Creep Strain Rate (Norton's Power Law, Simplified)
Creep Strain Rate (Norton's Power Law, Simplified)
At elevated temperature, materials slowly and permanently deform under stresses well below their yield strength — a time-dependent process called creep that governs the design life of turbine blades, boiler tubing, and any component that operates hot and under load for extended periods. Norton's power law is the standard empirical model for the steady-state (secondary) creep stage, where strain rate settles into a roughly constant value before accelerating again in tertiary creep toward rupture; because the stress exponent n is typically large (often 3-8), creep rate is extremely sensitive to even modest stress increases.
Norton's power law gives creep strain rate as edot = A*sigma^n, with stress treated as its plain numeric MPa value in this empirical form. where A_creep is an empirical material creep constant, sigma_creep is the applied stress expressed as a plain numeric MPa value, and n_creep is the stress exponent, both dimensionless model parameters.
Inputs
A_creep := 1e-14=1e-14
sigma_creep := 100=100
n_creep := 5=5
Because this empirical power law hides its true units inside the fitted constant A, the stress is evaluated as a plain numeric MPa value first, and only afterward is a conventional 1/hr rate unit attached to the result.
edot_num := A_creep·sigma_creep^n_creep=1e-04
Attaching the conventional per-hour unit turns the dimensionless model output into a usable engineering creep rate.
edot_creep := edot_num·(1 hr^-1)=2.78e-08 Hz
Results
A steady-state creep rate on this order accumulated over a component's design life (which can be tens of thousands of hours in power generation service) determines whether total creep strain stays within an acceptable limit, often around 1% total strain for many turbine and pressure-part applications. Because the exponent n is large, a stress increase of just 20-30% (from a pressure or temperature upset, for example) can multiply the creep rate several-fold, which is why creep-limited components carry conservative stress margins.
Assumptions & limitations
- Norton's law describes only steady-state (secondary) creep, not primary or tertiary stages.
- A and n are empirical, material- and temperature-specific constants.
- Stress is treated as a plain numeric MPa value per the conventional empirical form of this law.
- Does not predict time to rupture directly — that requires integrating strain or a separate rupture correlation.