Creep (deformation)
In materials science
Materials science
Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. This scientific field investigates the relationship between the structure of materials at atomic or molecular scales and their macroscopic properties. It incorporates...

, creep is the tendency of a solid material to slowly move or deform permanently under the influence of stress
Stress (physics)
In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

es. It occurs as a result of long term exposure to high levels of stress that are below the yield strength of the material.
Creep is more severe in materials that are subjected to heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

 for long periods, and near melting point. Creep always increases with temperature.

The rate of this deformation is a function of the material properties, exposure time, exposure temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 and the applied structural load
Structural load
Structural loads or actions are forces, deformations or accelerations applied to a structure or its components.Loads cause stresses, deformations and displacements in structures. Assessment of their effects is carried out by the methods of structural analysis...

. 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
Structural failure
Structural failure refers to loss of the load-carrying capacity of a component or member within a structure or of the structure itself. Structural failure is initiated when the material is stressed to its strength limit, thus causing fracture or excessive deformations...

 of the blade. Creep is usually of concern to engineers
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

 and metallurgists
Metallurgy is a domain of materials science that studies the physical and chemical behavior of metallic elements, their intermetallic compounds, and their mixtures, which are called alloys. It is also the technology of metals: the way in which science is applied to their practical use...

 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
Failure mode
Failure causes are defects in design, process, quality, or part application, which are the underlying cause of a failure or which initiate a process which leads to failure. Where failure depends on the user of the product or process, then human error must be considered.-Component failure:A part...

. 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
Strain (materials science)
In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal deformations of a continuum body...

 accumulates as a result of long-term stress. Creep is a "time-dependent" deformation.

The temperature range in which creep deformation may occur differs in various materials. For example, tungsten
Tungsten , also known as wolfram , is a chemical element with the chemical symbol W and atomic number 74.A hard, rare metal under standard conditions when uncombined, tungsten is found naturally on Earth only in chemical compounds. It was identified as a new element in 1781, and first isolated as...

 requires a temperature in the thousands of degrees before creep deformation can occur while ice will creep near 0 °C (32 °F). As a rule of thumb, the effects of creep deformation generally become noticeable at approximately 30% of the melting point
Melting point
The melting point of a solid is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at standard atmospheric pressure...

 (as measured on a thermodynamic temperature
Thermodynamic temperature
Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an "absolute" scale because it is the measure of the fundamental property underlying temperature: its null or zero point, absolute zero, is the...

 scale such as kelvin or rankine) for metals and 40–50% of melting point for ceramic
A ceramic is an inorganic, nonmetallic solid prepared by the action of heat and subsequent cooling. Ceramic materials may have a crystalline or partly crystalline structure, or may be amorphous...

s. Virtually any material will creep upon approaching its melting temperature. Since the minimum temperature is relative to melting point, creep can be seen at relatively low temperatures for some materials. Plastics and low-melting-temperature metals, including many solders, creep at room temperature as can be seen markedly in old lead
Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...

 hot-water pipes. Glacier
A glacier is a large persistent body of ice that forms where the accumulation of snow exceeds its ablation over many years, often centuries. At least 0.1 km² in area and 50 m thick, but often much larger, a glacier slowly deforms and flows due to stresses induced by its weight...

 flow is an example of creep processes in ice.

Stages of creep

In the initial stage, or primary creep, the strain rate is relatively high, but slows with increasing time. This is due to work hardening
Work hardening
Work hardening, also known as strain hardening or cold working, is the strengthening of a metal by plastic deformation. This strengthening occurs because of dislocation movements within the crystal structure of the material. Any material with a reasonably high melting point such as metals and...

. The strain rate eventually reaches a minimum and becomes near constant. This is due to the balance between work hardening and annealing
Annealing may refer to:*Annealing , a heat treatment that alters the microstructure of a material causing changes in properties such as strength and hardness and ductility*Annealing , heating a piece of glass to remove stress...

 (thermal softening). This stage is known as secondary or steady-state creep. This stage is the most understood. The characterized "creep strain rate" typically refers to the rate in this secondary stage. Stress dependence of this rate depends on the creep mechanism. In tertiary creep, the strain rate exponentially increases with stress because of necking
Necking can refer to:* Making out, a term for heavy kissing of the neck or petting of that area* Necking , the process by which a ductile material deforms under tension forming a thin neck* Necking, a behavior of giraffes...


Mechanisms of creep

The mechanism of creep depends on temperature and stress. The various methods are:
  • Bulk diffusion (Nabarro-Herring creep)
  • Climb — here the strain is actually accomplished by climb
  • Climb-assisted glide — here the climb is an enabling mechanism, allowing dislocations to get around obstacles
  • Grain boundary diffusion (Coble creep
    Coble creep
    Coble creep, a form of diffusion creep, is a mechanism for deformation of crystalline solids. Coble creep occurs through the diffusion of atoms in a material along the grain boundaries, which produces a net flow of material and a sliding of the grain boundaries.Coble creep is named after Robert L...

