A Modified Heat Source Model for Off-Axis Directed Energy Deposition of SS316L: Finite Element Modelling and Experimental Validation

Reliable prediction of the transient temperature field is essential for controlling melt-pool geometry, cooling rate, and microstructure in directed energy deposition-laser beam (DED-LB). Conventional Goldak and modified Gaussian double-ellipsoidal (GDE) heat sources retain an exponentially decaying energy distribution and therefore under-represent the nearly uniform energy input of high-power top-hat lasers, whereas existing top-hat models are mainly surface heat fluxes for normal-incidence processing. Neither accounts for the elongated, shallower footprint of an inclined beam in off-axis DED-LB. This study proposes a top-hat double-ellipsoidal (THDE) heat source that combines a uniform volumetric energy distribution with an explicit geometric correction for oblique incidence. The model was implemented in Abaqus using a DFLUX subroutine and progressive element activation and validated against a single SS316L track deposited on mild steel (3.3 kW, 1500 mm min−1 25° inclination) using infrared thermography, an embedded thermocouple, and metallography. The THDE model reproduced the elongated melt pool and predicted the track width within 6%, against 17% for the GDE model, while both models predicted the height within 7–9%. The peak surface and subsurface temperatures differed from the measurements by 8.9% and 2.4%, and the liquidus–solidus cooling rates were 6–9% lower, within the temporal resolution of the 27 Hz camera. These results indicate that the proposed THDE model offers an efficient representation of off-axis top-hat heat input at the track scale in off-axis DED-LB. The validation is currently limited to a single track, one set of process parameters, and its extension to multi-track and multilayer deposition is the subject of future work.