Titanium alloys have been used in engines since the 1950`s due to their outstanding mechanical properties, such as high specific (heat-) strength (ratio of strength to specific weight), good ductility, and acceptable stiffness (Fig. "Metal fires at titanium parts"). The more flight speeds increased, the higher the percentage of titanium in the aircraft became (Fig. "Metal fires at titanium parts"). Along with the use of titanium materials in aircraft engines came an awareness of titanium fires. These involve the ignition and rapid, partly explosive burning of massive titanium cross-sections with the outward appearance of an intensive fire (flames, sparks, bright white light, large amounts of heat). This kind of fire can destroy the surrounding structural parts, even those not made of titanium, e.g. Ni alloys (chapter 9.1.2). The burning of titanium is not a diffusion reaction of oxygen with the metal surface, but a reaction in which not only the solid, but also the liquid and gaseous states are involved (Ref. 9.1-3, ). In order to ignite a titanium alloy, an intense oxygen supply must be present and the metal temperature must reach about 1600°C (in standard atmosphere; ). For the burning to occur, a sufficient air pressure and/or a sufficient air flow speed with suitable flow conditions at the point of ignition/burning is necessary. For this reason, the duration of a titanium fire does not usually exceed a few seconds (chapter 9.1.2). The rapid spreading of a titanium fire in the direction of air flow can be explained by the impact of burning drops of Ti from the rubbing or burning structural parts ( ). This short period of time is until the compressor blading is damaged to the point that the flow conditions cannot sustain the fire. A titanium fire reaches burning temperatures of about 3300°C. Extensive consequential damages to the components located behind the point of ignition in the direction of the flow (blades, housings) can be expected (chapter 9.1.2). Therefore, it is important to contain a titanium fire inside the engine, even if sufficient safety measures suitable for prevention cannot be taken (chapter 9.1.3).
Figure "Metal fires at titanium parts" (Ref. 9.1.1-4): The top diagram shows the engine weight reduction due to the use of titanium alloys until 1970. Primarily, this involves replacing steels that, at the same strength, have twice the specific weight. In this way, rotor weight was reduced by about 52%. Relative to the entire engine, weight reduction in large engines was over 20%, or nearly double that in small engines (about 12%). This can be explained by the use of titanium alloys in the fan region. The large fan of an engine with a high bypass ratio is a large portion of the total engine weight. The recent increases in the use of fibre-reinforced synthetics in the fan region should result in a reduction of the proportion of titanium in the long term. However, this may increase the risk of dust explosions (chapter 9.3).
Evidently, the weight reduction in supersonic aircraft (tactical aircraft) becomes less and less. This is probably due to the high operating temperatures. The maximum continuous operating temperature of titanium alloys is roughly 500 °C due to the drop in creep resistance and surface oxidation. This necessitates the increased implementation of more heat resistant Ni-based alloys.
The bottom diagram shows the typical titanium structural parts in a large commercial turbofan engine with a high bypass ratio. In the engines of tactical aircraft, the bypass housings are made of titanium alloys, as well.
A further boost in the use of titanium alloys can be expected when burn resistant (e.g. “Alloy C”, chapter 9.3), especially heat and oxidation resistant, alloys (inter-metallic phases - IP) with sufficient mechanical specific values (e.g. acceptable toughness) become available for serial use. When this happens, their use could extend even to the blading of the low pressure turbine, for example.
Figure "Causes of titanium fires" (Ref. 9.1.1-4): This diagram shows the causes of known titanium fires from 1957-1979.
Ignition was primarily caused by two effects:
It is possible, that torching flames escaping from the combustion chambers of tactical aircraft at high speeds could ignite titanium fires (e.g. in the bypass housing). To date, however, such cases are not known.
The high number of unknown causes of titanium fires is astounding. This might be due less to the causes not being isolated than to their not being made public.
Experience also shows that titanium fires are often caused by a blade failure, but this cannot be conclusively shown due to the extensive consequential damages (e.g. surface damage examinations).
Turbine damage: One can only speculate about the relationship between causal turbine damages and titanium fires. Imbalances after turbine damage could be a cause. On the other hand, it can be argued that the turbine damages were a result of a titanium fire rather than its cause.
Testing rig damage: It is not clear, whether peculiarities of the testing rigs lead to titanium fires or simply if a high number of titanium fires were observed on testing rigs. This would be understandable in engines in development.
