13.2 Design Rules
There are many design rules and approaches that, if correctly and critically applied, can minimize the risk of damage. Unfortunately, design rules are not always without problems. Things that work positively in one situation can even increase the risk of damage in another. Here are a few examples:
In order to minimize imbalances and to better absorb unavoidable imbalances (e.g. under enemy fire; Fig. "Durability improvement of engine rotors"), welded rotors are seen as being very damage-tolerant. However, welds are always connected to an increased risk of flaws. Flaws, such as pores, bonding flaws (splices), and micro-cracks, are often very difficult to find and prevent. Cracks can spread further in integral parts (Ill.13-23) than in flange connections, which act as crack stoppers.
An additional problem is the reduced damping of integral parts (e.g. blisks and blings) due to the lack of friction (Fig. "Damping mchanisms"). This promotes high-frequency vibrations (resonance) with HCF crack initiation (Volume 2, Ill. 7.2.2-28).
Higher strengths are generally not conducive to damage-tolerant behavior. If, as is usually required, the strength potential is utilized as much as possible, the risk of crack initiation increases. At higher stress levels, smaller flaws become capable of growth, the cyclical crack growth rate increases, and fractures occur at shorter crack lengths (critical crack length; Fig. "Strength and danger of crack length").
Material properties can also have very different effects. High-strength, powder-metallurgical materials may have a high fracture toughness, but the typical small grain size in thick cross-sections can increase the crack growth rate (Fig. "Factors influencing crack growth"), thus shortening the available inspection intervals after crack initiation to the point that they are no longer sufficient to prevent fracture.
Usually, one attempts to orient material-specific flaws relative to the main stress directions in a way that they have the smallest possible influence on strength, especially cyclical fatigue. Forged parts, such as disks, are deformed in a way that flaws are located in an axial-radial plane, and therefore in the direction of centrifugal force-induced stresses. This is one reason that powder-metallurgical (HIP) parts are subsequently forged.
A further aspect of material selection within the context of damage tolerance is the tendency to cracking under function-specific damaging influences. Typical examples include parts with a seal function. Labyrinths are locally heated during rubbing to a degree that conditions for hot cracking occur (Volume 2, Ill. 7.2.2-9.2). Of course, labyrinth racks should be as hot crack-resistant as possible. However, this requirement may interfere with the strength demands. Rubbing blade tips are also heated up, and this can damage them to the extent that crack initiation occurs (Volume 2, Ill. 7.1.3-1).
The wide blade chords of modern compressors may be less sensitive to certain foreign objects and fundamental flexural modes than the narrow blades of older engine types (Fig. "Blade shape and aerodynamic damping"), but they tend to higher-order vibrations that can cause effects like corner cracks, which can combine with rubbing damage to increase the damage risk considerably.
In the case of large overloads, such as occur during a bird strike, clappers on narrow blades can ensure that fragments are smaller (blade section above the clapper; Volume 1, Ill. 18.104.22.168-13). Wide blades without clappers, on the other hand, can be overstressed at the root, causing the entire blade leaf to break off.
Even a fan rotor with bearings on both sides is not purely advantageous. While it does improve clearance behavior during maneuvers and reduce deflection during smaller imbalances, it also increases the risk of bearing failure and overstress of the fan blades in case of a high-speed impact such as a bird strike. In this case, having a bearing on only one side has its advanatges (Volume 1, Ill. 22.214.171.124-8).
Improved damage tolerance can also be achieved through the introduction of new principles and technologies. These include brush seals, which do not have the catastrophic failure mechanism of labyrinth seals, i.e. self-increasing rubbing (Volume 2, Ill. 7.2.2-4).
In the context of damage tolerance, the introduction of fiber-technical materials can more than compensate for their disadvantages in the case of FOD. These include consequential damages following unavoidable blade fractures (bird strikes, Fig. "Safety philosophy must match technology") or high inner damping, which makes them safe from HCF failures (Fig. "Advantage of a material needs design philosophy").
