CONTINUOUS-DISTRIBUTION DISLOCATION MODEL OF INTERNAL FRICTION ASSOCIATED WITH THE INHOMOGENEOUS SLIDING ALONG HIGH-ANGLE GRAIN BOUNDARIES

Abstract
Basing on a continuous-distribution dislocation model of high-angle grain boundaries, an integral-differential equation governing the inhomogeneous sliding along the boundaries was set up. This equation consists of three terms. The first term is the shear stress produced by the dislocations with a given continuous distribution linear density, the second term is the applied shear stress and the third term is the Newtonian viscous resistant stress. This equation was solved approximately and the approximate formulae for the internal friction and modulus defect were obtained. For high-purity isotropic metals, the viscosity for grainboundary sliding is correlated with the diffusion coefficient along grain-boundary, D_b, by an expression similar to Einstein-Stokes formula. The optimum temperature of grain-Poundary internal friction peak for a number of pure metals calculated according to this model and sliding mechanism are fairly close to the corresponding experimentally observed values. It is shown that for impure metals, the viscosity of some grain boundaries is considerably changed by the selective segregation of impurities along them, so that another internal-friction peak (the solute peak) appears at a different temperature. Also, in anisotropic pure metals and in the presence of internal stress, the migration of grain boundaries may cause another high temperature internal-friction peak or a higher internal-friction background in addition to the grain-boundary peak associated with grain-boundary sliding.