Figure "Fundamentals of LCF damage mechanism"

Figure "LCF as lifespan determining": The difference between LCF (low cycle fatigue) and HCF (high cycle fatigue) is explained well by the Woehler diagram (top diagram). This applies to materials that have a Woehler curve that becomes horizontal above about 10⁷ load changes, i.e. materials that have a fatigue limit (e.g. steels). Al alloys and titanium alloys do not have a fatigue limit below which no fracture can be expected; in this case the curve continues to decline. Loads in the range of the fatigue strength are above the fatigue limit. After a load-dependent period of time, a dynamic fatigue fracture occurs. Therefore, this breakdown of the Woehler diagram is load-oriented. Another method of classification common in the English-speaking world is based on the expected life span. Dynamic loads that lead to “noticeable plastic deformation” in the crack initiation zone are defined as lying in the LCF range between 10⁴ and 10⁵ crack initiation load changes. An interesting note is the imprecise definition of the deformation amplitude, which can be seen in the relatively broad life span range. In addition, at first glance it is often not clear how the deformations occurred, since parts that have a limited cyclical life (rotor disks, etc.) do not show any measurable expansion.
The bottom diagram uses an everyday situation to make the damage mechanism of (extreme) LCF stress understandable. If one desires to split a wire by hand, then it must be plastically bent several times. This causes the wire to experience an LCF fracture. Of course, the number of load cycles in engine parts is considerably higher, but the mechanism is comparable.
In a steel wire, an increase of bending force can be detected as the material hardens (Ills. 12.6.1-9 and 12.6.1-10). The wire breaks after several load changes. Heat creation is not important for explaining this process, and only reflects the bending force required to plastify the material. One might also notice that a rusty wire (with corrosion notches) tolerates less load changes to fracture than a smooth wire. Therefore, notches and flaws lower the LCF strength, i.e. shorten the LCF life of a part. For this reason, they must not occur in part zones that are subjected to this type of stress.
HCF fractures, on the other hand, do not show any noticeable signs of plastic deformation. Even in ductile (tough) materials, these fractures act brittly.
As the bottom left diagram shows, LCF-stressed part zones (of a rotor disk, in this case) are limited to small volumes in areas that experience increased stress levels due to a notch effect. These include radii between sectional jumps, bores for connecting bolts, and hub bores. These zones are subject to high stress levels due to centrifugal forces and thermal stress, and always result in plastic deformations at the load levels that are typical in today`s operating environments. After relief, residual stresses build up in the zones between the plastically deformed areas and the merely elastically deformed surrounding areas. These stresses are in a state of equilibrium when the engine is at a standstill. For this reason, the local plastic deformations are not apparent in external dimensional changes (in disk diameter, for example).
In order to avoid a common misconception, it must be pointed out that letter “F” in the terms HCF and LCF stands for “fatigue”, not “frequency”. Although the large number of fracture load changes and the comparatively moderate stress amplitude in HCF fractures are usually connected with high-frequency vibrations, it is also possible for HCF fractures to accumulate at “LCF-typical” low frequencies (e.g. startup/shutdown cycles). An example of this would be a peak load gas turbine which is only started a few times a day over several decades of operating time.
On the other hand, LCF fractures can also be caused by high-frequency vibrations with extreme amplitudes. These loads can occur during flutter vibrations or when blades run over a blade fragment that is caught in the housing, for example.

Figure "LCF lifespan determining critical zones": This example shows a radial compressor disk from the APU of a large helicopter. The disk is made from heat-treated steel. There were several instances in which these disks cracked and burst. The LCF cracks originated in small mounting holes for the shaft which was flanged onto the back of the disk. Due to the pronounced notch effect of these bores, centrifugal forces cause a small zone with plastic deformations to form around the holes. The number of cycles after crack initiation, i.e. the crack growth rate, could be estimated with the aid of a fracture surface analysis. It was discovered that the cyclical loads could be attributed to the startup/shutdown cycles. The total number of cycles for the cyclical crack growth led to the conclusion that crack initiation must have occurred during the first few load cycles. It is understandable that the deformations around the small bores would not have a measurable effect on the outer diameter of the disk at rest.

