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Nabarro–Herring creep

In materials science, Nabarro–Herring creep is a mechanism of deformation of crystalline materials that occurs at low stresses and held at elevated temperatures in fine-grained materials. In Nabarro–Herring creep, atoms diffuse through the crystals, and the rate of creep varies inversely with the square of the grain size so fine-grained materials creep faster than coarser-grained ones. NH creep is solely controlled by diffusional mass transport. This phenomenon is named after Frank Nabarro and Conyers Herring who discussed the phenomenon in 1950.

Derivation of the creep rate
Source: :\dot\varepsilon = {A_n} \frac{Db^3\sigma}{d^2kT} == Comparison to Coble creep ==
Comparison to Coble creep
Coble creep is closely related to Nabarro–Herring creep and is controlled by diffusion as well. Unlike Nabarro–Herring creep, mass transport occurs by diffusion along the surface of single crystals or the grain boundaries in a polycrystal. :\dot\varepsilon = \frac{ADGb}{kT}{\left(\frac{\sigma}{G}\right)}^n{\left(\frac{b}{d}\right)}^p is the shear modulus. The diffusivity is obtained form the tracer diffusivity, D^*. The dimensionless constant A_n depends intensively on the geometry of grains. The parameters A, n and p are dependent on creep mechanisms. Nabbaro–Herring creep does not involve the motion of dislocations. It predominates over high-temperature dislocation-dependent mechanisms only at low stresses, and then only for fine-grained materials. Nabarro–Herring creep is characterized by creep rates that increase linearly with the stress and inversely with the square of grain diameter. In contrast, in Coble creep atoms diffuse along grain boundaries and the creep rate varies inversely with the cube of the grain size. Lower temperatures favor Coble creep and higher temperatures favor Nabbaro–Herring creep because the activation energy for vacancy diffusion within the lattice is typically larger than that along the grain boundaries, thus lattice diffusion slows down relative to grain boundary diffusion with decreasing temperature. == Experimental and theoretical examples ==
Experimental and theoretical examples
• Creep in dense, polycrystalline magnesium oxide and iron-doped polycrystalline magnesia • Compressive creep in polycrystalline beryllium oxide • Creep in polycrystalline that has been doped with Cr, Fe, or Ti • Creep in dry synthetic dunite which results in trace melt and some grain growth • Reproduced for nanopolycrystalline systems in Phase Field Crystal simulations (theory matched in terms of creep stress and grain size exponents) ==References==
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