Incorporating crystallographic orientation in the development of resonant ultrasound spectroscopy

Abstract

Resonant ultrasound spectroscopy (RUS) measures the mechanical resonance of solids and uses the resonance frequencies to extract a complete set of elastic constants of the solid material. One of the advantages of the RUS method is its applicability to small single crystals. In the past two decades, the RUS technique has gained more acceptance as a nondestructive method to measure elastic properties. The inherent assumptions in the conventional RUS algorithm include free boundary condition on the specimen faces and the faces of the specimens are normal/parallel to the principal crystallographic axes. This assumption is fulfilled through a time consuming procedure that typically involves multiple iterations of sample cutting and inspection using an x-ray Laue method. Such an intensive method is not suitable for many samples in engineering applications. To estimate the elastic constants of such samples, a modified RUS algorithm has been developed to incorporate the sample crystallographic orientation expressed in terms of Euler angles. This modified RUS algorithm has been applied to estimate the elastic constants of cubic and hexagonal crystal structure samples with known orientation. The obtained values are comparable to literature values. With the incorporation of crystal orientation into the RUS algorithm, the elastic constants of samples with random crystal orientation were obtained.