Case study

Aircraft Fatigue Crack Inspection Interval Case Study

Aerospace engineering case study on aircraft fatigue crack growth, damage tolerance, critical crack size, inspection detectability, Paris-law life, residual strength, and maintenance interval decisions.

Branch: Aerospace Engineering
Content: Case study
Updated: Jun 22, 2026
Revision: v1.0.0 · reviewed

An aircraft fatigue crack finding is not only a material defect. It is a damage-tolerance decision that connects structural loads, fracture toughness, crack-growth rate, inspection capability, maintenance intervals, repair rules, and operational risk. A crack that is stable today can still invalidate the inspection interval if it can grow to critical size before the next scheduled inspection.

This case study follows a metallic wing attachment detail after a non-destructive inspection finds a crack near a fastener row. The case is hypothetical, but the calculations reflect the logic of a damage-tolerance review: define the detectable crack size, estimate critical crack size, integrate crack growth, convert spectrum cycles to flight cycles, compare with the inspection interval, and decide whether normal service can continue.

The central question is:

Can the aircraft remain on the existing inspection interval, or does the crack finding require repair, a shorter interval, or a special operating limitation?

The answer is controlled by the gap between detectable crack size and critical crack size, not by the fact that the crack has not yet caused static failure.

Case Context

During a heavy maintenance check, eddy-current inspection reports a crack indication at a lower wing skin attachment detail. The detail is a high-load metallic joint with local stress concentration at a fastener hole. The engineering team must decide whether the existing 1800-flight inspection interval remains acceptable.

Item	Value or assumption
Material fracture toughness, $K_{Ic}$	$40\ \text{MPa}\sqrt{\text{m}}$
Geometry factor, $Y$	$1.12$
Residual-strength tensile stress, $\sigma_{max}$	$140\ \text{MPa}$
Equivalent fatigue stress range, $\Delta \sigma$	$85\ \text{MPa}$
Paris-law coefficient, $C$	$2.0\times10^{-12}$
Paris-law exponent, $m$	$3.0$
Qualified detectable or missed crack size, $a_i$	$3.0\ \text{mm}$
Reported crack size, $a_{obs}$	$5.5\ \text{mm}$
Current inspection interval	$1800\ \text{flights}$
Equivalent stress cycles per flight	$650$
Inspection factor on growth life	$F=3$

The values are simplified. A real aircraft assessment would use the approved structural repair manual, certified load spectrum, material data for the exact product form and heat treatment, crack geometry, residual stress, corrosion condition, inspection probability of detection, and regulatory approval path.

Critical Crack Size

For a first linear-elastic fracture mechanics screen:

K=Y\sigma\sqrt{\pi a}

At critical fracture:

K_{Ic}=Y\sigma_{max}\sqrt{\pi a_c}

Solve for critical crack size:

\displaystyle a_c=\frac{1}{\pi}\left(\frac{K_{Ic}}{Y\sigma_{max}}\right)^2

Substitute the values:

\displaystyle a_c=\frac{1}{\pi}\left(\frac{40}{1.12(140)}\right)^2

a_c=0.0207\ \text{m}=20.7\ \text{mm}

The crack is not critical at $5.5\ \text{mm}$ , but that does not mean normal operation is automatically acceptable. Damage tolerance requires enough growth life between the crack that can be missed by inspection and the critical crack size.

Residual Strength Check at the Observed Crack

Check the stress intensity at the observed crack size:

K_{obs}=Y\sigma_{max}\sqrt{\pi a_{obs}}

With $a_{obs}=5.5\ \text{mm}=0.0055\ \text{m}$ :

K_{obs}=1.12(140)\sqrt{\pi(0.0055)}=20.6\ \text{MPa}\sqrt{\text{m}}

Margin to fracture toughness:

\displaystyle \text{margin ratio}=\frac{K_{Ic}}{K_{obs}}=\frac{40}{20.6}=1.94

The residual-strength check is positive in this simplified screen. The observed crack is below critical size. However, the aircraft cannot be released on residual strength alone because fatigue growth can consume the margin before the next inspection.

Crack-Growth Model

Use the Paris-Erdogan relationship in the stable growth region:

\displaystyle \frac{da}{dN}=C(\Delta K)^m

with:

\Delta K=Y\Delta\sigma\sqrt{\pi a}

For $m=3$ and constant $Y$ and $\Delta\sigma$ , the integrated growth life from $a_i$ to $a_c$ is:

\displaystyle N_{growth}=\frac{2\left(a_i^{-1/2}-a_c^{-1/2}\right)}{C(Y\Delta\sigma)^3\pi^{3/2}}

Use the qualified detectable or missed crack size as the starting crack:

a_i=3.0\ \text{mm}=0.003\ \text{m}

The stress-intensity range at $a_i$ is:

\Delta K_i=1.12(85)\sqrt{\pi(0.003)}=9.24\ \text{MPa}\sqrt{\text{m}}

The integrated crack-growth life is:

N_{growth}=2.35\times10^6\ \text{equivalent stress cycles}

This is the calculated life from a crack that might just be missed or detected at the inspection capability limit to the critical crack size. It is not the full fatigue life of the component from new condition.

