Fig. 1: One-dimensional law for keyhole aspect ratio controlled by the Keyhole number.

a Identified scaling law, which is universal because all the data collapse to a single curve, even though they correspond to various laser power (100–520 W), scan speed (0.3–1.2 m/s), laser spot size (44–70 µm), and three different materials (Ti-6Al-4V (Ti64)², Aluminum alloy 6061 (Al6061), and Stainless Steel 316 (SS316)). Time-dependent keyhole depth is measured from high-speed X-ray images at a 20-µs interval for each process condition. The maximum and minimum of keyhole aspect ratio during the time period when the laser scans 2 mm length at the middle of the sample are marked as vertical error bars. Horizontal error bars indicate 3% error amount to account for uncertainties of the process parameters and material properties. b Operando X-ray image series with a 20-µs interval showing the keyhole and melt pool morphologies in the stable keyhole region of Al6061. Laser power is 416 W and scan speed is 0.6 m/s. c Operando X-ray images showing keyhole morphologies in the chaotic keyhole region of Al6061. Laser power is 520 W and scan speed is 0.3 m/s. The fusion boundary (outlined by the black dashed line) can be identified by the X-ray imaging because of the density difference inside and outside the fusion region (some operando X-ray images without dashed lines are shown in Supplementary Fig. 10).