Aeroengine Safety

Figure "Effects of residual stresses": Residual stresses are stresses in a body that are in a state of equilibrium (Fig. "Equilibrium of residual stresses"). As long as they don`t change, they won`t make themselves outwardly apparent. A bow provides a good example. In its “designed” resting state (“A”), the bowstring is under tensile stress, and the bow is under bending stress (tension and compression). When the bow is drawn by an external force (“B”), the stresses from this “operating force” overlay with the residual stresses.
If the residual stresses lead to plastic deformation or, at higher temperatures, creep (relaxation, “C”) they will be reduced. This effect also occurs when the material yields through cracking (“D”), such as that caused by stress corrosion cracking or liquid metal embrittlement (“E”). At least in the case of cracking, this development should unallowably worsen the operating behavior.
Changes in the residual stresses also occur when the operating stresses exceed the flow limit and cause plastic deformation. In a deformation-restricting situation (e.g. thermal fatigue), very high residual stresses can be induced. In this case, cracking will reduce the residual stresses (Fig. "Processes to build up desired resiudual stresses") and/or fracture the part.
If the operating stresses, including the residual stresses, exceed the strength of the part, it will result in part failure and fractures (“F”)
Depending on the scale of their effects, residual stresses are grouped into three categories (Refs. 16.2.2.4-1 and 16.2.2.4-3). These residual stress types often influence one another.

Type I residual stresses: These macroscopic residual stresses are especially important in finishing processes (Volume 3, Ill. 12.2-13), and should be of interest to specialists in this field. These residual stresses act over a considerably larger part zone than the structural characteristics. Forces and moments are in equilibrium in the case of these residual stresses. If they change, it will result in dimensional changes, i.e. warpage (bottom diagram). In cases with symmetrical residual stress conditions, warpage will not occur. Examples include a plate that has been shot peened on both sides (Fig. "Equilibrium of residual stresses") or a disk that has been centrifuged in the plastic range (Fig. "Relaxation" and Volume 3, Ill. 12.6.1-13.1). Dimensional changes resulting from strain in the elastic range are relatively minor. Specialists will recognize them in tightly fitting parts. Rapid residual stress changes, such as are initiated by external forces, can be accompanied by noticeable movement of the part. One example is the snapping of a tin can lid when opened.

Type II residual stresses: These act on the scale of the structural properties (grain sizes). The deformations that occur when these stresses change are very minor, and are rarely noticed in practice. These residual stresses are present, for example, in electrical discharge machined or coated surfaces (Fig. "Electric discharge machining features").

Type III residual stresses: These are only inhomogenous on the scale of inter-atomic distances. Changes are not macroscopically visible. These residual stresses are typically found in hard structures (case-hardened, nitrided) or in phases in hardenable alloys.
The bottom diagram shows a case in which a disk made from a high-strength nickel alloy, which is difficult to machine, was face turned on one side. This created high residual stresses in the face turned side. Depending on the machining parameters, the residual stresses in the surface will either be tensile or compressive. As long as the disk is held fast by external forces, it remains symmetrical. In this situation, the asymmetrical residual stresses are in equilibrium with the external clamping forces. However, as soon as it is removed from the fastening equipment, the external forces disappear and the residual stresses have to shift in order to create a new equilibrium, which is now entirely dependent on the internal stresses. This forces the part to elastically deform as shown in the diagram (warpage). If the disk is heated, lowering the flow limit of the material, the warping will become even more pronounced as the residual stresses are broken down further.

Figure "Equilibrium of residual stresses": This model shows the residual stress conditions of a plate with symmetrical compressive stresses in the surface zone (bottom diagram). One can see that an equilibrium forms that can be explained with the aid of springs (top diagram, Ref. 16.2.2.4-11). The state of equilibrium can be seen in the symmetry and equal surface areas of the areas below the stress curves on the compression and tension sides (bottom diagram).

Figure "Process parameters influencing residual stresses": Residual stresses that are induced by machining processes can decisively influence operating characteristics. These include primarily HCF and LCF dynamic strength (Fig. "Increasing fatigue strength by compressive residual stresses"). The large number of influences on residual stresses can also act in combination. This is evident when considering the difficulty of using only machining to ensure defined residual stress conditions in highly stressed parts such as rotor components. The prerequisite for this is thoroughly tested finishing parameters. Other influences on the residual stresses, such as finishing steps and material conditions, must be sufficiently documented and reproduced. Even a change in the type of machining tool being used must be tested and verified in this way.

For example, depending on the material, a change in the cutting edge material can affect the height and pattern of the residual stresses, especially depending on the service life of the cutting edge (bottom diagrams, Ref. 16.2.2.4-2). Due to these difficulties, defined residual stresses are often subsequently created in the machined surfaces with the aid of shot peening.

Figure "Increasing fatigue strength by compressive residual stresses".: The mean stress s_m is the shift of the dynamic stress (2 s_a ) on the ordinate (top right detail). This type of shift occurs with the overlaying (addition (note algebraic sign), bottom diagram) of residual stresses and dynamic operating stresses. One can recognize that, as the mean stress increases, the usable dynamic fatigue strength (fatigue resistance!) approaches zero when the tensile mean stress has reached the flow limit.
Consider the example of a blade (left diagram) vibrating in its fundamental flexural mode in the area above the root platform, which is at risk of fatigue. If the blade face has been shot peened, then compressive stresses have been induced in its surface (bottom diagram). Tensile stresses from the bending loads (compressive stresses are not a problem) overlay with the compressive residual stresses from shot peening. This significantly reduces the (tensile) mean stress in the surface area, and the part experiences greater dynamic loads. In the opposite case, unfavorable machining parameters create powerful tensile stresses in the blade surface. These combine with the dynamic operating stresses and raise the mean stress, which lowers the fatigue resistance of the part.
In this case, the special difficulty is the fact that, unlike scratches and nicks, residual stresses in a part are not visible.

This demonstrates why changes in the finishing parameters (Fig. "Process parameters influencing residual stresses") without assuring verification can dangerously increase the risk of blade fractures in engines. The risk is especially high if damages only occur after longer operating times, and a large number of engines are affected.
In order to minimize risks, on the basis of statistical analysis, parts are taken from blade production batches and their dynamic fatigue strength (axf value, Fig. "Axf testing dynamic strength") is determined in a laboratory with the aid of fatigue tests. If the prescribed minimum value is met, the production batch can be released for installation.

Figure "Residual changes during finishing processes": Finishing processes create or change residual stresses. Typical examples have been selected to explain how this occurs, and what types of residual stresses are created.

