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Table of Contents

12.2 Crack Growth

Before covering the individual load-specific damage mechanisms in separate chapters, which also cover crack initiation (Chapter 12.6.3) and residual fractures (Chapter 12.3), the development and growth of cracks to unavoidable part failure will be discussed. Knowledge of fracture mechanics is an important prerequisite for understanding these processes. The initial crack and the sub-critical crack growth (Ills. 12.2-1 and 12.2-2 ) can occur under static loads (Ill. 12.2-12), dynamic loads (LCF, HCF; Ill. 12.2-3) or a combination of both (overlayed or at different times). In the field of fracture mechanics, crack growth rate is defined as the growth of the crack relative to the number of load cycles (Da/DN), independent of temporal progression. This means that the vibration frequency is not part of this value, even though cracks will naturally grow more quickly at higher frequencies. Fracture mechanical inspections are used in engine construction most frequently in relation to high cyclical loads, such as occur during startup/shutdown cycles. There are several reasons for this.
HCF is a type of dynamic stress that requires over 105 crack load changes. This many load changes are usually only reached by high-frequency vibration. This frequency means that crack growth will be very rapid, and it will hardly be possible to detect the crack in an intermediate inspection before fracture. It is rare for the operator to know the time of the dynamic loads, the number of cycles to cracking, or the load levels, making the time of crack initiation undeterminable. Therefore, fracture mechanical observations lose importance in the field of damage prevention.
If initial cracking and sub-critical growth occur under static loads, then they require the simultaneous action of additional effects such as stress corrosion cracking (Ills. 12.2-11 and 12.2-12) or temperatures (dwell time). If the time of initial cracking (e.g. due to corrosion) or the crack growth rate are not sufficiently predictable, then the usefulness of fracture mechanics for conducting risk assessments and setting inspection intervals is very limited.
In the case of LCF loads with cracking load cycles below 105 , the conditions are good for successful application of fracture mechanics to damage prevention in acute cases. This requires sufficiently exact knowledge of the number of relevant cycles to cracking and the size of the loads, e.g. as design data for the life span. The relevant states are primarily transient ones such as startup/shutdown processes or power changes. The cyclical loads are made up of centrifugal forces and temperature gradients (Chapter 12.6.1 and 12.6.2). This makes the time of initial cracking and the crack growth per load cycle estimable, provided the necessary material data are available. This allows the implementation of measures in cases of acute damage. These measures include setting safe remaining run times and/or sufficient inspection intervals before the risk of part failure due to fracture becomes too great.

Illustration 12.2-1:Fatigue fractures under cyclical loads occur in several phases. Fracture/crack surface analysis can allow retroactive conclusions regarding the dynamic loads and the mean stress (Ill. 12.2-19).

Incubation: Damage occurs at the most highly-loaded weak point (“A”), in which the loads are greater than the threshold value below which no crack growth occurs (Ill. 12.2-3). This damage increases with the number of load cycles until it results in an initial crack, which spreads (Ill. 12.6.3.2-1). Multiple cracks of almost equal length in other engine parts of the same type (e.g. same stage) indicate the presence of very high, and possibly brief, dynamic loads in the LCF range, which caused the crack to grow after only a few load cycles (Ills. 12.2-18 and 12.2-19).

Stable crack growth phase: In this phase, the increasing loads in the remaining cross-section, combined with the notch effect of the crack, cause stable, accelerated cyclical crack growth (“phase 1”, “phase 2” and “phase 3”, Ill. 12,6.3.2-1). The fracture surfaces often show curved concentric line patterns (lines of rest). These are created by an uneven crack growth rate. This is caused by fluctuations in the dynamic loads due to temporally varying excitement, changes in the resonant frequency due to the crack-induced loss of stiffness, and changing damping. Lines of rest in corrosion-resistant materials such as titanium alloys and nickel alloys are not caused by discoloration due to oxide formation while the engine is standing, as the term would seem to suggest. However, oxidation at high temperatures while the crack is at rest can create similar markings.

Residual forced fracture: This occurs when the crack has reached a critical length “ac” and becomes unstable (“R”). The surface of the residual forced fracture in relation to the dynamic fatigue fracture surface provides clues regarding the static loads during fracture. The loads can be estimated on the basis of the critical crack length ac (Ill. 12.2-3). This requires knowledge of the fracture toughness Kc for the specific case. In thin cross-sections (e.g. blades), Kc is greater than the critical fracture toughness KIc (Ill. 12.3-2). Shear surfaces indicate the stress conditions during the residual fracture (Ill. 12.3-3).

Illustration 12.2-2 (Refs. 12.2-1 and 12.2-2): Three types of crack opening are defined in fracture mechanics (top diagram). They are classified according to whether the force that causes the crack to grow acts perpendicular to the crack plane (“I”), in the crack plane in the direction of growth (“II”), or crossways to the growth (“III” ). The corresponding stress intensities are denoted with the respective indicators I, II, and III (KI, KII, KIII). Type I, in which the cracked surface is pulled apart, is the most common crack opening mechanism in technics. Type II places pure shear stress on the crack plane, causing the two sides to slide along one another. Type III also involves the surfaces sliding along one another. Shear surfaces also form in thin cross-sections under tensile stress. This is due to the pronounced plastic deformation at the surface (Ill.12.3-3).

