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MAT-26

Norton power-law creep

ε̇ = A σ^n. Secondary (steady) creep rate.

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CreepNorton 1929

Governing equation

ε˙=Aσn\dot{\varepsilon}=A\sigma^n

σ∈[5,400]\sigma \in \left[5, 400\right]

where

A
Norton A (1/s/MPa^n)
\sigma
Stress (MPa)
n
Creep exponent (—)
\dot{\varepsilon}
Creep rate (1/s)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

MAT-26 · curve
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①

Governing law — red

ε˙=Aσn\dot{\varepsilon}=A\sigma^n

σ∈[5,400]\sigma \in \left[5, 400\right]

σ=5\sigma = 5ε˙=3.12×10−13\dot{\varepsilon} = 3.12\times 10^{-13}

②

Domain of the variable — blue

σmin⁡=5,σmax⁡=400\sigma_{\min} = 5,\quad \sigma_{\max} = 400

σ∈[5,400]\sigma \in \left[5, 400\right]

σ=5\sigma = 5σ=5\sigma = 5

③

Response curve — green

ε˙=Aσn\dot{\varepsilon}=A\sigma^n

σ∈[5,400]\sigma \in \left[5, 400\right]

σ=5\sigma = 5ε˙=3.12×10−13\dot{\varepsilon} = 3.12\times 10^{-13}

④

Rate of change — amber

dε˙dσ\frac{\mathrm{d}\dot{\varepsilon}}{\mathrm{d}\sigma}

σ∈[5,400]\sigma \in \left[5, 400\right]

σ=7.484\sigma = 7.484ε˙′=1.92×10−12\dot{\varepsilon}^{\prime} = 1.92\times 10^{-12}

Lecture brief

Historical brief

Hooke (1678), Hall–Petch grain size, Arrhenius activation and Paris fatigue-crack growth are the spine of materials selection. The sheets relate stress, microstructure and life. This sheet (MAT-26 — Norton power-law creep) is the form associated with Norton 1929. Working symbols: AA, σ\sigma, nn →\rightarrow ε˙\dot{\varepsilon}. Norton fitted the steady creep rate of metals to a power of stress. Combined with Arrhenius it is the Norton–Bailey law.

Purpose

Purpose: compute ε˙\dot{\varepsilon} from AA, σ\sigma, nn in Materials via ε˙=Aσn\dot{\varepsilon}=A\sigma^n ε̇ = A σ^n. Secondary (steady) creep rate. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given A=1.000e−16 1/s/MPanA = 1.000e-16\,\mathrm{1/s/MPa^n}, σ=80.000 MPa\sigma = 80.000\,\mathrm{MPa}, n=5.000 —n = 5.000\,\mathrm{—}, the governing relation ε˙=Aσn\dot{\varepsilon}=A\sigma^n yields ε˙=3.277e−7 1/s\dot{\varepsilon} = 3.277e-7\,\mathrm{1/s}. A hot bar, a stress, a strain-rate arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Creep rate \dot{\varepsilon}0.000000 1/s
Reading speed

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MAT-26 · curve
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Narration of this film

A hot bar, a stress, a strain-rate arrow.

Norton fitted the steady creep rate of metals to a power of stress. Combined with Arrhenius it is the Norton–Bailey law.

Reading speed

Watch on YouTube