Model based laser-ultrasound determination of hardness gradients of gas-carburized steel

Gas carburizing is a common industrial process utilized for case hardening of low carbon steels. However, there is a lack of non-destructive evaluation systems for the measurement of hardness-depth profiles. We propose a novel measurement method for the determination of hardness-depth profiles of two-step gas carburized steel specimens. The method is based on the measurement of broadband laser excited Rayleigh waves. Rayleigh waves were generated by a pulsed Nd: YAG laser in the thermoelastic regime and measured with a heterodyne Mach-Zehnder interferometer in the near-field. From two measurements with different source to receiver distances the dispersion diagrams were calculated by means of the phase spectral analysis method. In order to simulate the observed dispersive behavior of the Rayleigh waves, first the two-step gas carburizing process was simulated using solutions of the diffusion equation. The resulting continuous hardness profile was then discretized into up to 100 layers. Thereafter the Rayleigh wave dispersion diagram was calculated from the discretized stack of layers using a delta-matrix formulation of the Thomson-Haskell transfer matrix method. In order to obtain best fitting hardness profiles, the simulated dispersion diagrams were fitted to measurements with a curve fitting algorithm. Comparison of the Rayleigh wave inversion method with destructively obtained Vickers hardness profiles shows good quantitative agreement.