Ideal and ultimate tensile strength of a solid body

The mechanical stability of an ideal elastic solid under infinitesimal and finitesimal changes in its state parameters is considered. The temperature and density dependences of the isothermic moduli of bulk compression $K$, simple shear $\mu$, and tetragonal shear $\mu'$ in a Lennard-Jones face-centered cubic (FCC) crystal have been determined by means of molecular dynamic experiments in the region of stable and metastable states. It has been shown that the crystalline phase remains stable under long-wave spatially nonuniform density fluctuations on the spinodal $(K = 0)$ at pressures below the pressure of the endpoint of the melting line $(p < p_K < 0)$. Here, the critical nucleus formation work is also finitesimal. Hence, spinodal states in quasisteady-state processes at $p < 0$ not only are attainable, but the transition across the spinodal without destroying the homogeneity in the substance also proves to be feasible. In this case, the boundary of the ideal strength of a solid is set by the vanishing of the uniaxial compression modulus $\tilde K$ for a certain specified deformation direction. The spinodal also is not the boundary of the ideal strength of a solid at positive and small negative pressures. A solid loses its ability for a restorative response to finitesimal spatially nonuniform density disturbances before the spinodal $(\tilde K = 0)$ is attained.