Illustration 12.2-3 (Refs. 12.2-8 and 12.2-19): The top diagram depicts the stable crack growth against the size of the dynamic loads (F). During stable crack growth, the growth rate can be decreased and even halted by reducing the dynamic loads.
The higher the loads, the fewer load changes are required to fracture. This expected relationship is based on two effects: faster crack growth, which is seen in the steeper curve, and the shorter critical crack length “ac”, above which crack growth is unstable, i.e. forced fractures occur.
The bottom diagram (re. Paris) shows the stable crack growth per load change (da/dN) relative to the load size “K” (stress intensity) during crack growth under static loads (e.g. under the influence of corrosion, Ill. 12.2-11). For dynamic loads, the corresponding load amplitude is D K. This value corresponds to the loads at the crack tip under the load cycles against the crack size (Ills. 12.2-4 and 12.2-5). One can see that, depending on the size of the nominal loads, crack growth only occurs above a minimum stress intensity Kth , i.e. a corresponding amplitude DKth. This minimum intensity depends on many factors, such as structure and environmental influences (Ills. 12.2-11 and 12.2-12).
The stable crack growth itself can be divided into three phases as shown in Ill. 12.2-1 (not to be confused with the three types of crack opening). Phase 1 after initial cracking, an intermediate Phase 2, and a Phase 3 in which the crack growth accelerates rapidly, before unstable crack growth and fracture occur (Ref. 12.2-8).

Illustration 12.2-4 (Ref. 12.2-19): Because crack growth occurs at the crack tip, the dominant stress and deformation conditions (top diagram) in this area are of decisive importance (Ill. 12.2-7).

Fracture mechanical evaluation of the crack tip requires two values: the stress intensity “K”, which in fracture mechanics corresponds to the loads (stress s ), and the crack toughness of the strength of the cracked materials (e.g. “KI” for crack opening type I, Ill. 12.2-2). If the stress intensity exceeds the fracture toughness, it results in a residual forced fracture (unstable crack growth). If the conditions at the crack tip are suitable for causing a cleavage fracture, then the lowest (critical) fracture toughness “KIC” has been reached (Ill. 12.3-3). Under conditions that create shear components in the fracture (narrow fracture cross-section, Refs. 12.2-2 and 12.2-8), the fracture toughness is greater, and is denoted by “KI”.
The bottom diagram shows the simple relationship between the stress intensity, the nominal stress “s” across the crack, and the effective crack value “a”, which is derived from the crack form and crack location (e.g. surface cracks, inner cracks).

Illustration 12.2-5 (Ref. 12.2-2): A plastically deformed zone forms ahead of the crack tip, and its volume and form depend on the width “B” of the cracking cross-section and the ductility of the material (left diagram). These zones can be easily recognized in plastically deformed, notched samples of ductile materials. If the plastically deformed zones are large in relation to the cross-section thickness (thin, flat cross-sections), then the crack opening type I changes to crack opening type III (Ills. 12.2-2 and 12.3-2). At the surfaces, the neighboring, less highly stressed volume has a relatively minor inhibiting effect on the deformations in the crack tip area. The result is uneven strain conditions. Inside the cross-section, the deformation is inhibited so much, that the strain ahead of the deformation progresses evenly. This is referred to as an even strain state. In this case, the deformation inhibition leads to macroscopically brittle behavior.
The right diagram shows important influences on the state of the crack tip, and therefore also on the behavior of the crack.

Illustration 12.2-6 (Ref. 12.2-9): Various stages of crack development are defined (top diagram). When a crack first develops near the surface (stage I), intercrystalline separation, which is often very smooth, occurs below about 45°. Intrusions and extrusions also form at the surface (detail).
During subsequent crack growth (stage II) under cyclical loads, linear markings are created along the crack front during every load cycle. These are microscopic crack growth striations, and not macroscopic lines of rest (Ill. 12.2-1). The explanation of striations is the plastic deformation at every load cycle: expansion when the crack opens, and compression when it closes (bottom diagram).
Under static loads (e.g. corrosion), a line pattern can form that is similar to that of cyclical crack growth (Volume 1, Ills. 5.4.2.1-4 and 5.4.2.1-5). There is a special danger of false interpretations in this case.

Illustration 12.2-7: Higher strength materials do not necessarily mean increased safety against part failure and fracture. Unfortunately, the opposite is true. Higher strength materials are generally also more highly stressed (Chapter 14.2). This increases the damage risk during fatigue, since the probability of initial cracking is increased and the part will fail sooner after initial cracking (shorter crack growth phase). The reasons for this behavior are:

  • Even small initial flaws tend to crack growth because while Kth remains constant as a specific material value, the increase in stress s means that the size of a growth-capable flaw at the initial crack decreases (Ill. 12.2-3).
  • The crack growth rate increases because a load change results in a larger step (Ill. 12.2-6).
  • The crack becomes unstable at shorter critical crack lengths (“ac”) due to the increased loads that result if the specific material value KIC is also the same for the higher-strength material. The more highly-stressed cracked part fractures sooner (Chapter 13). It is also possible that a higher-strength material is actually more crack-sensitive, i.e. has a lower critical fracture toughness (Ill. 12.2-8), further worsening its performance.

