Formulating mesodynamics for polycrystalline materials
Abstract
For materials consisting of polycrystalline grains, we formulate a minimal basis for mesoscale dynamics—mesodynamics—where the mass points are individual mesoscale grains that interact via a shortranged and pairwiseadditive mesopotential. Newton's equations of motion for the grains are augmented by relativevelocity viscous damping between grains, representing subgrain dissipative processes. We require, at minimum, two things of the mesopotential: i) in compression, it must be consistent with the nonlinear elastic equation of state, and ii) under tension, the mesoscale bonding between two grains must reflect the fact that grains separate at their mutual interface (grain boundary) rather than in the bulk. We then show that a polycrystalline system interacting by this minimal mesopotential fails under tension at a yield strength that decreases inversely with the square root of grain size, with a predicted coefficient that agrees remarkably well with HallPetch experimental values.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 November 2003
 DOI:
 10.1209/epl/i200300178y
 Bibcode:
 2003EL.....64..330H
 Keywords:

 45.05.+x;
 62.20.Fe;
 83.60.La;
 General theory of classical mechanics of discrete systems;
 Deformation and plasticity;
 Viscoplasticity;
 yield stress