Figure "Temperatur dependent damage mechanisms": This triaxial depiction is intended to provide a concept of the location of thermal fatigue in the stress environment. The range of thermal fatigue is limited by a curved plane, dependent on the parameters, mechanical loads, temperature, and life span. These limits have been somewhat subjectively selected by the author, since these are actually transition zones. Above this plane, damage occurs under the noticeable influence of mechanically-based loads such as dynamic stress and creep stress.

Figure "Cracks protecting from thermal fatigue": The top left diagram shows a model of the TF load process:

A metallic rod is moveably limited by two solid walls. If this rod is heated, it expands. Without the restriction of the walls, its heat strain is Dlt. The strain restriction of the walls causes plastic compression Dlp to occur when the flow limit is exceeded. After cooling, the rod is shortened by the length of this compression, and a gap is formed between the rod and the wall. The rod is now relieved.
Now imagine that the rod was firmly attached to the walls at the start of the experiment. In this case, the plastic compression with high compressive stress would still occur when the rod is heated (bottom left diagram). However, during cooling, tensile stress builds up in the shortened rod. Therefore, one temperature cycle (T) corresponds to one tension/compression stress cycle, which leads to mechanical fatigue (e.g. Figs. "LCF as lifespan determining" and "Cracks in integral turbine wheels") in the LCF range. This is called thermal fatigue (TF).

Crack initiation leads to relief. This also means that crack growth slows. The crack initiation in turbine guide vanes (Fig. "Influences on thermal fatigue") is depicted well by this model.
A more practice-oriented model of the depicted thermal fatigue process is shown in the right diagram. If one locally heats a cold metal plate on one side, the hot area, which has lower strength than the surrounding cold area, wants to expand. This induces compressive stresses that are in equilibrium with tensile stresses in the cold zones. Sufficiently high compressive stresses cause the heated zone to arch up and be plastically compressed. During cooling, tensile stresses form in the plastically compressed zone, while compressive stresses build up in the formerly cold zone. In addition, the residual stresses induced by this process cause warping.
The bottom right diagram shows the strain progression over temperature (Ref. 12.6.2-15) for typical TF cycles in wedge-shaped specimens, as well as a TMF cycle in hollow cylindrical specimens (Fig. "Representative specimens for thermal fatigue"). During the TF cycles (dotted line), which are induced by pure heating and cooling of the specimen edge, the compression in the pressure phase (heating) determines the strain amplitude. The TF cycle is caused by cyclical mechanical loads under cyclical temperature changes.

Figure "Symptoms of 'thermal shock' cracks": In the following, thermal shock is defined as a process in which a sudden temperature change leads to damage. In turbine blades, this type of damage generally takes the shape of a semicircular field of axially oriented cracks (right diagrams). This damage symptom can be especially pronounced if there are coatings that behave brittly during heating or cooling, depending on the temperatures.
The typical example for a thermal shock process is the shattering of a glass when filled with hot liquid. Comparable conditions are present if problems occur during ignition during engine startup or afterburner startup with the aid of a darting flame from the combustion chamber (bottom left diagram). This procedure is used in some engine types (Ref. 12.6.2-16).

Figure "Influences on thermal fatigue": Thermal fatigue damage depends on the combination of many different factors that can influence one another:

Operation: The temperature levels influence strength, toughness, and diffusion processes. Restricted thermal strain and the type and size of the created stresses depend on temperature gradients. The part temperatures are controlled through heating and cooling, whereby the temperature, pressure, and velocity of the cooling air/hot gas (heat transfer) play the decisive role.
The composition of the hot gas, especially contaminants such as salts (NaCl, etc.) and dusts (sulfuric, such as CaSO₄ ), can promote crack initiation and/or crack growth by causing preliminary damage to the part.
Due to their notch effect and/or frequency-lowering effect (resonance), thermal fatigue cracks can initiate cracks as the consequence of high-frequency vibrations. These damages are found in turbine disks in the form of annulus cracks, for example (Fig. "Cracks in integral turbine wheels").

