Figure "Unstable crack mechanism": The material offers resistance to crack growth. This manifests itself as energy consumption. In addition, as the part elastically opens, it stores potential energy like a spring. If the crack grows further (“1”, crack growth), stored elastic energy is released (“3”). During stable crack growth, less energy is released than is required for crack growth, and energy must be introduced from outside. If the crack reaches a certain critical length, it releases more stored potential energy in the part (“4”) than is necessary for crack growth. This accelerates the crack growth (“2”). This is called unstable crack growth, or overload fracture.

Figure "Factors causing a forced feracture": If the loads exceed the breaking strength in a cross-section, the result is an overload fracture. In cross-sections that were not already cracked, it means that the nominal stress was greater than the material strength. If a crack was present, then the overload conditions can be better explained using fracture mechanical values. The deciding factor is that the stress intensity at the tip of a crack with a critical length a_c exceeds the fracture toughness of the material (Fig. "Characteristic crack growth").

Overload fractures due to excessive stress levels: These are consequential damages resulting from loads that exceed design specifications (left column). These loads include overspeed, explosions, containment, and foreign object damage. One should remember that the material behavior itself is affected by the load. One example of this is embrittlement (bottom left diagram) under high deformation speeds during containment incidents (Fig. "Influences on fracture toughness"). When estimating fracture-causing loads, the data being used must sufficiently consider the material behavior at operating temperatures. In this respect, increasing temperatures will not always result in a higher degree of ductility. For example, Ni alloys can behave brittly at very high temperatures (Fig. "Temperature influence on material properties"). The state of the structure is also important. Single-crystal materials can react considerably differently to impact stress than directionally solidified or normally solidified structures.

Overload fractures due to decreased strength: The right column shows the possibilities of dangerous strength losses. These include, for example, consequential damage due to operating parameters that do not conform to the designed values (e.g. during overheating). However, in most cases a residual overload fracture will occur, resulting from an already present crack of critical length (Fig. "Stable and unstable crack growth"). Similar conditions are present with crack-like material flaws. Damages such as sharp notches (FOD, etc.) can increase the stress intensity (Fig. "Influences at crack tip behavior"), until unstable crack growth is incited. Further important changes to material properties include embrittlement due to structural changes (formation of brittle phases), corrosion (stress corrosion cracking, Fig. "Influences on fracture toughness") and gas absorption (such as during hydrogen embrittlement; Volume 1, Chapter 5.4.4).

Figure "Stable and unstable crack growth": A residual (overload) fracture is always preceded by stable crack growth (Figs. "Phases of fatigue fracture" and "Characteristic crack growth").
Stable crack growth is characterized by a need for energy from an outside source in order to grow. Reducing the loads can slow and even stop this type of crack. Stable crack growth occurs in such typical crack types as dynamic cracks (LCF and HCF, left diagram), creep cracks, and corrosion cracks.

Unstable crack growth can not be controlled or stopped, and therefore leads to fracture of the part. In thin cross-sections, the unstable crack occurs with macro-plastic deformations and the formation of shear planes (middle diagram, Fig. "Forced fracture behavior by section thickness"). If the external loads can be decreased sufficiently quickly, or if the stiffness of the system is high enough, even this type of crack can be caught in time. However, this is not usually possible in practice. Sufficiently thick cross-sections lead to macro-brittle crack growth (right diagram). However, SEMs can be used to detect micro-tough fracture characteristics. In this case, the critical fracture toughness (K_Ic) typical for the material and loads is exceeded by the acting stress intensity. If the elastic energy stored in the part (e.g. due to centrifugal force, etc.) is great enough that, above a critical crack length a_c , the energy released during crack growth is sufficient to cause the crack to grow further, then the part will certainly fracture.

Figure "Forced fracture behavior by section thickness" (Ref. 12.3-1): The fracture cross-section and the material toughness influence the type of crack that occurs (Fig. "Understanding fracture processes") and therefore also the type and appearance of the residual overload fracture (top diagrams, Ref. 12.3-2).
Shear fractures (tough fractures), i.e. fractures with shear components, occur with wedge-like deformations (bottom middle diagram) due to large plastic zones (“1” and “2”). The thinner the fracture cross-section (bottom left diagram “1” and “2”) and/or the tougher the material, the greater the shear plane component (tough fracture in top right diagram). In the plastic zones, there is an even stress distribution (Fig. "Influences at crack tip behavior"). Because of the shear components, the fractures have greater fracture toughness (“K_I”, Fig. "Influence of conditions at the crack tip") than the material-specific lowest fracture toughness (critical fracture toughness K_IC), of a purely brittle fracture (“3”).