“1” Machining (Ill. 16.2.2.5.1): Plastic deformations occur on a micro-scale along with the removal of shavings (Ref. 16.2.2.4-4), inducing residual stresses. The size and type of the residual stresses is dependent on many factors, primarily the material and machining parameters (Fig. "Process parameters influencing residual stresses"). If sufficiently high temperatures are reached during machining, especially grinding, steels can experience structural changes with volume changes and a building-up of residual stresses (Ref. 16.2.2.4-16).

“2” Welding (Fig. "Welding causing deformations and residual stresses"): Thermal stresses based on the temperature changes cause plastic and elastic deformations. The stresses change during welding and cooling (Fig. "Welding causing deformations and residual stresses", Ref. 16.2.2.4-5) until the residual stress conditions are reached at room temperature. If the materials experience structural changes with volume changes (e.g. steels) in the zones that are heated during welding, the stress patterns can deviate from that shown in Fig. "Changes by residual stresses from machining" (Ref. 16.2.2.4-17). The type, strength, and pattern of the residual stresses depends not only on the welding parameters, but is also decisively influenced by the resilience/stiffness of the part. High stiffness means that there will be limited warping, but results in high residual stresses because they cannot be relieved through deformation. Minimal warping after welding is not necessarily a sign of low residual stresses from the welding process.

“3” Blasting (Fig. "Residual stresses by shot peening"): Blasting, especially shot peening, creates compressive stresses in the part surface. Symmetrical treatment of both sides will not cause warping (Fig. "Equilibrium of residual stresses"). If a flat, sufficiently thin part is shot peened on one side, the compressive stresses on the one side must be balanced by deflection (warping; Fig. "Equilibrium of residual stresses", Refs. 16.2.2.4-6, 16.2.2.4-12, and 16.2.2.4-14). Blasting is used to ensure sufficient dynamic fatigue strength, which also applies to small cracks that remain in the compressive stress zone (Ill. 17.4-9). Comparable effects can also be achieved using other hardening processes such as rolling and laser peening.

“4” Thermal spraying (Fig. "Residual stresses at spray coatings after cooling"): Residual stresses that are created by thermal spraying are especially dependent on the differences in physical properties between the coating and base material. These include thermal strain, strength, and modulus of elasticity. In the following, the residual stress conditions after cooling following the spraying process are given simplified explanations:

“A”: Relative to a metallic base material, it is typical for ceramic coatings to have low thermal strain. Their low thermal conductivity is responsible for an especially large temperature difference between the coating and the cooler base material. Therefore, during cooling, compressive stresses are created that depend on the degree to which the base material was heated during the coating process. The modulus of elasticity of porous coatings is usually low and results in low residual stress levels.

“B”: Suitable temperature control in the base material can be used to create tensile stresses, at least temporarily, which will cause cracking. This creates the desired segmentation cracks in thermal barriers. They help with the breaking down of residual stresses. In order to attain residual stress conditions in the finishing process that are matched to the operating behavior of a part, it is necessary to have optimal temperature control. This also makes it possible to create compressive residual stresses in the coating or in the base material.

“C”: If the thermal strain of the base material is less than that of the coating, tensile stresses are created in the hot coating when it cools. The same effect can be realized by keeping the base material at a lower temperature during the coating process. This may be desirable in order to create compressive stresses in the base material and at least prevent the dynamic fatigue strength from decreasing.

“D”: If the coating has dynamic residual stresses, which means that the base material has tensile residual stresses, it will promote dynamic fatigue cracking beneath the coating, which is usually porous and not suited to crack detection. This danger is increased in coatings with a very low modulus of elasticity. At the same strain levels, these coatings, which are often porous, will have considerably lower stresses than the base material to which they are joined.

“5” Hard coatings (Fig. "Residual stresses from hardening coatings"): Volume increases during the hardening of surfaces will result in compressive stresses. This will increase both the hardness and the dynamic fatigue strength. This effect may be due entirely to the larger volume of the hardened structure, as in the case of induction hardening. The diffusion of carbon (case hardening) or nitrogen (nitriding) also increases the volume and induces desired compressive stresses. In the case of very thin cross-sections, such as small gear teeth (Ill. 16.2.2.4-6), powerful tensile stresses can be created in the core due to equilibrium. Experience has shown that, during case hardening, these stresses can cause internal cracking in connection with hydrogen embrittlement (Volume 1, Ill. 5.4.4.2-3). The high dynamic fatigue strength of the surface coating promotes dynamic fatigue cracks from the transition of the hard coating to the base material. These cracks may only be noticed when they reach a dangerous size shortly before fracture occurs, by which time it is usually too late.

“6” Chemical and galvanic coatings: (Fig. "Residual stresses of chemical and galvanic coatings"): The lowering of fatigue resistance through Cr and Ni coatings is widely known (Ref. 16.2.2.4-8). The decrease in dynamic fatigue strength in connection with Ni coatings is greater than with Cr coatings. This is probably due to the very high modulus of elasticity of the nickel coatings. At the same strain levels, considerably greater stresses will occur in Ni coatings. The lowering of the dynamic fatigue strength can be traced back to residual stresses in the coatings. Fig. "Residual stresses of chemical and galvanic coatings" shows the residual stress distribution around a hard chrome coating on cast iron. One can see that the tensile stresses reach a maximum at the transition of the coating to the base material. If these residual stresses are overlayed with dynamic loads, it considerably increases the mean stress and reduces the usable dynamic fatigue strength (Ill.16.2.2.4-4). The tensile stress minimum in the coating is significant, and is probably related to the coating buildup and therefore also the process parameters.

“7” EDM, laser boring, EB boring (Fig. "Residual stresses of non chipping boring proceses") melt local areas of the material very rapidly, although in different ways. This results in recast layers. In addition, the base material in a narrow adjacent zone will be heated to a high temperature. This compresses it and creates tensile stresses upon cooling, which results in very high tensile-shrinkage stresses in the recast layer. The recast layer is usually fortified with carbon from the dielectric, making it hard and brittle. This promotes micro cracks. The pattern of the residual stresses changes along with unevenness in the coating (Fig. "Electric discharge machining features") over very small distances and can serve as an example for type II residual stresses (Fig. "Effects of residual stresses"). Tensile stresses and/or micro cracks from these processes reduce the dynamic fatigue strength more drastically than other machining processes that do not have comparable thermal effects. Special caution is required when changing to a machining process that creates a recast layer. In any case, suitable, realistic and representative verification of the suitability of the machining process is required.

