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 mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield 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. Creep always increases with temperature.
The rate of deformation is a function of the material 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 will 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.
The temperature range in which creep deformation may occur differs in various materials. For example, tungsten requires a temperature in the thousands of degrees before creep deformation can occur, while ice will creep at temperatures 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 (as measured on a thermodynamic temperature scale such as kelvin or rankine) for metals, and at 40–50% of melting point for ceramics. Virtually any material will creep upon approaching its melting temperature. Since the creep minimum temperature is related to the melting point, creep can be seen at relatively low temperatures for some materials. Plastics and low-melting-temperature metals, including many solders, can begin to creep at room temperature, as can be seen markedly in old lead hot-water pipes. Glacier flow is an example of creep processes in ice.
Stages of creep:
Strain as a function of time due to constant stress over an extended period for a viscoelastic material.
In the initial stage, or primary creep, the strain rate is relatively high, but slows with increasing time. This is due to work hardening. The strain rate eventually reaches a minimum and becomes near constant. This is due to the balance between work hardening and annealing (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 phenomena.
Mechanisms of creep
The mechanism of creep depends on temperature and stress. Various mechanisms 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)
Thermally activated glide – e.g., via cross-slip
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.
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 = 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 is a form of diffusion 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 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 lays in an energetically favourable 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 neighbour 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 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 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 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 neighbours 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
a) Applied stress and b) induced strain as functions of time over a short period for a viscoelastic material.
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 Newtoniandashpot in parallel. The creep strain is given by the following convolution integral:
σ = applied stress
C0 = instantaneous creep compliance
C = creep compliance coefficient
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 (Spectra, Dyneema) will show time-linear creep, whereas polyester or aramids (Twaron, Kevlar) will show a time-logarithmic creep.
Creep of concrete
The creep of concrete, which originates from the calcium silicate hydrates (C-S-H) in the hardened Portland cement paste (which is the binder of mineral aggregates), is fundamentally different from the creep of metals as well as polymers. Unlike the creep of metals, it occurs at all stress levels and, within the service stress range, is linearly dependent on the stress if the pore water content is constant. Unlike the creep of polymers and metals, it exhibits multi-months aging, caused by chemical hardening due to hydration which stiffens the microstructure, and multi-year aging, caused by long-term relaxation of self-equilibrated micro-stresses in the nano-porous microstructure of the C-S-H. If concrete is fully dried, it does not creep, but it is next to impossible to dry concrete fully without severe cracking.
High Temperature Failure Analysis
Creep occurs under load at high temperature. Boilers, gas turbine engines, and ovens are some of the systems that have components that experience creep. An understanding of high temperature materials behavior is beneficial in evaluating failures in these types of systems.
Failures involving creep are usually easy to identify due to the deformation that occurs. Failures may appear ductile or brittle. Cracking may be either transgranular or intergranular. While creep testing is done at constant temperature and constant load actual components may experience damage at various temperatures and loading conditions.
The behavior of materials can be broadly classified into two categories; brittle and ductile. Steel and aluminum usually fall in the class of ductile materials. Glass and cast iron fall in the class of brittle materials. The two categories can be distinguished by comparing the stress-strain curves, such as the ones shown in Fig.
Figure : Ductile and brittle material behavior
The material response for ductile and brittle materials is exhibited by both qualitative and quantitative differences in their respective stress-strain curves. Ductile materials will withstand large strains before the specimen ruptures; brittle materials fracture at much lower strains. The yielding region for ductile materials often takes up the majority of the stress-strain curve, whereas for brittle materials it is nearly non-existent. Brittle materials often have relatively large Young’s moduli and ultimate stresses in comparison to ductile materials.
These differences are a major consideration for design. Ductile materials exhibit large strains and yielding before they fail. On the contrary, brittle materials fail suddenly and without much warning. Thus ductile materials such as steel are a natural choice for structural members in buildings as we desire considerable warning to be provided before a building fails. The energy absorbed (per unit volume) in the tensile test is simply the area under the stress strain curve. Clearly, by comparing the curves in Fig, we observe that ductile materials are capable of absorbing much larger quantities of energy before failure.
Finally, it should be emphasized that not all materials can be easily classified as either ductile or brittle. Material response also depends on the operating environment; many ductile materials become brittle as the temperature is decreased. With advances in metallurgy and composite technology, other materials are advanced combinations of ductile and brittle constituents.
A material is brittle if, when subjected to stress, it breaks without significant deformation (strain). Brittle materials absorb relatively little energy prior to fracture, even those of high strength. Breaking is often accompanied by a snapping sound. Brittle materials include most ceramics and glasses (which do not deform plastically) and some polymers, such as PMMA and polystyrene. Many steels become brittle at low temperatures (see ductile-brittle transition temperature), depending on their composition and processing.
When used in materials science, it is generally applied to materials that fail when there is little or no evidence of plastic deformation before failure. One proof is to match the broken halves, which should fit exactly since no plastic deformation has occurred.
When a material has reached the limit of its strength, it usually has the option of either deformation or fracture. A naturally malleable metal can be made stronger by impeding the mechanisms of plastic deformation (reducing grain size, precipitation hardening, work hardening, etc.), but if this is taken to an extreme, fracture becomes the more likely outcome, and the material can become brittle. Improving material toughness is therefore a balancing act.
Ductility is especially important in metalworking, as materials that crack or break under stress cannot be manipulated using metal forming processes, such as hammering, rolling, and drawing. Malleable materials can be formed using stamping or pressing, whereas brittle metals and plastics must be molded.
High degrees of ductility occur due to metallic bonds, which are found predominantly in metals and leads to the common perception that metals are ductile in general. In metallic bonds valence shell electrons are delocalized and shared between many atoms. The delocalized electrons allow metal atoms to slide past one another without being subjected to strong repulsive forces that would cause other materials to shatter.
Ductility can be quantified by the fracture strain , which is the engineering strain at which a test specimen fractures during a uniaxial tensile test. Another commonly used measure is the reduction of area at fracture . The ductility of steel varies depending on the alloying constituents. Increasing levels of carbon decreases ductility. Many plastics and amorphous solids, such as Play-Doh, are also malleable. The most ductile metal is platinum and the most malleable metal is gold.
Mechanisms of creep deformation
The chief creep deformation mechanisms can be grouped into;
1) Dislocation glide
Involves dislocation moving along slip planes and overcoming barriers by thermal activation.
Occurs at high stress.
2) Dislocation creep
Involves dislocation movement to overcome barriers by diffusion of vacancies or interstitials.
3) Diffusion creep
Involves the flow of vacancies and interstitials through a crystal under the influence of applied stress.
4) Grain boundary sliding
Involves the sliding of grains past each other.
Effects of stress and temperature on creep rate
Dependence on Temperature
Creep occurs faster at higher temperatures. However, what constitutes a high temperature is different for different metals. When considering creep, the concept of a homologous temperature is useful.
The homologous temperature is the actual temperature divided by the melting point of the metal, with both being expressed in K. In general, creep tends to occur at a significant rate when the homologous temperatures are 0.4 or higher.
Dependence on stress
Where n is termed the stress exponent. Prediction of the value of n from first principles is not easy, but its value does depend on which mechanism of creep is operating. For example, for diffusion creep its value is approximately 1, while for dislocation creep it is usually in the range 3-8.
Creep rate equation
Q = activation energy; n = stress exponent; A = constant;
The activation energy Q can be determined experimentally, by plotting the natural log of creep rate against the reciprocal of temperature.