Bird strikes: The intake of a bird can result in blade failure and/or bearing damage and thus ignite a titanium fire. Surprisingly, this seems to occur fairly frequently.
Experientially, compressor blade failure is the largest cause of titanium fires. This seems to be confirmed by the proportion of rotor blade failures. Oddly, the proportion of guide vane failures is relatively low. It can be assumed, that this is connected with the specific weak points of the engine types being evaluated. In other engine types, the guide vanes seem to be more likely to cause a fire.
Rotor damage: This must refer to damages to the rotor drum, i.e. the discs and intermediate rings. Causes might be rubbing occurrences due to rotor imbalances (e.g. due to rotor bow) or oscillation deflection.
Bearing damage: Main bearing damage leads to extreme axial and/or radial rotor offset and thus rubbing occurrences with danger of ignition.
Stalls as a cause of titanium fires: A stall in the compressor can dynamically overstress the blading and result in fatigue fractures and/or axially and radially offset the rotor and blading in such a way that it results in powerful rubbing occurrences and/or contact between the rotor and housing or stators. A further source of heating-up are the agitation losses following the interruption of flow after a stall. This heating-up due to air friction can bring the thin edges of the blading to ignition temperatures in a fraction of a second. On the other hand, an ignition due to a pressure or shock wave is unlikely. This could be expected in pure oxygen. It is more likely that an oil fire may break out in the storage chamber region.
FOD, OOD: Objects from inside and outside of the engine can directly initiate heavy rubbing occurrences by causing blades to fail and the fragment becoming jammed, but also by notching the blade and promoting fatigue fractures that result in a fire.
Air seals: Intermediate stage labyrinths (Fig. "Damage mechanisms of titanium fire ignition" and 9.1.2-7) or labyrinths made from titanium alloys (even in the low pressure turbine) subjected to serious rubbing occurrences with sufficient pressure gradients and bleed air flow (Fig. "Titanium fire ignition in labyrinths") can ignite and cause extensive fire damage.
Figure "Ignition of titanium fires" (Ref. 9.1.1-4 and Ref. 9.1.1-5): The top diagram shows a model of the “heat household” in the intake edge region of a compressor blade during a titanium fire as described by Glickstein in 1974. The flow of the titanium melt over the leaf surface is especially important. This effect was observed in trials in a high-speed wind tunnel. In the calculations, the mathematical model is based on the shown physical “burn model”. Among the variables considered were:
This “burn model” should be capable of estimating the probability of an ignition (see Ills. 9.1.1-4 to 9.1.1-7) due to various causes, such as
It is assumed, that liquid metal forms at the leading edge, of which some is carried away, and the rest dispersed across the surface by the air flow. The melt that resolidifies transfers its heat to the solid base material. This heat, together with the heat from the external heat source, acts as the stimulus of the burning process. If this is self-sustaining, then the burning speed is dependent on the energy balance between that lost to the surrounding regions through radiation and convection and that taken in.
The bottom diagram shows the influence the angle of a blade`s leading edge has on the spreading of a titanium fire. This influence is especially important because the outbreak of a titanium fire (see Fig. "Causes of titanium fires") is often accompanied by a deformation of the blading (e.g. after FOD) and/or flow interference, i.e. a change in the angle of flow.
In trials, the leading edge of a blade was ignited by a laser, so that the angle of flow was not changed by the ignition process. It was discovered that:
At hitchless angles of flow (a=0°), only a narrow burn area in the direction of flow is created (bottom left diagram). Even at a slightly off-center angle of flow (a=10°), the burn runs radially across the angle of flow (bottom right sketch), thus resulting in a considerably wider burn area. The larger angle of flow results in a loss of flow on the suction side and a steeper angle of impact of the flow on the pressure side. This influences a few different effects:
It is assumed that the difference in size and shape of a burned leaf region is related to the separation of the boundary layer on the suction side of the leaf.
Figure "Ignition of a Ti-fire y burning metal": It can be concluded from trials ( ) and experience (chapter 9.1.2) that creation of drops and sparks plays a critical role in the ignition of titanium fires.
