Theoretical study of the response of 12 cubic metals to uniaxial loading

Abstract

The theoretical mechanical response of 12 cubic metals (Al, Cu, Mo, Na, Li, K, Rb, Nb, Fe, Ni, Au, and Ag) to unconstrained uniaxial loadings, coaxial with each of the three principal symmetry directions, is analyzed, at finite strain, in the framework of the embedded-atom method model calculations. The models have been formulated to reproduce, identically, empirical values of the three second-order elastic moduli ${(C}_{11},$ ${C}_{12},$ and ${C}_{44})$ and the six third-order elastic moduli (${C}_{111},$ ${C}_{112},$ ${C}_{123},$ ${C}_{144},$ ${C}_{166},$ and ${C}_{456}),$ and thus both the linear (harmonic) and nonlinear (anharmonic) response of the metals is represented in the computations. The mechanical behavior, including theoretical strengths, is strongly influenced by crystalline symmetries and bifurcation phenomena. Characteristic anisotropies, both at infinitesimal and at finite strain, are associated with each of three subgroups, i.e., the fcc metals, the bcc alkali metals, and the bcc group-V and group-VI transition metals. The behavior of bcc Fe is intermediate to that of the bcc alkalis and that of the group-V and group-VI transition metals. For the fcc metals under [100] loading, the maximum stress generally is about 20--50 % of the value of Young's modulus, although a potential instability associated with the vanishing of the elastic moduli combination ${C}_{22}\ensuremath{-}{C}_{23}$ occurs at stresses of about 10--25 % of Young's modulus. Also, for the fcc metals, the maximum tensile stress in [111] loading is generally comparable with that in [100] loading, but in [110] loading, the maximum stresses are only about 2--5 % of the respective Young's modulus values. By contrast, in the bcc alkali metals, the maximum tensile stress in [100] loading is only about 1--3 % of Young's modulus, while in [111] and [110] loading, these percentages are about 10% and 30--35 %, respectively. The relative anisotropy of the bcc transition metals at finite strain is much less than that of the bcc alkali metals. For example, the maximum theoretical stresses in Nb range from about 25 GPa (in [100] loading) to 70 GPa (in [111] loading); for bcc Na, these values range from about 0.04 GPa (in [100] loading) to 2 GPa (in [110] loading).