Mesodynamics from Atomistics: A New Route to Hall-Petch

 

Brad Lee Holian

Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM

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.