Illustration 12.2-8: The size of a flaw that can result in an initial crack, and the crack growth, depend on the amplitude of the stress concentration (DK), the cross-section of the part in the crack zone, and the structure (diagram). In titanium alloys with rough structures, the crack growth rate is lower in thick cross-sections than in fine ones (diagrams, Ref. 12.2-22). This behavior can also be observed in fine-grain nickel alloys that were produced by forging or powder metallurgy (especially fine grains). In thin cross-sections, the crack grows more rapidly in rough grain structures than in fine grain structures (Ref. 12.2-11).
The framed values in the formula represent the influence of the structure and cross-section. “NS” is the number of load cycles, which takes into consideration the influence of the material structure on crack initiation (also see Ref. 12.2-21). Ns /p is dependent on the sample cross-section (Ref. 12.2-10).

Illustration 12.2-9 (Ref. 12.2-9): Crack-initiating notches must not necessarily be diagonal to the load direction (right diagram). Even lengthwise grooves (middle diagram) and ridges that act in a similar manner, can cause cracks due to their jagged notch base. The danger of ridges on dynamically highly-stressed bores and edges is often underestimated (Ill. 12.6.1-12 and Volume 2, Ill. 7.1.3-18 ).

Illustration 12.2-10: The “controllability” of a crack refers to the possibility of catching the crack before the part fails. The controllability of cracks is a prerequisite for being able to live with them, i.e. cracks that are specifically tolerated in operation (e.g. thermal fatigue cracks in turbine stator vanes, Ill. 11.2.3.2-7). They should be incorporated into the life span concept of the engine parts and can be monitored in some cases (e.g. boroscope inspections). Another situation in which cracks must be controlled is when damage occurs due to LCF cracking and corrective measures cannot be implemented quickly enough (Volume 2, Ill. 8.1-19). If safe inspection and/or replacement intervals can be set, then the problem is temporarily mitigated. This assumes that crack initiation, growth, and the acting influences are sufficiently understood and that crack growth can be traced.
The controllability depends especially on the crack growth rate and the critical crack length (Ill. 12.2-5). In the case of a known LCF load which can be attributed to certain traceable operating cycles, the safe life span can be defined and monitored (provided the crack is accessible). With high-frequency vibrations, experience has shown that the chances of identifying and replacing the cracked part after initial cracking but before the part fails are extremely slim. This is due to the following factors:

  • Size of dynamic loads usually not known
  • Time and duration of dynamic load not accurately known
  • High crack growth speed with regard to time rather than load cycles.

The crack growth per load change must not necessarily increase with the crack length (Ill. 12.2-1). Exponentially increasing crack growth occurs when the stress in the cross-section in the direction of crack growth is virtually constant (small gradient, also see Ill. 12.6.3.4-19) or even increases with the crack size (residual cross-section becomes smaller). In this case, the accelerated crack growth rate makes controllability of an LCF crack much more difficult, if not impossible. A typical example of this is the crack in the hub of a turbine disk (top left diagram).

If crack initiation is followed by sharply decreasing stress levels (high stress gradient), which possibly even change into a compressive zone (turbine disk annulus, Ref. 12.2-14), then crack growth slows and even stops temporarily at sufficiently low stress levels, provided the stress transfer during crack growth allows it (diagram). Cracks that are tolerated within specified limits are usually thermal fatigue cracks, i.e. strain-dependent loads. Thermal strain is usually an important factor in these cases (Chapter 12.6.2).
Dynamic fatigue and crack growth only occur under tensile stress. However, materials science has also discovered a special case in which fatigue cracks seem to occur under pulsing compressive stress. These cracks are not capable of completely separating a cross-section without the aid of additional loads. This process involves cracking in the notch bases of cross-sections that are subject to external pressure loads (right diagram). Due to the notch effect, the notch base plastically deforms under the compressive stress. In the strain-release phase, tensile stress occurs in this area, reaching an equilibrium with the elastically stressed residual cross-section. In the described case, it is easy to see that the tensile stress, which is the prerequisite for crack growth, decreases
as the crack grows. Parts undergoing thermal fatigue are subjected to a similar mechanism.

Illustration 12.2-11.1 (Ref. 12.2-16): The minimum flaw size capable of growth reacts sensitively to various influences. The Paris diagrams (Ill. 12.2-3) show the influence of frequency and temperatures on the crack behavior under dynamic loads.

Influence of frequency: At a constant frequency, the forged material IN 718 (top left diagram) becomes considerably more sensitive to flaws at high temperatures (550°C) than at 25°C. The threshold value has evidently decreased considerably (crack growth from small flaws) and the crack growth rate under the same cyclical loads is several times (log. plotting!) the growth rate at room temperature. he cast material IN 738LC (top right diagram) has higher growth per load cycle at a lower frequency (Refs. 12.2-21 and 12.2-22). The threshold does not seem to be affected by the frequency. The influence of the frequency on crack growth can most likely be traced to creep due to the relatively high temperature of 850°C (also see Ills. 12.6.1-20 and 12.6.1-21).

