Rigidity Modulus of Beta-Brass Single Crystals

The rigidity modulus of ten beta-brass single crystals has been measured as a function of crystal orientation and of temperature from 25° to 500°C by the method of the composite piezoelectric oscillator. The reciprocal of the rigidity modulus, $\frac{1}{G^{\prime }}$, 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 × ${10}^{-12\mathrm{}}$ ${\mathrm{cm}}^2$/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, $G_{}^{\prime }{}_{\mathrm{}\left[100\right]\mathrm{}}{}^{}=17.3\mathrm{}\times {10}^{11}$ dyne/${\mathrm{cm}}^2$, and a minimum in the [111] direction, $G^{\prime }\mathrm{}\left[111\right]=1.35\mathrm{}\times {10}^{11}$ dyne/${\mathrm{cm}}^2$, and at the critical temperature, $G^{\prime }\mathrm{}\left[100\right]=13.5\mathrm{}\times {10}^{11}$ dyne/${\mathrm{cm}}^2$ and $G^{\prime }\mathrm{}\left[111\right]=1.06\mathrm{}\times {10}^{11}$ dyne/${\mathrm{cm}}^2$. The elastic anisotropy as given by $\frac{G^{\prime }\mathrm{}\left[100\right]\mathrm{}}{G^{\prime }\mathrm{}\left[111\right]\mathrm{}}$ is 12.8 at room temperature, decreases to 12.3 at 250°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.