Figure "Design philosophy influences part failure" (Ref. 13-4): The design philosophy plays an important role in crack behavior and failure sequences.
- Statically determinate construction methods usually do not allow cracking, especially if a single element transfers the operating loads. These constructions do not exhibit fail safe behavior, because the fracture of a supporting element causes the entire system to fail. In addition, the crack growth leads to rapid load increases in the residual cross-section. This additionally accelerates the crack growth. After a relatively short operating time, which makes sufficiently early detection a matter of pure chance, this results in a fracture and catastrophic failure. In this case, the designed life span must be limited to the incubation phase (Fig. "Material changes during crack development"). A typical example from everyday life is three-legged variations of tables and chairs. As long as the three legs are supporting, the chair or table cannot wobble. However, if one of the legs fails, the entire system will collapse (top diagram).
- Multiple statically indeterminate construction methods behave in a more damage-tolerant way than statically determinate methods. Because there are several supporting elements, the load shifts during cracking and fracture so that the damaged element is relieved. Statical indeterminacy occurs if, for example, more than the absolutely necessary number of elements for force transmission are involved and/or the hinge action in the nodes is eliminated through rigid fastening (welds). With four supports, a chair will continue to stand if a leg breaks. A similar effect can be attained with three legs, if these are firmly connected to the floor. This is also a statically indeterminate variation. If one leg breaks, the intact legs absorb the loads, as long as they have sufficient flexural strength.
As an analogy, bearing braces in housings can be compared with the example of the chair. In this case, a brace failure in a statically indeterminate version would make itself known through vibrations and rubbing before catastrophic failure occurs.
The bottom diagram uses the example of a turbine stator vane to show the influences of fastening on the damage process. One-sided fastening relieves the part in the case of heat stress. However, cracking will cause a blade fragment to break off and cause extensive consequential damages. While the right variant leads to complex stresses, it will not immediately lose its function and cause consequential damages if it cracks. In this case, it is possible to catch the damage in time with the aid of a boroscope.
Figure "Part reacting at stress types": The load type plays an important role in the safe behavior of parts in spite of cracking.
The top left schematic diagram shows a force-controlled load. Creep tests and cyclical tests for determining fatigue strengh correspond to this type of load form. In the specimen, the stress is the controlling value. If the supporting cross-section is reduced due to deformation (constriction) and/or cracking, the remaining cross-section is subjected to a corresponding higher level of stress. If
there is no noticeable stress gradient, e.g. due to the part geometry, then the crack growth accelerates until fracture.
Strain-controlled loading (top right diagram) causes the part to expand within certain limits. If this strain is reduced due to higher elasticity (crack initiation) and/or plastic deformations, the loads are reduced accordingly. Damages such as crack growth or creep strain slow down in this manner. These damages under strain-controlled loads are considered to be controllable, and are often classified in maintenance manuals as being acceptable within limits in hot parts. This includes thermal fatigue cracks (Chapter 12.6). Stress relief annealing and relaxation are also strain-controlled processes. Strain-controlled operating loads on parts are usually related to a strain restriction. In this case, local strain is restricted by the surrounding cross-section (Fig. "Cracks protecting from thermal fatigue"). A typical example is residual stresses in welds, or LCF-stressed disk zones. Residual stresses can be reduced through relaxation, i.e. stress relief annealing.
One example of a structure with restricted strain is integral turbine stator blading (bottom diagram). The rigid outer and inner shrouds restricts the thermal strain of the blade leaves. The shrouds are considerably cooler than the blades during heating up (startup), and the temperature gradients can reverse during shutdown. This creates large cyclical thermal strains that are determined by the temperature differences. In addition, large temperature gradients are created between neighboring areas in the blade leaves, which stress each other with corresponding thermal strain differences.
