Question 1

What is the design philosophy of damage tolerance design?

Accepted Answer

Damage Tolerance Design assumes the existence of pre-existing defects or damage in a structure, and ensures safety by guaranteeing sufficient time for defects to grow from a detectable size to a critical size before failure. It is one of the three main fatigue design approaches alongside safe-life design (evaluating design life assuming no defects) and fail-safe design (redundant design preventing total collapse after partial failure). It is widely adopted in aircraft structures (FAR 25.571), pressure vessels (ASME), bridges (AASHTO), and other applications.

Question 2

How is the critical crack size a_crit calculated?

Accepted Answer

The critical crack size is the crack length at which residual strength equals the design stress, calculated as a_crit = (KIC / (F×σ))² / π, where KIC is the plane-strain fracture toughness, F is the geometry factor, and σ is the design stress level. Higher stress or lower fracture toughness results in a smaller critical crack length. The actual inspection interval is determined by integrating the Paris law from the minimum detectable crack length a_0 to a_crit to obtain total cycles N_total, then dividing by a safety factor (typically 2–4).

Question 3

What is a POD curve?

Accepted Answer

A POD (Probability of Detection) curve statistically represents the crack detection capability of an NDI method. The exponential model POD(a) = 1 - exp(-a/a₅₀) (where a₅₀ is the crack size giving 50% detection probability) and normal distribution models are commonly used. The a₉₀ value — the crack size at which 90% detection probability is achieved — serves as the practical minimum detectable crack size for design. POD curves vary by NDI method (UT, PT, MT, ET) and are also influenced by inspection conditions (frequency, sensitivity, inspector skill).

Question 4

How is the Paris law integration performed?

Accepted Answer

The Paris law da/dN = C(ΔK)^m is integrated from a₀ to a_crit to determine crack growth life. Substituting ΔK = F×Δσ×√(πa) gives N = ∫[a₀ to a_crit] da / [C(F×Δσ×√(πa))^m]. For the analytical form when m≠2: N = [a_crit^(1-m/2) - a₀^(1-m/2)] / [C(F×Δσ×√π)^m × (1-m/2)]. This tool uses Runge-Kutta numerical integration for high-accuracy computation. The inspection interval is set as N_interval = N_total / SF (SF = safety factor).

Damage Tolerance Design — Residual Strength & Inspection Interval

Governing Equations