Anharmonicity in Noble Metals; Nonlinear Elasticity in Whiskers

Abstract

A nonlinear stress-strain relation has been observed in copper whiskers with [100], [110], and [111] orientations using a sensitive apparatus for tensile-stress measurement. The nonlinearity was considered to be due to the lattice anharmonicity of the crystal. The nonlinearity constants of the specimens, which represent the amount of the deviation from linear elasticity, have been found to depend apparently on their yield stresses. Whiskers with low yield stresses showed large values of the nonlinearity constants. It was assumed that there was some kind of defects on the specimen surfaces and that the stress concentrations near the defects produced by the external forces lowered the yield stresses and increased the apparent nonlinearity constants. A simple analysis based on this assumption was enough to explain the experimental results, and the true nonlinearity constants which should be possessed by crystals without defects have been evaluated. The values of the true nonlinearity constants thus determined experimentally for three crystal orientations were consistent with the theoretical values from higher-order elasticity theory.