PSI - Issue 69

Mohammadjavad Abdollahzadeh et al. / Procedia Structural Integrity 69 (2025) 2–19

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constant' are respectively abbreviated as T, T LV , and R. Figure 5 provides a schematic representation of the recoil pressure, the Marangoni effect, and the buoyancy force.

Fig.5: Schematic of the Recoil pressure, Buoyancy force, and Marangoni effect

2.4. Boundary Condition The power density of the laser beam is generally assumed to adhere to a Gaussian distribution. In the context of laser scanning processes, the beam traverses linearly along the positive x-axis at a constant scan speed. Consequently, the power density of the laser beam can be described by Equation 24 [33, 40, 41, 59]. In this equation, γ indicates the laser absorption of the powder bed, P stands for the laser power, R a shows the radius of the laser beam, and v represents the scan speed. Furthermore, the coordinates (x m , y m ) mark the initial position of the laser beam center. q= F CD B E +# exp ,−2 ("4" , ) # 6(#4# , ) # B +# - (24) The presence of evaporation is critical in maintaining an accurate representation of the melt pool's surface. Thus, the energy balance at the melt pool's surface requires an appropriate equation, as denoted by Equation 25. In this equation, h stands for the convective heat transfer coefficient, T 0 stands for the temperature of the surrounding environment, σ stands for the Stefan–Boltzmann constant, q(r) is the heat flux at the distance r from the laser center, and ε stands for the emissivity. q ev is the amount of heat that is lost as a result of evaporation, which can be depicted by Equation 26 [31, 33, 40]. q(r)=k ! ! < GHH⃗ +h(T−T @ )+σε(T J −T @J )+q ev (25) q evap = exp 62.52 + 6.121 − 'K < K-L − 0.5log T7 L + (26) Figure 6 illustrates the various energy interactions occurring between the melt-pool's free surface and its surroundings. This depiction highlights the significance of all heat transfer modes, namely conduction, convection,