The reduction of grain size to the nanometer range (˜2-100 nm) has led to many interesting materials properties, including those involving mechanical behavior. In the case of metals, the Hall-Petch equation, which relates the yield stress to the inverse square root of the grain size, predicts great increases in strength with grain refinement. On the other hand, theory indicates that the high volume fraction of interfacial regions leads to increased deformation by grain-boundary sliding in metals with grain size in the low end of the nanocrystalline range. Nanocrystalline ceramics also have desirable properties. Chief among these are lower sintering temperatures and enhanced strain to failure. These two properties acting in combination allow for some unique applications, such as low-temperature diffusion bonding (the direct joining of ceramics to each other using moderate temperatures and pressures). Mechanical properties sometimes are affected by the fact that ceramics in a fine-grained form are stable in a different (usually higher pressure) phase than that which is considered “normal” for the ceramic. To the extent that the mechanical properties of a ceramic are dependent on its crystal-lographic structure, these differences will become evident at the smaller size scales.
It is uncertain how deformation takes place in very fine-grained nanocrystalline materials. It has been recognized for some time that the Hall-Petch relationship, which usually is explained on the basis of dislocation pileups at grain boundaries, must break down at grain sizes such that a grain cannot support a pileup. Even some of the basic assumptions of dislocation theory may no longer be appropriate in this size regime. Recently considerable progress has been made in simulating the behavior of extremely fine-grained metals under stress using molecular-dynamics techniques. Molecular-dynamics (MD) simulations of deformation in nanophase Ni and Cu were carried out in the temperature range of 300–500 K, at constant applied uniaxial tensile stresses between 0.05 GPa and 1.5 GPa, on samples with average grain sizes ranging from 3.4 nm to 12 nm.