This can be better understood through use of the model of drop-induced surface damage (Ref. 9.1.1-6). Titanium drops burn intensively during their flight in the air flow, which creates enough heat to bring the drop's temperature to over 1700°C. This prevents solidification and locally heats surface areas it comes into contact with up to the ignition temperature of about 1500°C. If this type of liquid drop strikes a metal surface with the high speeds of the air flow and the moving compressor parts, the protective oxide film (e.g. in Ti and Ni alloys) is mechanically and chemically destroyed. Even a water drop (drop strike) can plastically deform titanium surfaces. The pressure building at the contact surface (water hammer pressure) is proportional to the density of the drop material, the sonic speed in the drop, and the impact speed. The considerably higher density and sonic speed in titanium drops result in respectively heavier surface damage. This will result in the shattering and/or the erosion of the oxides, promoting the dissolving of the oxides into the melt, as is typical for titanium melts (Fig. "Requirements for ignition and burning"). New metal surfaces are created at both the drop and the base material, and these are penetrated by the aggressive titanium melt. This is followed by an initial fusing of the surface and an increase of the volume of burning titanium.
This plausibly explains the rapid spread of a Ti fire in the direction of the gas flow.
Figure "Ignition of titanium fires by rubbing": Trials in a “rubbing rig” (Fig. "Titanium fire ignition test"), in which a package of four 0.8 mm thick titanium sheets (spaced about 0.5 mm) was pressed against a rotating disc with a rubbing speed of roughly 300 m/s (top diagram), yielded unexpected results relevant to ignition:
In order to simulate the rubbing of blade tips against a housing or rotor (bottom left diagram), the sheet package was pressed against the disc at a speed of about 1 mm/s. The first sheet in the gas flow (“1”) simply formed burrs, whereas the three following sheets ignited and melted increasingly in the direction of the flow while burning. Astonishingly, the first sheet did not ignite, even though it was directly in the flow and thus must have had the largest oxygen supply. One explanation may be, that the air (ca. 400°C) could have cooled the sheet below the ignition temperature. The “lee” sheets, on the other hand, ignited. It is possible that the heated-up air flow and melts it carried could have promoted the burning of the following sheets. The increase of burning in the following sheets could also be explained by their early ignition.
The extreme rubbing resulting from a large axial and/or radial rotor offset was simulated by a higher pressing speed (center diagram). It resulted in an almost simultaneous ignition of all sheets and extensive burning down.
Because the first result could also be interpreted in such a way that erosion and energy transfer from the abrasion cloud could have caused the following sheets to ignite, the third trial included a separate titanium sheet placed behind the package at an angle of attack that kept it from being involved in the rubbing. This sheet was ignited by the abrasion cloud after a short rubbing of the sheet package, and this fire was sustained (right diagram). The burn area was of the typical wedge-shape that is observed in compressors after limited titanium fires (Fig. "Primary and secondary damages of titanium fires").
Figure "Requirements for ignition and burning" (Ref. 9.1.1-4): If the boiling point of the oxides (TSP oxide, Ref. 9.1.1-7) is higher than that of the metal melt (TSP metal), it often (not always, e.g. not when too much heat is radiated and the flame temperature falls beneath TSP metal) results in a burning in the vapor phase of the metal (top left diagram). The oxide absorption of the drop is relatively small. This behaviour is typical for light metals with low melting points and high melting point oxides such as magnesium and aluminium. Thus the oxide layer should hinder the ignition and burning process.
If the boiling point of the oxides is below that of the metal, the flame temperature can only reach the melting point of the metal. Burning occurs at the surface of the melt with a relatively high oxide content at the surface as well as in the drop. Metals that burn at the surface of the melt include titanium, iron, and nickel alloys. Refractory melted oxides can absorb large amounts of heat and thus increase the heat content of the drop, i.e. the melt. This high heat content is a reason for the transmission of the fire to other structural parts (see Fig. "Ignition of titanium fires by rubbing"). The burning temperature of metals usually reaches more than 3000°K, and those of light metals such as aluminium and magnesium lie higher than those of even iron, nickel, and titanium. Therefore, in alloys based on these metals, a significant hindering of burning through oxides cannot be expected.
A localized explosive burning is typical for titanium. This happens when the oxide reaction occurs so quickly, that the dissipation of the amount of created heat is no longer possible. The metal then superficially fuses at the surface, thus enabling the dissolving of the protective oxide film into the melt, so that the burning spreads.
