# Fatigue (material)

(Redirected from Thermal fatigue)
"Metal fatigue" redirects here. For other meanings, see Metal Fatigue (disambiguation).

In materials science, fatigue is the weakening of a material caused by repeatedly applied loads. It is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The nominal maximum stress values that cause such damage may be much less than the strength of the material typically quoted as the ultimate tensile stress limit, or the yield stress limit.

Fatigue occurs when a material is subjected to repeated loading and unloading. If the loads are above a certain threshold, microscopic cracks will begin to form at the stress concentrators such as the surface, persistent slip bands (PSBs), and grain interfaces.[1] Eventually a crack will reach a critical size, the crack will propagate suddenly, and the structure will fracture. The shape of the structure will significantly affect the fatigue life; square holes or sharp corners will lead to elevated local stresses where fatigue cracks can initiate. Round holes and smooth transitions or fillets will therefore increase the fatigue strength of the structure.

## Fatigue life

ASTM defines fatigue life, Nf, as the number of stress cycles of a specified character that a specimen sustains before failure of a specified nature occurs.[2]

One method to predict fatigue life of materials is the Uniform Material Law (UML).[3] UML was developed for fatigue life prediction of aluminum and titanium alloys by the end of 20th century and extended to high-strength steels[4] and cast iron.[5] For some materials, there is a theoretical value for stress amplitude below which the material will not fail for any number of cycles, called a fatigue limit, endurance limit, or fatigue strength.[6]

## Characteristics of fatigue

Fracture of an aluminium crank arm. Dark area of striations: slow crack growth. Bright granular area: sudden fracture.
• In metal alloys, when there are no macroscopic or microscopic discontinuities, the process starts with dislocation movements, which eventually form persistent slip bands that become the nucleus of short cracks.
• Macroscopic and microscopic discontinuities as well as component design features which cause stress concentrations (holes, keyways, sharp changes of direction etc.) are common locations at which the fatigue process begins.
• Fatigue is a process that has a degree of randomness (stochastic), often showing considerable scatter even in well controlled environments.
• Fatigue is usually associated with tensile stresses but fatigue cracks have been reported due to compressive loads.[7]
• The greater the applied stress range, the shorter the life.
• Fatigue life scatter tends to increase for longer fatigue lives.
• Damage is cumulative. Materials do not recover when rested.
• Fatigue life is influenced by a variety of factors, such as temperature, surface finish, metallurgical microstructure, presence of oxidizing or inert chemicals, residual stresses, scuffing contact (fretting), etc.
• Some materials (e.g., some steel and titanium alloys) exhibit a theoretical fatigue limit below which continued loading does not lead to fatigue failure.
• In recent years, researchers (see, for example, the work of Bathias, Murakami, and Stanzl-Tschegg) have found that failures can occur below the theoretical fatigue limit at very high fatigue lives (109 to 1010 cycles). An ultrasonic resonance technique is used in these experiments with frequencies around 10–20 kHz.[citation needed]
• High cycle fatigue strength (about 104 to 108 cycles) can be described by stress-based parameters. A load-controlled servo-hydraulic test rig is commonly used in these tests, with frequencies of around 20–50 Hz. Other sorts of machines—like resonant magnetic machines—can also be used, to achieve frequencies up to 250 Hz.
• Low cycle fatigue (loading that typically causes failure in less than 104 cycles) is associated with localized plastic behavior in metals; thus, a strain-based parameter should be used for fatigue life prediction in metals. Testing is conducted with constant strain amplitudes typically at 0.01–5 Hz.

