Creep (deformation)

Creep is the term used to describe the tendency of a material to move or to deform permanently to relieve stresses. Material deformation occurs as a result of long term exposure to levels of stress that are below the yield or ultimate strength of the material. Creep is more severe in materials that are subjected to heat for long periods and near melting point. The rate of this damage is a function of the material properties and the exposure time, exposure temperature and the applied load (stress). 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 will cause the blade to contact the casing, resulting in the failure of the blade. Creep is usually a concern to engineers and metallurgists when evaluating components that operate under high stresses and/or temperatures. Creep is not necessarily a failure mode, but is instead a damage mechanism. Moderate creep in concrete is sometimes welcomed because it relieves tensile stresses that may otherwise have led to cracking.

Overview
Rather than failing suddenly with a fracture, the material permanently strains over a longer period of time until it finally fails. Creep does not happen upon sudden loading but the accumulation of creep strain in longer times causes failure of the material. This makes creep deformation a "time-dependent" deformation of the material.

Creep deformation can be obtained in reasonable time frames under very high temperatures i.e., temperatures around half of the absolute melting temperature. This deformation behaviour is important in systems for which high temperatures are endured, such as nuclear power plants, jet engines, heat exchangers etc. It is also a consideration in the design of magnesium alloy engines. Since the relevant temperature is relative to melting point (usually at temperatures greater than half the melting temperature), creep can be seen at relatively low temperatures depending upon the alloy. Plastics and low-melting-temperature metals, including many solders creep at room temperature, as can be seen markedly in older lead hot-water pipes. Planetary ice is often at a high temperature (relative to its melting point), and creeps. Virtually any material will creep upon approaching its melting temperature. Glass windows are often erroneously used as an example of this phenomenon: creep would only occur at temperatures above the glass transition temperature (around 900°F/500°C).

An example of an application involving creep deformation is the design of tungsten lightbulb filaments. Sagging of the filament coil between its supports increases with time due to creep deformation caused by the weight of the filament itself. If too much deformation occurs, the adjacent turns of the coil touch one another, causing an electrical short and local overheating, which quickly leads to failure of the filament. The coil geometry and supports are therefore designed to limit the stresses caused by the weight of the filament, and a special tungsten alloy with small amounts of oxygen trapped in the grain boundaries is used to slow the rate of Coble creep.

Steam piping within fossil-fuel fired power plants with superheated vapour work under high temperature (1050°F/565.5°C and high pressure (often at 3500 psig/ 24.1 MPa or greater). In a jet engine temperatures may reach to 1000°C, which may initiate creep deformation in a weak zone. Because of these reasons, understanding and studying creep deformation behaviour of engineering materials is very crucial for public and operational safety.

Stages of creep
Initially, the strain rate slows with increasing strain. This is known as primary creep. The strain rate eventually reaches a minimum and becomes near-constant. This is known as secondary or steady-state creep. It is this regime that is most well understood. The "creep strain rate" is typically the rate in this secondary stage. The stress dependence of this rate depends on the creep mechanism. In tertiary creep, the strain-rate exponentially increases with strain.

Dislocation creep
At high stresses (relative to the shear modulus), creep is controlled by the movement of dislocations. Dislocations may move in a conservative fashion, retaining their length, or they move in a non-conservative fashion--increasing their length through atomic diffusion. The former process is known as 'glide' and the latter as 'climb.'

Glide-controlled
At lower temperatures, creep can be controlled by dislocation glide. Typically, this glide is opposed by obstacles (other dislocations, solute atoms or precipitates, grain boundaries, etc.). These control the creep rate, which is proportional to the square of the stress. Creep is much more prominent in BCC crystal structures due to its high symmetry.

