In materials science, Nabarro–Herring creep (NH creep) is a mechanism of deformation of crystalline materials (and amorphous materials[1]) 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.
[2][3] NH creep is solely controlled by diffusional mass transport.
[1] 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.
[4] 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.
, can be derived by considering an individual rectangular grain (in a single or polycrystal).
The atomic volume is decreased by compression and increased by tension.
Under this change, the activation energy to form a vacancy is altered by
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 (
These vacancy concentrations are maintained at the lateral and horizontal surfaces in the grain.
These net concentrations drive vacancies to the compressive regions from the tensile ones which causes grain elongation in one dimension and grain compression in the other.
This is creep deformation caused by a flux of vacancy motion.
is the volume changed per unit time during creep deformation.
the NH creep rate is given by: This equation can be greatly simplified.
The lattice self-diffusion coefficient is given by: As previously stated, NH creep occurs at low stresses and high temperatures.
is a constant that absorbs the approximations in the derivation.
Alternatively, this can be derived in a different method where the constant
In this case, the NH creep rate
Unlike Nabarro–Herring creep, mass transport occurs by diffusion along the surface of single crystals or the grain boundaries in a polycrystal.
[1] For a general expression of creep rate, the comparison between Nabarro–Herring and Coble creep can be presented as follows:[6] G is the shear modulus.
depends intensively on the geometry of grains.
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.
[2] 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.