Question

Fatigue is a condition which usually causes damage in aircraft structures. The damage of an
aircraft structure could possibly lead to failure.
(a) Discuss how to sustain damage in aircraft structures before an inspection can be done. Provide
appropriate mathematical equations to support your answer

Answer 1

ANSWER (a)-

Fatigue is a common occurrence among all metal airframes. Due to the repeated flight cycles and frequent use, the metal elements of planes become weakened over time, and they will eventually require attention and repair.

This weakness manifests in cracks, which are microscopic at first. With continued aircraft use over time, though, the cracks grow larger and eventually become visible. An aircraft begins to age after its first flight, and the effects of corrosion and fatigue occur almost immediately. Aging becomes an issue when the aircraft can no longer be effectively repaired or sustain the rigors of flight. Atmospheric pressure, G-loads, turbulence and other factors create the perfect environment for damaging stress.

Fatigue cracks mainly originate in three different areas:

• Internally, in load-bearing structural elements, potentially developing small points under high stress.
• Externally, in load-bearing aircraft skins, in the case that the skin is under pressure from a structural load.
• Around the edges of fastener holes, such as those for rivets, bolts or screws, or in any similar area of concentrated stress.

These areas of high pressure are more prone to premature cracking and exhibiting early signs of fatigue. In the same right, they are often the areas recorded as the original sites of failure.

In order to avoid fatigue failure in an aircraft, we have to take the following measures:

To determine how many cycles an aircraft or type of metal can take, there has to be a measurable factor with which to make a comparison. This factor is called the Limit of Validity, or LOV.

• Manufacturers should determine a model-specific LOV, make the limit available, uphold said limit as verification of airworthiness, report LOV accordance to regulating authority and provide and publish service bulletins of preventative modifications.
• Operators should maintain aircraft through a regular service program, integrate mandatory services into the program, utilize manufacturer provided LOV values and create and uphold a plan of action for the instance of airplanes reaching their LOV.

There are certain different methods following which can avoid the fatigue in an aircraft:

• Infinite lifetime concept methods- Infinite lifetime concept is a design to keep stress below threshold of fatigue limit. Fatigue limit, endurance limit, and fatigue strength are all expressions used to describe property of materials. It is the amplitude or range of cyclic stress that can be applied to the material without causing fatigue failure.
• Finite lifetime concept methods- Safe-life design (finite lifetime concept or safe-life design practice) is design for a fixed life after which the user is instructed to replace the part with a new one and the damaged part is recycled or disposed off easily.
• Damage tolerant design methods or methods of nondestructive testing- Damage tolerant design instructs the user to inspect the part periodically for cracks and to replace the part once a crack exceeds a critical length. This approach usually uses the technologies of non-destructive testing and requires an accurate prediction of the rate of crackgrowth between inspections. The designer sets some aircraft maintenance checks schedule frequently enough that parts are replaced while the crack is still in the "slow growth" phase. Methods for non-destructive testing (Non-Destructive Testing – NDT) are a set of methods for finding defects in material and in such a way that materials or devices after testing remain intact, and if there are not defects detected, they can be placed in normal exploitation.

The most commonly used methods of NDT are: visual, magnetic, penetrant, radiographic, ultrasonic and eddy current methods.