“8” Heat treatment, annealing: These processes can not only break down stresses (stress relief annealing), but they can also create residual stresses. This is the case when thick and/or very different neighboring cross-sections heat rapidly and create thermal stresses in the part that are above the flow limit. If parts are plastically compressed or stretched during annealing, residual stresses that are oriented in the opposite direction will be created during cooling. Compressive stresses can be expected in the stretched zone, while tensile stresses can be expected in the compressed zone. Therefore, the residual stresses at room temperature are the opposite of the thermal stresses at annealing temperature. The greater the thermal resistance of a part, the more difficult it is to break down residual stresses through repeated annealing at temperatures that are certain to not damage the material. In order to create as little residual stress as possible in parts during heat treatment, raw parts should be designed with favorable contours (heat treatment contours). Residual stresses can also be created by other finishing processes that occur at high temperatures, such as forging (Ills. 15.1-14 and 15.2-19).

“9” Casting: High residual stresses can be expected in thick cast cross-sections. A typical example is integral cast turbine disks in small gas turbines (e.g. helicopter engines). Because the material on the inside solidifies last, this zone experiences powerful shrinkage stress (tension). In addition, the inward temperature increase during cooling also creates tensile stresses. If this type of disk is cut open using a radial cut towards the center, tensile stresses will close the cut. Experience has shown that this will then trap the cutting disk or saw blade. High thermal resistance and thermal stress during heating and cooling only permit an unsatisfactory reduction of the residual stresses from casting.

“10” Forming processes (Fig. "Residual stresses in FRP and plastics"): If a part is plastically formed and not kept at temperature for a long period, it will spring back. In this case, it may not be noticed that the residual stresses after springing back will have the opposite orientation of the forming forces. If a metal sheet that is fastened on one side is placed under flexural stress, it creates a tension side and a pressure side. If the stresses exceed the flow limit, the most highly stressed point (fastened area) on the tension side will be plastically stretched, while the pressure side will be plastically compressed. After relaxation and springing-back, there will be tensile stresses in the plastically compressed zone and compressive stresses in the stretched zone. This effect leads to unexpected damage symptoms. One example of this is stress corrosion cracking on the inner radius of bent part zones.

“11” Shifting of residual stresses through contact material removal: This includes electrochemical processes (ECM) and etching. If material is removed from a part that has residual stresses, it will disturb the equilibrium of the residual stresses. This changes the size of the stresses and/or causes them to shift and warp or change the dimensions of the part. If the residual stresses are powerful enough, and the affected cross-section is large enough, this warping can cover up other effects, including residual stresses at the surface which were created by machining and can also cause noticeable warping. The combination of these effects can have a very unpleasant influence on the finishing process.

Figure "Changing of residual stresses during operation": Residual stresses in new parts also change during assembly and operation. The following are typical examples:

“A”: Residual stresses can already be induced in parts during assembly. The stresses are also related to finishing tolerances. In these cases, the assembly system can be viewed like a homogenous part, i.e. as a closed system that is not affected by external moments and forces. For example, if a pipe is installed that does not fit exactly (“A1”), it will induce stresses that can be viewed as residual stresses. The closed system in this case consists of the pipe and the force-transferring engine components.

In “A2” the closed system consists of the shaft and the shrink-fitted hub. Tangential tensile forces and radial compressive forces act in the hub and are in equilibrium with stresses in the shaft.

“B”: In turbine blades, in this case a guide vane, the relatively thin edges are heated much more intensively and quickly than thicker and/or cooled blade zones. The greater thermal expansion in the edges, relative to the neighboring blade zones, creates powerful compressive stresses in the hot edges. This causes the edges to be plastically compressed through creep and flow. When the blade cools, tensile residual stresses build up in the compressed zones, and are in equilibrium with compressive stresses in the undeformed areas.

“C”: In LCF-stressed rotor disks or rings, in especially highly stressed zones (bores, etc.), the flow limit is exceeded by tensile stresses and plastic deformation occurs. During rest, these strained areas are in equilibrium with the surrounding compressive zones that are merely under elastic stress.

“D”: The differences in thermal strain between a thermal spray coating, especially a ceramic thermal barrier, and the base material lead to stresses during operation (Ref. 16.2.2.4-7). If tensile stresses exceed the fracture strength of the ceramic at high temperature, it will result in gaping cracks and stress reduction (segmentation cracks). After cooling, the closing of the cracks prevents excessively high compressive residual stresses, which would cause the ceramic coating to spall.

“E”: During the production (HIP) of long fiber-reinforced titanium alloys, compressive stresses are created due to the very different heat strain in the fiber band. The relatively low heat strain of the ceramic fibers restricts the titanium matrix during cooling. This creates powerful tensile stresses in the matrix. Creep and flow in the matrix under operating conditions (temperature, stress) can change these undesired residual stress conditions. Residual stresses between individual fibers and the matrix can be categorized as type II residual stresses (Fig. "Effects of residual stresses"). They are very important for the strength properties of the band. These process-specific residual stresses cannot be broken down through stress relief annealing. On the contrary, it is expected that creep processes at high temperature would further increase the residual stresses in the cooled state, compromising the LCF strength even at relatively low operating temperatures (e.g. in the fan area).

“F”: If polymers, either with or without reinforcing fibers, are used in combination with metallic structures (e.g. abradable coatings), even during the production process, shrinkage during hardening will create tensile residual stresses that can cause the coating to spall and/or crack. Aging processes with volume losses, such as evaporation of components or oxidation, can create shrinkage stress (tensile) during operation, resulting in delamination of the edges and/or cracking (right diagram). If polymers such as silicon gum swell up in contact with fuel, it will result in compressive stresses that can lead to delamination that can be seen in the appearance of blisters (left diagram).

Figure "Verifying of bond strength by process monitoring": A suprisingly large variety of material properties can influence the residual stresses in a part. The following text examines these influences in greater detail:

Strength: The important parameters are the temperature-dependent flow limit and the time-dependent elastic limit (Fig. "Annealing time effect on residual stress level"). If the stresses exceed these limits, it will cause plastic deformation and stress limitation.
If the strength is locally exceeded by a high stress gradient, it will result in cracking, which reduces stress levels (Ill. 16.2.2.4-6). The strength determines the composition of residual stresses, i.e. their strength, changes (e.g. during deformation processes), and reduction (e.g. stress relief annealing).

Tendency to harden: The degree to which a material hardens during plastic deformation (left diagram) also determines the level of induced residual stresses. During shot peening, especially high compressive residual stresses will develop in materials that have a high tendency to harden. This tendency also influences residual stresses that are created when plastically deformed parts spring back (Ill. 16.2.2.4-5.10).