## Timeline of early fatigue research history

• 1837: Wilhelm Albert publishes the first article on fatigue. He devised a test machine for conveyor chains used in the Clausthal mines.[8]
• 1839: Jean-Victor Poncelet describes metals as being tired in his lectures at the military school at Metz.
• 1842: William John Macquorn Rankine recognises the importance of stress concentrations in his investigation of railroad axle failures. The Versailles train crash was caused by axle fatigue.[9]
• 1843: Joseph Glynn reports on fatigue of axle on a locomotive tender. He identifies the keyway as the crack origin.
• 1848: The Railway Inspectorate reports one of the first tyre failures, probably from a rivet hole in tread of railway carriage wheel. It was likely a fatigue failure.
• 1849: Eaton Hodgkinson is granted a small sum of money to report to the UK Parliament on his work in ascertaining by direct experiment, the effects of continued changes of load upon iron structures and to what extent they could be loaded without danger to their ultimate security.
• 1854: Braithwaite reports on common service fatigue failures and coins the term fatigue.[10]
• 1860: Systematic fatigue testing undertaken by Sir William Fairbairn and August Wöhler.
• 1870: Wöhler summarises his work on railroad axles. He concludes that cyclic stress range is more important than peak stress and introduces the concept of endurance limit.[8]
Micrographs showing how surface fatigue cracks grow as material is further cycled. From Ewing & Humfrey (1903)
• 1903: Sir James Alfred Ewing demonstrates the origin of fatigue failure in microscopic cracks.
• 1910: O. H. Basquin proposes a log-log relationship for SN curves, using Wöhler's test data.
• 1945: A. M. Miner popularises A. Palmgren's (1924) linear damage hypothesis as a practical design tool.
• 1954: L. F. Coffin and S. S. Manson explain fatigue crack-growth in terms of plastic strain in the tip of cracks.
• 1961: P. C. Paris proposes methods for predicting the rate of growth of individual fatigue cracks in the face of initial scepticism and popular defence of Miner's phenomenological approach.
• 1968: Tatsuo Endo and M. Matsuishi devise the rainflow-counting algorithm and enable the reliable application of Miner's rule to random loadings.[11]
• 1970: W. Elber elucidates the mechanisms and importance of crack closure in slowing the growth of a fatigue crack due to the wedging effect of plastic deformation left behind the tip of the crack.

## High-cycle fatigue

Historically, most attention has focused on situations that require more than 104 cycles to failure where stress is low and deformation is primarily elastic.

### S-N curve

In high-cycle fatigue situations, materials performance is commonly characterized by an S-N curve, also known as a Wöhler curve . This is a graph of the magnitude of a cyclic stress (S) against the logarithmic scale of cycles to failure (N).

S-N curves are derived from tests on samples of the material to be characterized (often called coupons) where a regular sinusoidal stress is applied by a testing machine which also counts the number of cycles to failure. This process is sometimes known as coupon testing. Each coupon test generates a point on the plot though in some cases there is a runout where the time to failure exceeds that available for the test (see censoring). Analysis of fatigue data requires techniques from statistics, especially survival analysis and linear regression.

The progression of the S-N curve can be influenced by many factors such as corrosion, temperature, residual stresses, and the presence of notches. The Goodman-Line is a method to estimate the influence of the mean stress on the fatigue strength.

### Probabilistic nature of fatigue

As coupons sampled from a homogeneous frame will display a variation in their number of cycles to failure, the S-N curve should more properly be an S-N-P curve capturing the probability of failure after a given number of cycles of a certain stress. Probability distributions that are common in data analysis and in design against fatigue include the log-normal distribution, extreme value distribution, Birnbaum–Saunders distribution, and Weibull distribution.

In practice, a mechanical part is exposed to a complex, often random, sequence of loads, large and small. In order to assess the safe life of such a part:

2. Create a histogram of cyclic stress from the rainflow analysis to form a fatigue damage spectrum;
3. For each stress level, calculate the degree of cumulative damage incurred from the S-N curve; and
4. Combine the individual contributions using an algorithm such as Miner's rule.

### Miner's Rule

In 1945, M. A. Miner popularised a rule that had first been proposed by A. Palmgren in 1924. The rule, variously called Miner's rule or the Palmgren-Miner linear damage hypothesis, states that where there are k different stress magnitudes in a spectrum, Si (1 ≤ ik), each contributing ni(Si) cycles, then if Ni(Si) is the number of cycles to failure of a constant stress reversal Si, failure occurs when:

$\sum_{i=1}^k \frac {n_i} {N_i} = C$

C is experimentally found to be between 0.7 and 2.2. Usually for design purposes, C is assumed to be 1. This can be thought of as assessing what proportion of life is consumed by stress reversal at each magnitude then forming a linear combination of their aggregate.