  • Thermally activated glide — e.g., via cross-slip
    Slip (materials science)
    In materials science, Slip is the process by which plastic deformation is produced by a dislocation motion. By an external force, parts of the crystal lattice glide along each other, resulting in a changed geometry of the material. Depending on the type of lattice, different slip systems are...

General creep equation

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.

Dislocation creep

At high stresses (relative to the shear modulus), creep is controlled by the movement of dislocation
In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials...

For dislocation creep, Q = Q(self 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 modified power law equation then becomes:

where A, Q and n can all be explained by conventional mechanisms (so 3 ≤ n ≤ 10).

Nabarro-Herring creep

Nabarro-Herring creep is a form of diffusion controlled creep. In Nabarro-Herring creep, atoms diffuse through the lattice causing grains to elongate along the stress axis; k is related to the diffusion coefficient of atoms through the lattice, Q = Q(self diffusion), m = 1, and b = 2. Therefore Nabarro-Herring 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 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
Potential well
A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy because it is captured in the local minimum of a potential well...

) to the nearby vacant site (another potential well). The general form of the diffusion equation is D = D0exp(E/KT) where D0 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 Schottky defect
Schottky defect
A Schottky defect is a type of point defect in a crystal lattice named after Walter H. Schottky.The defect forms when oppositely charged ions leave their lattice sites, creating vacancies. These vacancies are formed in stoichiometric units, to maintain an overall neutral charge in the ionic solid....

 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.

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 Nabarro-Herring creep. For Coble creep k is related to the diffusion coefficient of atoms along the grain boundary, Q = Q(grain boundary diffusion), m = 1, and b = 3. Because Q(grain boundary diffusion) < Q(self diffusion), Coble creep occurs at lower temperatures than Nabarro-Herring 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 Nabarro-Herring creep.

Creep of polymers

Creep can occur in polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...

s and metal
A metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...

s which are considered viscoelastic
Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like honey, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain instantaneously when stretched and just...

 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
Hooke's law
In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law...

 spring and a Newtonian
Newtonian refers to the work of Isaac Newton, in particular:* Newtonian mechanics, also known as classical mechanics* Newtonian telescope, a type of reflecting telescope* Newtonian cosmology* Newtonian dynamics...

A dashpot is a mechanical device, a damper which resists motion via viscous friction. The resulting force is proportional to the velocity, but acts in the opposite direction, slowing the motion and absorbing energy. It is commonly used in conjunction with a spring...

 in parallel. The creep strain is given by the following convolution
In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions. Convolution is similar to cross-correlation...


  • σ = applied stress
  • C0 = instantaneous creep compliance
  • C = creep compliance coefficient
  • = retardation time
  • = 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 at which the stress is relieved, at which time the strain immediately decreases (discontinuity) then continues decreasing gradually 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.

Both polymers and metals can creep. Polymers experience significant creep at temperatures above ca. –200°C; however, there are three main differences between polymeric and metallic creep.

Polymers show creep basically in two different ways. At typical work loads (5 up to 50%) ultra high molecular weight polyethylene
Ultra high molecular weight polyethylene
Ultra-high-molecular-weight polyethylene , also known as high-modulus polyethylene or high-performance polyethylene , is a subset of the thermoplastic polyethylene. It has extremely long chains, with molecular weight numbering in the millions, usually between 2 and 6 million...

 (Spectra, Dyneema) will show time-linear creep, whereas polyester
Polyester is a category of polymers which contain the ester functional group in their main chain. Although there are many polyesters, the term "polyester" as a specific material most commonly refers to polyethylene terephthalate...

 or aramid
Aramid fibers are a class of heat-resistant and strong synthetic fibers. They are used in aerospace and military applications, for ballistic rated body armor fabric and ballistic composites, in bicycle tires, and as an asbestos substitute. The name is a portmanteau of "aromatic polyamide"...

s (Twaron
Twaron is the brandname of Teijin Aramid for a para-aramid. It is a heat-resistant and strong synthetic fibre developed in the early 1970s by the Dutch company AKZO, division Enka, later Akzo Industrial Fibers. The research name of the para-aramid fibre was originally Fiber X, but it was soon...

, Kevlar
Kevlar is the registered trademark for a para-aramid synthetic fiber, related to other aramids such as Nomex and Technora. Developed at DuPont in 1965, this high strength material was first commercially used in the early 1970s as a replacement for steel in racing tires...

) will show a time-logarithmic creep.


Though mostly due to the reduced yield stress at higher temperatures, the Collapse of the World Trade Center
Collapse of the World Trade Center
The twin towers of the World Trade Center collapsed on September 11, 2001, as a result of al-Qaeda's September 11 attacks, in which terrorists affiliated with al-Qaeda hijacked four commercial passenger jet airliners, flying one into the North Tower and another into the South Tower...

 was due in part to creep from increased temperature operation.