Elasticity (modulus): The lower the modulus of elasticity, the lower the stresses that will be created by elastic deformation. This limits residual stresses in fiber-reinforced polymers. The matrix has a very low modulus of elasticity relative to reinforcing fibers such as glass and carbon fibers, and this usually drops even further as temperatures increase (right diagram). As a result, residual stresses decrease during heating, and rise during cooling (Fig. "Residual stresses in spite of stress-relief annealing"), making it ineffective to attempt residual stress relief through heating.

Thermal strain: Thermal strain plays an important role in the creation of residual stresses. Materials with high thermal strain coefficients tend to have correspondingly large strain differences and thermal stresses during heat cycles. If, in the course of thermal fatigue, these stresses cause plastic compression in the hot edges, it will create residual stresses. For this reason, the edges of cooled turbine blades have tensile stresses, while the inner zones have compressive stresses. Inhomogeneous materials such as fiber-reinforced metals develop pronounced inhomogeneous residual stresses due to the large differences in thermal strain between the matrix and fibers (Ill. 16.2.2.4-6). This is especially true of titanium alloys that are reinforced with ceramic fibers (SiC).

Thermal conductivity: Low thermal conductivity, which is typical of titanium alloys, leads to large gradients during temperature changes in cooling and heating processes. This results in correspondingly high stress peaks and the development of residual stresses (Ill. 15.2-19). For these materials, slow cooling is especially important after stress relief annealing in order to prevent new residual stresses from forming during the cooling phase.

Structural changes also influence type III residual stresses that act on a micro-scale (Fig. "Effects of residual stresses"), and therefore affect properties such as creep behavior. In steels, a hard structure at the surface (induction hardening, flame hardening) is under compressive residual stress due to volume increases, which increases dynamic fatigue strength considerably. A similar effect can be seen in hard coatings that are created by the diffusion of carbon (case hardening) or nitrogen (nitriding).

Inhomogeneities: These include both reinforcements (fibers, etc.) as well as hardening particles (g'-phase) and carbides. They affect all three types of residual stresses through the physical properties discussed above.

Figure "Influence by compressive surface zones": Compressive residual stresses at the part surface reduce the mean stress under bending loads (Fig. "Increasing fatigue strength by compressive residual stresses"). This increases the usable dynamic fatigue strength. Unlike an increase in tensile stress, an increase in compressive residual stress due to overlaying with the compressive operating stresses does not have a damaging effect. This is why compressive residual stresses are desirable in surface zones, and the reason for shot peening parts that experience high dynamic loads, such as disks and blades.
An additional positive effect is a certain protection against surface damages. This effect will be present as long as potentially damaging influences are limited to the compressive stress zone (top diagram, Fig. "Increasing fatigue strength by shot peening"). The thicker the compressive stress zone and the higher the compressive stresses, the more pronounced the protective effect.
Because compressive stresses at the surface are in equilibrium with tensile stresses inside the cross-section, the mean tensile stress within the part increases. This increase is minor in sufficiently thick cross-sections. However, in thin cross-sections with even, high tensile stress across the entire cross-section, an excessively pronounced compressive stress zone may cause problems. This applies to rotating rings and ring racks on disks with high tangential stresses (Fig. "Problems by compressive residual stresses").
Compressive stresses are usually induced in surfaces with the aid of hardening processes (rolling, shot peening, case hardening, induction hardening, nitriding, etc.). In addition to inducing compressive stresses, these processes increase the material strength in the surface zone. Hardening and compressive stresses are two different effects that occur in combination. Hardening results in a raised flow limit and increased dynamic fatigue strength. It is related to changes in the metal lattice (displacements) that reduce plastic deformability. The material type determines whether the hardening or the residual stresses are primarily responsible for the increase in dynamic fatigue strength. In pronounced strain-hardening materials such as steels (bottom left diagram), the hardness increase should have the greater positive effect. Materials that do not strain-harden, such as titanium alloys (bottom right diagram), primarily benefit from the compressive stresses.
If the hardening leads to pronounced embrittlement, the protective effect may be reduced by increased notch-sensitivity.

Figure "Problems by compressive residual stresses" and Figure "Flexual load and flat stress gradient": High compressive stresses in the surface cannot always be expected to result in clear increases in dynamic fatigue strength.

Very deep (relative to the whole cross-section) compressive stress zones (top detail) can unfavorably overlay with operating stresses. If the tensile stresses created inside the material during hardening (Ill. 16.2.2.5-5.5) combine with tensile stresses during operation, it can result in early dynamic fatigue cracks below the surface. This situation is especially dangerous if the operating stress has very small gradients. This is the case with thin ring racks such as labyrinth racks and flange lugs (left frame) that are subjected to tangential stress. Similar conditions occur during the bending of thick cross-sections. These also have a very flat stress pattern (Fig. "Influences at fatigue strength by shot peening"). Cracks below the surface are typical in case-hardened or nitrided surfaces.

The bending of thin cross-sections such as compressor blades (right frame), on the other hand, results in steep stress gradients. The tensile stress component from the operating loads is broken down by the compressive residual stresses at the surface, which has a positive effect on the dynamic fatigue strength.

Figure "Beneficial limits of compressive residual stresses": Compressive stresses at the surface are in equilibrium with corresponding tensile stresses underneath. This effect should be especially pronounced in edges and other thin cross-sections (Fig. "Residual stresses from hardening coatings"). If these tensile stresses are overlayed with tensile stresses from operation, it should result in a considerable lowering of the dynamic fatigue resistance in the area below the compressive stress zone. This situation is present in the edges of disk grooves that are subject to high tangential stress levels. This explains the special sensitivity of excessively shot-peened groove edges. Even minor damages such as PSEFs (shot overlap) or burrs (elephant tails) can evidently make LCF cracking more likely (Fig. "Peened surface extrusion folds").

Figure "Residual stresses affecting part life span": The phase`s crack initiation, crack growth, and residual fracture (top left diagram) can be decisively influenced by residual stresses. In the following, dynamic fatigue cracks are examined with the aid of examples.