Temperature influence: The widely used Fe based forged material A286 (bottom left diagram) shows a considerable increase in the crack growth rate with increasing temperature, while the threshold remains nearly constant. Similar behavior can be seen in the bottom right diagram in the Ni based forged material U700. However, the testing temperature of 850°C seems greater than the usual operating temperature of this material, which is closer to 700°C. The sharp bend in the curves to slower increase of the growth rate is evidently connected to a change in the growth stage (Ill. 12.2-6).

Illustration 12.2-11.2 (Ref. 12.2-12): The diagrams show the crack growth under dynamic and static loads under the influence of corrosion. In all cases it can be seen that the growth of short cracks (low stress concentration) is slower in inert atmospheres (no corrosion) than in the surrounding atmosphere (Ill. 12.2-12, Ref. 12.2-20). The difference in the crack growth rate is dependent on a combination of the corrosion type (Volume 1, Chapter 5.4) and loads (dynamic, static). At air pressures under about 0.01 mbar, atmospheric influences seem to disappear (Ref. 12.2-20). The effects increase at low frequencies. It is still debated which parts of the atmosphere cause these effects. There seems to be mounting evidence that the causal factor is not necessarily oxygen, but rather hydrogen that forms from water vapor. Ni alloys are prone to reacting to oxygen (also see Ill. 12.5-5), while Ti alloys, steels, and Al alloys react to H2O, i.e. H2 . This means:
Determination of design data or life span verifications under inert gases or in cyclical testing rigs must be tested for relevancy to engine parts subject to corrosion. Otherwise, there is a danger of the life spans, i.e. safety limits, being overestimated.
Under the influence of stress corrosion cracking, there is a threshold value KISCC above which the crack growth rate suddenly increases very rapidly. This effect can only be verified with samples that are suitably cracked.

Illustration 12.2-12 (Ref. 12.2-12): Not only the amplitude of the stress intensity DK influences the crack growth and limits it with DKth. Under the influence of corrosion, Kmax and Kmax th are further criteria. Kmax is determined by the overlaying of the residual stresses (type II, Ill. 12.2-13) ahead of the crack tip, and the outer loads. In notched areas, the outer loads act through the stress gradients.

These residual stress influences can have various causes, including:

  • Local plastic deformation due to the outer loads (Ill. 12.2-6).
  • Machining or handling of the surface
  • Temperature gradients

Short cracks are more sensitive to effects in the micro-range, such as residual stresses and inhomogeneities (Ills. 12.2-13 and 12.6.3.2-1). Due to the residual stresses, which are especially strong at the surface, the crack length/depth has an important influence. Here, “short” cracks are those with a length that corresponds to the material structure (e.g. grain size, Ill. 12.2-8). Due to their definition-specific visibility, “long” cracks are longer than the technical crack of 0.8 mm at the surface (Volume 1, Ill. 3.1). Depending on whether the residual stresses promote or retard crack growth, micro-cracks grow into macro-cracks when Kmax th is exceeded. Compressive residual stresses can even cause longer cracks to stop growing, or grow unusually slowly.

In summary, short and long cracks vary in the following ways:

  • Short cracks have no set threshold value above which crack growth occurs (Kmax th short range).
  • Short cracks grow at stress intensities below the threshold of long cracks (Kmax th long).
  • The growth of short cracks can accelerate, decelerate, or stop completely.
  • At high growth rates, short cracks continuously transform into long cracks. This is the case when tension residual stress ahead of the crack tip causes the threshold conditions of long cracks to be exceeded.
  • The growth data of short cracks scatter considerably.
  • Long cracks have minor scattering of growth data and a uniform crack growth threshold.

Illustration 12.2-13 (Ref. 12.2-15): Residual stresses can be categorized into three groups:

Type I residual stresses: Virtually homogenous over larger planar material areas (several grains). Inner forces and moments related to the residual stresses are in equilibrium throughout the entire body. Changes to this equilibrium always result in dimensional changes (deformations).

Type II residual stresses: These are virtually homogenous over small material areas (one grain or grain area). The corresponding inner forces and moments are in equilibrium across sufficiently many grains. Microscopic dimensional changes can occur if this equilibrium is disturbed.

Type III residual stresses: Are inhomogenous over small material areas (space of several atoms). The corresponding inner forces and moments are in equilibrium in small areas (part of a grain). No macroscopic dimensional changes occur when the equilibrium is disturbed.

Illustration 12.2-14: Naturally, hot gases influence the growth of cracks that are exposed to the atmosphere. This can sometimes make the crack shape in the structure visible (Ref. 12.2-17, Ills. 12.2.1-11 and 12.2.1-12). Changes to the following parameters have an especially pronounced effect (also see Volume 1, Ill. 5.4.3.1-2):

  • Strength and duration of static loads
  • Strength and time of dynamic loads
  • Part temperature levels and gradients
  • Load frequency
  • Microstructure (grain size, structure)
  • Damage (e.g. depletion, embrittlement)

The diagram shows tendencies of hot gas influences on the crack symptoms according to the author`s estimations. Oxidation/hot gas corrosion and the crack growth rate influence each other. A low crack growth rate allows intensive oxidation of the crack surface, which can round off the crack tip. The influence of the atmosphere is also indicated by the clear increase in creep strain under hot gas influence, relative to the levels in resting air (Ill. 12.5.1-5).

