Issue 53

P. Ferro et alii, Frattura ed Integrità Strutturale, 53 (2020) 252-284; DOI: 10.3221/IGF-ESIS.53.21 258 is the reason why in powder-scale models the volumetric heat source is not a good choice. For example, in SLM, heat is generated where the laser beam strikes the particle surface, and then it is diffused into the particle. Even the shadowing effect, where some bottom particles surfaces could be prevented from heating by shadows of other top particles, is a unique feature in PBFPs [34]. By using a volumetric heat source, melting occurs at anywhere inside the particle simultaneously. Thus, neither partial particles melting, nor the shadowing effect could be captured. Li and Tan [43] demonstrated how the light scattering through air voids dramatically change the distribution of energy absorption profile. It is experimentally verified that the total energy absorption of the powder depends on its parameters (size particle distribution, packing density, and so on) and is much higher than that absorbed by the bulk material [44, 45]. In literature, the Ray Tracing (RT) Model is used to capture the interaction between the still solid powder layer and the heat source [43,46]. Particles are assumed as rigid spheres fulfilling the relation , were D is the average diameter and λ is the wavelength. The Gaussian power distribution of the beam is then divided in a sufficient number of rays. Each ray is assigned with a certain size, a direction, and amount of power. Reflection on every gas-metal interface and propagation in the gas between two consecutive interfaces is explicitly studied for every ray until it is totally absorbed or reflected outside the power bed. Upon the incidence of a ray on the surface of a particle, a portion of its power is absorbed by the particle surface and the remainder power goes to the reflected ray. The law of reflection determines the direction of the reflected ray, and the absorptivity is calculated by Eq. (5), A(  )  1  1 2 (ncos   1) 2  k 2 cos 2  (ncos   1) 2  k 2 cos 2   (n  cos  ) 2  k 2 (n  cos  ) 2  k 2       (5) where γ is the incident angle and n and k are the optical constant of the material. Some authors [34,47] simplified the RT model by considering only the first laser-metal interaction without reflection. Using the RT model, the following conclusions were reached in literature [43, 46]: 1) a bed structure has a higher absorption and a deeper laser penetration compared to a flat surface (the powder bed (PB) structure can better enhance the absorption for materials with low absorptivity); 2) absorption distribution along the laser shooting direction doesn’t follow an exponential decay, rather, it increases until it reaches a “peak” and drops steeply after that; 3) thin powder bed has higher absorption near the substrate. The total absorption of thin PBs is of the same magnitude as those of thick PBs due to the enhancing effect of the substrate; 4) different laser absorption is calculated using smooth and wrinkled particles models: diffuse mode, due to not mirror-like particle surface, gives the best approximation. Molten pool Molten pool and parameters influencing its shape have been studied in literature by fluid-dynamic computation [48]. Vaporization/keyholing, spatter, surface tension-driven fluid flow, recoil pressure and porosity formation are some of the complex phenomena that can be studied by computational fluid dynamics (CFD). Results coming from powder deposition and power-source interaction are used as input for the fluid-dynamic analysis [46, 41, 34]. The laser heat-driven fluid flow problem is defined by a set of equations such as the conservation of mass (Eq. 6), ( ) 0 t        u (6) ( ρ is the density, t is the time, u is the flow velocity), the volume fraction conservation (Eqs. 7), 1 2 1 ( ) 0 t            u (7) (where  1 and  2 are the solid/liquid metal and the gas volume fractions, respectively) and the Navier-Stokes equation (Eqn. 8),  D/  1