Parameters
KI = Y σ √(πa)
σc = KIC / (Y√(πa)) ac = (KIC/(Yσ))² / π
rp = (1/6π)(K/σy)² plane strain
rp = (1/2π)(K/σy)² plane stress
da/dN = C(ΔK)m ΔK = YΔσ√(πa)
one common KIC size check: B ≥ 2.5 (KIC/σYS)²
Y is treated as constant: 1.12 for the ideal wide-plate edge-crack option and 1.0 for the ideal wide-plate central-crack option. Real geometry factors vary with crack and component geometry.
Live readout
What to watch for
Critical size falls with the square of stress
ac goes as 1/σ². Doubling the working stress quarters the flaw you can tolerate, which is why highly stressed designs need far finer inspection than lightly stressed ones made of the same steel.
Paris-law growth accelerates as the crack grows
On the fatigue tab, watch where the cycles go. In a single-region Paris model, growth rate rises strongly with ΔK, so much of the integrated interval is often spent near the smaller-crack end. The exact split depends on the initial flaw, critical size, stress range and material constants.
Toughness beats strength for flaw tolerance
Swap between the materials. A high-strength steel with low toughness has a far smaller critical crack than a softer, tougher one at the same stress. Strength decides when it yields; toughness decides how big a flaw it survives.
Thickness changes crack-tip constraint
The plastic-zone tab shows the plane-stress zone at three times the plane-strain one. That is why published KIC is the plane-strain value — the lower bound — and why the thickness validity check matters when interpreting a test.
Leak-before-break is a geometry argument
This page uses only a geometry screen: it compares the ideal central-crack critical half-length ccrit with wall thickness t, equivalently comparing full lengths 2ccrit and 2t. Real leak-before-break qualification also needs crack-shape, tearing and leak-rate analysis.
The exponent is where the risk lives
Change Δσ by 25 % with m = 3 and the life changes by about a factor of two. Fatigue predictions are therefore only as good as the load spectrum they are fed.
Sources and technical basis
Linear elastic fracture mechanics with Irwin plastic-zone estimates and a single-region Paris growth law; material values are representative teaching anchors, not design allowables.