In materials science, fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. In Engineering, buckling is a failure mode characterized by a sudden failure of a structural member subjected to high Compressive stresses where Corrosion means the breaking down of essential properties in a material due to Chemical reactions with its surroundings Creep is the tendency of a solid material to slowly move or deform permanently under the influence of stresses It occurs as a result of long term exposure to levels of A fracture is the (local separation of an object or material into two or more pieces under the action of stress. An impact force is a high Force or shock applied over a short time period Melting is a process that results in the phase change of a substance from a Solid to a Liquid. The failure or fracture of a product or component in a single event is known as mechanical overload. Thermal shock is the name given to cracking as a result of rapid temperature change In Materials science, wear is the erosion of material from a Solid Surface by the action of another substance The yield strength or yield point of a Material is defined in Engineering and Materials science as the stress at which a material Materials Science or Materials Engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of Science and The maximum stress values are less than the ultimate tensile stress limit, and may be below the yield stress limit of the material. Stress is a measure of the average amount of Force exerted per unit Area. Tensile strength \sigma_{UTS} or S_U is the Stress at which a material breaks or permanently deforms Tensile strength \sigma_{UTS} or S_U is the Stress at which a material breaks or permanently deforms

Fatigue life

ASTM defines fatigue life, N_f, as the number of stress cycles of a specified character that a specimen sustains before failure of a specified nature occurs. ASTM International ( ASTM) originally known as the American Society for Testing and Materials is an international Standards organization that develops and publishes ^[1]

Characteristics of fatigue

Fracture of an Aluminium Crank Arm. Dark area: slow crack growth. Bright area: sudden fracture.

• The process starts with dislocation movements, eventually forming persistent slip bands that nucleate short cracks. In Materials science, a dislocation is a Crystallographic defect, or irregularity within a Crystal structure.
• Fatigue is a stochastic process, often showing considerable scatter even in controlled environments. Stochastic (from the Greek "Στόχος" for "aim" or "guess" means Random.
• The greater the applied stress, 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, presence of oxidizing or inert chemicals, residual stresses, contact (fretting), etc. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature Roughness is a measure of the texture of a Surface. It is quantified by the vertical deviations of a real surface from its ideal form Redox (shorthand for reduction-oxidation reaction describes all Chemical reactions in which atoms have their Oxidation number ( Oxidation state In English to be inert is to be in a state of doing little or nothing Fretting (or fretting corrosion) refers to combined Wear and Corrosion damage at the asperities of contact surfaces
• Some materials (e. g. , some steel and titanium alloys) exhibit a theoretical fatigue limit below which continued loading does not lead to failure. Steel is an Alloy consisting mostly of Iron, with a Carbon content between 0 Titanium (taɪˈteɪniəm is a Chemical element with the symbol Ti and Atomic number 22 Fatigue limit, endurance limit, and fatigue strength are all expressions used to describe a property of materials the amplitude (or range of Cyclic stress
• In recent years, researchers (see, for example, the work of Bathias, Murakami, and Stanzl-Tschegg) have found that failures 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.
• High cycle fatigue strength (about 10³ to 10⁸ cycles) can be described by stress-based parameters. Fatigue limit, endurance limit, and fatigue strength are all expressions used to describe a property of materials the amplitude (or range of Cyclic stress 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, achieving frequencies up to 250 Hz.
• Low cycle fatigue (typically less than 10³ cycles) is associated with widespread plasticity; thus, a strain-based parameter should be used for fatigue life prediction. Testing is conducted with constant strain amplitudes at 1–5 Hz.