Though Miner's rule is a useful approximation in many circumstances, it has several major limitations:

1. It fails to recognise the probabilistic nature of fatigue and there is no simple way to relate life predicted by the rule with the characteristics of a probability distribution. Industry analysts often use design curves, adjusted to account for scatter, to calculate Ni(Si).
2. There is sometimes an effect in the order in which the reversals occur. In some circumstances, cycles of low stress followed by high stress cause more damage than would be predicted by the rule. It does not consider the effect of an overload or high stress which may result in a compressive residual stress that may retard crack growth. High stress followed by low stress may have less damage due to the presence of compressive residual stress.

### Paris' Law

Typical fatigue crack growth rate graph

In Fracture mechanics, Anderson, Gomez and Paris derived relationships for the stage II crack growth with cycles N, in terms of the cyclical component ΔK of the Stress Intensity Factor K[12]

$\frac {\mathrm{d}a} {\mathrm{d}N} = C (\Delta K)^m$

where a is the crack length and m is typically in the range 3 to 5 (for metals).

This relationship was later modified (by Forman, 1967[13]) to make better allowance for the mean stress, by introducing a factor depending on (1-R) where R = min stress/max stress, in the denominator.

### Goodman Relation

In the presence of a steady stress superimposed on the cyclic loading, the Goodman relation can be used to estimate a failure condition. It plots stress amplitude against mean stress with the fatigue limit and the ultimate tensile strength of the material as the two extremes. Alternative failure criteria include Soderberg and Gerber.[14]

## Low-cycle fatigue

Where the stress is high enough for plastic deformation to occur, the accounting of the loading in terms of stress is less useful and the strain in the material offers a simpler and more accurate description. Low-cycle fatigue is usually characterised by the Coffin-Manson relation (published independently by L. F. Coffin in 1954 and S. S. Manson 1953):

$\frac {\Delta \epsilon_p} {2} = \epsilon_f '(2N)^c$

-where:

• Δεp /2 is the plastic strain amplitude;
• εf' is an empirical constant known as the fatigue ductility coefficient, the failure strain for a single reversal;
• 2N is the number of reversals to failure (N cycles);
• c is an empirical constant known as the fatigue ductility exponent, commonly ranging from -0.5 to -0.7 for metals in time independent fatigue. Slopes can be considerably steeper in the presence of creep or environmental interactions.

A similar relationship for materials such as Zirconium, is used in the nuclear industry.[15]

## Fatigue and fracture mechanics

The account above is purely empirical and, though it allows life prediction and design assurance, life improvement or design optimisation can be enhanced using Fracture mechanics. It can be developed in four stages.

1. Crack nucleation;
2. Stage I crack-growth;
3. Stage II crack-growth; and
4. Ultimate ductile failure.

## Factors that affect fatigue-life

• Cyclic stress state: Depending on the complexity of the geometry and the loading, one or more properties of the stress state need to be considered, such as stress amplitude, mean stress, biaxiality, in-phase or out-of-phase shear stress, and load sequence,
• Geometry: Notches and variation in cross section throughout a part lead to stress concentrations where fatigue cracks initiate.
• Surface quality: Surface roughness can cause microscopic stress concentrations that lower the fatigue strength. Compressive residual stresses can be introduced in the surface by e.g. shot peening to increase fatigue life. Such techniques for producing surface stress are often referred to as peening, whatever the mechanism used to produce the stress. Low plasticity burnishing, laser peening, and ultrasonic impact treatment can also produce this surface compressive stress and can increase the fatigue life of the component. This improvement is normally observed only for high-cycle fatigue.
• Material Type: Fatigue life, as well as the behavior during cyclic loading, varies widely for different materials, e.g. composites and polymers differ markedly from metals.
• Residual stresses: Welding, cutting, casting, grinding, and other manufacturing processes involving heat or deformation can produce high levels of tensile residual stress, which decreases the fatigue strength.
• Size and distribution of internal defects: Casting defects such as gas porosity voids, non-metallic inclusions and shrinkage voids can significantly reduce fatigue strength.
• Air or Vacuum: Certain materials like Metals are more prone to fatigue in air than in a vacuum. Depending upon the level of humidity and temperature, the lifetime for metals such as aluminum or iron might be as much as 5 to 10 times greater in a vacuum. This is mostly due to the effect of the oxygen and water vapour in the air which will aggressively attack the material and so encourage the propagation of cracks. Other environments such as oil or seawater may reduce the fatigue life at an even greater rate.[16]
• Direction of loading: For non-isotropic materials, fatigue strength depends on the direction of the principal stress.
• Grain size: For most metals, smaller grains yield longer fatigue lives, however, the presence of surface defects or scratches will have a greater influence than in a coarse grained alloy.
• Environment: Environmental conditions can cause erosion, corrosion, or gas-phase embrittlement, which all affect fatigue life. Corrosion fatigue is a problem encountered in many aggressive environments.
• Temperature: Extreme high or low temperatures can decrease fatigue strength.
• Crack Closure: Crack closure is a phenomenon in fatigue loading, during which the crack will tend to remain in a closed position even though some external tensile force is acting on the material. During this process the crack will open only at a nominal stress above a particular crack opening stress. This is due to several factors such as plastic deformation or phase transformation during crack propagation, corrosion of crack surfaces, presence of fluids in the crack, or roughness at cracked surfaces etc. this will provide a longer fatigue life for the material than expected, by slowing the crack growth rate.

