A semi-analytical-numerical solution is theorized to describe the laser additive manufacturing via laser-bulk ceramic interaction modeling. The Fourier heat equation was used to infer the thermal distribution within the ceramic sample. Appropriate boundary conditions, including convection and radiation, were applied to the bulk sample. It was irradiated with a Gaussian spatial continuous mode fiber laser (λ = 1.075 µm) while a Lambert-Beer law was assumed to describe the laser beam absorption. A close correlation between computational predictions versus experimental results was validated in the case of laser additive manufacturing of silicon nitride bulk ceramics. The thermal field value rises but stays confined within the irradiated zone due to heat propagation with an infinite speed, a characteristic of the Fourier heat equation. An inverse correlation was observed between the laser beam scanning speed and thermal distribution intensity. Whenever the laser scanning speed increases, photons interact with and transfer less energy to the sample, resulting in a lower thermal distribution intensity. This model could prove useful for the description and monitoring of low-intensity laser beam-ceramic processing.