Construction: The stress levels depend on overlaying external forces (e.g. centrifugal forces, gas forces, clamping forces). The stress levels affect the location and time of crack initiation, as well as the crack growth rate. The stress gradient, which is dependent on the temperature gradients, has an especially strong influence on the direction and speed of a thermal fatigue crack. Abruptly decreasing tensile stresses, in some cases in transition to a compressive stress zone, can slow the crack growth rate to a standstill, making possible a fail safe behavior. Under these conditions, the crack can be a calculated value in the life span philosophy.
Changes to part cross-sections and geometry causes geometric notches and stiffness notches (e.g. on the transition between blade and shroud) that promote crack initiation. The cooling configuration inside the blade and the out-facing cooling air bores (air film cooling) act as geometric notches. Some designs that can tolerate a certain loss of cooling air (Ill. 12.5.1-13) make it possible to allow larger crack sizes.

Production: Producing the bores for the cooling air film affects crack sensitivity. If the surface is melted by the drilling process (electrical discharge machining = EDM, or laser drilling), it will create brittle recast layers with high tension residual stresses.

Material: Naturally, the material plays an important role in thermal fatigue cracking.

Behavior of the base material: Properties under mechanical loads, such as static and dynamic strength, stiffness (elasticity), and plastic deformability (toughness, ductility), influence the resistance to crack initiation. In the case of thermal fatigue, increased operating temperatures do not necessarily mean shorter life spans. If the toughness increases along with temperature, it can have a retarding effect on crack growth. The loads consist of thermal strain, which is dependent on thermal conductivity and specific heat, among other factors. The relationships become extremely complex if the material structure undergoes temperature- and stress-dependent changes during operation. An additional influence on crack initiation and growth may be the oxidation- and corrosion-resistance of the material.

Influence of the material condition: The size and orientation of the grains (crystal orientation, grain boundaries, inhomogeneities) influence crack initiation and growth considerably. This must be taken into consideration in specifications for unfinished parts, such as casting, forging, and heat-treatment. The surface topography (e.g. type, orientation, and size of machining grooves) can act as a notch, as well as influencing the local heat transfer and therefore also the temperature gradients. The part temperatures are influenced by the reflection and absorption of the surface. New part surfaces can change considerably with increasing oxidation during heat absorption. Blank metallic surfaces (new parts), especially reactively etched ones, are especially oxidation-sensitive. This makes them more susceptible to crack-initiating attacks.
In directionally-solidified materials and single-crystal materials, over long operating periods under TF stress, the g' phase comes into line in a charateristic manner depending on the stress levels (raftening, Ref. 12.6.2-10), similar to the creep stress process (page 12.4-13). The orientation is generally parallel to the tensile stress.
In single-crystal materials, the missing grain boundaries cause thermal fatigue cracks to occur primarily at the surface. The cracks are related to an oxidation-induced depletion of the surface zone. This cracking is supported by the notch effect of micropores from casting (Ref. 12.6.2-15).

Coatings: Hot parts can have various types of coatings (e.g. ceramic thermal barrier coatings, thermal sprayed coatings, diffusion coatings, and coating combinations) that affect the thermal fatigue behavior due to their mechanical properties (Ref. 12.6.2-19). It is possible to both improve and worsen the situation:
All aluminide diffusion coatings shorten the TMF life through brittle cracks.
An increased Al content in the coating reduces the breaking strain, i.e. has an embrittling effect.
The micro-structure (grain size) of the coating has a major influence on its toughness, but the coating thickness does not.
The coating properties also depend on the production process. This means that coatings with identical chemical compositions, but different production-specific structures, have considerably different behaviors. One example is erosion-resistant thermally-sprayed thermal barrier coatings with a typical lamellar structure, compared with columnar TF-resistant vapor-deposited coatings (Fig. "Thermal barrier coatings of turbine rotor blades"). Thermally insulating coatings (thermal barrier coatings) lower both temperature gradients and temperature levels in cooled parts. A similar effect can be attained with reflective coatings (gold, silver, platinum) if a large amount of heat is introduced and/or dissipated through radiance (Fig. "Influences on combustion chamber wall heating-up"). An important factor is the ductility of the coating at the specific operating temperatures. Unlike tough coatings, brittle coatings promote TF cracking (Ref. 12.6.2-9). Before a crack initiates in the base material, the protective coating itself may crack or spall. This leads to local temperature increases and/or increased oxidation. If the aging of coatings (cracking, sintering, diffusion, emaciation through oxidation and erosion) changes their TF-relevant properties, it must be taken into account in life span estimates and part design.