## Design against fatigue

Dependable design against fatigue-failure requires thorough education and supervised experience in structural engineering, mechanical engineering, or materials science. There are four principal approaches to life assurance for mechanical parts that display increasing degrees of sophistication:[17]

1. Design to keep stress below threshold of fatigue limit (infinite lifetime concept);
2. fail-safe, graceful degradation, and fault-tolerant design: Instruct the user to replace parts when they fail. Design in such a way that there is no single point of failure, and so that when any one part completely fails, it does not lead to catastrophic failure of the entire system.
3. Safe-life design: Design (conservatively) for a fixed life after which the user is instructed to replace the part with a new one (a so-called lifed part, finite lifetime concept, or "safe-life" design practice); planned obsolescence and disposable product are variants that design for a fixed life after which the user is instructed to replace the entire device;
4. damage tolerant design: Instruct the user to inspect the part periodically for cracks and to replace the part once a crack exceeds a critical length. This approach usually uses the technologies of nondestructive testing and requires an accurate prediction of the rate of crack-growth between inspections. The designer sets some aircraft maintenance checks schedule frequent enough that parts are replaced while the crack is still in the "slow growth" phase. This is often referred to as damage tolerant design or "retirement-for-cause".

### Stopping fatigue

Fatigue cracks that have begun to propagate can sometimes be stopped by drilling holes, called drill stops, in the path of the fatigue crack.[18] This is not recommended as a general practice because the hole represents a stress concentration factor which depends on the size of the hole and geometry, though the hole is typically less of a stress concentration than the removed tip of the crack. The possibility remains of a new crack starting in the side of the hole. It is always far better to replace the cracked part entirely.

### Material change

Changes in the materials used in parts can also improve fatigue life. For example, parts can be made from better fatigue rated metals. Complete replacement and redesign of parts can also reduce if not eliminate fatigue problems. Thus helicopter rotor blades and propellers in metal are being replaced by composite equivalents. They are not only lighter, but also much more resistant to fatigue. They are more expensive, but the extra cost is amply repaid by their greater integrity, since loss of a rotor blade usually leads to total loss of the aircraft. A similar argument has been made for replacement of metal fuselages, wings and tails of aircraft.[19]

Example of a HFMI treated steel highway bridge to avoid fatigue along the weld transition.

### High Frequency Mechanical Impact (HFMI) treatment of welds

The durability and life of dynamically loaded, welded steel structures are determined often by the welds, particular by the weld transitions. By selective treatment of weld transitions with the High Frequency Mechanical Impact (HFMI) treatment method,[20][21] the durability of many designs can be increased significantly. This method is universally applicable, requires only technical equipment and offers high reproducibility and a high grade of quality control.

## Notable fatigue failures

### Versailles train crash

Versailles train disaster
Drawing of a fatigue failure in an axle by Joseph Glynn, 1843

Following the King's fete celebrations at the Palace of Versailles, a train returning to Paris crashed in May 1842 at Meudon after the leading locomotive broke an axle. The carriages behind piled into the wrecked engines and caught fire. At least 55 passengers were killed trapped in the carriages, including the explorer Jules Dumont d'Urville. This accident is known in France as the "Catastrophe ferroviaire de Meudon". The accident was witnessed by the British locomotive engineer Joseph Locke and widely reported in Britain. It was discussed extensively by engineers, who sought an explanation.

