Ultrasonic determination of single crystal sapphire fiber modulus

Abstract

Single crystal α-Al2O3, (sapphire) fibers of ∼ 100 μm diameter have recently emerged as candidates for stiffening and strengthening high temperature composites. The Young's modulus of these fibers depends upon their crystallographic orientation, ranging from a high of 461 GPa for thec-orientation to a low of ∼373 GPa for orientations 45° off thec-axis. A deviation of the fibers' axial orientation from the c-axis and thus a reduction in the fibers' axial modulus can sometimes occur during the fiber growth process, and so a simple reliable method is needed to characterize the modulus and/or orientation of the fibers. A laser generated-piezoelectric transducer detected ultrasonic method has been used for this purpose. It has been found that a clear correlation exists between the velocity of the first arriving ultrasonic signal and the deviation of the fiber's axis from thec-axis. The measured velocity is found to be in reasonably good agreement with the calculated bar velocity,ν b =√E/ρ, for the fiber, providing an estimate of the fiber's orientation dependent Young's modulus. The small differences between the measured and the calculated velocities are believed to be caused by a combination of measurement errors, uncertainties in the reference elastic compliance constants of α-Al2O3 and the presence of small volume fractions of pores and other (low modulus) aluminum oxide phases in the fibers.