Primary Creep
Primary creep — the decelerating strain stage following initial load application, its physical origins in strain hardening, its mathematical representation and its significance for short-duration high-temperature operation.
The primary creep stage
Primary creep is the first stage of the creep curve, following the instantaneous elastic-plastic strain at load application. The creep strain rate is initially high and decreases over time. The total primary creep strain may be a small or a substantial fraction of the total creep strain, depending on the material, the stress and the temperature. At high stresses or at temperatures where creep is just becoming significant, primary creep may dominate the total deformation. At lower stresses or higher temperatures, the primary stage may be short and the secondary stage may dominate.
Physical mechanism
The decelerating strain rate in primary creep is attributed to strain hardening. As the material deforms, dislocations are generated and interact, increasing the dislocation density and the resistance to further deformation. The material becomes harder as it creeps, so the creep rate decreases. This is analogous to strain hardening in plasticity, but it occurs over time at elevated temperature. Eventually, the strain hardening is balanced by thermal recovery (dislocation annihilation by climb and cross-slip), and the creep rate stabilises — this is the transition to secondary creep.
Mathematical representation
Primary creep is often represented by a power-law or logarithmic function of time. A common form is the time-hardening expression, where the creep rate decreases as a power of time. The Norton-Bailey model combines primary and secondary creep by making the creep rate depend on both time and stress. The parameters of the primary creep model must be calibrated from creep test data that includes the primary stage. Some simplified models ignore primary creep and use only the secondary creep rate — this is conservative for deformation but may be non-conservative for stress redistribution in the early life.
Primary creep (power-law time hardening): eps_creep = A * sigma^n * t^m eps_dot_creep = A * sigma^n * m * t^(m-1) where: eps_creep = creep strain [dimensionless] eps_dot_creep = creep strain rate [1/s] sigma = applied stress [Pa] t = time [s] A, n, m = material constants (temperature-dependent) For primary creep: 0 < m < 1 (rate decreases with time) Note: A, n, m are illustrative constants that must be calibrated for each specific material and temperature.
Significance for short-duration operation
Primary creep is particularly significant for components with short high-temperature excursions — turbine blades during start-up, rocket engine components, heat exchangers during transients. In these applications, the operating time at temperature may be comparable to or shorter than the primary creep duration, and the primary creep strain may be the dominant deformation. A secondary-creep-only model would under-predict the deformation. The analysis must include the primary creep stage when the operating duration is short relative to the secondary creep stage.
Interaction with stress redistribution
Primary creep affects stress redistribution in statically indeterminate structures. The high initial creep rate in the primary stage causes rapid stress redistribution at the start of the high-temperature exposure. As the creep rate decreases, the redistribution slows. The time to reach the steady-state stress distribution depends on the primary creep duration. For components with stress concentrations, the primary creep may significantly relax the peak stress before the secondary stage begins. The analysis must capture the primary stage to predict the early-time stress redistribution correctly.
When primary creep must be represented explicitly
Primary creep is most important when the early-life strain or stress redistribution matters to function or subsequent damage. It can dominate short missions, proof or acceptance tests at temperature, start-up dwells and situations where clearances are small. If the design life is very long and secondary creep dominates almost all of the exposure, a steady-state model may be adequate for some purposes; however, omitting primary creep can still distort the initial redistribution and therefore the stress entering the long-term stage. The choice should be based on the time fraction and strain fraction contributed by primary creep at the relevant stress and temperature.
Calibration and verification of transient creep response
Primary-creep models require data with sufficient resolution near the start of the test. Fitting only the later portion of a curve can produce parameters that reproduce secondary rate but miss the early deceleration. Conversely, fitting a short test may give poor long-term predictions. A useful calibration separates instantaneous strain from time-dependent strain, fits several stress and temperature levels simultaneously, and then verifies the model against curves not used in the fit. In FEA, the resulting early-time response should be checked for time-step dependence because a large first increment can numerically smear the rapid initial evolution.