Quantification of Interdependent Dynamics during Laser Additive Manufacturing Using X‐Ray Imaging Informed Multi‐Physics and Multiphase Simulation

Abstract Laser powder bed fusion (LPBF) can produce high‐value metallic components for many industries; however, its adoption for safety‐critical applications is hampered by the presence of imperfections. The interdependency between imperfections and processing parameters remains unclear. Here, the evolution of porosity and humps during LPBF using X‐ray and electron imaging, and a high‐fidelity multiphase process simulation, is quantified. The pore and keyhole formation mechanisms are driven by the mixing of high temperatures and high metal vapor concentrations in the keyhole is revealed. The irregular pores are formed via keyhole collapse, pore coalescence, and then pore entrapment by the solidification front. The mixing of the fast‐moving vapor plume and molten pool induces a Kelvin–Helmholtz instability at the melt track surface, forming humps. X‐ray imaging and a high‐fidelity model are used to quantify the pore evolution kinetics, pore size distribution, waviness, surface roughness, and melt volume under single layer conditions. This work provides insights on key criteria that govern the formation of imperfections in LPBF and suggest ways to improve process reliability.


The pressure exerted in irregular pores
To support our hypothesis regarding the high-pressure gas pore (Supplementary Figure 1), the pressure force exerted from the pore , must equal to or exceed the sum of the applied forces , acting on the pore, including buoyant force ( ), drag force( ), and Marangoni-driven force ( ): Firstly, we can assume that the pore is spherical, and it is insoluble in the liquid metal, the force exerted by the surface tension, , equals to the force exerted by the gas pressure, otherwise, the pore will shrink or grow.
Based on the ideal's gas law, increases proportional to the density, , of the vapour plume, is assumed to be the gas constant of 8.3145 J mol -1 k -1 , is the temperature of the vapour plume, is the surface area of the pore, and is the molecular mass of the vapour plume (argon + metal vapour) inside the pore. Although it is not possible to deduce and from our experiments, we know that must exceed the metallostatic pressure, , of the thermal fluid exerted onto the pore surface. Given that >> , we can use Laplace's law to estimate the metallostatic pressure: where is the gas-liquid interfacial energy (or surface tension) and is the pore equivalent radius.
Due to the lack of thermophysical data for Inconel 625, we assume the thermophysical properties of Inconel 625 are similar to Inconel 718. 718 is 1882 mN m -1 at 1609K [1], is ca. 44 μm (taken from 3D pore analysis) and hence the is estimated to be 85.6 kPa or 0.85 atm. This is nearly 9 times the chamber pressure of 10 kPa.
where the pore surface area, is 33685 μm 2 , and hence is calculated as 2.89 mN. We expect the is much greater than that of .
The buoyant force ( ) calculation: where is the pore equivalent radius, is the density of the liquid metal, and is the gravitational acceleration, 9.8 m s -2 . Here, we also assume the density of Inconel 625 is similar to that of Inconel 718 where = 7440 kg m 3 at 1609 K [1], and hence the is estimated as 2.59 x 10 -8 N.
The drag force ( ) calculation: where is the drag coefficient, is the density of the liquid, is the pore equivalent radius, is the velocity of the pore, and is the velocity of the liquid metal.
where is the Reynold number must be lower than 1000 and is given by: where is the density of the liquid, is the pore equivalent radius calculated from AVIZO, is the velocity of the pore, is the velocity of the liquid metal, and is the dynamic viscosity. To find the maximum drag force, we assume that exerted on the pore with zero velocity, i.e, is null, and therefore is ca. 0.009 Pa s (1638 K) [2] and is ca. 1 m s -1 based on the radiography analysis. and are estimated as 1.27 and 72.7, respectively. is calculated as 6.46 x 10 -7 N.
The Marangoni-driven force ( ) calculation: Where is the temperature-dependent surface tension coefficient and is the temperature gradient

Powder characterisation
The morphology of a virgin nitrogen gas atomised Inconel 625 powder (LPW Technology Ltd., UK) was examined by a JEOL JSM-6610LV scanning electron microscope (SEM). Its particle size distribution was extracted using SEM images and image analysis techniques depicted in ref [3]. The showing an open pore on a powder particle and (b) the particle size distribution.

Phase identification by X-ray diffraction
The Inconel 625 powder and AM tracks were examined by XRD for phase identification using a Smartlab diffractometer (Rigaku, Japan) and Profex [5]. The SmartLab was set with a 5º soller slit, two 15 mm wide receiving slits, and a 2D detector (Rigaku's HyPix 3000, Japan). The X-ray beam (45 kV and 200 mA) was set to a 200 µm spot using a collimator. The position of the X-ray source and the sample was aligned using a video camera (located inside the diffractometer) and the Smartlab guidance software (Rigaku, Japan). We calculated the lattice parameters using Bragg's law on the acquired XRD patterns. X-ray diffraction (XRD) and phase identification were also performed using a PANalytical X′Pert Pro MPD series automated spectrometer (Malvern Instruments, UK) with a Cu Kα radiation (λ = 0. 1540 nm) and 2 angles ranging from 20° to 100°. Data analysis was carried out using open-source software -Profex [5]. The XRD analysis (Supplementary figure 4) only shows the presence of γ matrix in the Inconel 625 powder and AM tracks. The calculated lattice parameter, a, for powder and AM tracks is 3.599 Å ± a maximum scatter of 0.002 (see details in Supplementary Table   4) and is very similar to the reported value in ref [6].   ).