This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Creep" deformation – news · newspapers · books · scholar · JSTOR (March 2017) (Learn how and when to remove this message)

In materials science, creep (sometimes called cold flow) is the tendency of a solid material to undergo slow deformation while subject to 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.

Creep or cold flow is of great concern in plastics. Blocking agents are chemicals used to prevent or inhibit cold flow. Otherwise rolled or stacked sheets stick together.^[1]

Temperature dependence

The temperature range in which creep deformation occurs depends on the material. 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 the onset of creep deformation, lead may creep at room temperature, and ice will creep at temperatures below 0 °C (32 °F).^[2] 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.^[3] The effects of creep deformation generally become noticeable at approximately 35% of the melting point (in Kelvin) for metals and at 45% of melting point for ceramics.^[4]

Theoretical framework

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, primary 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.^[5]

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.^[6]

Mechanisms of deformation

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

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.^[7]

${\displaystyle {\frac {\mathrm {d} \varepsilon }{\mathrm {d} t}}={\frac {C\sigma ^{m}}{d^{b}}}e^{\frac {-Q}{kT}}}$

where ε 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.^[8]

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), 4 ≤ m ≤ 6, and b < 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," σ_th, below which creep can't be measured. The modified power law equation then becomes:

${\displaystyle {\frac {\mathrm {d} \varepsilon }{\mathrm {d} t}}=A\left(\sigma -\sigma _{\rm {th}}\right)^{m}e^{\frac {-Q}{{\bar {R}}T}}}$

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

Nabarro–Herring (NH) creep is a form of diffusion creep, while dislocation glide creep does not involve atomic diffusion. Nabarro–Herring creep dominates at high temperatures and low stresses. As shown in the figure on the right, the lateral sides of the crystal are subjected to tensile stress and the horizontal sides to compressive stress. The atomic volume is altered by applied stress: it increases in regions under tension and decreases in regions under compression. So the activation energy for vacancy formation is changed by ±σΩ, where Ω is the atomic volume, the positive value is for compressive regions and negative value is for tensile regions. Since the fractional vacancy concentration is proportional to exp(−Q_f ± σΩ/RT), where Q_f is the vacancy-formation energy, the vacancy concentration is higher in tensile regions than in compressive regions, leading to a net flow of vacancies from the regions under tension to the regions under compression, and this is equivalent to a net atom diffusion in the opposite direction, which causes the creep deformation: the grain elongates in the tensile stress axis and contracts in the compressive stress axis.

In Nabarro–Herring creep, 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 the 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) to the nearby vacant site (another potential well). The general form of the diffusion equation is

${\displaystyle D=D_{0}e^{\frac {E}{KT}}}$

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 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 the 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, thus, Coble creep will be more important in materials composed of very fine grains. 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) is less than 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. Generally, the diffusional creep rate should be the sum of Nabarro–Herring creep rate and Coble creep rate. Diffusional creep leads to grain-boundary separation, that is, voids or cracks form between the grains. To heal this, grain-boundary sliding occurs. The diffusional creep rate and the grain boundary sliding rate must be balanced if there are no voids or cracks remaining. When grain-boundary sliding can not accommodate the incompatibility, grain-boundary voids are generated, which is related to the initiation of creep fracture.

Solute drag creep

Solute drag creep is one of the mechanisms for power-law creep (PLC), involving both dislocation and diffusional flow. Solute drag creep is observed in certain metallic alloys. In these alloys, the creep rate increases during the first stage of creep (Transient creep) before reaching a steady-state value. This phenomenon can be explained by a model associated with solid-solution strengthening. At low temperatures, the solute atoms are immobile and increase the flow stress required to move dislocations. However, at higher temperatures, the solute atoms are more mobile and may form atmospheres and clouds surrounding the dislocations. This is especially likely if the solute atom has a large misfit in the matrix. The solutes are attracted by the dislocation stress fields and are able to relieve the elastic stress fields of existing dislocations. Thus the solutes become bound to the dislocations. The concentration of solute, C, at a distance, r, from a dislocation is given by the Cottrell atmosphere defined as^[9]

${\displaystyle C_{r}=C_{0}\exp \left(-{\frac {\beta \sin \theta }{rKT}}\right)}$

where C₀ is the concentration at r = ∞ and β is a constant which defines the extent of segregation of the solute. When surrounded by a solute atmosphere, dislocations that attempt to glide under an applied stress are subjected to a back stress exerted on them by the cloud of solute atoms. If the applied stress is sufficiently high, the dislocation may eventually break away from the atmosphere, allowing the dislocation to continue gliding under the action of the applied stress. The maximum force (per unit length) that the atmosphere of solute atoms can exert on the dislocation is given by Cottrell and Jaswon^[10]

${\displaystyle {\frac {F_{\rm {max}}}{L}}={\frac {C_{0}\beta ^{2}}{bkT}}}$

When the diffusion of solute atoms is activated at higher temperatures, the solute atoms which are "bound" to the dislocations by the misfit can move along with edge dislocations as a "drag" on their motion if the dislocation motion or the creep rate is not too high. The amount of "drag" exerted by the solute atoms on the dislocation is related to the diffusivity of the solute atoms in the metal at that temperature, with a higher diffusivity leading to lower drag and vice versa. The velocity at which the dislocations glide can be approximated by a power law of the form