Crack initiation: The causes of dynamic fatigue cracks are flaws, i.e. the dynamic fatigue strength is less than the design specifies, or overstress. In the latter case, the crack can originate in a weak point that has been incorporated into the design. The residual stress conditions largely determine whether the point of origin is a weak point or a flaw, such as a scratch. If there are sufficiently high tensile stresses, such as from a grinding process, then crack growth can occur early. In contrast, if there are sufficient compressive stresses, cracking will not occur even in flaws (Fig. "Increasing fatigue strength by shot peening"), because dynamic fatigue requires a sufficiently high tension phase. Usually, significant crack growth only occurs after a certain incubation period. During this phase, plastic deformations on a micro-scale can create residual stresses in the structure and/or around the flaw (type II and III residual stresses, Fig. "Effects of residual stresses"), which then cause crack growth to occur after the incubation period. In extreme cases under LCF stress, crack growth begins during the first load cycle. In this case there is no incubation time. Below a certain flaw size or crack length (threshold length), depending on the load levels, crack growth will not occur (top right diagram). However, if dynamic loads cause sufficiently high tensile stresses to occur on a micro-scale around the flaw (Volume 3, Ill. 12.6.3.2-1), it can cause cracks below the threshold length to become capable of growth (top right diagram). Important factors for the growth capability of flaws are the location, direction, and gradients of acting residual stresses. Growth-capable flaws are promoted by tensile residual stresses. These include corrosion cracks (stress corrosion cracking) and hydrogen embrittlement. In the case of hydrogen embrittlement, powerful type II and III tensile residual stresses are induced around inhomogeneities (Volume 1, Ill. 5.4.4.1-1). After an incubation period, these can create micro-cracks that later become the origin of dynamic fatigue cracks.

Stable crack growth: This is a type of crack growth (cyclical, creep) before residual fracture occurs. Therefore, spontaneous failure does not occur. The growth rate is clearly influenced by residual stresses. If plastic strain occurs under tensile stress in the base of a notch, compressive residual stresses will form during relaxation. These will initially slow crack growth. Tensile residual stresses can also be broken down by crack initiation, which slows crack growth. This behavior can be observed in thermal fatigue cracks (Volume 3, Ill. 12.6.2-2).

Unstable crack growth/residual fracture: Embrittlement of the material shortens the critical crack growth, i.e. shorter cracks will already cause the part to fail. Sufficiently high macro-residual stresses can cause violent fractures and failure if the material behaves brittly.

Figure "Benefits of compressive residual stresses": Compressive residual stresses can make part behavior safer in several different ways:

• Raising the usable dynamic fatigue strength: This effect is achieved by lowering the mean stress under operating loads (Fig. "Increasing fatigue strength by compressive residual stresses").
  

This is not only true for the surface area, which may have been shot peened or similarly treated. The principle of lowering the mean stress can also be applied to thick cross-sections such as rotor disk hubs. The centrifugal forces during overspeed rotation can plastically strain the especially highly-stressed hub. Following relaxation, this area will have corresponding compressive residual stresses (Ill. 16.2.2.4-6). If creep breaks down necessary compressive residual stresses, then these must be induced again. Typical examples of this are dovetail connections in compressors and the relatively hot fir-tree roots in the turbine. In these cases, regular regeneration through shot peening should be done during overhauls.

• Protection from operation-related damages, such as in areas subjected to fretting (Fig. "Fretting damage loweing by shot peening")). The surface can be damaged by wear notches, impressed wear products, and micro-cracking, resulting in an unacceptable loss of dynamic fatigue strength. Titanium alloys are especially sensitive to this type of damage (Volume 2, Chapter 6.2).
  

• “Defusing” surface damage: This effect can be expected from compressive stresses that act deeper than the surface damage. This reduces the danger of cracking originating in surface damage on highly stressed parts such as rotor components. Examples of surface damage include notches such as scratches and grooves created during handling, storage, or assembly.
  

• Compressive residual stresses prevent stress corrosion cracking: Because sufficiently high tensile residual stresses are a prerequisite for stress corrosion cracking (SCC), compressive residual stresses have a protective effect. This is the primary reason why toothed gears must be shot-peened before burnishing. Under sufficient tensile stress, burnishing baths will cause SCC in the form of caustic embrittlement (Fig. "Cracking in steels processed in burnishing baths").
  

• Ensuring that a defined surface state is created: The targeted creation of compressive residual stresses with the aid of hardening processes such as shot peening makes it possible to attain defined surface states. Even minor deviations from the parameters of machining can lead to unwanted tensile residual stresses (Fig. "Changes by residual stresses from machining"). However, it is vitally important for part safety that the surface conditions are the same as in the specimens that were used to determine the design values. If the burnishing bath penetrates through cracks in coatings with dangerous tensile stresses (e.g. Cr coatings), it is necessary that the base material has been shot peened. This can prevent SCC beneath the coating (Fig. "Dangers of residual stresses").
  

• Galvanic and chemical coatings have high tensile residual stresses (Fig. "Residual stresses of chemical and galvanic coatings"). The aim in this case is to prevent unacceptably large losses of dynamic fatigue strength (Fig. "Influence of Cr and Ni coatings at fatigue strength"). To ensure this, shot peening is used to induce compressive stresses in the base material and/or in the coating either before or, ideally, after the coating process.
  

Figure "Negative effects of residual stresses from finishing": Residual stresses from the production process can cause damages in many different ways. Cracks can occur both during the finishing process as well as afterwards. They may occur as delayed cracking during storage (Fig. "SCC of titanium-alloy in contact with chlorine") or under operating influences. These damages are very often related to tensile residual stresses.

Stress relief cracking: During heat treatment, tensile residual stresses in areas with restricted deformation, such as notches, can be relieved through cracking if the creep strain was not sufficient to relieve them.

Dynamic strength losses: If tensile residual stresses raise the mean stress significantly, it reduces the usable dynamic fatigue strength (Fig. "Increasing fatigue strength by compressive residual stresses").

Warping: If the equilibrium of the residual stresses and internal moments is disturbed, the part will change shape until a new state of equilibrium is attained. This means that warping during relaxation, such as during stress relief annealing, indicates success (Fig. "Annealing time effect on residual stress level").

Cracking beneath coatings: In Cr coatings, cracks due to high tensile residual stresses are typical. Stress corrosion cracking can result in the base material below these coatings. This is the case when cracking in the Cr coating allows a corrosive media (burnishing bath, Ills. 16.2.1.8-3 and 16.2.2.4-13) to reach the substrate. Tensile residual stresses from grinding processes will promote this behavior.

Hydrogen embrittlement: Hydrogen atoms in the metal lattice diffuse in the direction of increasing tensile stresses. In the case of welds, delayed cracking is a common occurrence. Moisture in contact with the melt bath is especially dangerous (Ills. 16.2.1.3-18 and 16.2.2.4-13). In thin, case-hardened cross-sections, such as small gear teeth (Fig. "Hydrogen embrittlement by coatings"), tensile stresses in the core are in a state of equilibrium with high compressive stresses in the hardened layer (Fig. "Residual stresses from hardening coatings"). Under these tensile stresses, hydrogen that was diffused-in during the hardening process causes cracking in the core.