The derailment had been the result of a broken locomotive axle. Rankine's investigation of broken axles in Britain highlighted the importance of stress concentration, and the mechanism of crack growth with repeated loading. His and other papers suggesting a crack growth mechanism through repeated stressing, however, were ignored, and fatigue failures occurred at an ever increasing rate on the expanding railway system. Other spurious theories seemed to be more acceptable, such as the idea that the metal had somehow "crystallized". The notion was based on the crystalline appearance of the fast fracture region of the crack surface, but ignored the fact that the metal was already highly crystalline.

### de Havilland Comet

The recovered (shaded) parts of the wreckage of G-ALYP and the site (arrowed) of the failure

Two de Havilland Comet passenger jets broke up in mid-air and crashed within a few months of each other in 1954. As a result systematic tests were conducted on a fuselage immersed and pressurised in a water tank. After the equivalent of 3,000 flights investigators at the Royal Aircraft Establishment (RAE) were able to conclude that the crash had been due to failure of the pressure cabin at the forward Automatic Direction Finder window in the roof. This 'window' was in fact one of two apertures for the aerials of an electronic navigation system in which opaque fibreglass panels took the place of the window 'glass'. The failure was a result of metal fatigue caused by the repeated pressurisation and de-pressurisation of the aircraft cabin. Also, the supports around the windows were riveted, not bonded, as the original specifications for the aircraft had called for. The problem was exacerbated by the punch rivet construction technique employed. Unlike drill riveting, the imperfect nature of the hole created by punch riveting caused manufacturing defect cracks which may have caused the start of fatigue cracks around the rivet.

The fuselage roof fragment of G-ALYP on display in the Science Museum in London, showing the two ADF windows at-which the initial failure occurred.[22]

The Comet's pressure cabin had been designed to a safety factor comfortably in excess of that required by British Civil Airworthiness Requirements (2.5 times the cabin proof pressure as opposed to the requirement of 1.33 times and an ultimate load of 2.0 times the cabin pressure) and the accident caused a revision in the estimates of the safe loading strength requirements of airliner pressure cabins.

In addition, it was discovered that the stresses around pressure cabin apertures were considerably higher than had been anticipated, especially around sharp-cornered cut-outs, such as windows. As a result, all future jet airliners would feature windows with rounded corners, greatly reducing the stress concentration. This was a noticeable distinguishing feature of all later models of the Comet. Investigators from the RAE told a public inquiry that the sharp corners near the Comets' window openings acted as initiation sites for cracks. The skin of the aircraft was also too thin, and cracks from manufacturing stresses were present at the corners.

### Alexander L. Kielland oil platform capsizing

Fractures on the right side of the Alexander L. Kielland rig

The Alexander L. Kielland was a Norwegian semi-submersible drilling rig that capsized whilst working in the Ekofisk oil field in March 1980 killing 123 people. The capsizing was the worst disaster in Norwegian waters since World War II. The rig, located approximately 320 km east from Dundee, Scotland, was owned by the Stavanger Drilling Company of Norway and was on hire to the U.S. company Phillips Petroleum at the time of the disaster. In driving rain and mist, early in the evening of 27 March 1980 more than 200 men were off duty in the accommodation on the Alexander L. Kielland. The wind was gusting to 40 knots with waves up to 12 m high. The rig had just been winched away from the Edda production platform. Minutes before 18:30 those on board felt a 'sharp crack' followed by 'some kind of trembling'. Suddenly the rig heeled over 30° and then stabilised. Five of the six anchor cables had broken, with one remaining cable preventing the rig from capsizing. The list continued to increase and at 18.53 the remaining anchor cable snapped and the rig turned upside down.

A year later in March 1981, the investigative report[23] concluded that the rig collapsed owing to a fatigue crack in one of its six bracings (bracing D-6), which connected the collapsed D-leg to the rest of the rig. This was traced to a small 6 mm fillet weld which joined a non-load-bearing flange plate to this D-6 bracing. This flange plate held a sonar device used during drilling operations. The poor profile of the fillet weld contributed to a reduction in its fatigue strength. Further, the investigation found considerable amounts of lamellar tearing in the flange plate and cold cracks in the butt weld. Cold cracks in the welds, increased stress concentrations due to the weakened flange plate, the poor weld profile, and cyclical stresses (which would be common in the North Sea), seemed to collectively play a role in the rig's collapse.

