**Mesodynamics**** from Atomistics: A New Route to Hall-Petch**

Brad
Lee Holian

Theoretical
Division,

87545

Mesoscale dynamics of polycrystalline
grains---mesodynamics---where the grain-grain
interactions have a functional form that is homologous to a simple, effective,
atomistic potential, can be derived under the following assumptions: (i) the mesoscopic nonlinear
elastic behavior must agree with the atomistic in compression; (ii) the mesoscale cold curve in tension represents surface, rather
than bulk cohesion, thereby decreasing inversely with grain size; and (iii) the
sub-grain dissipative processes are represented, to first order, by
relative-velocity viscous damping between grains. As a first consequence of this
formulation, the cubic anharmonicity of the mesopotential in the tensile regime is enhanced over the
atomistic potential by the square root of the grain size, which gives rise to a
dimensionality-independent yield strength that decreases inversely with the
square root of the grain size, in agreement with the familiar Hall-Petch ``Law'' of materials science.