compared to the available melt volume \({V}_{melt}\). The remaining keyhole height \(k\) was derived in case enough material is available to establish a keyhole.
2.4 Numerical melt flow analysis
A numerical fluid-dynamic model was developed to simulate the temperature field and melt flow characteristics when using different beam shapes. The keyhole dimensions were extracted from the high-speed images and the keyhole was inserted as a cylinder into the computation domain, penetrating the whole sheet (Fig. 4).
Mesh refinement was used around the keyhole in order to resolve the expected high thermal gradients and fast melt flows. The material was modelled as a fluid with high viscosity moving through the computational domain at the welding speed. The material was assumed to be pure iron. When the melting temperature is reached, the viscosity is set to the real material viscosity and gravity and Marangoni effects are considered to model the melt flow.
All process parameters were chosen as used in the experiments. No gas flow was assumed. The energy input was modelled using volumetric heat sources with Gaussian profiles, using one profile for the single spot welding and multiple spots arranged according to the experimental possibilities. Both temperature distributions and melt flow patterns were extracted from the simulation results.