Convert Growth Life to Flights

The structural spectrum is represented as $650$ equivalent stress cycles per flight:

\displaystyle N_{flights}=\frac{2.35\times10^6}{650}=3620\ \text{flights}

With inspection factor $F=3$ :

\displaystyle N_{inspect}\leq\frac{3620}{3}=1207\ \text{flights}

A practical interval would be rounded down, for example:

N_{inspect}=1200\ \text{flights}

The existing $1800$ -flight interval is therefore not acceptable under this simplified damage-tolerance screen.

Remaining Life from the Observed Crack

Because the observed crack is larger than the qualified detectable crack size, calculate the growth life from $a_{obs}=5.5\ \text{mm}$ :

N_{growth,obs}=1.36\times10^6\ \text{equivalent stress cycles}

Convert to flights:

\displaystyle N_{flights,obs}=\frac{1.36\times10^6}{650}=2093\ \text{flights}

With the same inspection factor:

\displaystyle N_{inspect,obs}\leq\frac{2093}{3}=698\ \text{flights}

This result is a decision warning. Even though the crack has residual-strength margin, a confirmed $5.5\ \text{mm}$ crack leaves less inspection-margin life than the generic detectable-crack interval. If the structural repair manual requires repair at any confirmed crack at this location, the aircraft should not be released to normal service. If a one-time ferry or limited operation is requested, it needs explicit engineering authorization, operating restrictions, and a repeat inspection or repair limit well below the calculated bound.

Inspection Capability

The inspection interval is only meaningful if the inspection can reliably find the assumed crack. The damage-tolerance record should state:

inspection method, such as eddy-current, ultrasonic, dye penetrant, or visual aided inspection;
access condition, surface preparation, paint removal, fastener removal, and local geometry;
qualified detectable crack size and probability-of-detection basis;
inspector qualification and calibration block;
crack orientation and whether the method is sensitive to that orientation;
record format, image, indication length, and reinspection procedure.

If the inspection method can only reliably detect $6\ \text{mm}$ cracks, using $a_i=3\ \text{mm}$ in the calculation is unconservative. If access is worse in service than during qualification, the detectable crack size should be revised or the interval shortened.

Engineering Decision

The engineering decision is:

the current 1800-flight interval is rejected for this damage-tolerance basis;
a revised routine interval should not exceed about 1200 flights when starting from the qualified detectable crack size;
the specific aircraft with a confirmed $5.5\ \text{mm}$ crack should not return to normal service without repair or an approved limited-operation disposition;
if limited operation is approved, the limit should be derived from the observed-crack remaining life, not from the generic inspection interval;
the stress model, NDI capability, crack sizing uncertainty, and repair configuration must be documented.

The most important distinction is between fleet interval and aircraft disposition. A fleet interval may be based on the crack that could be missed. A specific aircraft with a measured crack needs its own remaining-life decision.

Validation Evidence

A defensible closeout package should include:

Evidence item	Why it matters
Local stress basis	Shows that $\sigma_{max}$ and $\Delta\sigma$ apply to the detail, not only the global wing.
Load spectrum conversion	Justifies equivalent stress cycles per flight.
Crack geometry and sizing record	Defines whether $a$ is surface length, depth, half-length, or an equivalent crack.
Material data	Confirms $K_{Ic}$ , $C$ , $m$ , product form, heat treatment, and environment.
NDI qualification	Supports the assumed detectable or missed crack size.
Residual-strength check	Shows the structure can carry the required load with the assumed crack.
Growth-life integration	Supports the inspection interval and any limited-operation decision.
Repair or repeat-inspection record	Proves the actual aircraft disposition was completed.
Configuration-control note	Ensures future repairs, fastener changes, or load changes trigger reassessment.

Without this evidence, the number of flights is only a calculation artifact. Damage tolerance is an engineering control system built from loads, material data, inspection capability, repair action, and records.

Engineering Lessons

The first lesson is that residual strength and inspection interval answer different questions. A crack can be below critical size today and still make the scheduled interval unsafe.

The second lesson is that the starting crack size must match inspection capability. Damage-tolerance analysis is invalid if it assumes a crack smaller than the inspection can reliably detect.

The third lesson is that flight cycles are not automatically fatigue cycles. A load-spectrum conversion is required, and uncertainty in that conversion should be visible in the inspection factor.

The final lesson is that a confirmed crack changes the decision from fleet scheduling to aircraft disposition. Once a crack is measured, repair, repeat inspection, or limited operation must be justified using the observed crack size and the approved maintenance basis.

REF

Disciplines