${\displaystyle v=B{\sigma ^{*}}^{m}B=B_{0}\exp \left({\frac {-Q_{\rm {g}}}{RT}}\right)}$

where m is the effective stress exponent, Q is the apparent activation energy for glide and B₀ is a constant. The parameter B in the above equation was derived by Cottrell and Jaswon for interaction between solute atoms and dislocations on the basis of the relative atomic size misfit ε_a of solutes to be^[10]

${\displaystyle B={\frac {9kT}{MG^{2}b^{4}\ln {\frac {r2}{r1}}}}\cdot {\frac {D_{\rm {sol}}}{\varepsilon _{\rm {a}}^{2}c_{0}}}}$

where k is Boltzmann's constant, and r₁ and r₂ are the internal and external cut-off radii of dislocation stress field. c₀ and D_sol are the atomic concentration of the solute and solute diffusivity respectively. D_sol also has a temperature dependence that makes a determining contribution to Q_g.

If the cloud of solutes does not form or the dislocations are able to break away from their clouds, glide occurs in a jerky manner where fixed obstacles, formed by dislocations in combination with solutes, are overcome after a certain waiting time with support by thermal activation. The exponent m is greater than 1 in this case. The equations show that the hardening effect of solutes is strong if the factor B in the power-law equation is low so that the dislocations move slowly and the diffusivity D_sol is low. Also, solute atoms with both high concentration in the matrix and strong interaction with dislocations are strong gardeners. Since misfit strain of solute atoms is one of the ways they interact with dislocations, it follows that solute atoms with large atomic misfit are strong gardeners. A low diffusivity D_sol is an additional condition for strong hardening.^[11][12]

Solute drag creep sometimes shows a special phenomenon, over a limited strain rate, which is called the Portevin–Le Chatelier effect. When the applied stress becomes sufficiently large, the dislocations will break away from the solute atoms since dislocation velocity increases with the stress. After breakaway, the stress decreases and the dislocation velocity also decreases, which allows the solute atoms to approach and reach the previously departed dislocations again, leading to a stress increase. The process repeats itself when the next local stress maximum is obtained. So repetitive local stress maxima and minima could be detected during solute drag creep.

Dislocation climb-glide creep

Dislocation climb-glide creep is observed in materials at high temperature. The initial creep rate is larger than the steady-state creep rate. Climb-glide creep could be illustrated as follows: when the applied stress is not enough for a moving dislocation to overcome the obstacle on its way via dislocation glide alone, the dislocation could climb to a parallel slip plane by diffusional processes, and the dislocation can glide on the new plane. This process repeats itself each time when the dislocation encounters an obstacle. The creep rate could be written as:

${\displaystyle {\frac {\mathrm {d} \varepsilon }{\mathrm {d} t}}={\frac {A_{\rm {CG}}D_{\rm {L}}}{\sqrt {M}}}\left({\frac {\sigma \Omega }{kT}}\right)^{4.5}}$

where A_CG includes details of the dislocation loop geometry, D_L is the lattice diffusivity, M is the number of dislocation sources per unit volume, σ is the applied stress, and Ω is the atomic volume. The exponent m for dislocation climb-glide creep is 4.5 if M is independent of stress and this value of m is consistent with results from considerable experimental studies.

Harper–Dorn creep

Harper–Dorn creep is a climb-controlled dislocation mechanism at low stresses that has been observed in aluminum, lead, and tin systems, in addition to nonmetal systems such as ceramics and ice. It was first observed by Harper and Dorn in 1957.^[13] It is characterized by two principal phenomena: a power-law relationship between the steady-state strain rate and applied stress at a constant temperature which is weaker than the natural power-law of creep, and an independent relationship between the steady-state strain rate and grain size for a provided temperature and applied stress. The latter observation implies that Harper–Dorn creep is controlled by dislocation movement; namely, since creep can occur by vacancy diffusion (Nabarro–Herring creep, Coble creep), grain boundary sliding, and/or dislocation movement, and since the first two mechanisms are grain-size dependent, Harper–Dorn creep must therefore be dislocation-motion dependent.^[14] The same was also confirmed in 1972 by Barrett and co-workers^[15] where FeAl₃ precipitates lowered the creep rates by 2 orders of magnitude compared to highly pure Al, thus, indicating Harper–Dorn creep to be a dislocation based mechanism.

Harper–Dorn creep is typically overwhelmed by other creep mechanisms in most situations, and is therefore not observed in most systems. The phenomenological equation which describes Harper–Dorn creep is

${\displaystyle \frac{\mathrm{d}\mathrm{\epsilon <!--\; \epsilon \; -->}}{\mathrm{d}t}={\mathrm{\rho <!--\; \rho \; -->}}_0\frac{D_{}}{}}$Zdroj:https://en.wikipedia.org?pojem=Creep_(deformation)
Text je dostupný za podmienok Creative Commons Attribution/Share-Alike License 3.0 Unported; prípadne za ďalších podmienok. Podrobnejšie informácie nájdete na stránke Podmienky použitia.

---