About the Keyhole Model
In additive manufacturing a laser beam melts the powder, and at high energy density of the laser also evaporation of the liquid metal occurs. The evaporation causes transfer of momentum from the metal to the vapour, i.e. a recoil. The conservation of total momentum then leads to a recoil pressure that pushes down the liquid/gas interface to form a cavity, also known as a keyhole. However, this free surface is computationally expensive to calculate due to the very dynamic movements of the keyhole. To reduce the complexity, the Additive Manufacturing (AM) Module has an analytic model based on [1994Kap] to pre-compute the keyhole shape and the corresponding mesh.
Example AM_06b: Using the Calibrated Heat Source for a 316L Steel includes the use of the keyhole model. The different processing conditions are selected to simulate both the conduction mode as well as the keyhole mode.
Also see examples AM_07, AM_08a, AM_08b, AM_09a, AM_09b, and AM_13 where the keyhole model is used with fluid flow, or AM_14 without fluid flow
The analytical keyhole model approximates the heat conduction by a moving line source where the keyhole shape is obtained by heat balance at the keyhole wall using average material properties. A point-by-point scheme compares absorbed power and conduction losses to obtain the local inclination angle of the keyhole walls.
Figure 1: Side-view of a keyhole and melt pool for the material SS316L with Gaussian beam radius of 40 μm and the absorptivity set to 40%.
When a keyhole is formed, the energy is transmitted into the material through numerous reflections within the keyhole (see Figure 2).
For metals with an absorption factor of around 30% the reflections can increase the effective absorption to values around 90% or higher of the total laser beam energy. In the Additive Manufacturing (AM) Module, multiple reflections are implemented in the analytical keyhole mode according to the Coviello publication [2022Cov]. This strategy allows for computation of a keyhole shape, including multi reflections using ray tracing.
Figure 2: Ray tracking of the laser beam reflected at the wall of the keyhole. Blue, green and red lines highlight the path for three rays. Gray lines represent a fraction of all the reflected rays.
The keyhole model is limited to the surface heat sources (Gaussian, Core-ring and Top-hat) without separate material properties for powder. An additional input is the beam quality factor M2 of the laser beam where the default value is 1.0. The beam quality factor is a measure of laser beam quality, it relates the beam divergence of a laser beam to the minimum focused spot size that can be achieved.
To include the keyhole feature, go to AM Calculator Heat Source Settings where you can enable this feature.
See About the Heat Source Models for background details about the heat sources.
References
[1994Kap] A. Kaplan, A model of deep penetration laser welding based on calculation of the keyhole profile. J. Phys. D. Appl. Phys. 27, 1805–1814 (1994).
[2022Cov] D. Coviello, A. D’Angola, D. Sorgente, Numerical Study on the Influence of the Plasma Properties on the Keyhole Geometry in Laser Beam Welding. Front. Phys. 9, 1–9 (2022).