Figure "Ignition mechanisms in metals" (Ref. 9.1.1-4 and 9.1.1-7): In air pressure of one bar, titanium ignites at about 1600 °C. However, there are many effects that can lower this ignition temperature (top diagram). These include processes that transfer energy and/or create highly reactive fresh metal surfaces:
The ignition temperature in thin cross-sections (0,5 mm) is lowered dramatically due to higher heating-up rates (over 40°C/s). With heating-up rates of 100°C/s ignition temperatures can drop to 300-400°C.
The bottom left diagram (trials in a helium-oxygen mixture and a vapour-oxygen mixture) shows that conditions necessary for ignition depended on the type of trial in which they were ascertained. Dynamic trials are those with a gas flow present, while static trials take place in a resting atmosphere. It is easy to see that ignition is promoted by dynamic trial conditions. It occurs with lower oxygen supplies and less gas pressure. The conditions necessary for sustaining burning are considerably less than the conditions for ignition..
The bottom right diagram shows the relationship between the ignition temperature and the oxygen supply. It is clear, that in engine conditions with normal surface oxidation of the structural parts, ignition starts between 900°C ( under high pressure in the rear compressor region) and 1500°C (in the front compressor region). If fresh surfaces are created during a damage sequence, the ignition temperature can be considerably lower (from 500°C).
Figure "Influence on metal ignition": The ignition and burn process is heavily influenced by physical factors such as heat conductivity, specific heat, heat of fusion, and melting point. This should answer the question, why titanium fires are common in engines, whereas magnesium fires (Example "Magnesium dust catching fire" and Example "Combustion of magnesium hub during rollout accident") are seldom reported. It obviously is not due to the frequency in which these two materials are used, especially in older engine types. In these, magnesium alloys were common; e.g. in the forward compressor housing. However, magnesium was not used in bladings.
The specific values of the following materials only apply approximately to the alloys typical in engines, since the literatures they were taken from pertain to the pure metals.
Heat conductivity: heat conductivity (top left diagram) provides the most plausible explanation for the special fire danger which titanium engine parts present (Ref. 9.1.1-8). The top left diagram compares the heat conductivity of typical material families used in engine construction. It can be seen that the heat conductivity of titanium alloys is almost a whole order of magnitude lower than that of comparatively more reactive light aluminium- and magnesium-based metals. This means that during rubbing, the heat cannot be dissipated quickly enough and the ignition temperature of 1500°C is reached (
Specific heat (Ref. 9.1.1-7, top right diagram): The different amounts of heat necessary to heat a certain amount of various metals to the same temperature are compared in the top right diagram. The larger this amount of heat is, the more heating-up energy is necessary. If one is concerned with structural parts of similar volumes, the volume-based specific heat is relevant. One can see here that iron- and nickel alloys are about 30% above titanium alloys.
Heat of fusion: the heat of fusion (center right diagram) is the amount of heat required to superficially fuse a certain amount of material. It is relevant, because the melt plays an important role in the burning process of a metal (Fig. "Requirements for ignition and burning"). The bottom right diagram shows that aluminium has a somewhat higher heat of fusion, whereas the other metals are roughly equal.
Melting point (bottom right diagram): Al- and Mg-alloys melt at roughly half the temperature (°C) at which Ti- (Fig. "Melting temperatures of Ti-oxides"), Fe- and Ni-alloys melt. Despite their relatively high heat of fusion, the light metals should reach their melting points quickly. However, the high-melting pronounced surface oxides hinder the contact with oxygen and the escape of the melt (Fig. "Requirements for ignition and burning").
Heating-up sensitivity: This term was coined in order to give the sensitivity of a metal to reaching ignition temperature through a local heat addition (e.g. due to rubbing) in a comparative (relative heating-up sensitivity) manner (center left diagram). Titanium was set at 100 %t. The heating-up sensitivity is derived from the reciprocal value of the product of the volume-based specific heat and the heat conductivity. Therefore, the lower the specific heat and the worse the heat conductivity, the faster the structural part is locally heated and reaches ignition temperature. It can be observed, that the heating-up sensitivity of titanium is several times that of the other metals. This makes the, compared with other metallic materials, frequent ignition of titanium fires in engines understandable.
Figure "Melting temperatures of Ti-alloys" (Ref. 9.1.1-4): The two-material phase diagram for titanium and nickel (top) shows a pronounced low-melting eutectic with a melting temperature below 1000°C (arrow). This property is particularly important to the extent of typical consequential damages from a titanium fire. The melting-through of the compressor housings can, for example, be promoted by a reaction of the titanium melt with the nickel/graphite abradables ( ).
