Internal friction at grain boundaries in nanocrystalline material with pores

A mathematical model of the internal friction in a polycrystalline material with the nanoscale grain size is considered. Their boundaries contain pores, both in the triple joints of the grains and between them. Under the influence of the alternating normal boundary stresses, flat sections of the boundary are periodically active sources and sinks for vacancies. Due to the presence of these flows, the mutual displacement of adjacent grains is carried out. Depending on temperature, the diffusion length of the vacancies is smaller or compared with the distance between the pores. In the graph of the dependence of the internal friction on temperature, there is a break between the rectilinear sections. From the position of the fracture, the average size of the flat sections of the border can be estimated. The effective activation energy of the process in these cases depends on temperature and differs twice. At temperatures when the concentration of thermal vacancies in the boundary exceeds the geometrically necessary value of the concentration of structural vacancies, the activation energy increases even more. The transition temperature to this value is determined by the degree of imbalance of the boundary structure.

nanocrystalline material, grain boundaries, diffusion length, pores, vacancies, internal friction, activation energy