Theory 13/Engineering & Materials Failure /Fatigue theory/3 min
Fatigue Remembers in the Plastic Zone
Two identical cracks under identical current load can grow at different rates. The difference is what happened before.
A fatigue crack's growth rate is set by the residual stress field stored in its plastic zone, which encodes the load history, so history can be read from diffraction and remaining life predicted without a path-dependent damage rule.
01The evidence
- Cyclic plasticity and variable-amplitude fatigue have long shown that load sequence matters, with overloads retarding growth and underloads accelerating it in ways that current stress-intensity descriptions cannot capture.International Journal of Fatigue
- Damage evolution governed by microcrack nucleation has been modelled as a plastic-zone process, which gives a physical location for the memory.Journal of the Mechanics and Physics of Solids
02The tension
Design codes treat fatigue as path-independent: sum the damage from each cycle by a rule and compare with a limit. The rule is known to fail after overloads, and the usual fix is an empirical retardation parameter that has to be recalibrated for each material and spectrum.
03The theory
The plastic zone ahead of a crack is not erased by unloading. It retains a residual stress field that reflects the largest load the crack has seen and the sequence of smaller ones. That field changes the effective stress intensity at the tip, and therefore the growth increment.
If the memory is stored in the residual field, it can be measured directly by diffraction, which gives a physical state variable rather than a fitted parameter. The growth rate should be a function of the effective stress intensity computed from the measured field, with no additional history term.
This predicts that two specimens with identical current loads but different histories will differ in growth rate by an amount predictable from their residual fields, and that the difference disappears if the field is erased by annealing.
The applied payoff is a remaining-life method that works for variable amplitude without material-specific calibration, which is exactly where current approaches are weakest.
04What this is not
Miner's rule sums cycle fractions without regard to order. Retardation models add a fitted parameter for overload effects. This replaces the fitted parameter with a measured field that has a physical meaning.
05Predictions
- P1The residual stress field measured by diffraction should predict growth rate after an overload, with no additional fitting.
- P2Annealing the plastic zone should erase the sequence effect and restore the baseline growth rate.
- P3A single scalar derived from the field should capture history across different spectra.
06What would refute it
Growth rates that depend only on current stress intensity, with no residual-field dependence, would restore the path-independent account.
07What it would change
It would replace empirical retardation with a measurement, and make remaining-life assessment possible for components whose load history is unknown.
08Evidence base
- Cyclic plasticity and variable amplitude fatigue — International Journal of Fatiguehttps://www.sciencedirect.com/science/article/abs/pii/S0142112303001373
- Damage evolution governed by microcrack nucleation — JMPShttps://www.sciencedirect.com/science/article/abs/pii/S0022509699000149