PSI - Issue 71

Ravi Prakash et al. / Procedia Structural Integrity 71 (2025) 325–332

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Fig. 3. Meshed assembly with adaptive non-linear mesh utility applied across the entire solution domain.

where the thermal conductivity (W/m/°C) in each direction is represented by the variables k i , k j , and k k . The rate of heat production per unit volume in the solution domain during the deposition phase is referred to as the heat capacity per unit (h cp ). In addition, the alloy under study has two more parameters: C p , or specific heat capacity (J/kg °C), and ρ, or density (kg/mm³). The current time in seconds is represented by t, while the scanning velocity (mm/s) along the X-axis is indicated by v. The present study employed a reputable double-ellipsoidal volumetric heat source to generate a molten pool. The subsequent spatial and temporal mobility of the laser beam facilitated metal powder deposition. The optimized double ellipsoidal heat source parameters used in the Goldak model were employed in the investigation (Kumar & Nagamani Jaya, 2023). This volumetric heat source primarily consists of a front ellipsoid and a rear ellipsoid, with semi-axes denoted as c f and c r , respectively. The following describes the energy distribution for the front ellipsoidal moving heat sources according to Goldak's double ellipsoidal moving heat source; further information and nomenclature are available in Ref. (Kumar et al., 2024). Q f (x, y, z) = 6√3 √ (−3 2 2 −3 2 2 −3 2 2 ) , (x ⩾ 0) (2) where Q f , the power distribution inside the front ellipsoid, is located under the ellipsoid along the X, Y, and Z axes. The parameter P stands for power in watts. The front ellipsoid-related weighting fraction of heat deposition is represented by f f , and the other parameters indicate the length of the transverse, depth, and longitudinal semi-axes of the ellipsoid, respectively. The boundary conditions of heat were applied by subjecting the deposited alloy to heat transfer through radiation, conduction, and convection, while the substrate material experienced conduction and convection only. The latent heat of fusion was incorporated to account for liquid-solid phase transformation (Gan et al., 2019). To simulate the metal deposition process, the *MODEL CHANGE tool in the ABAQUS ® 2020 software was used for element activation and deactivation. The "element birth technique" (Behseresht & Park, 2024) was employed, where wall elements were initially deactivated and then reactivated sequentially to match the laser's movement. A DFLUX subroutine based on Fortran and an interface programmed in Python were created to map the transient thermal field across the build/substrate structure. Structural modelling entailed solving a governing equation based on Lagrangian theory at every node throughout the solution domain to evaluate the thermo-mechanical behaviour of the built-substrate structure. The field of time temperature derived from the heat transfer analysis was utilized as input for calculating the residual stress field. The governing equations and mechanical boundary conditions required for sequentially coupled modelling over the 3D geometry are thoroughly discussed in references (Dandekar, 2024; Kumar & Nagamani Jaya, 2023). 4. Results and discussions A cuboid Ti-alloy component developed through multi-pass, multi-layer modelling enabled the observation of thermal field evolution and stress distribution during layer-by-layer deposition. In layered manufacturing, the temperature field is highly transient and spatially non-uniform. Fig. 4 represents the temperature contours during deposition of layers and after the completion of build part for different cases. The maximum temperatures after