Stress corrosion cracking (SCC): If the prerequisite of a material sensitive to a specific media are met, then sufficiently high tensile stresses will cause SCC. Typical examples include areas of halogen-contaminated titanium parts that are near welds (Fig. "Chlorine in process baths causing stress corrosion" and 16.2.2.3-16) or under residual forging stresses.

Bond strength losses and the separation of coatings: High tensile residual stresses, such as occur due to differences in heat strain between ceramic thermal barriers and the base material, can lead to cracking across the coating (segmentation cracks, Ills. 16.2.1.8.2-3 and 16.2.1.8.2-4) and/or separation of the coating at the edges.
Excessively high compressive residual stresses can also have damaging effects. On convex surfaces they can cause coatings to separate (Ill. 16.2.2.8-4.3).

Figure "Warping by residual stresses from one-sided peening"

Figure "Dangers of residual stresses": Production-related residual stresses can dangerously affect the operating characteristics of parts. This can be seen in the following examples:

Housings: Longitudinally-split, titanium alloy compressor housings in a small shaft-power turbine engine showed unallowably severe signs of rubbing after the first run. The longitudinal flange (top left diagram) showed signs of overheating with tarnishing and embrittlement, making continued operation impossible. The rubbing was due to warping caused by residual stresses in the new parts. The residual stresses were apparently related to the machining of the outer contour. The rubbing occurred as a self-increasing process caused by the deformations, which were in turn accelerated by the resulting thermal stresses. Only specific shot peening of the flange zones was able to solve the problem.
The bottom right diagram shows a welded housing made from steel sheets and forged parts. These housings are typical in older engine types. The melt absorbed hydrogen from moist surrounding air. This combined with high tensile residual stresses around the weld seam to cause delayed cracking (Fig. "Negative effects of residual stresses from finishing").

Turbine disk: An internal LCF crack caused a disk made from a forged alloy with high thermal strength to burst following a cyclical overspeed test (top right diagram). The internal crack location indicates powerful tensile residual stresses in the cross-section. The forging process and/or excessively high cooling rates can induce these tensile residual stresses in the hot interior of the part. It can be assumed that they were in equilibrium with compressive stresses near the surface. They evidently protected the surface from cracking. On the basis of the design, cracking would be expected at the surface. Apparently, an optimal strength-specific annealing temperature and the extreme high-temperature strength did not allow residual stresses to be broken down sufficiently.
An additional, comparable case attributed to residual forging stresses is shown in Fig. "Residual process stresses in titanium rotor disk", and concerns the operating fracture of fan disks made from a titanium alloy.

Toothed gears: High tensile residual stresses in ground sliding surfaces on seals and bearing seats caused stress corrosion cracking during the burnishing of toothed gear shafts (bottom left diagram). Cracking occurred beneath the Cr coating, which is typically cracked (Fig. "Aftertreatment cracks on Cr-coating"). Even around uncoated machined surfaces with high tensile residual stresses, especially multi-spline, burnishing cracks have been found that also led to disk fractures (Fig. "Cracking in steels processed in burnishing baths").

Figure "Residual stresses in spite of stress-relief annealing": The most commonly used method to reduce residual stresses is annealing. However, it is not possible to completely eliminate stresses using this method.
During stress relief annealing, the part is heated to a temperature at which the flow limit of the material has already dropped as far as possible (bottom diagram, Ref. 16.2.2.4-9). It is assumed that, when the flow limit (elastic limit) is exceeded, the plastic deformation will break down the strain that is causing the residual stresses. Therefore, as thermal strength increases, the remaining residual stress levels following annealing also increase. The maximum temperature must not damage the material. The annealing temperature of heat-treated steels must not be exceeded, or it will permanently lower their strength. Unsuitable annealing temperatures can make high-alloy steels become corrosion-sensitive (sensitized to grain boundary attack), while low-alloy steels can embrittle. Annealing temperatures of nickel alloys are determined by unallowable structural changes such as the influencing of hardening phases, thermo-mechanically induced strength properties, and grain growth. Usually, materials with high thermal strength, such as disk materials, require especially optimized structures. This limits the annealing time and temperature, and poses a risk of high, non-removable residual stresses (Fig. "Dangers of residual stresses"). If possible, residual stresses should be minimized during the production process of raw parts and blanks. It is highly recommended that unallowable residual stresses are also determined in cross-sections of samples. These findings may have to enter into the strength design.

Seemingly minor characteristics of raw part production can have a considerable effect on the residual stress levels. For this reason, it is understandable that an optimized production process, especially a raw part production process, will prohibit changing suppliers (e.g. due to costs or delivery problems) without extensive approval processes.
Breaking down residual stresses depends decisively on the annealing time. Unlike hot tensile tests, the important factor here is not short-time strain, but creep. The strain mechanism during creep deformations is called relaxation (Ills. 16.2.2.4-15.1 and 16.2.2.4-16).

The stiffness of a metallic material, i.e. its modulus of elasticity, typically decreases as temperatures rise (top left diagram). This means that strain at annealing temperatures will create less residual stresses. During cooling from the annealing temperature, the remaining residual stresses increase along with the modulus of elasticity. For this reason, it is not possible to reduce the residual stresses in the cooled part to the level at annealing temperature.

As temperatures increase, the thermal expansion coefficient also rises (top right diagram). This means that thermal stresses from temperature gradients can become unexpectedly pronounced during heating to annealing temperature and subsequent cooling. Excessively rapid cooling, especially in thick cross-sections and/or parts with cross-section jumps, induces tensile stresses in cooler zones near the surface. These are in equilibrium with compressive stresses in the hotter inner zone. Depending on the stress levels and patterns, this can cause plastic deformations. Accordingly, after cooling, compressive stresses can be expected in the surface area, which was strained at high temperature, while tensile stresses can be expected inside the cross-section. These tensile stresses can promote internal fatigue cracks (LCF, Fig. "Dangers of residual stresses").

Excessively rapid heating is less problematic. In this case, if thermal stress has led to plastic deformation, relaxation during the subsequent annealing period should defuse the situation. However, it is possible that the pattern and direction of the remaining residual stresses will be different from those of the original residual stresses. Of course, the thermal stresses in the heating and cooling phases should be kept below crack initiation levels.
The annealing time must be selected in a way that the most even possible temperature distribution can occur. Depending on the cross-section, this can necessitate long and costly annealing times.

