Nabarro-Herring

It was shown earlier that the Nabarro-Herring model of creep in solids involved the migration of vacancies out of the stressed solid accompanied by counter-migration of atoms to reduce the length of the solid in the direction of the applied stress. This property could clearly contribute to densiflcation under an external pressure, given sufficient time of application of the stress... 

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Figure 14-3. Nabarro-Herring creep in a grain of a polycrystalline sample which is (inhomogeneously) stressed (ct2

Let us finally mention that in polycrystalline samples, Nabarro-Herring(-Coble) creep occurs as already introduced in Section 14.3.2. The Nabarro-Herring creep rate is inversely proportional to the square of the average grain size, l2, if volume diffusion of point defects prevails. It is inversely proportional to /3 if grain boundary diffusion determines the transport. 

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. 

Figure 16.5 Deformation mechanism map for Ag polycrystal a = applied stress, p = shear modulus, grain size = 32 pm, and strain rate = IGF8 s 1. The diffusional creep field is divided into two subfields the Coble creep field and the Nabarro-Herring creep field. From Ashby [20].

W. Beere. Stress redistribution during Nabarro-Herring and superplastic creep. Metal Sci., 10(4) 133—139, 1976. 

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... 

Note that in the context of both the Nabarro-Herring analysis and that of Coble, the strain rate is found to vary linearly with the applied stress. In particular, this result is consistent with dubbing this process diffusional viscosity as did Herring (1950) in his original work. Indeed, the identification of a material parameter such as the viscosity and its associated scaling properties with grain size and temperature represents another example of the type of micro-macro connection... 

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

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