The creep rate of hot pressure-loaded components in a nuclear reactor
Nuclear reactor
A nuclear reactor is a device to initiate and control a sustained nuclear chain reaction. Most commonly they are used for generating electricity and for the propulsion of ships. Usually heat from nuclear fission is passed to a working fluid , which runs through turbines that power either ship's...

 at power can be a significant design-constraint, since the creep rate is enhanced by the flux of energetic particles.

Creep was blamed for the Big Dig tunnel ceiling collapse in Boston, Massachusetts that occurred in July 2006.

An example of an application involving creep deformation is the design of tungsten light bulb 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
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

 trapped in the crystallite
Crystallites are small, often microscopic crystals that, held together through highly defective boundaries, constitute a polycrystalline solid. Metallurgists often refer to crystallites as grains.- Details :...

 grain boundaries is used to slow the rate of Coble creep
Coble creep
Coble creep, a form of diffusion creep, is a mechanism for deformation of crystalline solids. Coble creep occurs through the diffusion of atoms in a material along the grain boundaries, which produces a net flow of material and a sliding of the grain boundaries.Coble creep is named after Robert L...


In steam turbine power plants, pipes carry steam at high temperatures (566 °C or 1050 °F) and pressures (above 24.1 MPa or 3500 psi). In jet engines, temperatures can reach up to 1400 °C (2550 °F) and initiate creep deformation in even advanced-coated turbine blades. Hence, it is crucial for correct functionality to understand the creep deformation behavior of materials.

Creep deformation is important not only in systems where high temperatures are endured such as nuclear power plant
Nuclear power plant
A nuclear power plant is a thermal power station in which the heat source is one or more nuclear reactors. As in a conventional thermal power station the heat is used to generate steam which drives a steam turbine connected to a generator which produces electricity.Nuclear power plants are usually...

s, jet engine
Jet engine
A jet engine is a reaction engine that discharges a fast moving jet to generate thrust by jet propulsion and in accordance with Newton's laws of motion. This broad definition of jet engines includes turbojets, turbofans, rockets, ramjets, pulse jets...

s and heat exchanger
Heat exchanger
A heat exchanger is a piece of equipment built for efficient heat transfer from one medium to another. The media may be separated by a solid wall, so that they never mix, or they may be in direct contact...

s, but also in the design of many everyday objects. For example, metal paper clips are stronger than plastic ones because plastics creep at room temperatures. Aging glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...

 windows are often erroneously used as an example of this phenomenon: measurable creep would only occur at temperatures above the glass transition temperature around 500 °C (900 °F). While glass does exhibit creep under the right conditions, apparent sagging in old windows may instead be a consequence of obsolete manufacturing processes, such as that used to create crown glass
Crown glass (window)
Crown glass was an early type of window glass. In this process, glass was blown into a "crown" or hollow globe. This was then transferred from the blowpipe to a pontil and then flattened by reheating and spinning out the bowl-shaped piece of glass into a flat disk by centrifugal force, up to 5 or...

, which resulted in inconsistent thickness.

See also

  • Biomaterial
    A biomaterial is any matter, surface, or construct that interacts with biological systems. The development of biomaterials, as a science, is about fifty years old. The study of biomaterials is called biomaterials science. It has experienced steady and strong growth over its history, with many...

  • Biomechanics
    Biomechanics is the application of mechanical principles to biological systems, such as humans, animals, plants, organs, and cells. Perhaps one of the best definitions was provided by Herbert Hatze in 1974: "Biomechanics is the study of the structure and function of biological systems by means of...

  • Brittle-ductile transition zone
    Brittle-ductile transition zone
    The brittle-ductile transition zone is the strongest part of the Earth's crust. For quartz and feldspar rich rocks in continental crust this occurs at an approximate depth of 13–18 km . At this depth rock becomes less likely to fracture, and more likely to deform ductilely by creep...

  • Deformation mechanism
    Deformation mechanism
    In structural geology, metallurgy and materials science, deformation mechanisms refer to the various mechanisms at the grain scale that are responsible for accommodating large plastic strains in rocks, metals and other materials.-Mechanisms:...

  • Hysteresis
    Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...

  • Stress relaxation
    Stress relaxation
    Stress relaxation describes how polymers relieve stress under constant strain. Because they are viscoelastic, polymers behave in a nonlinear, non-Hookean fashion...

  • Viscoelasticity
    Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like honey, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain instantaneously when stretched and just...

  • Viscoplasticity
    Viscoplasticity is a theory in continuum mechanics that describes the rate-dependent inelastic behavior of solids. Rate-dependence in this context means that the deformation of the material depends on the rate at which loads are applied...

External links

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