2.0 THE LEAD CRACK FRAMEWORK METHOD

A fatigue life prediction framework using a lead crack framework has been developed by the Australian Defence Science and Technology (DST) Group for primarily metallic airframe components^{(Reference Molent, Barter and Wanhill6)}. This framework builds on the observation that (near) exponential (i.e., log crack size versus linear cycles) FCG is a common occurrence for naturally nucleating lead cracks (i.e. those leading first to failure) in test specimens, components and airframe structures subjected to variable amplitude load histories^{(Reference Molent, Barter and Wanhill6,Reference Molent, Sun and Green11–Reference Jones, Molent and Pitt18)} .

Lead cracks have the following general characteristics (adapted from^{(Reference Molent, Barter and Wanhill6)}):

1. 1. They start to grow shortly after testing begins or after the aircraft is introduced into service from material or production discontinuities. Significantly, this implies that the threshold cyclic stress intensity factor (ΔK _thr) is small (i.e. close to zero). For more details, see (Reference Molent, Barter and Wanhill6,Reference Wanhill10,Reference Barter, Molent, Goldsmith and Jones16–Reference Jones, Molent and Walker20). Other cracks where nucleation is time-dependant need separate consideration (e.g. in-service induced damage, poor repairs, corrosion nucleated). Also, it should be noted that a conventional FSFT will not provide information relating to such cracks.

2. 2. Subject to several caveats^{(Reference Molent, Barter and Wanhill6)}, they grow approximately exponentially with consistent loading history, i.e. an FCG may be approximated by an equation of the form:

   (1)\begin{equation}{\rm a}={\rm a}_{{\rm 0}} {\rm e}^{\lambda {\rm t}}\end{equation}

   • where a = Crack depth (or length)

   • a₀ = Initial crack size (or EPS)^{(Reference Molent, Sun and Green11–Reference Gallagher and Molent15)}

   • λ = Growth rate parameter that includes the finite geometry factor β

   • t = Fatigue life in terms of Cycles/Number of Load Blocks/Simulated Flight Hours (SFH)

3. 3. A significant portion of their lives is spent in the physically short crack regime (i.e. at depths less than approximately 1mm).

4. 4. They grow in an optimum manner generally unaffected by such factors as crack-closure or material grain size, etc.

5. 5. The fastest possible lead crack is more likely to be revealed in a larger component than in a small coupon (i.e. the area or volume effect). Having a concurrent combination of ‘favourable’ grain orientation, local stresses and large initial discontinuities is more probable for a larger sample of material or a component containing multiple fastener holes.

6. 6. For a given material, spectrum, peak stress level and structural detail, the λ parameter of the exponential equation, e.g. the slope of the FCG curve shown in Fig. 1, is approximately a constant.

7. 7. The mean EPS for a 7050-T7451 aluminium alloy (AA) plate is approximately equivalent to a 0.01 mm deep (semi-circular) surface fatigue crack^{(Reference Molent, Barter and Wanhill6,Reference Molent7,Reference Molent, Sun and Green11–Reference Molent and Sun14)} . In other words, in this material, a 0.01 mm deep crack is a good starting point for estimating the average fatigue life using the lead crack framework, see Fig. 1. Note that this EPS value is well below the surrogate initial flaw/crack size usually assumed in the damage tolerant method (i.e., 1.27 mm⁽⁴⁾).

8. 8. The metallic materials used in highly stressed areas of high-performance aircraft, where load shedding has not occurred, typically have a_CRIT of less than 10 mm deep^{(Reference Molent, Barter and Wanhill6,Reference Molent, Barter, Gordon and Weibler9,Reference Molent, Sun and Green13,Reference Molent and Sun14,Reference Molent and Barter17)} .

9. 9. The framework is designed to produce a conservative FCG curve (e.g. the quasi-static crack tearing close to end-of-life is ignored).

Figure 1. Schematic of typical (lead) crack growth (note: each point represents one spectrum block of growth derived from QF).

Exponential FCG represents an optimum path for the crack to reach a_CRIT for a given spectrum, stress level and detail – thus analyses based on the framework will tend to result in conservative fatigue life management outcomes.

3.0 THE LEAD CRACK BASED METHOD

Let us assume for illustrative purposes that the FSFT is ready to commence cycling and the program’s aim was to demonstrate structural durability via two lifetimes of cycling. The lead crack framework predicts that cracks (with lives short enough to pose a meaningful risk of failure within the service life of the airframe) will commence growing from inherent material discontinuities shortly after the test starts.

