Nabarro-Herring expression

This expression is the well-known Nabarro-Herring expression for creep, and it predicts that... 

Fine-grained materials, when subjected to high temperatures and low applied stresses, deform by mutual accommodation of grains assisted by grain boundary sliding and transport of matter (diffusion). Under conditions where lattice diffusion dominates, the diffusional creep rate is reasonably well characterized by the Nabarro-Herring creep process. (For a review of this and other classical creep mechanisms, see Refs. 5 and 6.) Here the strain rate is expressed as... 

Derive an expression for the critical grain size below which Coble creep dominates and above which Nabarro Herring creep dominates (at constant temperature). 

The experimental data on diffusion creep in 25 mol% yttria stabilized cubic zirconia may be seen in Fig. 6.44, where a grain-size, normalized strain rate versus stress is illustrated. The data may be expressed as Nabarro-Herring diffusion creep... 

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