A dislocation model for the minimum grain size obtainable by milling

Primary among the processing techniques that are now available for synthesizing bulk nanocrystalline materials is ball milling, which produces nanostructures by the structural decomposition of large-grained structures as the result of severe cyclic deformation. It is well-documented that during milling, the grain size decreases with milling time, reaching a minimum grain size, d(min), which is a characteristic of each metal. In this paper, a dislocation model that redicts the value of d(min) as a function of material parameters, such as hardness, melting temperature, and stacking fault energy, has been developed. The model is based on the concept that d(min) is governed by a balance between the hardening rate introduced by dislocation generation and the recovery rate arising from dislocation annihilation and recombination. It is demonstrated that the model provides possible explanations for several recent observations regarding the characteristics of d(min). (C) 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.