Creep Coble

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].

Coble creep -for ceramics [CERAMICS - MECHANICALPROPERTIES AND BEHAVIOR] (Vol 5)... 

In the present analysis, large-scale spallations of alumina scales on NiAl were always connected with the presence of interfacial voids. In the absence of large voids and for small strain rate, it was found that the scale was well adherent under compressive substrate deformation even for large specimen deformations (cf. Fig. 7a).This suggests the presence of an effective stress relief mechanism by a slight scale wrinkling or by oxide Coble creep. 

Figure 10.29 (a) Coble creep, in which atoms diffuse along grain boundary surfaces to grain boundaries parallel to... 

In general, one should not suppose that the properties of bulk materials will apply to materials at the nanoscale level. With respect to the mechanical properties of small-scale solids, it is known that the elastic behaviour, due to bond stretching and twisting, does not vary significantly in nanoparticles compared with that in the bulk. Other properties are more sensitive. For example, the rate of diffusion creep (Nabarro-Herring and Coble creep) is dependent on grain size. Hence, creep will be enhanced in compacts of nanoparticles and in thin films. 

Both Coble creep and Herring-Nabarro creep describe ... 

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

Nabarro-Herring and Coble creep can take place in parallel so that actual creep rates will involve both components and both diffusion coefficients. In ceramics we also have a situation in which both anions and cations are diffusing adding further complications to the creep rate equations. If there is a large difference in the diffusion rates then the creep rate is controlled by the slower diffusing species along the faster diffusing path. 

Coble, Robert (Bob) L. (1928-1992) was best known for showing that small additions of MgO made it possible to form polycrystalline translucent alumina (Lucalox). This occurred while he was at the General Electric Research Laboratory in Schenectady, New York. He joined MIT in 1960. [More about this appears in the special alumina issue of J. Am. Ceram. Soc. 77(2), 1994.] He is also known for Coble creep. 

The densification by plastic deformation and power-law creep is, in principle, independent of particle (grain) size. In the case of diffusion (both lattice and grain boundary), on the other hand, densification depends on not only the effective pressure but also the grain size. The densification by diffusion under an external pressure is similar to diffusional creep Nabarro-Herring creep due to lattice diffusion, and Coble creep due to grain boundary diffusion. The dependency of densification on grain size is the same as that of diffusional creep. 

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