Generalized type III internal stress from interfaces, triple junctions and other microstructural components in nanocrystalline materials

The microstructure in polycrystalline materials consists of four types of geometric objects: grain cells, grain boundaries, triple junctions and vertex points. Each of them contributes to internal stress differently. Due to experimental limitations, the internal stresses associated with the microstructural components are difficult to acquire directly, particularly for polycrystalline materials with nanometer-scale grain sizes. Using newly developed computational methods, we obtained the type III internal stress associated with each of these microstructural objects in a stress-free nanocrystalline Cu. We found significant variation of the internal stresses from grain to grain, and their magnitudes descended in the order of vertex point, triple junction, grain boundary and grain cell. We also examined the effect of grain size and temperature. The change in the internal stresses inside the grains is found to follow a scaling relation of Ad^-x, using the mean grain diameter d from our results. For pressure, we found x = 1 and the effective interface stress A ∼ 1 N m^-1, and for shear stress x = 0.75 and A ∼ 14.12 N m^-1. On the other hand, the directly calculated interface stress is about 0.32-0.35 GPa for hydrostatic pressure and 12.45-12.60 GPa for von Mises shear stress. We discuss issues in treating the two-dimensional interface stress and one-dimensional triple junction line tension in nanocrystalline materials, as well as the potential impact of the type III internal stress on mechanical behavior of poly- and nano-crytalline materials.