SEDL / STP / STP1045-EB / STP24618S

Resonating-Orthotropic-Cube Method for Elastic Constants

Heyliger, P
assistant professorresearch metallurgistmaterials research engineer, Colorado State UniversityNISTNBS, Fort CollinsBoulder, ColoradoColorado

Ledbetter, H
assistant professorresearch metallurgistmaterials research engineer, Colorado State UniversityNISTNBS, Fort CollinsBoulder, ColoradoColorado

Austin, M
assistant professorresearch metallurgistmaterials research engineer, Colorado State UniversityNISTNBS, Fort CollinsBoulder, ColoradoColorado

Pages: 10    Published: Jan 1990

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Abstract

Following studies by Demarest (1969) and by Ohno (1976), we describe measurements and analysis that yield, from a single cube-shape specimen, in a single measurement, the complete set of anisotropic elastic-stiffness constants, the C^ij. Experimentally, we place a cubic specimen between two piezoelectric transducers, which excite and detect the cube's macroscopic free-vibration (fundamental-mode) frequencies, up to 10 MHz. From the specimen's shape, size, and mass, and from the measured resonance-frequency spectrum, we analyze for the C^ij within a given tolerance ϵⁱ: λi(Cij)-λi¯=ϵi. (No sum on i.) Here ƛⁱ relates to the measured resonance frequencies, and λⁱ represents eigenvalues calculated by a Rayleigh-Ritz method using Legendre-polynomial approximating functions. Legendre-polynomial orthogonality ensures a diagonal mass matrix [m], which simplifies the resulting eigenvalue problem: ([k]-λ[m]){x}={0}. For materials with certain symmetries, the coefficient matrix [k] reduces to a block-diagonal matrix, which reduces computational effort and simplifies vibration-mode identification.