Yield stress of ultrafine-grained or nanocrystalline materials with a bimodal grain size distribution

An attractive processing route for enhancing the yield strength of high-strength nanocrystalline metals and alloys while maintaining high ductility is to develop a bimodal grain size distribution (GSD), in which, supposedly, the finer grains provide strength, and the coarser grains maintain or even enhance ductility. We present a theoretical model predicting the strength of such a system, and show, analytically, how the yield stress is related to the various parameters of the bimodal GSD, such as volume fraction of the two components of the bimodal distribution and their standard deviations.