Theory of the response of an fcc crystal to [110] uniaxial loading

The response of an fcc crystal to unconstrained [110] uniaxial loading has been studied theoretically. Numerical calculations were made of load, stress (${\sigma }_{110}$), lattice parameters, and elastic moduli ($C_{\mathrm{rs}}$) along the primary loading path, and the domain of $M$ stability (as defined by Hill and Milstein) was determined. The crystal model was that used by Huang et al. to study the shear of a crystal. In tension, the limit of $M$ stability was at the maximum load (with corresponding ${\sigma }_{110}=8.78\mathrm{}\times {10}^{10}$ dyn/${\mathrm{cm}}^2$ at a strain of 7.5%; these values are comparable to other estimates of the "theoretical strength" of crystals, including experimental values of whisker strengths). The domain of $M$ stability in compression was remarkably large, and the magnitude of ${\sigma }_{110}$ in compression at the limit of $M$ stability was about 100 times the maximum tensile stress. With very large compression, the Poisson's ratios along the two principal axes normal to the load approached zero, and the lattice tended to arrange itself with successive planes in a particular "two-dimensional close-packed relationship." This latter tendency, in a sense, can "explain" the difference in algebraic sign of the Poisson's ratios along the principal axes normal to the [110] direction in some fcc crystals. In elongation, the primary equilibrium path intersects the path corresponding to unconstrained [100] uniaxial loading of a fcc or bcc crystal at the invariant eigenstate $C_{22}=C_{23}$. The Poisson's ratios approach infinity as this state is approached along a primary equilibrium (but unstable) path. Such studies of crystal response are of interest in a variety of applications, including, possibly, martensitic transformations.