Coble creep

In materials science, Coble creep, a form of diffusion creep, is a mechanism for deformation of crystalline solids. Contrasted with other diffusional creep mechanisms, Coble creep is similar to Nabarro–Herring creep in that it is dominant at lower stress levels and higher temperatures than creep mechanisms utilizing dislocation glide.^[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 $${\displaystyle {\begin{aligned}{\frac {d\varepsilon _{C}}{dt}}\equiv {\dot {\varepsilon }}_{C}&=A_{C}{\frac {\delta '}{d^{3}}}{\frac {\sigma \Omega }{k_{\rm {B}}T}}D_{0}\exp \left(-{\frac {Q_{f}+Q_{m}}{k_{\rm {B}}T}}\right)\\[4pt]&=A_{C}{\frac {\delta '}{d^{3}}}{\frac {\sigma \Omega }{k_{\rm {B}}T}}D_{\rm {GB}}\end{aligned}}}$$ where

${\displaystyle A_{c}}$ is a geometric prefactor

${\displaystyle \sigma }$ is the applied stress,

${\displaystyle d}$ is the average grain diameter,

${\displaystyle \delta '}$ is the grain boundary width,

${\displaystyle D_{\rm {GB}}=D_{0}\exp \left(-{\tfrac {Q_{f}\,+\,Q_{m}}{k_{\rm {B}}T}}\right)}$ is the diffusion coefficient in the grain boundary,

${\displaystyle Q_{f}}$ is the vacancy formation energy,

${\displaystyle Q_{m}}$ is the activation energy for diffusion along the grain boundary

${\displaystyle k_{\rm {B}}}$ is the Boltzmann constant,

${\displaystyle T}$ is the thermodynamic temperature (in kelvins)

${\displaystyle \Omega }$ is the atomic volume for the material.