Evaluation of the Stiffness Coefficients for Beryllium from Ultrasonic Measurements in Polycrystalline and Single Crystal Specimens

The pulsed ultrasonic method has been applied to the determination of the stiffness coefficients for beryllium. The constants c₁₁=30.8×10¹¹ dynes/cm², c₃₃=35.7 were evaluated from compressional wave velocities in single crystals by extrapolating a plot of the effective stiffness coefficient versus sin²θ θ being the angle between the hexagonal axis and the direction of wave propagation) to the points θ=π2 and 2and 0. The values c₁₂=-5.8, c₄₄=11.0 were derived from an analysis relating the average effective stiffness stiffness coefficients for compressional and shear waves with the shear modulus and Lame's constant. The latter data were calculated from measurements of longitudinal and transverse body wave velocities in polycrystalline metal. To find the coefficient c₁₃=0.87, the established values for the other constants were employed in the general relation for the effective stiffness coefficient of the form Cₗ=f(c_jk^'s,θ). Several criteria have been used to assess the validity of the cⱼₖ data: (1) The ratio of c₁₁c₃₃ is in accord with the c/a ratio for the hexagonal close-packed structure of beryllium; (2) the compressional and shear wave anisotropy factors of c₃₃c₁₁=1.16 and c₄₄1/2(c₁₁-c₁₂)=1.68, respectively are in harmony with the observed transmission properties of polycrystalline beryllium; and (3) the experimental and theoretical curves for the directional variation of the effective compressional stiffness coefficient agree quite well.