Macroscopically brittle cleavage fractures (“3”) form under hinge-like deformations (bottom right diagram). No significant plastic deformations occur in the surface area. Prerequisites are a sufficiently large fracture cross-section (bottom left diagram “3”) and/or brittle material. This means that even strain levels are present at the crack tip across the entire cross-section. Even cleavage fractures in ductile material exhibit micro-toughness that can be seen with an SEM. Cleavage fractures have the lowest fracture toughness. The corresponding critical fracture toughness is denoted by K_Ic in crack opening type I, for example. If crack growth-promoting corrosion occurs, it becomes K_ISCC (stress corrosion cracking, Volume 1, Chapter 5.4.2). This type of influence further reduces the critical fracture toughness (Fig. "Influences on fracture toughness").
The cross-section-dependent fracture behavior can cause damage to have widely differing fracture symptoms, even if the material is in accordance with specifications. Effects such as the embrittling effect of high deformation speeds (Volume 2, Ill. 8.1-13), can occur under impact stress.
When attempting to use a fracture-mechanical estimate to draw conclusions about the damage process (e.g. critical crack length, loads that caused the residual fracture, etc.), the representative fracture toughness of the affected cross-section and operating conditions must be used.

Figure "Crack opening displacement" (Ref. 12.3-3): If there is heavy local flow at the crack tip, then the linear elastic fracture mechanics (zones “O” and “A”) and the critical threshold values of the fracture toughness (K_Ic ) are no longer valid (Fig. "Characteristic crack growth"). The measurement category is the displacement of the crack sides, as determined through the use of notched samples with fatigue cracks (Fig. "Stable and unstable crack growth", detail in diagram). The resulting specific value is the critical crack opening displacement (COD). The COD concept should also be valid for the elastic-plastic behavior. Therefore, it can still be used in cases such as thin sample cross-sections that fail in the range between “A” and “B”. From “B” to “C”, the “conservative” procedure of calculation and design applies. In this case, the instability is due to unallowably large plastic deformations.

Figure "Influences on fracture toughness": The critical fracture toughness (K_Ic) is influenced by many parameters. These can occur separately or in combination, and therefore reinforce each other. This must be considered especially when conducting risk assessments, because overestimating the fracture toughness results in critical crack lengths that are too long. This can cause the “safe” inspection intervals to be too long.

Influence of temperature: If temperatures cause embrittlement of a material (low temperatures in steels, bottom diagram; high temperatures in Ni-base alloys, e.g. ductility minimum at temperatures near 600 °C, long-term development of brittle phases, or reaching of the solidus temperature), the fracture toughness is decreased. If corrosion also occurs, then even minor temperature increases in the surrounding area can have a pronounced effect on K_ISCC . Like the impact toughness, the fracture toughness of steels increases sharply with rising temperatures. However, the sharp increase in fracture toughness occurs at considerably lower temperatures than the increase in impact toughness. This means that the fracture toughness is less sensitive to temperature levels. This characteristic should be remembered when making decisions regarding low-temperature operation limits.

Corrosion influence: Stress corrosion cracking can reduce the threshold for stable crack growth considerably (top right diagram). This is very important for determining tolerable flaw sizes. If the influence of corrosion during operation was not taken into account when the data were calculated, overly large flaws may be defined as “tolerable”. If the critical crack length “a_c” is reached, the instability occurs at K_Ic . Because there are corrosion processes that act through embrittlement of the crack tip (e.g. hydrogen absorption; Volume 1, Chapter 5.4.4), it can be assumed that K_Ic also decreases under the influence of corrosion.

Specimen thickness: Up to a certain material-specific cross-section thickness (middle left diagram), the critical fracture toughness decreases (Figs. "Stable and unstable crack growth" and "Forced fracture behavior by section thickness"). With the critical fracture toughness K_Ic , estimates of tolerable crack lengths and/or remaining part life of thin cross-sections will be on the safe side. However, it is dangerous to estimate the residual fracture behavior if the only available data were taken from even thinner cross-sections.

Elastic limit: In general, the critical fracture toughness increases out of proportion to the elastic limit of a material. This is especially important because high-strength materials are also highly stressed, resulting in high stress intensity in the case of cracking. In this case, the relatively low fracture toughness can quickly be exceeded, resulting in a fracture. For especially hard material types, the tolerable flaw size and the increased risk in case of damage (scratches, etc.) must be analyzed especially carefully. The affected value is the life span of stable crack growth until the relatively short critical crack length is reached. It may be safer to use a material type that is less strong.

Load rate: The load rate during impacts (FOD, containment; Volume 2, Chapter 8.1) and pressure waves (dust explosion, Volume 2, Chapter 9.4; surge shocks) is very high. This can result in a reduction of the critical fracture toughness (top left diagram). Design and verification of engine parts for this type of load must take into account any special sensitivities of the materials.

