# Difference between revisions of "Creep"

Started by Lauren Hartle, Fall 2011.

## Definition

Creep is the time dependent change in Strain of a material subject to a constant Stress. A Creep test attempts to quantify the relevant timescales and functional forms of molecular and/or atomic rearrangement that occur when a material creeps. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations (Dislocation Creep) and the diffusion of atoms along grain boundaries (Coble Creep) or through the bulk (Nabarro-Herring creep).

The general equation for describing creep is:

$\frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}$

where the left hand side is the strain rate due to creep, Q is the activation energy of creep, d is the grain size, $\sigma$ is the stress in the material, T is the temperature, and m and b are constants that depend on the mechanism of creep. In dislocation creep, m = 4 to 6 and b = 0. In Nabarro-Herring creep, m = 1 and b = 2. In Coble creep, m = 1 and b = 3. Depending on the mechanism being modeled, the exponents m and b can be tuned.

For viscoelastic materials like many polymers, a number of models can be used to describe time dependent deformation. One approach is to combine two fundamental units (the spring, which represents elastic response, and the dashpot, which represents viscous response) in different configurations to create a simplified mechanical model of the system. The Zener model, for example, models a linear viscoelastic response as a "dashpot" (Newtonian flow behavior) in parallel with a spring, and spring in series with the combined unit. A polymer's creep behavior is often substantially more pronounced above its Glass Transition Temperature, where chains more freely slide across one another.

## Examples

Polymers can be characterized as cross-linked (where chains are chemically linked), uncross-linked (where chains are free to slide over one another), or crystalline. Uncross-linked polymers behave most like linearly viscoelastic materials, while cross-links in polymer chains limit the degree to which chains can slide past one another, and depending on the degree of cross-linking, can substantially impact the ability of the polymer to flow in a Newtonian manner. For more details, see Introduction to the Mechanics of a Continuous Medium, Chapter 6.4 (linear viscoelastic response) by Malvern.