Figure "Annealing time effect on residual stress level": Residual stresses can be reduced through annealing, which causes plastic flow. This means that the residual stresses must be sufficiently high, i.e. the strength of the material at the annealing temperature must be lower than the residual stresses. Because, depending on the material, strength decreases as temperatures rise (Volume 3, Ill. 12.2.2.4-14), the residual stresses can be reduced considerably at the annealing temperatures. Usually, the hot yield point, i.e. the flow limit at high temperatures, acts as a threshold value for the level of the possible remaining residual stresses following the heat treatment.
The diagram shows that the annealing temperature is the decisive influencing factor on the strength, i.e. the beginning of noticeable plastic deformations. During the steep drop that is pronounced in many materials with high temperature strength, it means that a very slight increase in annealing temperature will result in a considerable residual stress reduction. Unfortunately, the annealing temperature cannot be raised as high as one desires. Otherwise, especially the high-strength forged materials used in engines will suffer unallowable strength losses due to structural changes (Fig. "Residual stresses in spite of stress-relief annealing").

The diagram shows this using the example of the high-strength, heat-resistant forged disk material IN 718. After short annealing times, during which no noticeable creep deformation occurs, relatively high remaining residual stresses can be expected. Naturally, the annealing time is also cost-related. If the annealing time is raised, the residual stresses can be reduced to a fraction (arrow) of their earlier levels through relaxation (Fig. "Processes to build up desired resiudual stresses").
If the maximum annealing temperature is not sufficient to reduce the residual stress levels to the desired levels, the only option is to extend the annealing time.

Sufficiently long annealing times can reduce the remaining residual stresses to levels well below the hot yield point.

Figure "Influence of surface hardening treatment at residual stresses" (Ref. 16.2.2.4-20): This diagram shows the temperature-related drop in compressive stresses that were induced in a high-strength titanium alloy with hardening processes. The Larson-Miller parameter is plotted abscissa. It describes the combined time-temperature influence on creep. One can see that high temperatures or long annealing times are necessary for lower compressive stresses to decrease as rapidly as high compressive stresses, which are already close to the flow limit.
Because of this, it can be concluded that, at operating temperatures, high compressive residual stresses of the type typical in shot-peened blade roots will be rapidly broken down. However, this decrease will slow down and after a certain period of time will stabilize sufficiently to make it possible for the part to not require subsequent peening during the long overhaul intervals that are common today.

Figure "Processes to build up desired resiudual stresses": The residual stress reduction during stress relief annealing usually does not occur in a fast process, such as during a hot tensile test, but through creep. This process is called relaxation.
Relaxation occurs in closed systems such as structures with residual strain due to strain restrictions. Every homogeneous part such as a turbine blade or disk can be viewed as a closed system in this context. Relaxation can also occur in closed systems that consist of several individual components that are fastened to one another. These can be shrink-fit connections or joined heat-treatment equipment to minimize part deformation. The term relaxation is also used for describing the decrease
in a threaded connection at high temperatures over longer periods with loads below the flow limit (short-time value; Ref. 16.2.2.4-10).
The top left diagram explains the relaxation process with the aid of a turbine guide vane. It assumes that when the blade was cast and solidified, powerful tensile stresses with plastic strain occurred in the more rapidly cooling edges. After cooling, compressive residual stresses remain in the edges. These are in equilibrium with the tensile residual stresses in the thicker, slowly cooling blade cross-section.
If plastic deformation then occurs when the cast part is annealed, it reduces the elastic strain, and the inner stress breaks down (Fig. "Annealing time effect on residual stress level"). The creep strain slows accordingly (bottom left diagram). Therefore, unlike a creep test (right diagram), there is no constant stress that would result in increasing creep strain.

Figure "Relaxation": In order to ensure the design-specific operating behavior of a part, the influence of residual stresses must be controlled. This can be done in several ways:

• Limiting or reducing unwanted (usually tensile) residual stresses: This usually involves heat treatments, i.e. stress relief annealing (Fig. "Processes to build up desired resiudual stresses", middle right diagram).
  

• Limiting the buildup of residual stresses during the finishing process: Testing and optimization can be used to optimize a finishing process with regard to the resulting residual stresses. Examples include machining processes and coatings (e.g. thermal spraying, electroplating). In order to ensure the reproducibility of this residual stress state, all relevant process parameters must naturally be specified and strictly observed.
  

• Induction of defined desired (compressive) residual stresses with the aid of suface hardening processes such as shot peening, drift, or rolling).
  

Another possibility is to use overstress from external forces. If a part zone is plastically deformed (stretched, etc.), compressive residual stresses will be created in this zone after the force is removed (top diagrams). This effect is used to induce compressive residual stresses in the hub area of disks through overspeed (Ill. 16.2.2.4-6).
Cold straightening uses the same principle. Plastic bending is used to induce or overlay residual stresses with the aid of local plastic deformation. In this case, the spring-back effect occurs (Ill. 16.2.2.4-5.10).
With the aid of thermal stresses (middle left diagram), residual stress conditions can be suitably changed for straightening. This involves large temperature gradients with plastic deformations in areas of restricted strain. Typical examples are local hot spots on a metal sheet.
In the bottom left diagram, asymmetrical residual stress distribution has caused deformation, in this example through one-sided fastening or one-sided coating of a thin, flat part zone. This type of warping can be avoided if the treatment is done symmetrically (bottom right diagram).

Figure "Design to prevent damages by residual stresses": The design engineer can decisively extend the life span of a part through targeted design. This especially applies to large temperature gradients and accordingly high thermal stresses, which can be seen as residual stresses. Typical examples are charging racks used to insert parts into a heat treatment oven. Experience has shown that the many thermal cycles lead to life-shortening warping and cracking in the base of charging racks. The more solidly these are designed (left diagram), the more intensive the residual stresses and cracking.
In contrast, filigreed elastic structures (right diagram) show considerably better behavior. Their thin cross-sections heat and cool quickly with no damaging thermal gradients. In addition, their elasticity allows them to elastically accept thermal stresses. This means that residual stresses cannot build up in a damaging way. The non-continuous structure gives the oven atmosphere and radiation access to the parts. This allows them to heat sufficiently evenly. In addition, symmetrical configuration of the structure prevents one-sided warping that could also influence the parts being carried.

Figure "Minimizing residual stresses by form-fitted parts": Problematic residual stresses can occur even in closed connected systems such as pipelines. The residual stresses lower the usable dynamic fatigue strength. Typical causes of this are:

• Warping due to problems with measurements and/or assembly: These can overlay with residual stresses from straightening processes during finishing and/or assembly.
  