Figure "When is a weak point a flaw limiting LCF" (Ref. 12.6.1-17): The following is a guideline for estimating the allowable flaw size (maximum weak point) for LCF-stressed turbine parts. Ill. 12.6.3.4-19 provides information for HCF.
In the part areas that determine life span, the cyclical loads on turbine engine disks are in the LCF range, and therefore far above the yield strength. The failure rate must be below 10^-8 per disk and hour of operation (or cycle, depending on the definition; Volume 1, Chapter 2). This means that at the present volume of 60,000 civilian flights per day worldwide, there must be no disk failures in the space of a year. In order to estimate the maximum flaw size for LCF loads that conform to the designed values, the following procedure can be used for turbine disks:

“1”: Experience has shown that life-determining LCF cracks occur at flaws (material, production). An important factor is whether the load-induced stress concentration leads to immediate crack growth due to a flaw size that cannot be sufficiently safely detected (4), or whether there is an incubation period (Fig. "Phases of fatigue fracture").
This is a determining factor for the design philosophy that will be used. If the required part life is within the incubation period, then this is a very safe situation. However, this means that the potential strength of the material is not being fully utilized, resulting in higher disk weight and/or lower RPM. The more the potential strength is utilized, the smaller the flaws that must be safely found. This at the very least increases the complexity of quality assurance considerably (4). If the demand to keep the life span within the incubation period cannot be met, the crack growth rate must also be considered. This results in uncertainties that must be sufficiently minimized with elaborate verification procedures such as part tests and comprehensive determination of fracture-mechanical material data.

“2”: A fracture-mechanical inspection must determine the allowable flaw size of the expected crack growth rate, as well as the life span to critical crack length (crack length at fracture). This requires sufficient understanding of the relevant material characteristic data (Paris relationship, Ill. 12.2.3) and part loads (Ills. 12.6.1-16 and 12.6.1-17). If, for example, the fracture toughness that determines crack growth is clearly dependent on the orientation of the structure and temporal load progress (Fig. "Lifespan verification by cyclic spin test "), then crack growth (Fig. "Characteristic crack growth") can occur with unexpected rapidity (Fig. "LCF fracture of a fan disk").

“3”: This diagram provides the expected number of flaws of specific sizes in typical disk materials (also see Examples 12.6.1-1, 12.6.1-2, and 12.6.1-3). However, the estimation of the maximum allowable flaw sizes as given in this diagram does not attain the level of safety required for the failure rate of 10^-8 /hour of operation. We know, for example, that very hard inclusions have an especially negative effect on LCF strength (Example "Dwell time fatigue"). Therefore, the allowable operating loads are based on operating experience with comparable disks and engine parts. The interpretation of this type of experience must be possible despite different acceptance criteria, verifications, production processes, and loads in the cases being evaluated.

“4”: In order to sufficiently safely keep the flaw size below the value that is fundamental to the design (“1”), a serially implementable, non-destructive testing procedure and/or an equivalent quality assurance strategy (such as procedural monitoring) must be available. This must be used to guarantee the detection of unallowably large flaws.
Many surface flaws such as grooves and damages from production and handling (such as structural changes due to overheating), can be mitigated through hardening procedures (shot peening, rolling). In this case, the hardening effect evidently plays a deciding role, since the induced residual stresses should quickly dissipate under the plastic deformations in the part areas critical to LCF.
Residual stresses that act over larger cross-sections seem to behave differently (Ill. 12.6.1-17)
It must be mentioned that these hardening procedures have, up to now, been used as additional safety measures, but are not part of the original design. If the LCF strengths attainable through surface hardening become part of the design, it could result in the creation of new uncertainties (Fig. "Material behavior depending on design and technology").

Figure "LCF lifespan estimation" (Ref. 12.6.1-2): In order to design an engine part to meet the required LCF life (safe load cycle number), suitable material data are required. These are obtained by conducting sample tests as follows:

Step 1: Tensile specimens are put under strain-controlled loads in pulsers (usually hydraulic). Therefore, unlike in normal dynamic strength tests, no specific cyclical force (i.e. stress amplitude) is applied. In strain-controlled tests, the strain amplitude remains constant (forced). This remains the case even if the force required for the strain (plastic and elastic) changes due to hardening or softening of the specimen. The plastic deformation can be seen in the s-e diagram as a hysteresis between the expansion and compression processes.

Step 2: The specimen is cycled until the mean stress amplitude drops by 5%. This means that the specimen has failed. The progression of the maximum stress amplitude over the load cycles (life span) is used to calculate the tolerable stress/plastic strain amplitude. By definition, this is the stress relevant to half of the crack initiation-load cycle number N_A/2 .

Step 3: Many sample tests of the type depicted in steps 1 and 2, with varying strain amplitudes, are used to plot a cyclical stress/strain curve. Unlike in normal tensile tests, this curve is NOT determined with a constant load speed until a single sample fails! The cyclical stress/strain curve can now be used to determine the design-relevant stress and strain amplitudes necessary for calculating the allowable part load levels.

