Secondary Creep
Secondary creep — the steady-state stage where strain hardening and recovery are balanced, the minimum creep rate, its dependence on stress and temperature, and its role as the workhorse of creep analysis.
The secondary creep stage
Secondary creep is the middle stage of the creep curve, where the strain rate is approximately constant. The strain hardening from primary creep is balanced by thermal recovery — dislocations are generated and annihilated at equal rates, giving a steady-state microstructure and a constant creep rate. The secondary creep rate is the minimum creep rate on the creep curve. It is the most widely used creep parameter because it is relatively easy to measure, it represents the long-term steady-state behaviour, and it is the basis of the Norton creep law.
Stress dependence — the Norton power law
The secondary creep rate depends on stress, typically as a power law. This is the Norton creep law, the most widely used creep constitutive relation. The stress exponent n is typically in the range 3–8 for many metals under dislocation-creep conditions, though it varies with the material and the creep mechanism. At very low stresses, the exponent may approach 1 (diffusion creep, Nabarro-Herring or Coble creep). At very high stresses, the power law may break down and an exponential or hyperbolic-sine form may be needed. The Norton law parameters must be calibrated from secondary creep data at the relevant stresses and temperatures.
Temperature dependence — the Arrhenius term
The secondary creep rate depends strongly on temperature, typically following an Arrhenius relationship. The activation energy Q is a material constant that reflects the energy barrier for the rate-controlling creep mechanism. A modest temperature increase may double or triple the creep rate because of the exponential dependence. The Arrhenius term is combined with the Norton stress term to give the full secondary creep rate expression. The activation energy must be measured for the specific material — it is not universal.
The minimum creep rate
The secondary creep rate is the minimum creep rate on the creep curve. It is used as a design parameter in several ways. First, it is used to estimate the time to a specified strain (assuming the secondary stage dominates). Second, it is used to compare the creep resistance of different materials or conditions. Third, it is used in parametric rupture correlations (e.g. Larson-Miller) as a surrogate for the creep rate. The minimum creep rate is typically measured from a creep test by fitting a straight line to the secondary portion of the strain-time curve.
When secondary creep dominates
Secondary creep dominates the total creep strain when the primary stage is short and the tertiary stage has not yet begun. This is the case at moderate stresses and temperatures where the component operates for a long time in the steady-state regime. Many engineering creep analyses use a secondary-creep-only model for simplicity — the creep strain is the minimum creep rate multiplied by the time. This is a good approximation for long-duration steady-state operation but may under-predict the strain when primary creep is significant or when the component enters tertiary creep before the end of life.
The secondary creep rate is the most commonly used creep parameter, but it is not always the dominant stage. Always assess whether primary or tertiary creep contributes significantly to the total strain for the specific stress, temperature and duration before using a secondary-creep-only model.
Why the minimum creep rate is so useful
The minimum or approximately steady creep rate provides a compact measure of long-term deformation and is the basis of many engineering correlations. When secondary creep occupies most of the component life, integrating this rate can give a useful first estimate of accumulated strain and can support screening calculations before a full transient FEA. Its simplicity is also why the Norton law is widely used. The limitation is equally important: a constant-rate model cannot reproduce primary deceleration or tertiary acceleration, so it should not be used to infer rupture or early-life relaxation unless those behaviours are addressed separately.
Stress exponent, temperature sensitivity and extrapolation
Secondary creep is highly sensitive to both stress and temperature. A modest increase in either can produce orders-of-magnitude change in rate, so parameters should be fitted on logarithmic plots and checked across the full data range. A change in slope with stress may indicate a change in mechanism or a transition towards power-law breakdown. Similarly, an Arrhenius fit may not remain linear over a wide temperature range. These features are not merely academic: extrapolating a single stress exponent or activation term through a regime change can produce very large life errors. The model range should therefore be stated explicitly in any substantiation report.