Crack shape and branching react similarly under corrosion cracking at low temperatures (watery media) and high temperatures (titanium alloys above about 500 °C; Volume 1, Ill. 5.4.2.1-8).

Illustration 12.2-15: With equal flaw distribution, thick cross-sections have more volume flaws than surface flaws, relative to thin cross-sections (top diagram). However, surface flaws are more susceptible to crack initiation than equally large volume flaws under the same cross-section stress levels (not only during flexure). This is because the stress intensity responsible for the crack growth is determined by the diameter in circular flaws that border the surface, and by the radius in volume flaws (Ill. 12.2-5).
The bottom right diagram shows the circular spreading of a volume flaw in an evenly loaded cross-section. At first, the crack growth of the volume flaw is considerably slower than that of surface flaws. Once the volume flaw has reached the surface, the stress intensity and growth increase dramatically, corresponding to the square root of the effective double crack length. At the same time, the crack growth that has already occurred means that its volume is considerably greater
than the initial flaw. If this type of crack can be visually detected from the outside, it will already be relatively large and have a correspondingly high growth rate. This rapid growth at the surface (bottom diagram) minimizes the chances of sufficiently early detection during inspections.
In contrast to volume flaws, the stress intensity of a circular initial flaw that just reaches the surface (bottom left diagram) is effective according to the flaw diameter (Ill. 12.2-5). This makes surface flaws capable of growth even if volume flaws of the same size would not grow. In addition, as explained above, the crack growth rate of surface flaws is much greater from the start than that of a corresponding volume flaw.

Illustration 12.2-16: There are various influences that determine whether crack development and growth occur at the surface or in the volume:

  • Surface conditions (dynamic strength differences between surface and volume)
  • Flaw distribution (surface, volume)
  • Loads (e.g. tension rather than flexure, compressive residual stresses at the surface, Ill. 12.6.3.4-21).
  • Thicker cross-section (flat stress gradient, Ill. 12.6.3.4-19).

Surface with increased dynamic strength (top diagram): Diffusion coatings (e.g. nitrogen hardening, case hardening) and/or plastic hardening (e.g. shot peening, rolling) can increase the hardness of the surface considerably. This can result in dynamic flexural overstress causing dynamic fatigue cracks below the surface, where they spread more rapidly before breaking through to the surface. The crack growth at the surface then accelerates at a rate that depends on the notch sensitivity of the surface zone and the size of the present inner crack (Ill. 12.2-15).

Thermal strain (bottom left diagram): The wall of an internally-cooled part that is externally heated (e.g. a cooled turbine rotor blade) has a temperature distribution that drops towards the inside. The high outer temperature causes greater thermal expansion in this zone. Deformation due to expansion is restricted by the cooler inner section, causing compressive stress in the outer zone. Equilibrium is reached by the creation of tensile stress in the inner zone. This process promotes cracking inside the part, such as at grain boundary damage around cooling air bores that was caused by the production process (Ill. 12.6.2-9).

Compressive residual stress (bottom middle diagram): This usually occurs along with a strength increase during a manufacturing procedure (e.g. chipping, etc.), or intentionally through coating (e.g. case hardening) or hardening (e.g. shot peening) processes. These compressive stresses overlay with the stresses from the external loads, reducing dangerous tensile stress peaks near the surface and lowering the mean stress. Because this stress-reducing effect barely affects the volume, cracking is now caused by flaws near the surface in the volume, rather than flaws in the surface itself (also see Ill. 12.6.3.4-20).

Volume flaws (bottom right diagram): There are certainly cases in which the surface is not prone to flaws, but the volume is. A typical example is lost-wax cast parts with a thin, fine-grained, cavity free surface zone, but with solidification-induced cavity fields in thicker cross-sections (missing remaining melt). If this type of engine part is subjected to dynamic loads that are even or have a sufficiently flat stress gradient, the cavities are likely crack initiation zones. A typical example is the thick hub area of an integral-cast turbine disk (Ill. 11.2.3.1-7).

Illustration 12.2-17: During flexure, the stress gradient becomes flatter as the cross-section becomes smaller. This influences the reaction to flaws considerably:

  • Volume flaws become more important relative to surface flaws (also see Ill. 12.2-15). This means that in a thicker cross-section, more volume flaws are subjected to high stress levels and tend to cracking than in a thin cross-section, in which the stress has already decreased considerably immediately below the surface.
  • Crack growth in the cross-section increases: The flat stress gradient of the thicker cross-section leads to more rapidly accelerating growth of the crack (Ill. 12.2-10).
  • The dynamic fatigue-resistant effect of hardened areas and compressive residual stresses near the surface decreases rapidly further inside thicker cross-sections. This compromises the effectiveness of procedures such as shot peening. The result is an increased probability of sub-surface cracks (Ill. 12.2-16).

