Diffusional Viscosity of a Polycrystalline Solid

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.

Finite element modelling of creep cavity filling by solute diffusion

“…This solution is similar to the simplified solution of Herring [11], describing the axial diffusional growth of creep cavities, which means that like the 3D case, the time exponent for the diffusional flux tends to ν = 1 for large times.…”

“…Creep cavity growth by the diffusional flux of vacancies over grain boundaries has been described by Herring [11], and Hull and Rimmer [12], who propose that the driving force for vacancies to migrate to the creep cavities is a function of the applied stress. The effect of strain rate in the bulk material on the creep cavity growth was treated in finite-element calculations by Needleman and Rice [13].…”

Activation volume of Si diffusion in San Carlos olivine: Implications for upper mantle rheology

“…Jaoul's approach, described in details in the appendix, is similar to the Nabarno-Herring (NH) mechanism [Herring, 1950] and shows that the activation energy (Ec) and volume (Vc) of olivine creep at high temperature can be simply written as (5) and (6) that were first proposed for metals. On the other hand, the methods chosen by Battegay [1986] and Jaoul [1990] were specifically developed for olivine, with its particular property of very different diffusion coefficients for the three major species Dsi << Dox <• DMe, where Me represents the octahedral ions, in the domain of T and pO2 where dislocation climb controls creep (i.e., for mantle conditions).…”

Morphological Study of Oxide Scales and Iron Substrate Surfaces Formed at Elevated Temperatures

“…At first, a partial separation of oxide scale from the substrate over a small circular area takes place either by the coalescence (5) of vacancies or by a slight blistering due to stresses (2)(12) acting at the scale/iron interface or by a combination of both. Stress directed diffusion of vacancies may be considered to be likely for the latter (15). The void formation by the coalescence of vacancies preceding the creation of a crater shaped protrusion from a substrate alloy has been reported by Tien et al (9), though the source of vacancies in their case was not clear.…”