Elastic constant identification method for irregularly shaped solid materials based on resonant ultrasound spectroscopy

Abstract

Resonant ultrasound spectroscopy (RUS) is a well-established method for identifying the elastic coefficients of solid materials. The Rayleigh-Ritz method is usually used to calculate the natural frequencies of a sample, where the sample needs to be processed into certain regular bodies. This requirement is hard to meet for some materials with size limitations or special physical/chemical properties. To deal with these situations, a method that combines a finite element (FE) method and RUS is proposed in this paper to measure the elastic constants of an irregularly shaped solid. This method first measures the experimental resonant frequencies of a sample under ultrasonic excitation. Then, a micro-CT scan is used to obtain the three-dimensional shape information of the sample and a FE model is built to calculate the theoretical resonance frequencies. Finally, the Levenberg-Marquardt algorithm is chosen to optimize the elastic constants until the errors between the resonant frequencies calculated from the FE model and those determined experimentally reach a minimum. An irregularly shaped titanium sample was used to calibrate this method. The results show that the elastic constants of the irregular titanium sample estimated by this method were in good agreement with those of a rectangular titanium sample estimated by traditional RUS, with the relative differences below 4%. This study avoided the complicated processing of regular samples by traditional methods and makes it possible to measure the elastic properties of irregularly shaped solid materials.