Multiscale finite element analysis of bulk nano-particle fabrication by a mechanical method

A heterogeneous multiscale finite element approach is used to study the bulk mechanical alloying (BMA) process for nano-particles. Mechanical characteristics such as the load versus displacement relations and the heterogeneous distribution of maximum principle stress are calculated from the global analysis to support the subsequent local, small-scale, analysis. A simple local quasi-microscopic analysis of a six-ball contacting problem is conducted to determine the stress distribution in a particular particle. The Griffith fracture criterion is adopted to determine whether a particle will be forced to break into smaller fragments. To simulate the mixing process in the extruding stroke, particles in each element are randomly redistributed according to the uniform random distribution rule. The volume shrinkage effect is also considered. The relationships between the particle size, the fracture stress, and the applied stress in BMA are thus established. The goal of this paper is to explore fundamental mechanism for the nano-particle formation in BMA of brittle materials such as NaCl and Li2NH.