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Norton's Power Law (Creep Rate)
Describes the steady-state (secondary) creep strain rate of a material as a power-law function of applied stress.
Interpretation
ε̇ = A·σ^n. Steady‑state creep rate as a power‑law function of stress. Used to describe secondary creep. A and n are temperature‑dependent constants. Common in metals.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| epsilon_dot | Steady-state creep strain rate | 1/s |
| A | Material and temperature-dependent constant | |
| sigma | Applied stress | MPa |
| n | Creep stress exponent (typically 3-8) |
What it means
Norton’s power law (or the Norton‑Bailey creep law) describes the steady‑state (secondary) creep strain rate ε̇ as a function of applied stress σ: ε̇ = A σⁿ. Here, A is a material constant that depends on temperature, and n is the stress exponent (typically between 3 and 8 for metals). This empirical relation is widely used in creep analysis and design, as it simplifies the complex physics of dislocation climb and glide. It is valid for moderate stresses and temperatures where power‑law creep dominates. In engineering, it helps estimate the deformation rate of components under constant load, aiding in life prediction and material selection for high‑temperature service. Understanding this law is essential for power plant engineers and designers of creep‑limited structures.
Worked example
Norton's Power Law – Two Examples
Real‑World| Parameter | Value |
|---|---|
| A | 1×10⁻¹⁸ |
| σ | 100 MPa |
| n | 5 |
| Parameter | Value |
|---|---|
| A | 1×10⁻¹⁶ |
| σ | 80 MPa |
| n | 4 |
Common mistakes
- Norton’s power law: ε̇ = A·σⁿ – describes steady‑state creep rate as a function of applied stress.
- Stress exponent n: Typically between 3 and 8 for metals – depends on creep mechanism (e.g., dislocation climb, diffusion).
- Pre‑exponential A: Temperature‑dependent – often expressed as A = A₀·exp(−Q/(RT)).
- Units: ε̇ in s⁻¹, σ in Pa – A must have units that make the equation dimensionally consistent.
- Assumptions: Applicable for steady‑state (secondary) creep – not for primary or tertiary creep.
Applications
Norton's power law (ε̇ = A·σ^n) describes the steady‑state creep rate as a function of applied stress. It is used to model creep deformation in metals and alloys at high temperatures. Engineers use the constants A and n (stress exponent) to predict creep rates, to design components for high‑temperature service, and to select materials for creep‑resistant applications. The equation is central to the design of gas turbine engines, nuclear reactors, and chemical plant equipment. By understanding Norton's law, materials scientists can develop alloys with enhanced creep resistance and predict service life under complex loading.
- Creep deformation analysis of high‑temperature components
- Material selection for creep‑resistant alloys
- Design of gas turbines, steam turbines, and reactors
- Life assessment of pressure vessels and piping
- Development of new creep‑resistant materials
Frequently Asked Questions
Norton's power law describes the steady‑state creep strain rate as a function of stress: ε̇ = A · σ^n, where ε̇ is the creep rate (1/s), σ is the applied stress, A is a material constant (temperature‑dependent), and n is the stress exponent (typically 3‑8 for metals).
Applying it to the primary or tertiary creep stages, where it is only valid for the steady‑state (secondary) creep regime. Also, using a single A and n over a wide stress range where the mechanism changes.
n indicates the dominant creep mechanism. n ≈ 1 for diffusion creep, n ≈ 3‑5 for dislocation climb (power‑law creep), and n > 5 for dislocation glide (power‑law breakdown).
A is strongly temperature‑dependent, following an Arrhenius relationship: A = A₀ · exp(–Q_c / (RT)), where Q_c is the activation energy for creep. n is relatively temperature‑insensitive.
By plotting log(ε̇) vs log(σ) from creep test data. The slope gives n, and the intercept gives log(A) at a given temperature.
- Pure metals: n ≈ 4‑5.
- Solid solutions: n ≈ 3‑4.
- Precipitation‑strengthened alloys: n ≈ 5‑8.
- Ceramics: n ≈ 1‑2.
At high temperatures, grain boundary sliding can contribute, and the creep rate may depend on grain size. The standard Norton law assumes a fixed microstructure.
- Only valid for steady‑state creep.
- Assumes a constant mechanism over the stress range.
- Does not account for tertiary creep (damage accumulation).
- Predicting creep deformation in high‑temperature components.
- Designing for creep‑limited life.
- Material selection for creep resistance.
Primary creep is often modelled using time‑hardening or strain‑hardening laws, which are more complex. Norton's law is used only for the steady‑state portion.