Abstract
In typical coarse-grained alloys, the dominant plastic deformations are dislocation gliding or climbing, and material strengths can be tuned by dislocation interactions with grain boundaries, precipitates, solid solutions, and other defects. With the reduction of grain size, the increase of material strengths follows the classic Hall-Petch relationship up to nano-grained materials. Even at room temperatures, nano-grained materials exhibit strength softening, or called the inverse Hall-Petch effect, as grain boundary processes take over as the dominant deformation mechanisms. On the other hand, at elevated temperatures, grain boundary processes compete with grain interior deformation mechanisms over a wide range of the applied stress and grain sizes. This book chapter reviews and compares the rate equation model and the microstructure-based finite element simulations. The latter explicitly accounts for the grain boundary sliding, grain boundary diffusion and migration, as well as the grain interior dislocation creep. Therefore the explicit finite element method has clear advantages in problems where microstructural heterogeneities play a critical role, such as in the gradient microstructure in shot peening or weldment. Furthermore, combined with the Hall-Petch effect and its breakdown, the above competing processes help construct deformation mechanism maps by extending from the classic Frost-Ashby type to the ones with the dependence of grain size.