Figure "Notch types threatening constructions": Notches often act as areas with strain concentrations to determine the life span of parts. The design engineer must keep notch stresses as low as possible. However, in order to accomplish this, one must be conscious of the notch, which only seems obvious at first glance. Notches can have negative effects in two different ways. They minimize the fatigue strength, and long notches can direct and strongly accelerate crack growth (Fig. "Danger of notches in pressure chambers").
Notches can occur in different ways:
Form notches/stiffness notches (“1”): These are geometrical notches. They are based on two effects, the notch radius and/or a stiffness jump. Even “insignificant” increases in the notch radius can reduce the notch effect and thus decisively increase the life span (Fig. "Danger of notches in pressure chambers"). Appropriate re-machining of the radius can be used at least as a temporary measure in accute cases.
Relaxation bores in flanges and disks (Example "AS HIP") or scallops are capable of balancing stresses, i.e. reducing dangerous stress peaks. Form notches can also have an effect in less obvious areas, such as the transitions of coatings. The negative effect on dynamic strength increases along with the bond strength, strength, brittleness, and E modulus of the coating.
Machining notch (“2”): Machining transitions between different material-removing processes, and between different speeds of the same machining process, can create a strength jump with a notch-like effect, as well as residual stress conditions, in the surface. This is also true of the transition to hardened zones (e.g. shot peening). These zones should be located outside areas that are under high dynamic loads and, if possible, have “soft” transitions.
Detachable connections (“3”): If form notches are created, micro-movements can increase the dynamic strength losses in the notch area. In the case of elastic deformation, micro-movements also lead to stress increases (exertion) and damage (fretting, Volume 2, Chapter 6.1). If a corrosive media is present (pump effect), there is a danger of corrosion notches (pitting, Volume 1, Chapter 5.4.1).
Connections (“4”): Weld seams act as notches in several different ways. Form notches occur in unworked weld seams due to excessive seam height and undercuts. Even if the seam is reworked, other notch influences are in effect. In the transition of the solidification-dependent, oriented cast structure of a weld to the uninfluenced base material (e.g. fine-grained forged material), a notch effect is created (structural notch, see Fig. "Development of fracture surface features" and Fig. "Strength and danger of crack length"). Strength differences, hardness differences, and residual stresses increase the notch effect.
Solders act as notches due to their different material properties relative to the base material. In addition, bonding flaws must always be expected in soldered connections. The notch effect of solders is evident in the low shear strength of soft solders (“tuna can effect”). Same-material solders such as high temperature solders usually have high strength and sufficient hardness. However, their brittleness promotes notch effects. Therefore, soldered areas must have suitable geometries that relieve the transition areas.
Notch effects due to local temperature influences (“5”): Both during finishing (e.g. high-speed machining, grinding, welding, separating) and operation (rubbing), metal droplets can be created. If these strike a part surface, they can damage it in various ways. Droplets of titanium alloys are especially dangerous. While traveling through the air, droplets of titanium burn and reach high temperatures. When the fuse to the surface that they strike, the can act as form notches. Even if the droplet does not remain on the surface, it can dangerously alter the structure of the base material at the point of contact (structural notch):
- embrittlement (brittle phases, oxidation)
- changes in hardness/strength (annealing, hardening, diffusion)
- tension residual stresses
Surface notches (“6”): Scratches can be created during handling (finishing, assembly, maintenance). The more notch-sensitive a material is, the more seriously scratches must be taken. For this reason, the transition between steel pipe and titanium pipe can be a problem area.
Cracks in coatings can increase the risk considerably. The risk usually increases with coating strength and brittleness. For this reason, critical coatings (e.g. nickel-plating, chrome-plating) should be avoided in the areas of form notches. This is especially true for LCF-stresses areds, since these determine the part life. If noticeable plastic deformations occur, they will cause cracking in brittle coatings (Fig. "Coatings sensitive to thermal fatigue").
Inner notches (“7”): These are usually material flaws such as cracks, pores, and cavities. Even areas with lower strength, such as segregations and abrupt structural transitions (Fig. "Grain size influencing static and dynamic fatigue"), act as notches. A special problem is the poor detectability of the small, already dangerous notches of highly-stressed parts.