Figure "Melting temperatures of Ti-oxides": The titanium-oxygen phase diagram (bottom) shows that oxygen stabilizes the condition of the a- structure. Titanium oxides have relatively low melting points (under 1800 °C). This is relevant for titanium`s behaviour when burning (Fig. "Requirements for ignition and burning"). Because the melting point does not rise due to oxide formation, the drops remain liquid for a long time. From 20% oxygen (by weight) on, the solid state is made up entirely of oxides. The high solubility of the oxygen in the melt (up to 35% by weight) promotes the burning process, because no protective oxide film is formed.
Figure "Titanium fire burn test" (Ref. 9.1.1-5): These picture sequences depict images taken with a high speed camera in chronological order. The titanium was ignited with laser ( ). The trial duration of only a few seconds corresponds to titanium fires in engines. This is confirmed by observations in damage cases, where the titanium fire went out in the same moment that the compressor blades were destroyed. This interrupted the air flow which provided the basic conditions for a titanium fire.
The top sequence shows an ignition at the leading edge in the middle of a leaf under conditions typical for guide vanes. At first, the fire spreads in direction of the flow (axially). Only when the leaf is completely burned through does the fire accelerate across the direction of flow (radially). One should take note of the trial conditions: relatively high air temperature (427 °C) and a pressure of 6.8 bar. These are the conditions in the rear compressor region.
The bottom sequence corresponds to conditions for a rotor blade in the forward compressor region. In this case, ignition took place at the blade tip. Here, as well, the fire spreads rapidly in the direction of flow. The accelerated burning across the direction of flow (radially) occurs from the start of the trial in this case. This cannot be explained by the flow speed, since it was virtually the same in both trials.
At low air pressure (about 1 bar), the burning rate was barely influenced by the air flow speed. At higher air pressures, however, a relationship with air flow speed was observed.
The diagram compares the burn rates of different titanium alloys typically used in engine construction. Evidently the aluminium content of an alloy hinders burning. The intermetallic phase “TiAl” is considered unburnable and thus has no burn rate (Fig. "Titanium alloys preventing titanium fire").
Figure "Titanium fires risk of flight mission" (Ref. 9.1.1-4 and 9.1.1-5): There are several approaches that can be taken when diagramming the boundary conditions for ignition and sustained burning of titanium alloys, i.e. the boundary conditions for a titanium fire in a compressor (top left diagram). The static temperature of the flow is applied to the axis of ordinate. The fire`s strong dependence on flow conditions around the blade profile is applied to the axis of abscissae in Reynold`s numbers (Re). The Reynold`s number is the product of the speed of the uninfluenced flow and a “typical length” for the flow instance divided by the kinematic viscosity of the air. The kinematic viscosity is dynamic viscosity relative to the air density and is thus dependant on air temperature. In this case it refers to the stage entry. The problem most often experienced is with the “typical length”. It is commonly assumed to be double the radius of the leading edge (leading edge diameter). The diagram is divided by a curve, under which an ignited titanium fire is extinguished or not ignited at all, above which sustained burning can be expected after an ignition.
Damage events in engines (bottom left diagram) have clearly shown, however, that fires also occur below the limits published by Glickstein, Pyne, or the CAA. Points marked with “R” signify cases, in which rotor blades were ignited. “S” signifies the ignition of a stator blade (bottom right diagram). The light grey area covers modern tactical aircraft engines in serial use. The dark grey area covers older model tactical aircraft engines.
The following can be used to explain the observed discrepancy between damage events in engines and trial conditions with relation to the “burn limit”: Titanium fires are usually secondary damages and require igniting. For this, extreme local heating-up of a structural part in the air flow is necessary. To cause this, a primary damage sequence that causes heating-up must have occurred (e.g. blade failure, foreign object damage) This primary damage leads to mechanical damaging (FOD, OOD) of the blading (top right diagram). This can alter the geometry of the leading edge decisively (e.g. burrs, sharp edges, shear planes across the flow direction, see detail description). Deformation of a blade leaf due to torsion and/or deflection also changes the flow of the profile, which makes the leading edge radius of the undamaged blade no longer relevant to the ignition of a fire. Instead, a dispersion of the Reynold`s number corresponding to the damage-induced radii must be assumed.