Illustration 12.2-18: The macroscopic external appearance of cracking in several identical, similar, or different parts can yield information about the time and strength of the damage-causing dynamic loads.
Dynamic fatigue in the HCF range:
Typical examples are cracks and/or fractures in compressor blades (left diagram).
If several identical parts (usually blades of the same stage) are cracked, the causes may vary:
This is usually a clear sign of loads that were powerful enough to cause all parts to crack almost simultaneously (Ills. 12.2-19 and 12.6.3.4-22). These loads may have been temporarily in the LCF range when the crack occurred, but the crack growth may have taken place under HCF conditions at considerably lower loads. Possibilities include multiple surge shocks (Ill. 11.2.1.2-3) or, as in the depicted case, malfunctioning of the bleed valve.
If the stress distribution (e.g. nodal line of a vibration) causes the crack to pass into a sufficiently low dynamic and static stress level, then the crack may come to a standstill and cracks can initiate in several parts.
Crack formation and growth can cause the dynamic loads to decrease far enough for the cracking to stop. Reasons for this are damping due to the friction between crack sides and/or the drop in frequency (weakened cross-section) as it goes out of resonance.
If the crack is in a similar location on all parts, it indicates that the main cause of cracking is not a discrete flaw (e.g. groove or weak point caused by welding splash, etc.). If the cracks have a systematic or periodic distribution, e.g. around the circumference, it can indicate the mode of vibration (Ills. 12.6.3.1-5 and 12.6.3.1-8). This makes it possible to recognize cases of resonance and implement proper measures.
If parts such as blades from different stages with different resonant frequencies exhibit cracking, resonance is fairly unlikely. In this case, a free vibration is probably the cause (e.g. surge shocks striking blades).
Dynamic fatigue in the LCF range: Typical examples are thermal fatigue-induced annulus cracks in integral turbine disks (right diagram, Ill. 12.6.2-19). If the part or parts have cracks of similar length, it can be assumed that they are thermal fatigue cracks, the growth of which slows considerably or even stops as crack length increases (Ills. 12.2-10 and 12.2-14). This type of cracking can be monitored and “controlled”. Unlike HCF cracks, LCF cracks often occur in several parts simultaneously (e.g. rotor blade roots).

Illustration 12.2-19: Not only the external damage symptoms (Ill. 12.2-18), but also the analysis of the crack/fracture surface can yield valuable information concerning the damage causes and mechanisms. Both macroscopic and SEM analyses are reccommended.
Macroscopic inspection with the naked eye and stereo microscope: fracture surfaces with similar dynamic fatigue fracture sizes, i.e. crack lengths (top diagrams), indicate that a high dynamic overstress occured at a certain time (probably in the LCF load range, Ill. 12.6.3.4-22). If the cracks originate in weak points that are within part specifications (e.g. machining grooves or erosion pitting) and have similar locations on the parts, the likelihood of high dynamic overstress is increased (Ill. 12.2-18).
Comparative rest line patterns further confirm the suspicion of simultaneous cracking (bottom left detail). In some cases the temporal development of the damage can be traced by analyzing the spacing between and width of the lines of rest at the end of the dynamic fatigue fracture (final progression of the dynamic crack tip), and also by comparing the cracks. Corresponding development of the lines of rest indicates that all parts were dynamically overstressed at the same time. The number and distribution of the lines of rest indicates the time of crack initiation, as well as its cause (e.g. rubbing, flow disturbance, imbalance, etc.).
Electron microscope analysis (SEM): This device can be used to analyze the striations (bottom right detail). Each one of these lines represents a load change (Ill. 12.2-6). If the analysis is successful, it allows estimation of the number of load changes in the entire crack growth, as well as the number of load changes in specific occurrences that can be attributed to the lines of rest. The distance between striations can be used to directly determine the corresponding crack growth rates (Da/DN). This makes it possible to estimate the dynamic loads during the crack growth, if a Paris diagram (Ill. 12.2-3) is available for the material in question. Unfortunately, it is not possible to make reliable conclusions about the dynamic loads during the damage phase (incubation) before the macrocrack was formed. Analysis of the striation pattern (Ref. 12.2-10) can clearly identify the location of the initial crack and thereby usually also identify the crack-inducing weak point or flaw (also see Volume 1, Ill. 3-1).

Illustration 12.2-20: The startup/shutdown cycles alone are often enough for a sufficiently accurate and reliable estimation of the damage accumulation (Ills. 2.6.3.2-10 and 12.6.1-20). This is especially true for helicopter and fighter engines, which are subject to frequent extreme power output changes during a mission (RPM and temperature changes). In the depicted case of a military helicopter (Ref. 12.2-18), a turbine disk fractured before a dangerously high number of startup/shutdown cycles was reached, according to the new part specifications. It was discovered that several flight operations or training missions contributed considerably to the fatigue, increasing the danger of underestimation of the life span that had been used up. In order to make estimation of the remaining life span of the affected parts as accurate as possible, electronic cycle counters that use special algorithms (Ill. 12.6.1-20) and have a directly accessible indication of the used part life, i.e. the safe remaining part life, have come into widespread use.

Illustration 12.2-21: Estimating the risk of an entire affected fleet in acute damage cases is of supreme importance for the implementation of corrective measures. These include determining inspection intervals, defining the procedure to be used, and developing and implementing solutions. This process requires estimation of the probability that cracks will be discovered before the part fails (usually fracture) and the defective part replaced or repaired.

