Question 1

How is residual fatigue life calculated using Paris law?

Accepted Answer

Paris law da/dN = C·ΔK^m is integrated from initial crack size a₀ to critical crack size a_c. Substituting ΔK = Δσ·√(πa), the analytical solution for m ≠ 2 is Nf = (a_c^(1−m/2) − a₀^(1−m/2)) / (C·(Δσ√π)^m·(1−m/2)). The critical crack size is derived from K_IC = Δσ·√(π·a_c), giving a_c = (K_IC/(Δσ·√π))².

Question 2

How do Paris law constants C and m vary between materials and environments?

Accepted Answer

Paris law constants depend strongly on material, environment, and stress ratio R. Typical values for steel in air: C ≈ 10⁻¹¹ m/cycle/(MPa√m)^m, m ≈ 3.0. In seawater, C can increase by more than one order of magnitude. For accurate design, constants from ASTM E647 fatigue crack growth tests are used. The Walker equation or NASGRO model can correct for stress ratio R effects not captured by the basic Paris law.

Question 3

Why is the last 10% of crack growth disproportionately dangerous?

Accepted Answer

Because ΔK grows as the crack lengthens, da/dN accelerates exponentially as the crack approaches the critical size. The final 10% of crack extension (from 0.9·a_c to a_c) typically consumes only a small fraction of total fatigue life — often less than 5%. This asymmetry means that most of the usable life is spent in the slow-growth early stage, which has critical implications for inspection interval design: NDT must be sensitive enough to detect cracks well before the rapid-growth phase.

Question 4

How should I choose the initial crack size a₀ when it is unknown?

Accepted Answer

In damage-tolerant design, the initial crack size is set equal to the detection threshold of the applicable NDE method (e.g., ultrasonic, dye penetrant). When this threshold is unknown, a nominal initial crack of 0.5–1.0 mm is a common conservative assumption for machined metallic components. For certified structures (aircraft, pressure vessels), regulatory bodies (FAA, ASME) specify mandatory assumed flaw sizes that must be used regardless of actual NDE capability.

Paris Law Fatigue Crack Growth & Residual Life Calculator

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