The proposal is to terminate cycling early, for example after one lifetime, and then perform a thorough teardown and detailed inspection of the test article (noting that the regulations already contain a requirement for a teardown inspection). The teardown is driven (but not limited) by a pre-knowledge of hotspots and from collected strain data to prioritise the order in which details are inspected. It is envisaged that the hotspots and surrounding details will be subjected to loads that would cause fracture to occur and reveal the largest crack (as well as, in many instances, the surrounding smaller cracks). Many hotspots can be assessed in parallel subject to availability of resources. When cracking is detected, QF is conducted to derive an FCG curve, see example in Fig. 1. This step also confirms the appropriateness of the lead crack framework or informs the need for the use of an alternative model to predict the FCG at the hotspot under consideration. The a_CRIT can be calculated from the geometry and material fracture toughness or separate tests.

The lead crack framework is then used to extrapolate (or interpolate) the FCG to a_CRIT or a_RST (Residual Strength Test (RST)) depending on certification requirements, as shown in Fig. 1. The example in Fig. 1 from the FT55 fighter aircraft FSFT^{(Reference Wanhill21)} shows the crack depth (log scale) versus time history (linear scale) for a complex AA 7050-T7451 fuselage detail, as determined via QF. The growth curve for the left-hand-side crack has been extrapolated to the estimated critical crack size for RST loading conditions (a_RST) and to estimate the achievable life to a_RST. For the right-hand-side crack, the crack growth curve to the critical crack size has been interpolated back to a_RST.

The demonstrated fatigue life was calculated from the geometric mean of the lives to a_RST for both sides. Note the approximately exponential crack growth, which was used to estimate the EPS values for each crack. The early departure from exponential is thought to result from the transition of a discontinuity into a crack. Nonetheless, the use of the lead crack concept coupled with QF enables the generation of EPS to facilitate any probabilistic or risk analyses.

Once FCG curves are available, the certification requirements outlined above can be evaluated. Given that the QF of the principal cracks can be conducted in a significantly shorter timeframe than the continuation of cycling for another lifetime, it is suggested that this approach could make the required certification data available to the regulator and the original equipment manufacturer at an earlier stage, enabling the introduction of any necessary modifications during production or at least more efficiently in-service. This facilitates a more agile approach to introducing new capability to service.

FSFTs are used to validate damage tolerance analysis including the generation of test-based data for in-service inspection programs to detect damage in the fleet. Damage tolerance analysis is typically performed using deterministic methods based on the crack growth information generated from FSFTs. In this instance, the lead crack concept along with the interpolation and extrapolation methods shown in Fig. 1 could be applied to generate the master crack curves required for deterministic analysis. The master crack curves could be developed by either using correlated or corrected FCG codes against fatigue crack data from QF or using the λ parameter of the exponential equation with the rogue flaw as the initial crack size. Increasingly, damage tolerance analyses are being conducted employing risk analysis based on probabilistic methods^(4,5) . The single flight probability of failure (SFPOF) methodology employed by DST^{(Reference Simpson, Landry, Roussel, Molent, Graham and Schmidt22,Reference Torregosa, Hu, Ogden and Maxfield23)} is one approach that could be employed to conduct such analysis. Again, the lead crack concept is well-suited to generate key input data to conduct SFPOF assessments of a particular structural component (e.g. using EPS to generate Equivalent Initial Flaw Size (EIFS) distributions).

The lead crack concept could also be used to assist in WFD assessments, possibly triggering this effort much earlier. Most certification requirements^(3–5) typically favour an FSFT, which provides essential evidence to assist in assessing if a structure is susceptible to WFD and determines an appropriate operational life limit equivalent to a Limit of Validity (LOV)Footnote ². The use of the lead crack concept could be applied, for example, after one lifetime of testing to generate the necessary data to ascertain evidence of global fatigue damage in large areas of structure, whether characterised as multiple site damage or multiple element damage or bothFootnote ³. This will aid in a much quicker identification of WFD-susceptible structures. The data generated from the lead crack concept may then allow the manufacturer or regulator to determine whether sufficient data is available (supplemented with analysis where necessary) to establish the LOV of that structure or if further, more dedicated testing is required. If further test evidence is required, then it is possible to consider testing a full-scale portion of the structure, or a component in question subjected to representative loading rather than testing the entire airframe⁽⁵⁾. This may allow the manufacturer or regulator to consider multiple full-scale component-level tests to fully explore the influence of WFD. Testing components would also enable a_Crit to be determined.

As with good practice, a mid-life teardown and detailed inspection^{(e.g. (Reference Molent, Dixon, Barter and Swanton24))} of a high-life airframe would mitigate many potential concerns with the above proposal.