Rigidity Modulus of Beta-Brass Single Crystals

Abstract

The rigidity modulus of ten beta-brass single crystals has been measured as a function of crystal orientation and of temperature from 25\ifmmode^\circ\else\textdegree\fi{} to 500\ifmmode^\circ\else\textdegree\fi{}C by the method of the composite piezoelectric oscillator. The reciprocal of the rigidity modulus, $\frac{1}{{G}^{\ensuremath{'}}}$, is linearly related to the orientation function. When these data are combined with Rinehart's previous measurements of Young's modulus, the principal elastic parameters are found to be 3.88, --- 1.52 and 0.578 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{2}$/dyne, respectively, at room temperature. Curves and tables give them as functions of temperature up to and slightly beyond the critical temperature for order-disorder. At room temperature, the rigidity modulus is a maximum in the [100] direction, $G_{}^{\ensuremath{'}}{}_{[100]}{}^{}=17.3\ifmmode\times\else\texttimes\fi{}{10}^{11}$ dyne/${\mathrm{cm}}^{2}$, and a minimum in the [111] direction, ${G}^{\ensuremath{'}}[111]=1.35\ifmmode\times\else\texttimes\fi{}{10}^{11}$ dyne/${\mathrm{cm}}^{2}$, and at the critical temperature, ${G}^{\ensuremath{'}}[100]=13.5\ifmmode\times\else\texttimes\fi{}{10}^{11}$ dyne/${\mathrm{cm}}^{2}$ and ${G}^{\ensuremath{'}}[111]=1.06\ifmmode\times\else\texttimes\fi{}{10}^{11}$ dyne/${\mathrm{cm}}^{2}$. The elastic anisotropy as given by $\frac{{G}^{\ensuremath{'}}[100]}{{G}^{\ensuremath{'}}[111]}$ is 12.8 at room temperature, decreases to 12.3 at 250\ifmmode^\circ\else\textdegree\fi{}C and has a value of 13.0 at the critical temperature. The bending-torsion effect was found to be large and in agreement with theory.