Figure "Improving durability of turbine rotor by design" (Ref. 13-5): This two-stage high-pressure turbine from a fighter engine is designed for 8000 cycles. The two-stage design was chosen over a single-stage configuration. The better efficiency relative to the single-stage version allows the gas temperatures and blade loads (RPM) to be kept lower. At the same time, increased weight, longer axial length, and higher cooling air consumption were consciously accepted.
The focus was on the lowest possible stress concentration. This includes avoiding bolt bores and cooling air bores in the disk membranes and annulus areas.
The selection of the disk material was done in consideration of the aspect of damage tolerance and, therefore, crack resistance (crack toughness). The material was powder-metallurgical. This material was able to attain the predicted life span after the incubation time (crack initiation life) even if there was a flaw capable of growth. This was not possible with the conventional material. It must be noted that the two-stage turbine made possible lower disk loads than the single-stage version, which contributed decisively to the flaw tolerance and reduced crack growth rate. This also reduces the life cycle costs and makes the inspection intervals longer. This makes it easier to take action according to the retirement for cause philosophy (Ref. 13-15). This reasoning assumes that cracked parts are discovered and removed in time. Crack-free parts continue to be used within the potential crack growth phase (Ref. 13-10). Because the literature is from 1984, it can be said that the retirement for cause concept has not been widely accepted despite its seductive cost-reducing advantages of life span utilization. This is primarily due to the not sufficiently safe verification limits of the serially applicable testing procedures. Labyrinth rings near the annulus and fastening rings for the blades are parts with similarly limited life spans, due to to thermal fatigue stress. In the depicted example, these rings are positive-fitted and fastened with piston ring-like fasteners. These fasteners are tightened by centrifugal force, ensuring a good seal effect without threads or rivets.
The stepped intermediate stage labyrinth has four armored tips in order to minimize the circulation of hot gases with the leakage flow. This is intended to keep the annulus area of the disks as cool as possible. The armor is intended to minimize heat development during rubbing and thus minimize hot cracking.
The disks are jammed on the shaft over a cone, which is screwed onto the disk flange in an externally centered location. This creates an especially rigid connection.
The rotor parts were produced in a superplastic forming process that was close to the final dimensions. This improves material properties and lowers costs. In order to increase the fatigue strength and defuse flaws, the transitions to the flange were soft, and the surfaces were shot peened.
Figure "Threaded LCF loaded connections in a turbine": These single-stage high-pressure and low-pressure turbines from a fighter engine show two very different threaded rotor connections. The high-pressure turbine disk has bolts through the disk membrane. This disk zone is under relatively high LCF loads (Fig. "LCF as lifespan determining") from centrifugal forces and thermal stress. The bolt bore should represent a life-determining area of the disk. In the case of cracking, rapid crack growth is to be expected.
The low-pressure turbine is connected to the shaft via a flange. The flange bore is located in an area that should be subjected to relatively little stress from the startup and shutdown cycles, and therefore does not greatly limit the LCF life of the disk.
Figure "Bayonet coupling in LCF loaded turbine disks": The left diagram shows the two-stage turbine rotor of a large, first-generation, civilian fan engine. In both disks, the blade connections, labyrinth rings, and annulus are weakened by bolt bores. In addition, the pronounced structure of the annulus areas, which is necessary for the cooling air supply, creates problematic stiffness jumps. These have been causally related to serious damage (Volume 2, Ill. 8.1-19, Ref. 13-6). The second stage has bolt bores for the shaft connection in the disk membrane. This creates areas with high stress peaks that should have a limiting effect on part life.
