In materials science, Nabarro–Herring creep is a mechanism of deformation of crystalline materials (and amorphous 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. This type of creep results from the diffusion of vacancies from regions of high chemical potential at grain boundaries subjected to normal tensile stresses to regions of lower chemical potential where the average tensile stresses across the grain boundaries are zero. Self-diffusion within the grains of a polycrystalline solid can cause the solid to yield to an applied shear stress, the yielding being caused by a diffusional flow of matter within each crystal grain away from boundaries where there is a normal pressure and toward those where there is a normal tension. Atoms migrating in the opposite direction account for the creep strain (εNH). The creep strain rate is derived in the next section. NH creep is more important in ceramics than metals as dislocation motion is more difficult to effect in ceramics.
Derivation of the creep rate Source: The Nabarro–Herring creep rate, ε ˙ N H {\displaystyle {\dot {\varepsilon }}_{\rm {NH}}} , can be derived by considering an individual rectangular grain (in a single or polycrystal). Two opposing sides have a compressive stress applied and the other two have a tensile stress applied. The atomic volume is decreased by compression and increased by tension. Under this change, the activation energy to form a vacancy is altered by ± σ Ω {\displaystyle \pm \sigma \Omega } . The atomic volume is Ω {\displaystyle \Omega } and the stress is σ {\displaystyle \sigma } . The plus and minus indication is an increase or decrease in the activation energy due to the tensile and compressive stresses, respectively. The fraction of vacancy concentrations in the compressive ( N ν C {\displaystyle N_{\nu }^{C}} ) and tensile ( N ν T {\displaystyle N_{\nu }^{T}} ) regions are given as:
N ν C ≈ exp ( − Q f k T ) exp ( − σ Ω k T ) N ν T ≈ exp ( − Q f k T ) exp ( σ Ω k T ) {\displaystyle {\begin{aligned}N_{\nu }^{C}&\approx \exp \left(-{\frac {Q_{f}}{kT}}\right)\exp \left(-{\frac {\sigma \Omega }{kT}}\right)\\[4pt]N_{\nu }^{T}&\approx \exp \left(-{\frac {Q_{f}}{kT}}\right)\exp \left({\frac {\sigma \Omega }{kT}}\right)\end{aligned}}}
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