Figure "Parameters influencing thermal fatigue": Determining thermal fatigue properties and transferring them to realistic part behavior in operation is fraught with uncertainties due to the large variety of influences.
LCF tests at constant temperatures have been demonstrated to be insufficiently realistic for estimating the life span of complex engine parts (see Ill. 12.6.1-10). Today, TMF tests use independent overlaying of cyclical external forces and temperatures on round specimens to determine life spans (load changes to failure) with relation to the strain amplitude (Fig. "Representative specimens for thermal fatigue"). The test cross-section of the commonly-used round specimen has even stress throughout, unlike the TF loads in the part. This type of test yields reproducible results. The influence of coatings can also be determined in this manner. These results are entered into the finite element calculations for the temperature and strain cycles in the part. This allows life span estimates to be made even for complex parts, at least as far as the first crack initiation is concerned. However, these estimates demand critical analysis, especially if they deviate considerably from events during operation. For example, unlike the specimen, the engine part may have a stress gradient that correspondingly changes the crack growth rate. One problem with these tests is that the structure (grain size, grain orientation, inhomogeneities, and weak points) and test cross-section do not sufficiently represent the actual part (Fig. "Representative specimens for thermal fatigue").
In the case of comparative material evaluation under TF loads, tests with cyclical local heating can be useful. In these tests, the crack growth can be observed in its early phase. If the heat introduction is done with the use of hot gas, then the influence of effects such as oxidation and hot gas corrosion is evident (also see Ill. 12.5.1-5). The specimens used in these tests generally have a sharp edge (prismatic or wedge-shaped cross-sections, bottom left diagram). The heat is introduced at the edge, i.e. taper. A special problem is the limited quantitative evaluability for obtaining reliable data for calculation. If one combines the test results with a finite element calculation of the heated zone, it increases the relevance of the tests.

Another possibility for determining the TF behavior more realistically is cyclical heating tests on representative engine parts such as turbine blades (middle diagram). If necessary, even internal convection cooling can be simulated. These tests make it possible to draw conclusions regarding the location of the crack initiation zones in the part (e.g. cooling air ducts, Fig. "Damaging colder part zones by thermal fatigue"). However, these tests are elaborate and complicated. They also do not generally simulate an overlaying of the thermal stresses with external forces such as gas bending loads and centrifugal force.
The most realistic, but also most elaborate, is a TF life span estimation in the engine (bottom right diagram). In this case, as well, it must be ensured that the parts used are representative of the series (e.g. cast structure, coatings, production processes, etc.). In addition, the test cycles must enable comparisons with the behavior in serial operation. For example, temperature distribution at the combustion chamber exit is of major engine-specific importance (Fig. "Temperature variation at the combustion chamber outlet").
“Rainbow tests”, in which parts with different properties (e.g. base material, coatings) are used in the same engine run, make comparative investigations possible.

Figure "Grain size influencing static and dynamic fatigue" (Ref. 12.6.2-3): Next to the grain orientation, the grain size is of major importance for the strength properties of a material (Figs. "Grain structure influencing metal properties" and "Fatigue behavior by grain structure"). In general, larger grains have greater creep resistance (top left diagram). However, the dynamic strength (LCF and HCF) tends to decrease with larger grain sizes (top right diagram, Ref. 12.6.2-7). In addition, fine grains are generally more ductile than coarse grains.
As far as the grain development is concerned, parts with very different strength requirements are especially demanding. These include integral cast turbine disks (Fig. "Cracks in integral turbine wheels") of the type common in small output engines (for helicopters). The hub area, which is heavily stressed by cyclical centrifugal forces and thermal stress (Fig. "Turbine disk loads during operation cycles") should have fine grains, while the more highly heat-stressed blades should have coarse grains. Unfortunately, the casting process often results in the exact opposite configuration. Coarse grains form in the thick, slowly solidifying hub, while fine grains form in the thin blade cross-section. In addition, due to the temperature gradients during solidification, the fine grains in the blade edges are oriented crossways to the centrifugal forces in operation. In the annulus area, the grain also tends to form grain boundaries that are oriented across the tangential stress, promoting the typical annulus cracks which can be traced back to thermal fatigue (Fig. "Cracks in integral turbine wheels").
In an investment cast part, it is important that the (usually) more highly dynamically stressed surface has globular fine grains.
This can be accomplished by applying a special coating with many solidification seeds to the inside of the ceramic form (on the side of the melt) during the investment casting process. In this way, a fine grain layer forms at the surface (bottom diagram). This retards thermal fatigue crack initiation. The coarse-grained inner cross-section contributes to sufficient creep resistance. In this way, the creep resistance and dynamic strength of the part are optimized specifically for the expected loads.

