Creep in which the steady-state creep rate is proportional to the stress raised to the power n (n is about 3 to 8). It arises from dislocation glide combined with recovery by climb, and dominates at high stresses.
Japanese name: べき乗則クリープ
Power-law creep appears in 3 practice questions across 1 topic, including High-temperature materials and creep.
The steady-state creep rate in power-law creep is written ε̇ = Aσⁿexp(−Q/RT). Dividing the stress by the shear modulus G and using the self-diffusion coefficient D to write ε̇ ∝ D(σ/G)ⁿ makes different materials easier to compare. n is the stress exponent; for pure metals and many single-phase alloys it is about 4 to 7, and values close to 5 are especially common. Because n is large, with n = 5, for example, lowering the stress by only 10% changes the rate by a factor of 0.9⁵ ≈ 0.59. That the activation energy Q is close to that of self-diffusion shows that atomic diffusion sets the rate of deformation.
Dislocations move on their slip planes, but they stop when they catch on precipitates or become tangled with other dislocations. At high temperature, vacancies gather at or leave a dislocation, so it climbs out of its slip plane; this lets it get past obstacles or annihilate with a dislocation of opposite sign. Because the rate of this recovery is set by vacancy diffusion, power-law creep, although carried by dislocations, shows the same temperature dependence as diffusion. As deformation proceeds, dislocations line up into low-angle grain boundaries, and subgrains form inside the grains. The higher the stress, the smaller the subgrains.
The stress exponent is not a fixed constant for each material. In alloys such as Al-Mg, where solute atoms drag on moving dislocations, glide itself becomes the slow step and n ≈ 3, distinguished from the value of about 5 for pure-metal behavior. At still higher stresses the rate rises faster than a power of stress and the equation no longer holds (power-law breakdown). In alloys strengthened by dispersed oxide particles and similar materials, the apparent stress exponent can far exceed 10, and the apparent activation energy can exceed that of self-diffusion. This is due to a threshold stress σ_th at which particles stop dislocations; using σ − σ_th in place of σ brings n back toward ordinary values.
n and Q are determined by creep tests. Measuring the steady-state creep rate at several stresses at constant temperature and plotting it on log-log axes gives n as the slope. Stress-change tests, in which the stress on a single specimen is changed in steps, reduce the effect of microstructural differences between specimens. Similarly, holding the stress constant, varying the temperature and plotting ln ε̇ against 1/T gives Q from the slope −Q/R. In design, the equation found this way is used to find, for example, the stress that produces the allowable strain (such as 1%) in 100,000 hours. Extrapolating to stresses below those tested, however, may cross into another mechanism such as diffusion creep.
Answer: A. About 2.5 times
At the same temperature A and exp(−Q/RT) do not change, so the ratio of the rates is the stress ratio raised to the power n: (1.2)⁵ ≈ 2.49, about 2.5 times. That a mere 20% increase in stress more than doubles the rate is characteristic of dislocation creep (power-law creep), where n is large, about 3 to 8, and a small error in the design stress greatly affects the life. About 6.0 times is the value obtained by multiplying the stress ratio by the exponent n, and about 1.2 times assumes that the rate is proportional to stress (n = 1), which is the case for diffusion creep operating at low stress. Plotting rate against stress on log-log axes gives a slope of n.
Answer: B. Coble creep by diffusion of atoms along grain boundaries
In diffusion creep, atoms diffuse from grain boundaries under tension to those under compression, elongating the grains, and the rate is proportional to stress (n = 1). When the diffusion path runs along the grain boundaries it is called Coble creep, and the rate is inversely proportional to the cube of the grain size. When it is lattice diffusion through the grain interiors it is called Nabarro–Herring creep, and the rate is inversely proportional to the square of the grain size. Grain boundary diffusion has a lower activation energy than lattice diffusion, so Coble creep dominates at relatively low temperatures and fine grain sizes, while the contribution of Nabarro–Herring creep grows at high temperatures near the melting point. Power-law creep by dislocations has a large n of 3 to 8 and hardly depends on grain size.
They are used with almost the same meaning. Power-law creep is the name that focuses on the form of the equation, with the rate proportional to a power of stress; dislocation creep focuses on dislocations carrying the deformation. When contrasting it with diffusion creep, it is more often called dislocation creep.
For many metals, the Monkman–Grant relation is known, in which the product of the minimum creep rate and the rupture time is nearly constant. Measuring the minimum creep rate in a short test gives a rough idea of the rupture time, but the constant must be determined by measurement for each material.
The larger n, the more a small difference in stress changes the rate. With n = 5, doubling the stress raises the rate 32 times. Stress concentrations, residual stresses and errors in estimating loads strongly affect life, so the actual stress distribution is checked with the finite element method or similar tools, and a margin is built into the design.
That a mere 20% increase in stress more than doubles the rate is characteristic of dislocation creep (power-law creep), where n is large, about 3 to 8, and a small error in the design stress greatly affects the life.
The steady-state creep rate of a heat-resistant alloy follo…Power-law creep by dislocations has a large n of 3 to 8 and hardly depends on grain size.
A fine-grained polycrystalline metal was creep tested at a …Dislocation glide dominates at high stresses close to the ideal strength, power-law creep involving dislocation climb at intermediate stresses and high temperatures, and diffusion creep at low stresses and high temperatures.
Which statement about the deformation mechanism map of Ashb…Diffusion creep Creep Dislocation Deformation mechanism map Larson–Miller parameter Nickel-based superalloy Parabolic rate law Pilling–Bedworth ratio Thermal barrier coating