Step 4: The specimen values from steps 1 and 2 can also be used to create a dynamic strength diagram. This is done by plotting the plastic strain amplitude over the crack initiation load cycles (technical cracking, semi-elliptical with a length of 0.8 mm; Fig. "LCF as lifespan determining"). If the plotting is done logarithmically on both axes, the result for all metallic materials used in engine construction is a scatter band that decreases as crack initiation load cycles increase (Fig. "Fundamentals of LCF damage mechanism").

Figure "Strain hardening under cyclical loads" (Ref. 12.6.1-2): These diagrams show the static and cyclical stress-strain curves of a low-strength material (left) and a high-strength forged disk material. The low-strength material of type V2A is an austenitic steel with a very low yield strength and large elongation at fracture. Due to its special hardening properties, its cyclical stress-strain curve is far above the static curve, and its stress amplitude is close to that of the high-strength material. If the cyclical curve is above the static curve, the material has hardening properties (also see Fig. "Material changes during crack development"). Due to its good deformability and low flow limit, this material is used for sheet metal components that experience low mechanical stress but must be highly resistant to thermal fatigue (e.g. hot gas-carrying parts).
The stress-strain curves for a standard material used in HPC and turbine disks are shown at right. Here, the cyclical stress-strain curves are below the static curves both at room temperature and at the typical operating temperature of 600°C. This is referred to as softening behavior, even though material hardening can be observed.

Figure "LCF specimen in test device": At first glance it is not necessarily evident how the LCF loads in a part, in this case a turbine disk, correspond to the strain-controlled loads of a specimen in a pulser. These specimen tests are the basis for life span design calculations. Fig. "Cracks protecting from thermal fatigue" gives an explanation for thermal fatigue, which is also a type of LCF load.
The centrifugal forces in a disk, as well as the LCF loads they create, build up to an amount limited by the allowable RPM. During this process, small, but life-determining notch-influenced disk zones are plastically deformed. The entire large surrounding area has merely expanded like a spring. When the disk is at rest, the plastified zones are under compressive residual stresses, while the neighboring elastic zones experience tension residual stress. When the disk begins to run again, the plastically deformed zones only deform as much under tension as the elastic strain of the surrounding area permits. This corresponds to strain-controlled tension-pressure loading in a pulser. The pulser represents the large elastically strained part zones, the small plastically deformed zones correspond to the LCF specimen.

Figure "Determining strain in critical zones" (Ref. 12.6.1-3): The form coefficient a_k can only be used with loads in the fatigue strength range (elastic deformations, HCF) for designing the dynamic part strength (top left diagram). It cannot be used for modern engine parts that are subjected to loads in the LCF range (plastic deformation). If the stress in the notch exceeds the yield strength, it will result in plastic deformation and a reduction in stress levels. Any noticeable plastic deformations in the crack initiation zone must be taken into consideration. In this case the life span is determined on the basis of the stress levels in the notch.
In order to determine the number of load cycles to crack initiation in a notched part on the basis of the crack initiation characteristic diagram of un-notched specimens (Fig. "Fundamentals of LCF damage mechanism"), the strain amplitude in the notch must be determined. This can be done through the use of mathematical (finite elements) and experimental procedures (top right diagrams).
If an estimation is sufficient, then Neuber`s approximation procedure can be used (bottom diagram). This requires the cyclical stress-strain curve, the nominal stress, the crack initiation characteristic diagram, and the form coefficient a_K . The intersecting point of the Neuber hyperbola with the cyclical stress-strain curve provides the plastic and elastic strain with the corresponding stress levels in the notch base.

Note: The notch stress is relevant for treating the crack initiation phase, but is less relevant to crack growth. For estimation of the latter, the “nominal stress concept” is more suitable.

Figure "Bores as problematic zones": Based on the notch effect, it can be assumed that the walls of bores and surrounding areas are highly stressed both statically and dynamically. They are some of the life-determining zones in disks and flanges. For this reason, special attention must be paid to flaws and weak points in these areas.

Production-related weak points: Grooves and damages can occur as early as during production. Typical damages include those caused by hot-running drills (Volume 1, Ill. 4.5-11) or metal shavings that have been pressed into the material. These damages are generally not detectable with penetrative tests and require eddy current testing. The difficulty of finding dangerous weak points is made clear by examples such as the failure of a fan disk during startup (Volume 1, Ill. 4.5-11).
Another problem is burrs. These can be created during production or through improper handling. Due to their notched structure, they have a considerable notch effect and reduce LCF strength.

