Measurement of Elastic Constants of Polycrystals by the Resonance Method in a Cylindrical Specimen

Abstract

An analytical method of three-dimensional vibrations on a cylindrical specimen was developed, in order to determine the elastic constants by the resonance method. As trial functions on the Rayleigh-Ritz method of eigenvalue approximation, trigonometrical functions on circumference and Legendre polynomials along a column were used. A finite element method was applied to concentric cylinders divided in the radial direction. Many resonant frequencies in a small cylindrical specimen (φ6×6 mm) were easily measured over 20th of the higher mode by the newly devised techniques. The elastic constants G=26.2 GPa, ν=0.345, E=70.4 GPa of pure aluminum and G=30.2 GPa, ν=0.33, E=80.3 GPa of Al-12%Si eutectic alloy were obtained.