Diffusional Viscosity of a Polycrystalline Solid

TLDR

Nabarro proposed that self‑diffusion under shear can make a polycrystalline solid behave like a viscous fluid, potentially explaining creep at very high temperatures and low stresses. The study proposes that only grain boundaries with large orientation differences act as diffusion sources or sinks, so creep depends on their configuration, and calls for further experiments. A quantitative theory is presented that calculates creep rates and effective viscosities for aggregates of quasi‑spherical grains and cylindrical‑grain wires, including the effect of tangential stress relaxation at grain boundaries. Comparison with high‑temperature creep data for wires supports this theory but remains only partially satisfactory.

Abstract

According to a suggestion of Nabarro, any crystal can change its shape by self-diffusion in such way as to yield to an applied shearing stress, and this can cause the macroscopic behavior of a polycrystalline solid to be like that of a viscous fluid. It is possible that this phenomenon is the predominant cause of creep at very high temperatures and very low stresses, though not under more usual conditions. The theory underlying it is developed quantitatively, and calculations of rate of creep, or equivalently of effective viscosity, are given for aggregates of quasi-spherical grains and for wires composed of cylindrical grains. Allowance is made for the effect of tangential stress relaxation at the grain boundaries. It is suggested that mosaic boundaries and boundaries between grains of nearly the same orientation may be unable to serve as sources or sinks of the diffusion currents, in which case the creep rate will depend only on the configuration of grain boundaries having a sizable orientation difference. Numerical comparison of the theory with experiments on the high temperature creep of wires favors this view, but is not entirely satisfactory. Suggestions for further experiments are made.