Assembly and handling: Installing screws and bolts during assembly or disassembly may result in the creation of longitudinal grooves. These are especially dangerous because their orientation is perpendicular to high mechanical loads (tangental or radial stresses).

Visual inspection and crack testing: Bores are usually difficult to see into. If cracks or flaws are overlayed by fretting or corrosion, visual identification or verification with penetrative testing is difficult.

Fretting: In bores, elasticity differences, vibrations, and thermal strain often lead to micro-movements between the screw or bolt shaft and the bore wall. These damages are especially dangerous in titanium alloys, since they can result in dangerous drops in dynamic strength (Volume 2, Chapter 6.1).

Corrosion: Gaps between a bore and the shaft of a clamp bolt can suck in corrosive media through a capillary effect. For titanium alloys, these are watery solutions of silver compounds (Fig. "Problems using silver in engines"), while steels are threatened by saline condensation water. The corrosion forms occur in combination with crack initiation (corrosion cracking) and/or pitting (Volume 1, Chapters 5.4.1 and 5.4.2). In order to balance the different thermal strains, steel disks are placed between disks made from titanium alloys and those of Ni-based materials. Due to the close tolerances (fitting diameter), satisfactory corrosion protection cannot be applied to the steel disks.
Unsuitable auxiliary materials such as oils and greases can also initiate corrosion in bores. For example, several turbine disk fractures (cast Ni alloy) in a helicopter engine were traced back to the improper use of a lubricant containing MoS. This lubricant entered into the space between the clamp bolt and the wall of the highly stressed central disk bore. At operating temperatures, this resulted in stress corrosion cracking in the turbine disk. A further possibility for corrosive damage of bore walls in Ni-based alloys is connected to silver deposits and the sulfidation processes they promote (Fig. "Problems using silver in engines").

Fatigue cracks: If fatigue cracks (LCF) occur in bores during operation, experience has shown that they are not easy to detect with a sufficient degree of safety during overhauls. Detecting them with penetrating procedures can be made more difficult by the cracks closing up due to residual stresses induced by the LCF loads (Ill. 12.6.1-13).

Illustrations 12.6.1-13.1 and 12.6.1-13.2 (Ref. 12.6.1-5): According to the definition, LCF loads occur with noticeable plastic deformations (Figs. "LCF as lifespan determining" and "LCF lifespan determining critical zones"). This leads to a buildup of and/or change in residual stresses. These can also be used to increase the number of tolerable load cycles in operation (top diagram). This is done by spinning the unfinished parts at overspeed.
Residual stresses can make penetrative testing more difficult, if the LCF cracks in the hub area are pressed shut.
Desired residual stresses created by hardening processes (e.g. shot peening, piercing) and chipping machining of new parts are reduced or covered up by the plastic deformations. In order to minimize this effect in engine construction, if possible, parts are pre-stressed and shot peened (springs, etc.). The use of this type of process, i.e. shot peening at high overspeed, has not been reported for rotating engine parts.
Example1: Aside from special notched areas (bolt bores, transition radii of ring-shaped accretions, etc.), rotor disks with a typical shape experience the greatest stress in the area around the hub bore. This zone is often subject to life-determining LCF loads. When it is run for the first time, high tensile stresses with plastic deformations are created by the centrifugal force (top left diagram). Afterward, the relaxed disk will have compressive stresses in the plastically strained hub area (top right diagram). These are in equilibrium with the tension residual stresses in the surrounding areas that are only elastically stressed. This effect can be used to increase LCF life.
This is accomplished by spinning the unfinished part at overspeed before the final machining and material removal. This puts greater stress on the hub area than it will experience during later engine operation. The unfinished part now has high compressive residual stresses in the life-determining hub region. This lowers the mean stress (Fig. "Terms and examples of dynamic loads"), i.e. the tensile stress peaks, during operation. This increases the tolerable LCF strength (Fig. "Terms and examples of dynamic loads"). This procedure has found widespread use and has proven itself in practice.
Pre-spinning unfinished parts in the plastifying load range can also be used to even out residual stresses. Otherwise, these can cause warping during the final material-removing shaping process. This procedure is particularly useful in ring-shaped parts that have an especially filigreed final geometry.

Example 2: The thermal fatigue process (Chapter 12.6.2) occurs in the LCF load range. These stresses are created through restricted thermal strain. During the heating-up phase, compressive stresses build up in the hotter part zones. During cooling, tension residual stresses build up in the compressed area, and are in equilibrium with the part zones that were cooler during operation (bottom left diagram). A typical example is turbine blade leaves. In the edges, which are hottest during operation, tension stresses are present after cooling, putting compressive strain on the internally located cooling configuration (bottom right diagram).