Predictive analytical modeling of single-track cross-sections in directed energy deposition

Directed energy deposition (DED) enables the fabrication and repair of metallic components with high geometric flexibility. However, variations in laser power, travel speed, and mass flow rate critically affect the geometry of the deposited tracks, particularly their cross-sectional profiles. While simulations have shown acceptable approximations, they are typically computationally expensive. This study proposes and validates a low-cost analytical model for predicting single-track cross-sections using geometric curve fitting and a full factorial 3 k design. The model incorporates key process parameters and material thermophysical properties, using AISI 304 as the substrate and AISI 316L powder. Experimental validation under standoff distances of 3.5 mm and 4.0 mm yielded root mean square errors (RMSE) as low as 0.093 for width and 0.025 for height, particularly at a mass flow rate of 3.12 g/min. Among the geometric fits evaluated, the semielliptical model provided better accuracy for height predictions. Beyond performance metrics, residual analysis revealed that laser power had the strongest influence on model deviations (r = 0.64, p < 0.001 at 3.5 mm), followed by mass flow rate (r = 0.39, p < 0.05 at 4.0 mm), while travel speed showed weak, non-significant effects. These results highlight the model’s effectiveness in capturing geometric trends and identifying key process sensitivities, offering a physically grounded tool for process optimization in DED applications.