Power-law
The rate of dislocation creep tends to have a power law dependence on the stress in the material.

$$ \frac{d\epsilon}{dt} = A \sigma^n e^\frac{-Q}{\bar R T} $$

$$A$$ is a parameter relating to the material being crept and the sub-mechanism controlling creep.

$$Q$$ is the activation energy for creep.

$$ \bar R $$ is the universal gas constant.

$$T$$ is the absolute temperature

This mechanism readily occurs at temperatures above 0.3Tm in pure metals and above 0.4Tm in most ceramics and alloys, where Tm is the melting temperature of the material. These are the temperatures where diffusion within the material becomes significant. The stress exponent n usually lies between 3 and 10, and is determined by the sub-mechanism and the material composition. Some alloys exhibit a very large stress exponent ($$n>10$$), and this has typically been explained by introducing a "threshold stress," $$\sigma_{th}$$, below which creep can't be measured. The modfied power law equation then becomes: $$\frac{d\epsilon}{dt} = A \left(\sigma-\sigma_{th}\right)^n e^\frac{-Q}{\bar R T}$$ where $$A$$, $$Q$$ and $$n$$ can all be explained by conventional mechanisms (so $$3\leq{n}\leq{10}$$).

Diffusional creep
Diffusional creep occurs at lower stresses than dislocation creep. Atoms diffuse (due to a chemical potential gradient) through and around grain boundaries when a material is under stress. The relationship between this type of creep and stress is linear.

At low temperatures, creep is controlled by grain-boundary diffusion, and is known as Coble creep. It scales inversely to the cube of the grain size.

At higher temperatures, creep is controlled by lattice diffusion, and is known as Nabarro-Herring creep. It scales inversely to the square of the grain size.

Creep of Polymers
Creep can occur in polymers and metals which are considered viscoelastic materials. When a polymeric material is subjected to an abrupt force, the response can be modeled using the Kelvin-Voigt Model. In this model, the material is represented by a Hookean spring and a Newtonian dashpot in parallel. The creep strain is given by:
 * $$\epsilon(t) = \sigma C_0 + \sigma C \int_0^\infty f(\tau)(1-exp[-t/ \tau]) d \tau$$

Where:
 * $$\sigma$$ = applied stress
 * $$C_0$$ = instantaneous creep compliance
 * C = creep compliance coefficient
 * $$\tau$$ = retardation time
 * $$f(\tau)$$ = distribution of retardation times

When subjected to a step constant stress, viscoelastic materials experience a time-dependent increase in strain. This phenomenon is known as viscoelastic creep.

At a time t0, a viscoelastic material is loaded with a constant stress that is maintained for a sufficiently long time period. The material responds to the stress with a strain that increases until the material ultimately fails. When the stress is maintained for a shorter time period, the material undergoes an initial strain until a time t1, after which the strain immediately decreases (discontinuity) then gradually decreases at times t > t1 to a residual strain.

Viscoelastic creep data can be presented in one of two ways. Total strain can be plotted as a function of time for a given temperature or temperatures. Below a critical value of applied stress, a material may exhibit linear viscoelasticity. Above this critical stress, the creep rate grows disproportionately faster. The second way of graphically presenting viscoelastic creep in a material is by plotting the creep modulus (constant applied stress divided by total strain at a particular time) as a function of time. Below its critical stress, the viscoelastic creep modulus is independent of stress applied. A family of curves describing strain versus time response to various applied stress may be represented by a single viscoelastic creep modulus versus time curve if the applied stresses are below the material's critical stress value.

Additionally, the molecular weight of the polymer of interest is known to affect its creep behavior. The effect of increasing molecular weight tends to promote secondary bonding between polymer chains and thus make the polymer more creep resistant. Similarly, aromatic polymers are even more creep resistant due to the added stiffness from the rings. Both molecular weight and aromatic rings add to polymers' thermal stability, increasing the creep resistance of a polymer. (Meyers and Chawla, 1999, 573)

Both polymers and metals can creep. Polymers experience significant creep at all temperatures above ~-200°C, however there are three main differences between polymetric and metallic creep. Metallic creep :
 * is not linearly viscoelastic
 * in not recoverable
 * only significant at high temperatures

Other examples
The Collapse of the World Trade Center was credited in part to creep.

The creep rate of hot pressure-loaded components in a nuclear reactor at power can be a significant design-constraint, since the creep rate is enhanced by the flux of energetic particles.