The right diagram shows another two-stage high-pressure turbine from the same manufacturer, but from a newer engine type. The self-supporting labyrinth carrier was fastened between the disks with the aid of a bayonet coupling. The disks are each connected directly to the shaft with socket connection lugs in the hub area. The axial blade fastening is evidently accomplished with form-fitted rings (Ill. 13-19) that tighten under centrifugal force. This avoids having any bores in the disk, annulus, or seals. An optimal cyclical life span can be expected from this type of design.
Figure "Improving LCF behaviour by redesign" (Ref. 13-6): In this case, a life-critical part of an older engine was improved by reducing the stresses in the hub by enlarging the supporting cross-section and avoiding bolt bores in the disk membrane through the use of flange lugs.
Figure "Durability improvement of engine rotors" (Ref. 13-5): The fan (top diagram) is vital for the total efficiency of an engine. Therefore, maintaining efficiency, i.e. minimizing deterioration (Volume 2, Ill. 7.0-2) is an especially important consideration with this component. Wide chord blades do a better job of preventing stalls because they make larger play to the surge limit possible, and are less sensitive to disturbances in the inlet flow or during unsteady operation. This minimizes rubbing and clearance gap increases. The rotor blades of the first stage are outfitted with clappers in order to prevent flutter and high-frequency vibrations, as well as making them less sensitive to combat influences. The contact surfaces in the roots and clappers have hard coatings in order to prevent wear. However, this seems problematic because hard coatings on the blade roots could reduce dynamic strength. The number of flanges and threaded connections is reduced with the aid of welding. This eliminates notches and improves imbalance behavior (no shifting). The rotor has bearings on both sides in order to maintain clearances during flight maneuvers (Volume 2, Chapter 7). However, this principle can have considerable drawbacks relative to one-side bearings (Volume 1, Ill. 126.96.36.199-18) in case of bird strikes or containment incidents. All stators have an inner shroud to prevent vibrations and minimize foreign object damage. The stiffness of the intermediate housing with the fixed bearings is guaranteed by a cast housing.
Modern high-pressure compressors (bottom diagram) use welded rotors to minimize the number of flanges with stress-increasing bores. However, it should be noted that sufficiently flawless welding (pores, micro-cracks, splices, poor structures) must be guaranteed. The utilized materials are selected based on damage tolerant considerations, i.e. high crack toughness and minimal crack growth (Fig. "Notch types threatening constructions"). Blades with wide chords (low aspect ratio) are used due to their more robust behavior towards the common fundamental flexural modes (Fig. "Blade shape and aerodynamic damping"), combat influences, and erosion. For the same reasons, the stators have inner shrouds. It must be noted that wide chord blades have been proven to be sensitive to higher-order vibrations. The risk of edge cracks, especially, is considerably greater. Special emphasis is placed on erosion-resistant seal coatings (Volume 1, Ill. 5.3.2-10) with good abradable behavior (Volume 2, Chapter 7(. Another focal point is a robust guide vane adjustment mechanism. In order to prevent wear in the bearings, long guides are used and the number of connections is minimized. Ball joints can be avoided through the use of counterbalancing, adjustable control levers with flexible torsion. Increased adjustment forces due to the spring effect of the levers are consciously accepted. The fastening of the levers to the blade pivot is redundant. Under no circumstances may the blade be turned to a wrong angle, as this would cause consequential damages due to the flow disturbance in the compressor.
Figure "Blade design improving LCF failure safety": Strategies for damage tolerance in rotor disks. The object is to discover hub cracks in time, i.e. before catastrophic failure. This requires a sufficiently long crack growth phase and an externally recognizable indicator, such as imbalance or a certain inspection characteristic (recognizable crack). The best situation is if the crack growth slows or even stops for a period of time. In any case, the highest possible crack toughness is desirable in the disk material. This slows crack growth and increases the critical crack length at which a residual fracture occurs.
The crack growth rate can be slowed by suitably segmenting a single thick disk, of the type typical in modern fans with wide chord blades, into several thinner disks (left diagram, Refs.
13-7 and 13-10). However, cracks cannot be prevented from spreading into the neighboring disks.
