Creep (deformation)
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| Mechanical failure modes |
|---|
| Buckling |
| Corrosion |
| Creep |
| Fatigue |
| Fracture |
| Melting |
| Thermal shock |
| Wear |
In materials science, 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 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.
[edit] Overview
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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 temperature of the melting point. 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.
[edit] 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.
[edit] Mechanisms of creep
[edit] General creep equation
where 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 temperature.
[edit] Dislocation creep
At high stresses (relative to the shear modulus), creep is controlled by the movement of dislocations. When a stress is applied to a material, plastic deformation occurs due to the movement of dislocations in the slip plane. Materials contain a variety of defects, for example solute atoms, that act as obstacles to dislocation motion. Creep arises from this because of the phenomenon of dislocation climb. At high temperatures vacancies in the crystal can diffuse to the location of a dislocation and cause the dislocation to move to an adjacent slip plane. By climbing to adjacent slip planes dislocations can get around obstacles to their motion, allowing further deformation to occur. Because it takes time for vacancies to diffuse to the location of a dislocation this results in time dependent strain, or creep.
For dislocation creep Q = Qself diffusion, m = 4-6, and b=0. Therefore dislocation creep has a strong dependence on the applied stress and no grain size dependence.
Some alloys exhibit a very large stress exponent (n > 10), and this has typically been explained by introducing a "threshold stress," σth, below which creep can't be measured. The modfied power law equation then becomes: 
where A, Q and n can all be explained by conventional mechanisms (so 
).
[edit] Nabarro-Herring Creep
Nabarro-Herring creep is a form of diffusion controlled creep. In N-H creep atoms diffuse through the lattice causing grains to elongate along the stress axis. For Nabarro-Herring creep k is related to the diffusion coefficient of atoms through the lattice, Q = Qself diffusion, m=1, and b=2. Therefore N-H creep has a weak stress dependence and a moderate grain size dependence, with the creep rate decreasing as grain size is increased.
Nabarro-Herring creep is found to be strongly temperature dependent. For lattice diffusion of atoms to occur in a material, neighboring lattice sites or interstitial sites in the crystal structure must be free. A given atom must also overcome the energy barrier to move from its current site (it lies in an energetically favorable potential well) to the nearby vacant site (another potential well). The general form of the diffusion equation is D = DoExp(Ea / KT) where Do has a dependence on both the attempted jump frequency and the number of nearest neighbor sites and the probability of the sites being vacant. Thus there is a double dependence upon temperature. At higher temperatures the diffusivity increases due to the direct temperature dependence of the equation, the increase in vacancies through Shottky defect formation, and an increase in the average energy of atoms in the material. Nabarro-Herring creep dominates at very high temperatures relative to a material's melting temperature.
[edit] Coble Creep
Coble creep is a second form of diffusion controlled creep. In Coble creep the atoms diffuse along grain boundaries to elongate the grains along the stress axis. This causes Coble creep to have a stronger grain size dependence than N-H creep. For Coble creep k is related to the diffusion coefficient of atoms along the grain boundary, Q = Qgrain boundary diffusion, m=1, and b=3. Because Qgrain boundary diffusion < Qself diffusion, Coble creep occurs at lower temperatures than N-H creep. Coble creep is still temperature dependent, as the temperature increases so does the grain boundary diffusion. However, since the number of nearest neighbors is effectively limited along the interface of the grains, and thermal generation of vacancies along the boundaries is less prevalent, the temperature dependence is not as strong as in Nabarro-Herring creep. It also exhibits the same linear dependence on stress as N-H creep.
[edit] 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](../../../math/3/a/2/3a2e3f7e66509dd105f76163347ec731.png)
Where:
- σ = applied stress
- C0 = instantaneous creep compliance
- C = creep compliance coefficient
- τ = retardation time
- f(τ) = 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.[1] 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.[2] Polymers experience significant creep at all temperatures above ~-200°C, however there are three main differences between polymetric and metallic creep. Metallic creep:[2]
- is not linearly viscoelastic
- in not recoverable
- only significant at high temperatures
[edit] Other examples
The Collapse of the World Trade Center was due 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.
[edit] See also
- Stress relaxation
- Hysteresis
- Viscoelasticity
- Biomaterial
- Biomechanics
- Brittle-ductile transition zone
[edit] References
- ^ Rosato, et. al (2001): "Plastics Design Handbook," 63-64.
- ^ a b McCrum, N.G, Buckley, C.P; & Bucknall, C.B (2003). Principles of Polymer Engineering. Oxford Science Publications. ISBN 0-19-856526-7.
- Ashby, Michael F.; & Jones, David R. H. (1980). Engineering Materials 1: An Introduction to their Properties and Applications. Pergamon Press. ISBN 0-08-026138-8.
- Frost, Harold J.; & Ashby, Michael F. (1982). Deformation-Mechanism Maps: The Plasticity and Creep of Metals and Ceramics. Pergamon Press. ISBN 0-08-029337-9.
- Turner, S. (2001). "Creep of Polymeric Materials". Encyclopedia of Materials: Science and Technology: 1813-1817. Oxford: Elsevier Science Ltd.. ISBN 0-08-043152-6.
- Van Vliet, Krystyn J. (2006); "3.032 Mechanical Behavior of Materials", [1]