Figure "Fatigue behavior by grain structure" (Ref. 12.6.2-3): In the thinner cross-sections of investment-cast turbine stator and running blades, the grain size and shape is determined by the solidification conditions. The grains develop in the direction of the temperature gradients at a right angle to the surface. This results in long, directional fine grains (columnar grains, stem crystals). The rapid solidification in thinner cross-sections results in smaller grains. This grain development is typical for thin edges and shrouds (bottom diagrams). In thicker cross-sections, evenly shaped grains form inside and at the surface (equiaxed, globular).
Unfortunately, the grain boundaries of the columnar grains are often oriented perpendicular to the main direction of stress. One example is the back edges of blades. Grain boundaries are weak points with regard to creep stress and thermal fatigue. These weak points promote hot gas corrosion, crack initiation, and crack growth (Figs. "Pore formation as creep damage" and "Grain boundaries influencing thermal fatigue"). Therefore, columnar structural development is prohibited by the designer in certain parts. Globular grains ensure that the cracks run into grain boundaries and are diverted into a zigzag. This absorbs energy and slows crack growth.
In a grain/crystal, the modulus of elasticity is dependent on the orientation of the crystal (Fig. "Single crystal material for mistuning"). Parallel to the direction of solidification, i.e. in a lengthwise direction, columnar grains have a 30-40% lower modulus of elasticity than globular grains. This greater resiliency leads to 30-40% lower stress levels under even, localized elastic stress at the surface. Two different grain types (columnar and equiaxial) in a thin cross-section result in a stress distribution in the grain size region that corresponds to the stress distribution of the E-moduli. For this reason, a notch effect and stress jump are created at the transition between the two grain types (top diagrams). This is also true of thermal stresses (Ds =a . E . DT) that are created due to restricted strain. This has a noticeable effect on thermal fatigue behavior.
As a result, cracks tend to form at the surface in the transition from columnar to globular structure.

Figure "Different behave of part zones under thermal fatigue": Thermal fatigue (TF) is caused by strain cycles in combination with temperature changes. An important factor for the damage is whether the temperature and strain over time occur in-phase or phase-shifted.
In the cool center of a turbine blade, tensile stresses occur that are in equilibrium with the compressive stresses in the hotter edges. Strain (tensile stress) and temperature are in-phase in the blade center and phase-shifted at the edges.

Figure "Damaging colder part zones by thermal fatigue" (Ref. 12.6.2-1): The top right diagram shows the typical temperature distribution in a cooled turbine blade with large temperature gradients. The temperatures are relatively low around the cooling air bores. These zones absorb a large share of the centrifugal force-related operating loads. The cooling is designed in a way that the blade temperature decreases towards the root in order to cope with the increasing centrifugal force loads and to keep the disk temperatures low (at the blade connections). The edges are especially hot despite the intense cooling. The greater heat strain in this area acts counter to the centrifugal force. Blade edges are especially strongly affected by oxidation and structural changes due to their high operating temperatures.
The uneven temperature distribution and stresses in the blade cross-section are also the reason why simple measurement of lengthwise strain to determine creep strain is usually not suitable for estimating the remaining life span. Creep deformations are more likely to cause warping in the blade leaf than analyzable changes in length. A more promising method may be newer laser measuring techniques that measure the entire blade geometry and compare the previously documented individual new blade with the same blade after running.
In the case of thermal stress, the colder zones of a part are usually under especially high tensile stress. The warmer areas with greater thermal strain induce these tensile stresses in the cooler areas due to the restrictions the latter put on the thermal strain. One example is turbine disk hubs (Figs. "Loading of a turbine disk in the startup phase" and "Turbine disk loads during operation cycles"). Another typical example is cooled hot parts such as turbine blades (Fig. "Temperature caused damages at high pressure turbine vanes"). The areas around cooling air bores become tensile stress zones which tend to initiate thermal fatigue cracks (top detail). These can only be visually detected from the outside when they break through to the surface and have already weakened the part considerably. This type of damage is promoted by oxidation or hot gas corrosion in the cooling air bores (Example "Airflow leak causing fatigue failure").
The bottom diagram shows “unbuttoning” through impingement bores inside the blade. The catalyst is high shearing stress from the different temperatures on the pressure and suction sides (Ref. 12.6.2-8).