• Visual inspection- Visual testing is the oldest and most common form of inspection. It consists of an overview using human eye, a magnifying glass, a light source or special optical devices. The reliability of this method depends on the ability and experience of personnel who must know how to look for structural defects and how to identify an area where such defects are found. Basic equipment for the visual inspection is endoscopes. Endoscopes allow the technician to view the interior of the equipment, components or structures that have closed or hidden areas not accessible to ordinary visual inspection.
• Penetrant testing- Penetrant method (penetrant testing) is used to reveal discontinuities opened towards the surface of the parts made of material that is not porous. The method depends on the ability of liquid to penetrate the discontinuity of the material on which it is applied.
• Ultrasonic testing- Ultrasonic testing method (ultrasonic inspection) is suitable for the examination of most metals, plastics and ceramics and defects on the surface or below the surface. Ultrasound examination requires that at least one part of surface near the surface to be tested is available. Examination of aircraft structures can be achieved by inducing ultrasonic waves on the object with the contact probe and receiving of reflected waves from that point. Reflection of ultrasonic waves is projected electronically into the tube of oscilloscope and is used to indicate defects.
• Magnetic particle inspection- Magnetic testing method (magnetic particle inspection) is a method used to detect surface and subsurface discontinuities in ferromagnetic materials. Testing is done by inducing a magnetic field in observed part and applying the particles of a dry powder or a liquid suspension of iron oxide. If there is a discontinuity in the material (in the form of cracks, nicks, or inclusions), it leads to increased resistance in magnetic field at the site of the cracks.
• Radiographic testing- The radiographic testing of material, material irregularities are obtained in the way that the object of testing is aired with appropriate ionizing radiation. Radiographic testing will therefore show internal and external structural details of all portions of the material.
• Eddy current testing- Eddy current testing is used to detect fractures on the surface or near the surface in most metals. It can be used for aircraft parts or assemblies where the damaged area is accessible to contact probe. Examination is done by inducing eddy currents in the part to be tested and monitoring electronically variations in the induced field.
• Low coherence interferometry- New materials such as polymer composites and ceramics have found a wide variety of applications in modern industries including energy, aviation and infrastructure. This is due to their superior properties as compared to traditional materials. For process enhancement, quality control and health monitoring where these types of materials are used, sophisticated techniques are needed to non-destructively inspect the complex geometries inside the structures produced. Lowcoherence interferometry has been developed as a powerful tool for the cross-sectional imaging of microstructures.
• BITE concept- All modern transport aircraft today have some form of permanent monitoring of technical condition which is integrated on the aircraft (On-board Maintenance Systems). For mechanical components it means that there are sensors placed that continuously measure a parameter of the system by which the technical condition can be evaluated. Examples are sensors that measure pressure, temperature, vibration, shifts, etc. These systems allow the detection of defects during operation and are called BITE (Built In Test Equipment).
• Cold expansion methods- Over the past 40 years, cold expansion processes have impacted fatigue crack mitigation, structural integrity and airworthiness. Methods to reduce fatigue problems: thicken the structure locally to reduce stress levels with a structural weight penalty; install interference fit fasteners (props’ hole); reduce amplitude of the applied strain; fastener preload or clamp up or bridge hole via interface friction; and induce a compressive hoop pre-stress associated with a cold working process.

Fatigue scatter factor-

Fatigue scatter factors are used to determine the structural safe life and ensure the predefined reliability of the aircraft. The fatigue scatter factor can be defined as

SF = T50/Tp

Tp = service life with a certain reliability level

In fleet management, variations of load spectra and structural properties are considered when the fatigue life scatter factor is determined. But in fatigue monitoring, only the variation of structural properties will be considered since the load-time history of each aircraft can be obtained, which will lead to a lower scatter factor.

Assuming that fatigue life follows the lognormal distribution, we have the following relationship:

SF = 10u_pσ₀

where u_p is the pth percentile of the standard normal distribution and σ₀ the standard deviation of logarithmic life.

Fatigue analysis procedure can be described as follows:

(1). Obtain corresponding stress spectra for critical locations, based on the load spectrum of an individual aircraft

(2). Determine fatigue property for realistic structures-

The constant life curve is described as

σa = σa0 {1- σm/σs} ----eq 1

where σa is the stress amplitude, σa0 the peak value of fluctuating stress, σm the mean stress, and σs the yield stress of material.

(3). Cycle-by-cycle fatigue life calculation-

Each stress cycle can be expressed as (σai,σmi) or (σmaxi,Ri), where σmaxi is the peak stress, and Ri the stress ratio, and the latter is usually used in engineering. Thereinafter, σmaxi will be referred to σ_i.

According to eq 1 upon converting (σi,Ri) into (σi∗,R∗) σi∗ can be written as

σi∗=(1-Ri)σsσi / σs(1-R∗)+Si(R*-Ri) ----eq 2

where R∗ is the stress ratio with the same fatigue life of (σi,Ri), and σi∗ the corresponding peak stress.

Substituting eq. 2 we have the fatigue life as

Ni = CA/ (σi∗-C1α) 1/@ -----eq 3

4). Fatigue damage evaluation-

According to Miner’s rule, fatigue damage for a load spectrum block can be given by

D = k∑(i=1) = ni/Ni

where k represents the loading series, n_i the number of Load i in one block, and N_i the corresponding mean fatigue life, which can be obtained eq 3

(5). Fatigue life calculation-

Mean fatigue life can be obtained using the following expression:

t50 = t0 / k∑(i=1) ni/Ni = t0/D

where t₀ is the flight hour corresponding to one spectrum block (per base life period).

(6). Safe life calculation-

With the scatter factor of SF, we have structural safe life as

tP = t50 / SF

(7). Remaining fatigue life estimation-

Fatigue Life Expended Index (FLEI) can be used to illustrate the fatigue life consumption at any time t_e, which is denoted as FLEI (t_e) and can be obtained by

FLEI(te) = SF·D(te)·100%

where D(t_e) is the total damage accumulated in service.

The remaining fatigue life can be calculated by

LR(te)=1-FLET(te) / SF·d(F)

where d(F) is the predicted mean damage rate in subsequent service for critical structures, which is determined by predicted individual spectrum.