Nabarro-Herring creep process

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... 

Steady-state or secondary creep (Fig. 17) is characterized by a constant or minimum strain rate, dddt n- Two theories have typically been used to explain the constant strain rate (Ref 54) (a) There is a balance between the creation and annihilation of defects during steady-state creep. The rate processes are thermally activated and dependent upon the applied stress. The defect velocity is assumed to be a constant and (b) There is a relatively constant supply of defects having a constant velocity that establishes the creep rate. The creep rate is determined by the stress level and temperature and is also a thermally activated process. This theory is referred to as the Nabarro-Herring creep process. 

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Mass diffusion between grain boundaries in a polycrystal can be driven by an applied shear stress. The result of the mass transfer is a high-temperature permanent (plastic) deformation called diffusional creep. If the mass flux between grain boundaries occurs via the crystalline matrix (as in Section 16.1.3), the process is called Nabarro-Herring creep. If the mass flux is along the grain boundaries themselves via triple and quadjunctions (as in Sections 16.1.1 and 16.1.2), the process is called Coble creep. 

This relation defines a simple, ideal, viscous solid. One sees that increasing grain size reduces creep rate. Creep-rate change is proportional to d . Nabarro-Herring creep is a low-stress and high-temperature process. 

Here, Anh is a material parameter, a the external stress, fl the volume of a vacancy, d the grain size, and Dy the diffusion coefficient for self-diffusion through the bulk material. This process is called Nabarro-Herring creep. Since the stress dependence is linear, Nabarro-Herring creep is most important at low stresses, whereas dislocation creep is more important at high stresses. 

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