Norton Creep Law

At temperatures above roughly forty percent of its absolute melting point, a metal under constant load does not simply deform and stop. It keeps deforming, slowly, indefinitely, and that is creep. The classic creep curve has three stages: primary, where the rate falls as the metal hardens; secondary, where hardening and thermal recovery balance and the rate is nearly constant; and tertiary, where damage accumulates and the rate accelerates to rupture. Norton's law describes the secondary stage, which is where most of the component's life is spent and where design is done.

The form is a power law in stress multiplied by an Arrhenius term in temperature. F. H. Norton set out the stress dependence in 1929; the Arrhenius factor came out of Dorn's later work, and the two are usually written together as the Norton–Bailey or Norton–Dorn equation. Neither half is derived from first principles for a general alloy. The value of the equation lies in the two exponents, both of which are diagnostic.

The stress exponent n is a fingerprint of the creep mechanism, not a fitting parameter. An n near 1 means diffusional creep — atoms migrating from boundaries under compression to boundaries under tension, either through the lattice (Nabarro–Herring, dominant at higher temperatures) or along the grain boundaries themselves (Coble, dominant at lower ones). Both scale as 1/d² or 1/d³ in grain size, which means coarse grains are an advantage in this regime — the exact opposite of Hall–Petch, and the reason turbine blades progressed from equiaxed to directionally solidified to single crystal. An n near 2 means grain-boundary sliding, which is the superplastic regime. An n from 3 to 8 means dislocation creep by climb and glide, which is what most engineering alloys do in service, and where grain size scarcely matters. An n above about 10 almost always means a threshold stress is being ignored: oxide-dispersion and precipitation-strengthened alloys have a stress below which they simply do not creep, and forcing a plain power law through data that has one produces an absurd apparent exponent. Refit against (σ − σ_threshold) instead.

Q tells a parallel story. When the fitted activation energy comes out near the self-diffusion activation energy of the base metal — about 250 to 280 kJ/mol for iron, 142 for aluminium, 197 for copper, 285 for nickel — lattice diffusion is the controlling step and dislocation climb is the mechanism. A markedly lower Q says diffusion is running along a faster path, usually grain boundaries or dislocation cores, which is what happens at lower temperatures and in fine-grained material.

The temperature in the exponent is ABSOLUTE, and Celsius here is not an approximation, it is nonsense. An Arrhenius exponent is Q/RT with T in kelvin, and substituting a Celsius number produces an answer wrong by many orders of magnitude with no warning. Work the arithmetic once: 900 K is 626.85 °C, and putting 626.85 in place of 900 changes exp(−Q/RT) from 5.6 × 10⁻¹⁷ to 5.2 × 10⁻²⁴ for a Q of 280 kJ/mol. That is a factor of ten million, and the result still looks like a small number.

A is unit-bound and its dimensions depend on n. A has units of reciprocal time divided by stress to the power n, so it means nothing without knowing both the stress unit and the rate unit it was fitted with — and because the exponent multiplies the stress-unit error, a wrong unit is wrong by orders of magnitude rather than by a factor. This site takes A in s⁻¹·MPa⁻ⁿ: stress in megapascals, rate per second. A and n also are not independent. They are fitted together from the slope and intercept of log(rate) against log(stress) at constant temperature, and changing n means refitting A. Carrying an A across from a source that used a different exponent is one of the most reliable ways to get a creep calculation badly wrong.

Finally, keep the equation's scope in view. It describes steady-state creep of a uniformly stressed section. It says nothing about primary creep, which matters for clearances and for bolted joints losing preload; nothing about tertiary creep or the damage accumulation that ends the component's life; and nothing about stress redistribution around notches, section changes and welds, which is where creep components actually fail. For those, a creep-damage model — Kachanov–Rabotnov continuum damage, or a finite-element creep analysis with this law as the constitutive input — is the next step, not a bigger version of this page.