Figure "Titanium fire ignition in labyrinths": Titanium fires can ignite due to rubbing and be sustained by strong leaking air flow even in the region of titanium alloy labyrinth rings. In order to estimate the ignition tendency of a labyrinth, as well, the question of the typical length characteristic of the flow recurs. In the ignition diagram above (compare Fig. "Titanium fires risk of flight mission") two different flow-characteristic lengths (tip width “b” or hydraulic diameter “2s” of the tip crack) result in very different Reynold`s numbers, i.e. ignition zones.
Figure "Titanium fire ignition test": These trials are very useful for understanding the ignition of titanium fires in engines (Fig. "Ignition of titanium fires by rubbing"). In order to research the influence of the ignition source on the ignition process, a rubbing occurrence is simulated in a pressure chamber. A package of titanium sheets is pressed against a rotating disc and subjected to an air flow in the direction of rotation. The abrasion cloud affects the sheet package, but can also impact a sample placed behind it (blade simulation).
Figure "Containment test rig for Titanium fire" (Ref. 9.1.1-3): This testing rig is used for the testing and development of housings that can safely contain titanium fires inside the engine (compressor). It has been shown, that this testing rig concept makes the development of suitable housing wall configurations possible in an easy and reproducible manner.
The following approach has proven itself in this type of trial: A housing configuration is chosen as a reference model, the fire resistance of which corresponds to the accepted highest technical levels available given the weight limitations.
The amount of energy for the trial is simulated by burning down a strip of titanium sheeting (“C”). The mass of the strip of sheeting (“A”) is chosen in a way that ensures that the reference sample does not burn all the way through.
The samples, whose weight has been optimized for housing walls, are now tested against the determined standard and must contain the fire.
Functioning of the testing rig and testing procedure: The head accumulator “E” is pre-heated before the trial. During the trial, compressed air (intake “I”, pressure measurement at “P”) is heated to trial temperature (“Tg”) by the heat exchanger for the duration of the titanium fire (a few seconds). The air is directed into an exchangeable protective pipe “H” made of an Fe-alloy and the leading edge of the strip of sheeting inside it “C” is ignited by an arc (device “D”). The strip of sheeting burns down in a few seconds. The air flow blows the burning melt onto a housing wall sample “A” affixed at an adjustable angle. The back side of the sample is equipped with a thermal element that measures the temperature changes during the trial (“TP”). The behaviour of the sample while being struck by the melt is documented by a high-speed camera through the glass-covered observation shaft“G”. The waste gases leave the testing rig through a cone valve “F” that is used to adjust the air pressure to the required level before the trial begins.
9.1.1-1 “NTSB Aviation Accident/Incident Database Report”, SEA85FA134, 1985
9.1.1-2 “NTSB Aviation Accident/Incident Database Report”, CHI86LA140, 1986.
9.1.1-3 T. Uihlein, H. Schlegel, “Titanium Fire in Jet Engines”, Proceedings AGARD-CP-587 of the AGARD conference “Aircraft Fire Safety”, 14-17 October 1996, Chapter 25-1 to 25-12.
9.1.1-4 T.R. Strobridge, J.C. Moulder, A.F. Clark, “Titanium Combustion in Turbine Engines”,
Report Nos. FAA-RD-79-51 and NDSIR 79-1010 , July 1979, roughly 100 pages.
9.1.1-5 M.R. Glickstein, B.A. Manty, S.R. Lyon, C.W. Elrod, “Ignition and Self-Sustained Combustion of Titanium Alloys”, proceedings of the “Third DoD Conference on Laser Effects, Vulnerability and Countermeasures”, July 19-22, 1977, Naval Training Center, San Diego, CA.
9.1.1-6 Metal Handbook Ninth Edition, Volume 11 “Failure Analysis and Prevention”, American Society for Metals (ASM), Metals Park, Ohio 44073, page 164.
9.1.1-7 E.L.White, J.J. Ward, “Ignition of Metals in Oxigen”, Defense Metals Information Center, Battelle Memorial Institute, Columbus. Ohio 4301, DMIC Report 22N, February 1, 1968, Updata 1976.
9.1.1-8 J.A.Auger, “Les Risques Affectant la Resistance Structurale et la Securité des Propulseurs Modernes”, Proceeding AGARD-CP-215 of the AGARD conference “Power Plant Reliability”, page 6.1-6-14.