In materials science, creep (sometimes called cold flow) is the tendency of a solid material to move

slowly or deform permanently under the influence of persistent mechanical stresses. It can occur as
a result of long-term exposure to high levels of stress that are still below the yield strength of the
material. Creep is more severe in materials that are subjected to heat for long periods and generally
increases as they near their melting point.
The rate of deformation is a function of the material's properties, exposure time, exposure
temperature and the applied structural load. Depending on the magnitude of the applied stress and
its duration, the deformation may become so large that a component can no longer perform its
function — for example creep of a turbine blade could cause the blade to contact the casing,
resulting in the failure of the blade. Creep is usually of concern to engineers and metallurgists when
evaluating components that operate under high stresses or high temperatures. Creep is a
deformation mechanism that may or may not constitute a failure mode. For example, moderate
creep in concrete is sometimes welcomed because it relieves tensile stresses that might otherwise
lead to cracking.
Unlike brittle fracture, creep deformation does not occur suddenly upon the application of stress.
Instead, strain accumulates as a result of long-term stress. Therefore, creep is a "time-dependent"
deformation. It works on the principle of Hooke's law (stress is directly proportional to strain).

Contents

 1Temperature dependence
 2Stages
 3Mechanisms of deformation
o 3.1Deformation mechanism maps
 4General equation
o 4.1Dislocation creep
o 4.2Nabarro–Herring creep
o 4.3Coble creep
o 4.4Solute drag creep
o 4.5Dislocation climb-glide creep
o 4.6Harper–Dorn creep
o 4.7Sintering
 5Examples
o 5.1Polymers
o 5.2Wood
o 5.3Concrete
 6Applications
 7Prevention
o 7.1Superalloys
 8See also
 9References
 10Further reading
 11External links

Temperature dependence[edit]
The temperature range in which creep deformation may occur differs in various materials. Creep
deformation generally occurs when a material is stressed at a temperature near its melting point.
While tungsten requires a temperature in the thousands of degrees before creep deformation can
occur, lead may creep at room temperature, and ice will creep at temperatures below 0 °C (32 °F).
[1]
 Plastics and low-melting-temperature metals, including many solders, can begin to creep at room
temperature. Glacier flow is an example of creep processes in ice. [2] The effects of creep
deformation generally become noticeable at approximately 35% of the melting point for metals and
at 45% of melting point for ceramics. [3]

Stages[edit]

Strain as a function of time due to constant stress over an extended period for a Class M material.

Creep behavior can be split into three main stages. In primary, or transient, creep, the strain rate is a
function of time. In Class M materials, which include most pure materials, strain rate decreases over
time. This can be due to increasing dislocation density, or it can be due to evolving grain size. In
class A materials, which have large amounts of solid solution hardening, strain rate increases over
time due to a thinning of solute drag atoms as dislocations move. [4]
In the secondary, or steady-state, creep, dislocation structure and grain size have reached
equilibrium, and therefore strain rate is constant. Equations that yield a strain rate refer to the
steady-state strain rate. Stress dependence of this rate depends on the creep mechanism.
In tertiary creep, the strain rate exponentially increases with stress. This can be due
to necking phenomena, internal cracks, or voids, which all decrease the cross-sectional area and
increase the true stress on the region, further accelerating deformation and leading to fracture.[5]

Mechanisms of deformation[edit]
Depending on the temperature and stress, different deformation mechanisms are activated. Though
there are generally many deformation mechanisms active at all times, usually one mechanism is
dominant, accounting for almost all deformation.
Various mechanisms are:

 Bulk diffusion (Nabarro–Herring creep)

 Grain boundary diffusion (Coble creep)
 Glide-controlled dislocation creep: dislocations move via glide and climb, and the speed of
glide is the dominant factor on strain rate
 Climb-controlled dislocation creep: dislocations move via glide and climb, and the speed of
climb is the dominant factor on strain rate
 Harper-Dorn creep: a low-stress creep mechanism in some pure materials
At low temperatures and low stress, creep is essentially nonexistent and all strain is elastic. At low
temperatures and high stress, materials experience plastic deformation rather than creep. At high
temperatures and low stress, diffusional creep tends to be dominant, while at high temperatures and
high stress, dislocation creep tends to be dominant.

Deformation mechanism maps[edit]

Main article: Deformation mechanism map
Deformation mechanism maps provide a visual tool categorizing the dominant deformation
mechanism as a function of homologous temperature, shear modulus-normalized stress, and strain
rate. Generally, two of these three properties (most commonly temperature and stress) are the axes
of the map, while the third is drawn as contours on the map.
To populate the map, constitutive equations are found for each deformation mechanism. These are
used to solve for the boundaries between each deformation mechanism, as well as the strain rate
contours. Deformation mechanism maps can be used to compare different strengthening
mechanisms, as well as compare different types of materials.[6]

General equation[edit]
where  is the creep strain, C is a constant dependent on the material and the particular creep
mechanism, m and b are exponents dependent on the creep mechanism, Q is the activation
energy of the creep mechanism, σ is the applied stress, d is the grain size of the
material, k is Boltzmann's constant, and T is the absolute temperature.[7]

Dislocation creep[edit]
Main article: Dislocation creep
At high stresses (relative to the shear modulus), creep is controlled by the movement
of dislocations. For dislocation creep, Q = Q(self diffusion), m = 4–6, and b is less than 1.
Therefore, dislocation creep has a strong dependence on the applied stress and the intrinsic
activation energy and a weaker dependence on grain size. As grain size gets smaller, grain
boundary area gets larger, so dislocation motion is impeded.
Some alloys exhibit a very large stress exponent (m > 10), and this has typically been explained
by introducing a "threshold stress," σth, below which creep can't be measured. The modified
power law equation then becomes:
where A, Q and m can all be explained by conventional mechanisms (so 3 ≤ m ≤ 10), R is
the gas constant. The creep increases with increasing applied stress, since the applied
stress tends to drive the dislocation past the barrier, and make the dislocation get into a
lower energy state after bypassing the obstacle, which means that the dislocation is inclined
to pass the obstacle. In other words, part of the work required to overcome the energy
barrier of passing an obstacle is provided by the applied stress and the remainder by
thermal energy.

Nabarro–Herring creep[edit]
Main article: Nabarro–Herring creep