The middle diagram shows a variant in which an additional isolation slot is placed between neighboring disks in order to stop crack growth. Proper matching of the disk loads and the geometry can cause the crack to stop before it spreads into the neighboring disk.
In bling designs (bottom right diagram), it is desirable that the supporting fiber winding has slow crack-growth properties (Fig. "Advantage of a material needs design philosophy"). Whether or not this can be realized is a technological question and remains to be seen.
In general, from the standpoint of damage tolerance, it can be said that welded rotors (Fig. "Improving LCF behaviour by redesign") can also have drawbacks compared to flange. For example, flange can catch cracks and prevent spontaneous bursting of the rotor. This can be especially important in intermediate stage labyrinths on drum rotors (Volume 2, Ill. 7.2.2-11).
Figure "Danger of notches in pressure chambers": This diagram shows the problems of a weld in a highly stressed area; in this case, an outer combustion chamber liner. Even a minor shifting of the seam (crack initiation zone 1) can lead to crack initiation on the inside of this pressurized container. This will be noticed only when it results in instable bursting.
One can frequently observe parts that have been weakened with sharp-edged design notches, even when these are not necessary (crack initiation zone 2).
The notch promotes faster crack growth and reduces the probability that the crack can be found during an inspection.
Even slightly enlarged notch radii reduce the stress in the notch considerably. This fact can also be used when reworking parts to obtain a sufficiently safe life span.
Figure "Safety problems of joined constructions": Welds and solders should, if possible, be located in areas that do not determine part life, i.e. areas with lower stress levels. The hollow fan blade (left diagram) made from a titanium alloy is an excellent example of this. The connection between the two blade halves is parallel to the centrifugal force. In the range of high dynamic loads (fundamental flexure), it is not located at the surface (Ref. 13-7), but near the neutral fibers.
The dual property turbine disk shown at top has a diffusion bond between the cast annulus and forged disk. Typical flaws of this type of bond are splices, which cannot be sufficiently safely detected with serially implementable non-destructive testing. This leads to spontaneous separation of the annulus after widely varying operating times. It may be possible to sufficiently defuse the problem with a HIP treatment.
If parts such as blings (right diagram) are manufactured with HIP connections, it should be ensured that required connection zones are not subjected to cross-stress.
Under certain conditions, it is evidently possible to use welds in areas of rotating parts that are statically and potentially dynamically highly-stressed parts. Blisks (bottom left diagrams) with blades that are welded in at the blade root, are soon to enter serial use. The welding process (linear friction welding) is subject to special procedural controls. Additional, specific non-destructive tests could increase safety even further. Ultimately, however, only serial operation will allow statistical safeguarding.
Figure "Reworkability and testability of rotor weld seams": Sufficient testing and/or reworking conditions must be ensured with welds and solders. These determine the design-relevant flaw size and therefore the stress tolerance of the part. In the case of electron beam welding, splashes must also be safely removed from the root side. Friction welds must be reworked and inspected due to the typical burrs on the root side.
Figure "Accessibility of threaded connections": Assembly, for example, the safely controlled tightening of nuts, must be provided for. For example, there must be no danger of the torque wrench jamming and indicating a proper tightening torque in error. In this case, modern, computer-supported methods such as assembly simulators in computers and/or using parts manufactured with rapid prototyping can be very useful aids.
Figure "What can be installed wrongly is endangered": The design engineer must concern him or herself with the seemingly simple, but not always easily accomplished, task of ensuring foolproof assembly. In the depicted case, it was possible to install the blades the wrong way at a 180° angle, although this was easily visible due to the profile orientation. Despite this, this type of faulty installation occurred, leading to flow disturbances and compressor damage. An additional task of the design engineer is to inform the relevant personnel in case new technologies or special assembly procedures are introduced (Fig. "Risks of technology implementation in practice").
Figure "Safety concept based on function separation": The functions of a part can, in some cases, be distributed among different components in such a way that controllable failure, i.e. fail safe behavior, is guaranteed.