Figure "Symptoms of thermal fatigue cracks" (Ref. 12.6.2-2): Thermal fatigue cracks have characteristic symptoms from the damage mechanism. If crack growth is retarded to standstill, heavy oxidation of the crack sides and edges can occur. When the oxide coating breaks out,the base and edges of cracks are rounded off under compression and strain. If oxidation is minor, then the cracks will gape open and the edges will be thrown up. The gaping is a result of the compression process during heating and subsequent shrinking during cooling. The raised crack edges are also evidence of the compression phase (Fig. "Cracks in integral turbine wheels").
If the oxides do not break away, then the crack will be filled with oxide to the rounded base. This is a sure indicator of very slow crack growth. The oxides filling a crack can make penetrative verification considerably more difficult (Example "Unequal thermal load leading to stress "). In comparison, the rapid crack growth of a dynamic fracture progressing at high frequency does not show similar oxidation.
In the case of extreme temperature gradients, one can often see fields of shallow parallel surface cracks (Fig. "Turbine guide vane thermal damages", Ref. 12.6.2-20) that contribute to orange peel texture through oxidation. This type of damage is typical for the front edges of high-pressure turbine blades and combustion chamber liners.

Illustration 12.6.2.11: During the thermal fatigue process the compressive stresses in the cycle decrease while the tensile stresses increase. This trend is caused by relaxation. Relaxation is a process by which stresses in a strain-controlled system are broken down by creep. At the same time, the creep speed decreases with the stress levels. The conditions for this type of behavior are met, for example, by a strain-controlled system such as a turbine part with temperature gradients. A typical example is the front edge of a turbine blade (top diagram). Due to the deformation-restricting role of the neighboring cold blade areas, temperature cycles in the hot zones lead to powerful compressive stresses that are broken down by relaxation (bottom diagram). During the cooling phase, the compressive stresses turn into tension stresses. With every cycle the stress levels increase in the direction of tension stress, since the compressive stresses decrease more and more in the hot phase due to relaxation, while the cold material does not relax in the tension phase. The top left detail shows the trans-crystal crack surface of an only slightly oxidized thermal fatigue crack at the front blade edge. At the time of crack initiation, the crack zone shows concentrical crack growth lines (striations) near the crack edge. The striations can be attributed to the thermal cycles (usually startup/shutdown cycles). This makes it possible to gain important information regarding the time of crack initiation, crack spread, and the crack growth rate. This information can yield insights into the failure risk. Angled, crack field-like rupture structures (Stage I fractures, Fig. "Development of fracture surface features") spread out from the crack initiation zone. These are typical for dynamic fatigue fractures in austenitic alloys such as Ni-based alloys (especially coarse-grain cast alloys), and are especially pronounced in the HCF range. This indicates that the diagram shows a case in which the initial thermal fatigue crack weakened the part so much that high-frequency blade vibrations led to accelerated crack growth. This is not surprising, since a thermal fatigue crack represents a pronounced notch, which promotes dynamic cracks. Experience has shown that the probability of being able to identify evaluable crack growth lines on such pronounced rupture surfaces is very low.
The clearly recognizable crack initiation point is easily identifiable due to the concentric edges of the LCF crack. This point should be inspected for damage-promoting or even causal flaws (e.g. coating cracks, hot cracks, or cavities). If there are no flaws, thermal fatigue cracks often originate at oxidized carbides on the grain boundaries (Ref. 12.6.2-10). The structure of the fracture surface of the TF crack depends considerably on the temperature (Ref. 12.6.2-10). Structures develop that are similar to those in LCF tests at high and low temperatures. TMF loads in the temperature range between 400-1000°C result in a mixture of crystallographic fracture surfaces (rupture surfaces) and other fracture structures.