Universal scaling laws of keyhole stability and porosity in 3D printing of metals

Zhengtao Gan*, Orion L. Kafka, Niranjan Parab, Cang Zhao, Lichao Fang, Olle Heinonen, Tao Sun, Wing Kam Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

76 Scopus citations


Metal three-dimensional (3D) printing includes a vast number of operation and material parameters with complex dependencies, which significantly complicates process optimization, materials development, and real-time monitoring and control. We leverage ultrahigh-speed synchrotron X-ray imaging and high-fidelity multiphysics modeling to identify simple yet universal scaling laws for keyhole stability and porosity in metal 3D printing. The laws apply broadly and remain accurate for different materials, processing conditions, and printing machines. We define a dimensionless number, the Keyhole number, to predict aspect ratio of a keyhole and the morphological transition from stable at low Keyhole number to chaotic at high Keyhole number. Furthermore, we discover inherent correlation between keyhole stability and porosity formation in metal 3D printing. By reducing the dimensions of the formulation of these challenging problems, the compact scaling laws will aid process optimization and defect elimination during metal 3D printing, and potentially lead to a quantitative predictive framework.

Original languageEnglish (US)
Article number2379
JournalNature communications
Issue number1
StatePublished - Dec 1 2021

ASJC Scopus subject areas

  • General
  • Physics and Astronomy(all)
  • Chemistry(all)
  • Biochemistry, Genetics and Molecular Biology(all)


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