A substantial fraction of the volume in a nanocrystalline material was occupied by intercrystalline grain boundaries; as the grain sizes decreased below about 30nm these boundaries begin to play a major role in the inelastic deformation of the material. For such grain sizes, and under ambient pressures and moderate strain rates, dislocation-based slip processes in the grain interiors were essentially shut off and inelastic deformation occurred primarily by slip and separation at the grain boundaries. Here, a continuum mechanical theory of such grain boundaries was developed which was based upon the notion of a cohesive interface across which the displacement suffers a jump discontinuity, an approach that permitted the development of elastic and inelastic descriptions of slip and separation. As a means of capturing the small length-scales involved, allowance was made for a microscopic polar stress that expends power over the surface gradient of the inelastic slip rate. Using the principle of virtual power interfacial force balances were deduced for the grain boundaries which, when combined with thermodynamically consistent constitutive equations, resulted in visco-inelastic flow rules for the grain boundaries in the form of partial differential equations. A second application of the virtual-power principle yields non-standard conditions that balance grain-boundary tractions at a triple junction.

Nanocrystalline Grain Boundaries that Slip and Separate - a Gradient Theory that Accounts for Grain-Boundary Stress and Conditions at a Triple-Junction. M.E.Gurtin, L.Anand: Journal of the Mechanics and Physics of Solids, 2008, 56[1], 184-99