Criteria include:

  • Stress gradients (see Ill. 12.2-10)
  • Stress amplitude (LCF, HCF, see Ill. 12.2-3)
  • Load frequency: at high frequencies, a large amount of damage accumulates in a very short time (e.g. seconds) due to the many load changes, and the temporal crack growth becomes uncontrollable.
  • The number of cracked parts (see Ills. 12.2-18 and 12.2-19).

Illustration 12.2-22: It is easy to see that the location of a crack relative to the damage-relevant load direction is of great importance to crack growth. If the crack is in a good location relative to the main load direction, safe operation may still be assured. One example is a grinding crack across the tooth tip of a turbine blade fir-tree root (left diagram). This crack runs parallel to the main load direction (centrifugal force).
The right diagram shows flaw locations in a hollow shaft. A typical example is flaws in an electron-beam weld. While flaw “1” is not expected to cause unallowable operating problems, due to its position parallel to the main loads (circumferential stress), flaw “2” must be critically considered and can only be permitted in very small lengths, if at all.

Illustration 12.2-3: Usually, the weakening of the carrying cross-section and the notch effect caused by the crack lead to accelerated crack growth. However, there are several exceptions in which crack growth slows or the crack even stops completely. Some of these exceptions are described in the following:

“1”: The weakening of the cross-section increases the elastic compliance of the part. This lowers the eigenfrequency of the vibration form that causes the cracking. If the difference in frequency between the excitement and the vibrating frequency is sufficiently large, the part will come out of resonance and the dynamic loads will decrease considerably.

“2”: During vibration, the (at least microscopically) jagged crack sides move against one another. This can create sufficient friction to have a damping effect on the vibration, reducing the dynamic loads.

“3”: If there is a sharply decreasing tensile stress gradient (stress gradient, see Ill. 12.6.3.4-18) in the direction of crack growth, or if a compressive stress zone is reached, the crack growth rate decreases (Ill. 12.2-3). The crack stops growing below the threshold of the stress concentration. This type of stress gradient forms under the influence of thermal strain (Ill. 12.6.2-2). Compressive residual stress can also have a braking effect on cracks.

“4”: If a crack already has a very slow growth rate (e.g. thermal fatigue), oxidation can round off the crack tip and reduce the stress concentration so much that the crack stops growing.

“5”: Structural inhomogeneities can slow crack growth. A typical case is in fiber-reinforced materials (Ill. 14-30). For a crack-stopping effect, the fibers must not be too tightly connected with the matrix, in order to prevent cracks from passing into the fibers from the matrix.

“6”: As mentioned in “4”, compressive residual stress can lower the stress concentration during crack growth so much that it causes the crack to stop growing, at least temporarily. This type of residual stress can be expected in surface-hardened steel parts (case hardening, nitrogen hardening; Ill. 12.2-16). Cracks can form inside the cross-section and grow much more slowly towards the outside than within the cross-section.

“7”: If the fracture toughness of the material increases considerably ahead of the crack tip, then the crack stops growing. This is the case in very thin, brittle coatings on a tough material, for example. The short cracks in the thin coating have a relatively low stress concentration. A typical example is diffusion coatings on nickel alloys (Ill. 12.6.2-15). This also includes hard chromed parts, the chrome coating of which usually has cracks that do not spread into the base material at sufficiently low dynamic loads. An additional effect is achieved by inducing compressive stress through shot peening.

“8”: If the loads necessary for crack growth are sufficiently brief, and the crack has not grown far enough to continue growth under normal operating loads, it will stop growing. These conditions can occur in the case of rubbing or surge shocks.

“9”: If the hardness of a ductile material increases considerably ahead of the crack tip, as is the case in thermal barrier coatings on nickel alloys, cracks will remain in the thermal barrier coating and not pass into the substrate (segmentation cracks, Ill. 11.2.3.1-4). This behavior is a prerequisite for the function of ceramic thermal barrier coatings.
“10”
: If a crack spreads from a material with a high E module into one with a considerably lower E module, then consistent strain across the cross-section will result in corresponding reduction in stress and slowing of crack growth.

“11”: Inhomogeneities such as cracks or zones with low bond strength that run across the direction of crack growth can deflect the crack or cause it to stop growing. This type of weakness can be expected in poorly bonded coatings or soft solders.

“12”: Fiber-reinforced materials can considerably increase damping through delamination, decisively reducing the dynamic loads (Ills. 14-29 and 14-30). In many cases, this does not result in breakage of the fibers, resulting in a high level of residual strength.

References

12.2-1 K. Heckel, “Einführung in die technische Anwendung der Bruchmechanik”, Carl Hanser Verlag, Munich 1970.

12.2-2 W. Schmidt, “Die Beurteilung des Bruchverhaltens von Stählen höherer Festigkeit mit Hilfe der Bruchmechanik”, TEW-Technical Reports, Volume 1 1975, Issue 1, pages 39-55.

12.2-3 H.Leis, W. Schütz, “Bewertung neuer Flugzeugbauwerkstoffe mit den Methoden der Bruchmechanik”, Zeitschrift “LRT 16” Nr. 10, October1970, pages 247-251.

