Coble creep
[1] Coble creep occurs through the diffusion of atoms in a material along grain boundaries.
This mechanism is observed in polycrystals or along the surface in a single crystal, which produces a net flow of material and a sliding of the grain boundaries.
American materials scientist Robert L. Coble first reported his theory of how materials creep across grain boundaries and at high temperatures in alumina.
Here he famously noticed a different creep mechanism that was more dependent on the size of the grain.
[2] The strain rate in a material experiencing Coble creep is given by
where Coble creep, a diffusive mechanism, is driven by a vacancy (or mass) concentration gradient.
and taking a high temperature expansion, where the first term on the right hand side is the vacancy concentration from tensile stress and the second term is the concentration due to compressive stress.
If we consider the vacancy concentration across the grain under an applied tensile stress, then we note that there is a larger vacancy concentration at the equator (perpendicular to the applied stress) than at the poles (parallel to the applied stress).
Therefore, a vacancy flux exists between the poles and equator of the grain.
The vacancy flux is given by Fick's first law at the boundary: the diffusion coefficient
where we've divided the total concentration difference by the arclength between equator and pole then multiply by the boundary width
due to a flux of vacancies diffusing from a source of area
has absorbed constants and the vacancy diffusivity through the grain boundary
They are both diffusion processes, driven by the same concentration gradient of vacancies, occur in high temperature, low stress environments and their derivations are similar.
For example, the activation energy for dislocation climb is the same as for Nabarro–Herring, so by comparing the temperature dependence of low and high stress regimes, one can determine whether Coble creep or Nabarro–Herring creep is dominant.
[3] Researchers commonly use these relationships to determine which mechanism is dominant in a material; by varying the grain size and measuring how the strain rate is affected, they can determine the value of
Dislocation creep, sometimes called power law creep (PLC), has a power law dependence on the applied stress ranging from 3 to 8.
[1] Dislocation movement is related to the atomic and lattice structure of the crystal, so different materials respond differently to stress, as opposed to Coble creep which is always linear.
This makes the two mechanisms easily identifiable by finding the slope of
Dislocation climb-glide and Coble creep both induce grain boundary sliding.
[1] To understand the temperature and stress regimes in which Coble creep is dominant for a material, it is helpful to look at deformation mechanism maps.
These maps plot a normalized stress versus a normalized temperature and demarcate where specific creep mechanisms are dominant for a given material and grain size (some maps imitate a 3rd axis to show grain size).
These maps should only be used as a guide, as they are based on heuristic equations.
[1] These maps are helpful to determine the creep mechanism when the working stresses and temperature are known for an application to guide the design of the material.
Since Coble creep involves mass transport along grain boundaries, cracks or voids would form within the material without proper accommodation.
[1] This process typically occurs on timescales significantly faster than that of mass diffusion (an order of magnitude quicker).
Because of this, the rate of grain boundary sliding is typically irrelevant to determining material processes.
The processes underlying grain boundary sliding are the same as those causing diffusional creep[1] This mechanism is originally proposed by Ashby and Verrall in 1973 as a grain switching creep.
[5] This is competitive with Coble creep; however, grain switching will dominate at large stresses while Coble creep dominates at low stresses.
[1] The relation to Coble creep is clear by looking at the first term which is dependent on grain boundary thickness
