Functionally graded materials (FGMs) are widely applied in aerospace, energy, biology and other fields. Simultaneous determination of the thicknesses of all the graded layers is of great importance in evaluating the quality of an FGM. A model is set up to characterise the ultrasonic
waves reflected from an FGM composed of thin layers at normal incidence. The reflection spectrum is derived to simultaneously obtain the thicknesses of the various graded layers. To prove the feasibility of the proposed method, it is applied to measure the layer thicknesses of a prepared Al-Ti
bi-layered material specimen without delaminations. An inverse algorithm based on the Gauss-Newton method is introduced to determine the thicknesses by comparing the theoretical and measured reflection spectra. The effects of the frequency bandwidth of the transducer on the thickness convergence
zones and the thickness measurement results are investigated. The sensitivity of the proposed method to the thickness parameters is studied. The results indicate that the frequency bandwidth plays an important role in the thickness measurement. The relative thickness errors of the Al layer
and the Ti layer in this experiment are –5.28% and +2.77% using 5 MHz and 15 MHz transducers. It is concluded that a combination of reflection spectra and inverse techniques can be employed to simultaneously obtain the graded layer thicknesses.
Оптические свойства кремниевых нанопилларов со встроенным вертикальным p-n-переходом
