A three-dimensional, unsteady heat transfer model has been developed for predicting the temperature field in partially stabilized zirconia (PSZ) undergoing laser-assisted machining (LAM). PSZ is a semi-transparent ceramic which volumetrically absorbs, emits and scatters radiation across a spectral region extending from approximately 0.5 to 8 μm. As a first approximation, it is treated as optically thick within this spectral band, and the high density of scattering centers, as well as the random orientation of grain boundaries, permits the assumption of isotropic scattering. Accordingly, the Rosseland diffusion approximation is used to model internal radiative transfer. Since most of the CO2 laser radiation (λ = 10.6 μm) is absorbed in the first layer of control volumes adjacent to the surface, incident laser radiation is treated as a surface phenomenon.
The equivalent radiation conductivity of PSZ is strongly temperature dependent and enhances thermal energy transfer within regions of the workpiece which are close to the location of laser irradiation. However, the effective thermal conductivity of PSZ remains relatively low, even at the highest temperatures achieved during LAM, and is responsible for large temperature gradients near the irradiated surface of the workpiece. For representative operating conditions, comparative calculations are performed with and without the radiation model to assess the influence of volumetric radiation effects on the temperature field. Numerical simulations are also performed to consider the effect of operating conditions, such as the laser power, laser/tool feed and depth-of-cut, on thermal conditions in close proximity to the material removal zone. The results are contrasted with those for silicon nitride, which is an opaque ceramic that exhibits quasi-plastic deformation when its temperature is raised above a threshold value at the depth-of-cut and can therefore be machined with a cutting tool.