By the time a fatigue spectrum reaches the analyst it has already been through a chain of assumptions — mission mix, exceedance curves, gust/manoeuvre models, rainflow counting into a list of cycles. Two more decisions, often made for run-time reasons and almost never written down, can move the predicted life by a large factor: omission at the low end and truncation at the high end. They sound like housekeeping. They are engineering.
Two ends, two risks
- Omission (low end). Small-amplitude cycles are deleted to shrink the spectrum and speed the run. Individually they may sit below the fatigue limit and do nothing. But omit too aggressively and you remove cycles that do real damage in aggregate — especially near a notch, where the local mean stress is elevated and there effectively is no fatigue limit, so even small cycles accumulate damage. The honest way to set an omission level is to demonstrate it: drop the small cycles, recompute the damage, and show the life changed by less than some small, agreed amount. Setting it by gut is how a “harmless” clip quietly eats margin.
- Truncation (high end). Rare high loads are clipped down (or up) to some ceiling. This one is genuinely two-edged. Clip the real high loads out and, for crack growth, you can be unconservative — you removed the cycles that do most of the tearing, because da/dN scales steeply with ΔK (the exponent m is typically 2–4, so a big cycle does far more than its count suggests). But leave an artificially high load in — or truncate the spectrum by capping at a level you’ll never actually see — and you can over-credit retardation and flatter the life. There is no single safe direction.
Why it bites hardest in damage tolerance
Crack growth is load-interaction sensitive, and that is what makes the high end so treacherous. A single tensile overload drives a large plastic zone at the crack tip; as the crack subsequently grows into that zone, the compressive residual stresses left behind retard growth — sometimes for thousands of cycles, occasionally arresting it entirely. The constant-amplitude Paris law, da/dN = C·(ΔK)^m, knows nothing about this; you need a retardation model (Wheeler, Willenborg, or a crack-closure approach à la Elber) to capture it.
The consequences cut both ways:
- Truncate the overload out → you lose the retardation it would have caused → predicted growth is faster → potentially non-conservative if growth governs.
- Leave a non-physical overload in → you credit retardation that won’t happen in service → predicted growth is slower → unconservative in a sneakier way, because the life looks great until the real spectrum, which lacks that load, grows the crack faster than you predicted.
And it is sequence-dependent: a high-low block order retards; a low-high order can accelerate. Rainflow counting throws away the sequence, so a spectrum that’s been counted and re-ordered may not retard the way the real load history would. Whether the “conservative” direction is up or down depends on whether initiation or growth governs the region, and on the retardation model — which is exactly why you cannot decide it by reflex.
What I actually do
- Set omission by demonstration, not by gut: show the dropped small cycles change life by less than the agreed tolerance, document the level.
- Be deliberate about truncation level and direction, and state which way it errs for this region — initiation-governed or growth-governed.
- Treat retardation modelling as a declared assumption. If I’m crediting retardation, I say which model and which parameters; if I’m ignoring it (often the conservative choice for growth), I say that too. Crediting retardation you can’t substantiate by test is borrowing against a life you haven’t earned.
- Keep the un-clipped spectrum archived so the clipping is reversible and auditable.
The discipline
Write the truncation and omission levels into the report with the rationale and the direction of conservatism. Future-you, re-running the spectrum two years later when the mission mix changes, needs to know whether a life change came from the structure or from where someone drew the clip. A fatigue life quoted without its spectrum edges is half a result.
The spectrum is a model of a lifetime of loads. Document its edges as carefully as you document its middle — that is where the quiet unconservatism lives.
