A mean field approach including an internal length scale was developed in order to capture the particle size effects on the overall mechanical behavior of particle-reinforced alloys. A generalized self-consistent scheme (with coated particles) was employed, with a new “phase” representing the “layers” where orderly dislocations between the matrix and the particles were present. The thickness of these “layers” was the internal length scale introduced in the model. It was determined dynamically by using a one-dimensional field dislocation mechanics model, where localized geometrically necessary dislocation densities accommodate the lattice incompatibility between matrix and inclusions. The beneficial influence of this scheme, as compared to mean field approaches, was shown from comparisons with experimental data on the particle size effects in Al/SiC composites.

On Particle Size Effects: an Internal Length Mean Field Approach using Field Dislocation Mechanics. V.Taupin, S.Berbenni, C.Fressengeas, O.Bouaziz: Acta Materialia, 2010, 58[16], 5532-44