Reconstruction of depth profiles of thermal conductivity of case hardened steels using a three-dimensional photothermal technique

A method of retrieving thermophysical depth profiles of continuously inhomogeneous materials is presented both theoretically and experimentally using laser infrared photothermal radiometry. This method represents the three-dimensional (3D) extension of earlier one-dimensional thermal-wave inverse-problem techniques for reconstructing inhomogeneous thermal-conductivity or diffusivity depth profiles. A 3D theoretical model suitable for characterizing solids with arbitrary continuously varying thermophysical property depth profiles and finite (collimated or focused) laser beam spotsize is developed. A numerical fitting algorithm to retrieve the thermophysical profile was demonstrated with three case hardened steel samples. The reconstructed thermal conductivity depth profiles were found to be well anticorrelated with microhardness profiles obtained with the conventional indenter method.