## References

1. ^ Kim, W.H>; Laird, C. (1978). Crack Nucleation and State I Propagation in High Strain Fatigue- II Mechanism. Acta Metallurgica. p. 789-799.
2. ^ Stephens, Ralph I.; Fuchs, Henry O. (2001). Metal Fatigue in Engineering (Second edition ed.). John Wiley & Sons, Inc. p. 69. ISBN 0-471-51059-9.
3. ^ A. Bäumel, Jr and T. Seeger (1990). Materials data for cyclic loading, supplement 1. Elsevier. ISBN 978-0-444-88603-3.
4. ^ S. Korkmaz (2010). Uniform Material Law: Extension to High-Strength Steels. VDM. ISBN 978-3-639-25625-3.
5. ^ S. Korkmaz (2011). A Methodology to Predict Fatigue Life of Cast Iron: Uniform Material Law for Cast Iron. Journal of Iron and Steel Research, International 18:8, 2011. doi:10.1016/S1006-706X(11)60102-7
6. ^ Bathias, C. (1999). "There is no infinite fatigue life in metallic materials". Fatigue & Fracture of Engineering Materials & Structures 22 (7): 559–565. doi:10.1046/j.1460-2695.1999.00183.x.
7. ^ N.A. Fleck, C.S. Shin, and R.A. Smith. "Fatigue Crack Growth Under Compressive Loading". Engineering Fracture Mechanics, 1985, vol 21, No 1, pp. 173-185.
8. ^ a b W. Schutz (1996). A history of fatigue. Engineering Fracture Mechanics 54: 263-300. DOI
9. ^ W.J.M. Rankine. (1842). "On the causes of the unexpected breakage of the journals of railway axles, and on the means of preventing such accidents by observing the law of continuity in their construction". Institution of Civil Engineers, Minutes of Proceedings, 105-108.
10. ^ F. Braithwaite. (1854). "On the fatigue and consequent fracture of metals". Institution of Civil Engineers, Minutes of Proceedings, 463–474.
11. ^ Matsuishi, M., Endo, T., 1968, Fatigue of Metals Subjected to Varying Stress, Japan Society of Mechanical Engineers, Jukvoka, Japan.
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13. ^ [1]
14. ^ http://www.roymech.co.uk/Useful_Tables/Fatigue/Stress_levels.html
15. ^ O'Donnell, W.J. and B. F. Langer. Nuclear Science and Engineering, Vol 20, pp. 1-12, 1964.
16. ^ P. P. Milella (2013), "In Vacuo Fatigue", Fatigue and Corrosion in Metals, Springer, pp. 768 et seq., ISBN 9788847023369
17. ^ Tapany Udomphol. "Fatigue of metals", p. 54. sut.ac.th, 2007.
18. ^ http://www.prnewswire.com/news-releases/material-technologies-inc-completes-efs-inspection-of-bridge-in-new-jersey-58419432.html "Material Technologies, Inc. Completes EFS Inspection of Bridge in New Jersey". Press release regarding metal fatigue damage to the Manahawkin Bay Bridge in New Jersey
19. ^ "Horrors in the Skies." Popular Mechanics, June 1989, pp. 67-70.
20. ^ Halid Can Yıldırım, Gary Marquis, Fatigue strength improvement factors for high strength steel welded joints treated by high frequency mechanical impact, International Journal of Fatigue, 44, pp. 168-176, 2012.http://www.sciencedirect.com/science/article/pii/S0142112312001648#!
21. ^ Halid Can Yıldırım, Gary Marquis, Zuheir Barsoum, Fatigue assessment of High Frequency Mechanical Impact (HFMI)-improved fillet welds by local approaches, International Journal of Fatigue, 52, pp. 57–67, 2013. http://www.sciencedirect.com/science/article/pii/S0142112313000637#!
22. ^ "ObjectWiki: Fuselage of de Havilland Comet Airliner G-ALYP". Science Museum. 24 September 2009. Retrieved 9 October 2009.
23. ^ The Alexander L. Kielland accident, Report of a Norwegian public commission appointed by royal decree of March 28, 1980, presented to the Ministry of Justice and Police March, 1981 ISBN B0000ED27N