Figure "Estimating risks with fracture mechanics": As the following example shows, fracture mechanics is an important tool for minimizing risks in this ongoing case. This diagram shows an early case in which electron beam welding was used. The affected part is the turbine rotor of a small engine (top diagram). The Ni-based, cast-alloy turbine disk of the first stage was to be connected to the compressor by the hollow shaft (middle diagram). Evidently, this was not possible without pronounced axial hot cracks developing in the weld seam. In order to prevent delays in engine development, it was necessary to conduct longer cyclical test runs (RPM, thermal) with cracked parts.
A flat sample (bottom diagram) was prepared with a “blind weld point”, which corresponded to the weld seam width on the engine part. The sample inevitably developed cracks that were comparable to those in the engine part (bottom detail). The sample was sufficiently thick, and the low ductility of the material made it possible to determine the critical fracture toughness K_Ic for typical weld cracks. It was thus possible to estimate the critical crack length under the known maximum operating loads on the engine part that were relevant to crack development. With the aid of crack growth data gained from similar tests on engine parts, it was possible to calculate a remaining life span that was sufficiently safe for the part tests. This was then reinforced by sufficiently long inspection intervals.

Figure "Strength of ceramics": The fracture toughness of brittle materials depends largely on on the stressed volume (in the case of volume flaws) and/or the stressed surface area (in the case of surface flaws; see Chapter 14.2). This behavior must be especially considered with new materials such as ceramics and intermetallic phases (at low temperature), and also with less ductile cast materials. This is because the probability of a growth-capable flaw or a flaw with critical size (spontaneous failure) developing increases with its volume/surface area size. This relationship is described by the Weibull modulus (m), i.e. the slope of the line in the Weibull probability diagram (also see Volume 1, Ill. 4.5-14). The greater “m” is, the steeper the line and the smaller the scattering of the strength levels. “m” for the tensile strength of metal alloys used in engine construction is roughly 30 (bottom left diagram, Ref. 12.3-4). In high-strength ceramics (carbides, nitrides), “m” is about 10. This means that the fracture toughness of the turbine disk of a small gas turbine, which was determined with the aid of the usual small three-point bending samples, is reduced considerably (top right diagram). In the hub area, the stressed volume of the disk is about 1000 times greater than that in the samples. This means that the usable strength in the part is about 60% lower (example in bottom right bar diagram). If this is not taken into account during design, then spontaneous failures can be expected even at low RPM. In ductile materials with a similar sample geometry for strength verification, the loss of strength due to the influence of the difference in volume is only about 20%.

Figure "Fracture behavior of britte materials" (Ref. 12.3-5): In brittle materials, overstress due to impact loads sometimes results in unexpected effects.
If an impact load strikes the front side of a prismatic rod (top diagram), then a pulse (in this case, a triangular pulse) travels through the rod at the material-specific sonic speed. The pulse is reflected at the opposite side of the rod, which converts the compressive stress to tensile stress. If the tensile stress exceeds the fracture strength of the rod, the end of the rod breaks off at this location due to an overload fracture. This effect is known in military technology from firing at armor (bottom diagram). It can also occur in containment situations, when high-energy fragments moving at high speed strike a housing made of sensitive materials.

Figure "Applications of fracture mechanics": Fracture mechanics has proven itself in many important applications. One special use is the prevention of residual overload fractures and crack initiation within the framework of problems in serial operation. Fracture mechanics finally made possible analytically verifiable procedures to analyze the effect of cracks on the residual part strength and to estimate remaining part life. This can be used, in combination with data from analyzed damage cases, to determine sufficiently safe inspection intervals.
The high strength levels of the materials used in engine construction, which are usually pushed close to their limits, demand a corresponding reduction of the (effective) sizes of weaknesses caused by production and operation. Fracture mechanics can be used to determine the threshold values for specifications. These threshold values define the requirements for non-destructive testing or procedure-specific safeguards (such as multiple remelting procedures).
Fracture surfaces (spacing between crack growth lines) and knowledge of the material-specific crack growth behavior (Paris-diagram, Fig. "Characteristic crack growth") can be used to estimate the loads over the crack growth process. The crack growth lines (Fig. "Development of fracture surface features") can also reveal information regarding the temporal progress of the dynamic loads, which can in turn indicate damage-causing operating conditions (stall, resonance, etc.).
In the case of production/finishing flaws (cracking, local strength losses, porosity, etc.), it is possible to make decisions about the extent and type of reworking. This is also true for reparable damages within the framework of an overhaul, and determining the limits for reparable damage for inclusion in overhaul manuals.