12.2-4 D. Schütz, “Derzeitiger Stand der Lebensdauervorhersage für Bauteile”, “Zeitschrift für Werkstofftechnik” Nr. 9, 1978 3, pages 77-85.

12.2-5 W. Schütz, “Lebensdauer-Berechnung bei Beanspruchungen mit beliebigen Last-Zeit-Funktionen”, VDI-Berichte Nr. 268, 1976, pages 113-125.

12.2-6 H. Zenner, “Niedrig-Lastwechsel-Ermüdung (low cycle fatigue)”, VDI-Reports Nr. 268, 1976, pages 101-111.

12.2-7 J.P. Gallagher, “Estimating Fatigue-crack Lives for Aircraft: Techniques”, proceedings paper of the “SESA Spring Meeting”, Chicago IL., May 11-16, 1975, pages 113-125.

12.2-8.1 E. Macherauch, “Grundprinzipien der Bruchmechanik”, paper from the materials testing conference, “Gefüge und Bruch”, Leoben 25/28 November, 1976, pages 3-36.

12.2-8.2 E. Macherauch, P. Mayr, “Strukturmechanische Grundlagen der Ermüdung metallischer Werkstoffe”, VDI-Repots 268, 1976, pages 5-18.

12.2-8.3 E. Macherauch, O. Vöhringer, “Das Verhalten metallischer Werkstoffe unter mechanischer Beanspruchung”, periodical “Werkstofftechnik”, 9, 1978, pages 370-391.

12.2-9 L.Engel, H. Klingele, “Rasterelektronenmikroskopische Untersuchungen von Metallschäden”, ISBN 3-9800043-0-9, Gerling Institut für Schadensforschung und Schadensverhütung GmbH, Cologne, 1974, pages 63, 82.

12.2-10 D.W. Hoeppner, P.E. Cockburn, “Parameters that Input to Application of Damage Tolerance Concepts to Critical Engine Components”, proceedings paper AGARD-CP-393, of the conference “Damage Tolerance Concepts for Critical Engine Components” pages 4-1 to 4-16.

12.2-11 J.K. Gregory, contribution to DGM-Workshop “Titan”, Munich, 30-31st March, 2000.

12.2-12 A.K. Vasudevan, K Sadananda, “Environmental Effects on Fatigue Crack Initiation and Growth”, RTO Meeting Proceedings 18, “Fatigue in the Presence of Corrosion”, AGARD Structures and Materials Panel, Corfu, Greece, 7-9. October 1998, pages 17-1 to 17-12.

12.2-13 M.Beck, K.H. Lang, “Zulässigkeit von Fehlstellen in Feingussbauteilen bei thermisch-mechanischer Wechselbeanspruchung”, final report of the Forschungsvereinigung Verbrennungskraftmaschinen, Issue 723 . 2001, 30. June 2001, pages 1-138.

12.2-14 A.K. Koul, “Hot Section Materials for Small Turbines”, Proceedings Paper AGARD-CP-537 of the conference “Technology Requirements for Small Gas Turbines”, Montreal Canada, 4-8 October 1993, pages 40-1 to 40-9.

12.2-15 E. Macherauch, H. Wohlfart, U. Wolfstieg, “Zur zweckmäßigen Definition von Eigenspannungen”,periodical “HTM 28”, Issue 3, 1973, pages 201-211.

12.2-16 H.E. Boyer, “Atlas of Fatigue Curves”, American Society for Metals“, Metals Park, Ohio 44073, pages 274-314.

12.2-17 R. Wiswanathan, “Damage Mechanics and Life Assessment of High-Temperature Components”, ASM International, page 443.

12.2-18 U. Hesseler, “LCF-Failure Analysis of an Aero-Engine Turbine Wheel”, procedings paper of the “Third International Conference on Low Cycle Fatigue and Elasto-Plastic Behaviour of Materials ”, Berlin, FRG, 7-11. September 1992, pages 664-670.

12.2-19 H. Spähn, H.W. Lenz, “Die Bruchmechanik und ihre Anwendung auf Fragen der Bauteilzähigkeit - Anwendungsbeispiele”, “Zeitschrift für Werkstofftechnik”, Volume 4, 1973, Nr. 7, pages 351-362.
12.2-20 W.J. Evans, J.P. Jones, M.R. Bache, “High-Temperature Fatigue/Creep/Environment Interactions in Compressor Alloys”, paper 2001-GT-477 of the “Int. Gas Turbine and Aeroengine Congress and Exhibition”, New Orleans, LA, June 4-9, 2001 and periodical “Transactions of the ASME”, Vol 125, January 2003, pages 246-251.

12.2-21 M.R. Bache, W.J. Evans, “Dwell Sensitive Fatigue Response of Titanium Alloys for Power Plant Applications”, paper 2001-GT-424 of the “Int. Gas Turbine and Aeroengine Congress and Exhibition”, New Orleans, LA, June 4-9, 2001 and periodical “Transactions of the ASME”, Vol 125, January 2003, pages 241-245.

12.2-19 A.A. Shaniavski, A.I. Losev, “The effects of loading waveform and microstructure on the fatigue response of titanium aero-engine compressor disk alloys”,Blackwell Publishing, periodical : “Fatigue Fracture Engineering Material Structures, 26, pages 329-342.

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