• Warping under operating loads such as thermal strain and operating pressure in the pipe.
  

Residual stresses from operating loads and warping can be minimized through suitable elasticity of the pipe. Typical measures are flexible boots (left diagram) or offsets.

Figure "Change of residual stresses during heat treatment" (Refs. 16.2.2.4-3 and 16.2.2.4-11): Stress reducng annealing begins with heating, followed by a holding time, and then cooling. Stresses from heating can break down through relaxation during the holding time (Fig. "Processes to build up desired resiudual stresses"). However, excessively rapid cooling presents a danger of new residual stresses being created. The heat dissipation through the surface and from the inside of the cross-section results in a maximum temperature difference at a certain time (top diagram). If the thermal stresses (middle diagram) at this point exceed the thermal yield point (= high-temperature limit of elasticity), it will result in plastic deformations (bottom left diagram). The relatively thin edge zone in the depicted case was plastically stretched. During cooling, the stresses were reversed. The compressed core experiences tensile residual stresses that are in equilibrium with the compressive stresses in the previously stretched edge zone (bottom right diagram). The stress levels will be higher after cooling, because the modulus of elasticity increases as temperatures drop.

Figure "Measuring residual stresses and its interpretation" (Ref. 16.2.2.4-2): The effect of residual stresses on the operating behavior of parts, whether it is positive or negative, is extremely important. It means that the residual stresses must be specified in order to ensure the desired part behavior. This process can be applied in the following instances:

• Monitoring finishing processes
• Optimizing finishing processes and repairs
• Quality assurance
• Understanding part behavior
• Selecting processes, materials, coatings, etc.
• Risk estimates
• Damage investigation

Practically applicable measuring methods are:

X-ray diffraction analysis: This utilizes the diffraction of X-rays, which allows conclusions regarding the inter-atomic distance in the metal lattice. The lattice spacing is influenced by mechanical stresses and determined using a goniometer. Tensile stresses spread the lattice, while compressive stresses press it together. Unfortunately, this non-destructive method can only determine stresses in a surface layer with a depth of 0.1 mm. If the stress pattern is to be determined over a greater depth, material must be removed and measured layer by layer. The minimal measuring depth makes the results difficult to interpret. Usually, in a machined surface, plastic deformation can be expected. This means that residual stresses equal to the flow limit can be expected (Ills. 16.2.2.4-5.1 and 16.2.2.4-23). Often, the measurement results will contribute to confusion regarding the operating behavior and consequences.

Hole bore method (top diagram): This analysis requires a small (0.8-1.5 mm diameter) bore. Therefore, it cannot be described as non-destructive when used on parts with final contours. Usually, a diamond “dentist drill” is used for this process. It is important that the boring process does not create falsifying residual stresses. This requires a careful approach with minimal heat development. For this, the drill works similar to a cutter and carves out the bore walls and base in an orbital movement. When using a spiral drill, undesired hardening and residual stresses at the drill tip must be expected. As material is removed, the bore changes the equilibrium of the residual stresses in the surrounding surface area, resulting in stress shifts with measurable strain. This is measured using special strain gauges. It takes about one hour to obtain a measurement value. While the drill penetrates, the measurement data are analyzed step-by-step by a computer program. This provides depth-specific information regarding the stress distribution.

Almen intensity: This is an indirect measurement process. The “beam intensity” is determined by the warping (bending, Fig. "Blasting (Almen) intensity") of a metal plate (almen strip, bottom left diagram) that is shot-peened on one side (Refs. 16.2.2.4-12 and 16.2.2.4-13). The plate material is a low-alloy steel and not the same as that of the part in question. The beam intensity is related to the residual stress levels.
This process makes it possible to document the desired peening effect during the peening process by simultaneously peening an almen plate that is affixed in a suitable, i.e. relevant, position on the part.
Fig. "Measuring in situ residual stresses in galvanic coatings" shows a measuring method for residual stresses in galvanically and chemically deposited coatings.

Figure "Measuring in situ residual stresses in galvanic coatings": Electroplated coatings made from chrome and nickel are especially prone to high tensile residual stresses (Fig. "Influence of Cr and Ni coatings at fatigue strength"). They lower the dynamic fatigue strength of the parts considerably. From the point of view of residual stresses, the coating processes can be optimized with the aid of measuring procedures. These usually operate on the basis of the principle that a (thin) elastic cross-section that is coated on one side will deform due to the residual stresses of the coating. This deformation (bending, torsion) is mechanically measured. Therefore, this is not measurement on the part, but an indirect process for optimizing the coating process.
Direct measurements on the part are possible after the coating process with the aid of the methods described in Fig. "Measuring residual stresses and its interpretation", i.e. X-ray diffraction analysis and hole boring.

Figure "Increasing fatigue strength by hardening": Plastic deformation can be used to induce compressive residual stresses and hardening in surfaces (Fig. "Hardness and dynamic fatigue strength by plastic deformation"). Both effects increase dynamic fatigue strength. The hardening effect is based on disturbances in the atomic lattice (dislocations) that occur along with plastic deformation (top left diagram). These disturbances hinder sliding planes along which plastic deformation occurs. This leads to an increase in the flow limit (strain hardening) and a reduction in toughness. This effect is easy to observe in incremental tensile stress tests (top right diagram). The diagram shows the pattern of the “true” stress/strain curves. It takes into account the constriction during the tensile test, which is not usually done. The interaction of compressive residual stresses and strain hardening is shown in the bottom right diagram (Ref. 16.2.2.4-18).

The positive influence on the dynamic fatigue strength decreases along with decreasing strength in materials with pronounced hardening, while the influence of the residual stresses increases. Materials such as titanium alloys, which do not strain-harden significantly, understandably benefit from compressive residual stresses induced by targeted surface deformation (e.g. shot peening).
The verification of strain hardening is done through micro-strength measurement. This can also determine the strength pattern vertical to the surface (bottom left diagram).

Figure "Hardness and dynamic fatigue strength by plastic deformation": Plastic deformation strengthens materials (Fig. "Increasing fatigue strength by hardening"). Both plastic compression (under pressure) and plastic stretching (under tension) have strengthening effects. The strengthening can be seen in a hardness increase that is linearly related to an increase in dynamic fatigue strength (Ref. 16.2.2.4-19). This means that the strengthening is different from the influence of residual stresses. If the residual stress influence is dominant, then compressive residual stresses will increase the usable dynamic fatigue strength, while tensile residual stresses will reduce it.