In the top diagram, the fan-side fixed bearing of the low-pressure shaft sits on a shaft collar that does not transfer any torque. The fan is powered by the clearly radially offset low-pressure shaft. This makes it unlikely for bearing failure to cause the shaft to break. This prevents consequences such as uncontrollable overspeed in the low-pressure turbine (Volume 1, Ill. 4.5-4) or releasing of the fan (Ill. 4.5-5 and Ill. 4.5-6).
Figure "Seal function separation from compressor disks": In this case, the operating behavior of an engine is made safer through separation of different tasks of intermediate stage labyrinths, such as sealing and rotor bracing. In a modern drum rotor with integral labyrinth fins (left diagram), overheating and/or crack initiation due to labyrinth rubbing can result in unallowable weakening of the rotor (Volume 2, Ill. 7.2.2-11).
Such weakening of the rotor is not expected from labyrinth carriers that are not integrated into the rotor (right diagram), inset labyrinth rings, or labyrinth rings that are offset with the aid of radial brackets (middle diagram). Of course, there are other factors that go against this type of solution (e.g. cost, weight, complexity).
13-1 Z.S. Palley, I.M. Korolev, E.V. Rovinskiy, “Structure and Strength of Aircraft Gas-Turbine Engines”, Translated from Russian, Foreign Technology Division FTD-HT-23-903-68, 1967, pages 25-28.
13-2 R. Whitford, “Fundamentals of Fighter Design”, Airlife Publishing Ltd, ISBN 1 84037 112 9, 2000, page 82.
13-3 D.W. Hoeppner, “Parameters that Input to Application of Damage Tolerance Concepts to Critical Engine Components”, Proceedings Paper AGARD-CP-393 of the conference “Damage Tolerance for Critical Engine Components”, pages 4-1 to 4-16.
13-4 W. Schütz, “Lebensdauer-Berechnung bei Beanspruchungen mit beliebigen Last-Zeit-Funktionen”, VDI-Berichte Nr. 268, 1976, page 113.
13-5 B.L. Koff, “Design for durability in fighter engines”, periodical “International Journal of Turbo and Jet Engines”, 1, 1984, pages 209-222.
13-6 B.L. Koff, “Aircraft Engine Design & Development”, Proceedings Paper AGARD-CP-215, Chapter 9, page 9-3.
13-7 B. Gunston, “The Development of Jet and Turbine Aero Engines”, Publisher: Patrick Stephens Ltd, Chapter 8.
13-8 A.K. Vasudevan, K. Sadananda, “Environmental Effects on Fatigue Crack Initiation and Growth”, Paper RTO-MP-18 of the RTO AVT-Workshops on “Fatigue in the Presence of Corrosion” Corfu, Greece, 7-8 October 1998, pages 17-1 to 17-13.
13-9 D. Schütz, “Derzeitiger Stand der Lebensdauervorhersage für Bauteile”, VDI-Berichte Nr. 268, 1976.
13-10 “GE90 Program Summary”, Seminar lecture at the TU Munich, Institut fuer Flugantriebe, November 1995.
13-11 “FAA expected to announce further PW4000 compressor inspections”, periodical “Flight International”, 17-23 July, 2002, page 9.
13-12 “P&W set to certificate fix for PW4000 surge”, periodical Flight International“, 10-16 December, 2002, page 9.
13-13 R.M. Wood, S.X.S. Bauer, “Discussion of Knowledge-Based Design”, periodical “Journal of Aircraft”, Vol. 39, No. 6, November-December 2002, pages 1053-1060.
13-14 M.E. Taverna, “Ariane 5 EC-A Upgrade Faces Long, Costly Flight Delay”, periodical “Aviation Week & Space Technology”, January 13, 2003, page 402.
13-15 “New engine maintenance strategy: Throw it out just before it breaks”, periodical “Machine Design”,March 10, 1983, pages 25-30.