Timeline of early fatigue history

• 1837: Wilhelm Albert publishes the first article on fatigue. Wilhelm August Julius Albert ( January 24, 1787 - July 4, 1846) was a German Mining administrator best remembered as the He devised a test machine for conveyor chains used in the Clausthal mines. A belt conveyor consists of two or more Pulleys with a continuous loop of material - the conveyor belt - that rotates about them Clausthal-Zellerfeld is a Town in Lower Saxony, Germany. It is located in the southwestern part of the Harz mountains Mining is the extraction of valuable Minerals or other geological materials from the earth usually (but not always from an Ore body ^[2]
• 1839: Jean-Victor Poncelet describes metals as being tired in his lectures at the military school at Metz. Jean-Victor Poncelet ( July 1, 1788 &ndash December 22, 1867) was a French Engineer and Mathematician who served Metz (mɛs in French) is a city in the northeast of France, capital of the Lorraine région and Préfecture
• 1842: William John Macquorn Rankine^[3] recognises the importance of stress concentrations in his investigation of railroad axle failures. William John Macquorn Rankine FRS ( July 5, 1820 &ndash December 24, 1872) was a Scottish engineer and A stress concentration (often called stress raisers or stress risers) is a location in an object where stress is concentrated An axle is a central shaft for a rotating Wheel or Gear. In some cases the axle may be fixed in position with a bearing or Bushing The Versailles train crash was caused by axle fatigue. One of the worst rail disasters of the 19th century the Versailles train crash, occurred on May 8 1842 at Meudon ( Versailles) France.
• 1843: Joseph Glynn reports on fatigue of axle on locomotive tender. He identifies the keyway as the crack origin. A keyway is the shaped channel in a lock cylinder into which the key slides to gain access to the lock tumblers
• 1848: Railway Inspectorate report 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. Eaton A Hodgkinson ( February 26, 1789 - June 18, 1861) was an English Engineer, a pioneer of the application of Mathematics The Parliament of the United Kingdom of Great Britain and Northern Ireland is the supreme legislative body in the United Kingdom and British overseas territories
• 1854: Braithwaite^[4] reports on common service fatigue failures and coins the term fatigue.
• 1860: Systematic fatigue testing undertaken by Sir William Fairbairn and August Wöhler. Sir William Fairbairn, 1st Baronet ( of Ardwick) ( February 19, 1789 - August 18, 1874) was a Scottish August Wöhler ( June 22, 1819 - March 21, 1914) was a German Engineer, best remembered for his systematic investigations
• 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. ^[2]

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. Sir James Alfred Ewing KCB ( 27 March 1855 - 7 January 1935) was a Scottish Physicist and Engineer, best known
• 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. Year 1924 ( MCMXXIV) was a Leap year starting on Tuesday (link will display the full calendar of the Gregorian calendar.
• 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. Tatsuo Endo (1925 - 1989 was a Japanese Engineer who in 1968 along with M Matsuiski devise the rainflow-counting algorithm and enable the reliable application of Miner's rule to random loadings. The rainflow-counting algorithm (also known as the "rain-flow counting method" is used in the analysis of fatigue data in order to reduce a spectrum of varying Randomness is a lack of order Purpose, cause, or predictability
• 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 primarily elastic. A material is said to be elastic if it deforms under stress (e

The S-N curve

In high-cycle fatigue situations, materials performance is commonly characterised by an S-N curve, also known as a Wöhler curve. This is a graph of the magnitude of a cyclical stress (S) against the logarithmic scale of cycles to failure (N). Definition and base Logarithmic scales are either defined for ratios of the underlying quantity or one has to agree to measure

S-N curves are derived from tests on samples of the material to be characterised (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). In Statistics and Engineering, censoring occurs when the value of an observation is only partially known Analysis of fatigue data requires techniques from statistics, especially survival analysis and linear regression. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. In statistics linear regression is a form of Regression analysis in which the relationship between one or more Independent variables and another variable called

Probabilistic nature of fatigue

As coupons sampled from a homogeneous frame will manifest 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 lognormal distribution, extreme value distribution, Birnbaum-Saunders distribution, and Weibull distribution. In Probability and Statistics, the log-normal distribution is the single-tailed Probability distribution of any Random variable whose Extreme value theory is a branch of Statistics dealing with the extreme Deviations from the Median of Probability distributions The general The Birnbaum-Saunders distribution (also known as the fatigue life distribution) is used extensively in reliability applications to model failure times In Probability theory and Statistics, the Weibull distribution (named after Waloddi Weibull) is a continuous Probability distribution.

Complex loadings

Spectrum loading

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

1. Reduce the complex loading to a series of simple cyclic loadings using a technique such as rainflow analysis;
2. Create an histogram of cyclic stress from the rainflow analysis;
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. The rainflow-counting algorithm (also known as the "rain-flow counting method" is used in the analysis of fatigue data in order to reduce a spectrum of varying In Statistics, a histogram is a Graphical display of tabulated frequencies, shown as Bars It shows what proportion of cases fall into each of

Miner's rule

In 1945, M. Year 1945 ( MCMXLV) was a Common year starting on Monday (link will display the full calendar A. Miner popularised a rule that had first been proposed by A. Palmgren in 1924. Year 1924 ( MCMXXIV) was a Leap year starting on Tuesday (link will display the full calendar of the Gregorian calendar. 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, S_i (1 ≤ i ≤ k), each contributing n_i(S_i) cycles, then if N_i(S_i) is the number of cycles to failure of a constant stress reversal S_i, failure occurs when:

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 two 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.
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 overload or high stress which may result in a compressive residual stress. High stress followed by low stress may have less damage due to the presence of compressive residual stress.

Paris' Relationship

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

where a is the crack length and m is typically in the range 3 to 5 (for metals). Stress Intensity Factor, K is used in Fracture mechanics to more accurately predict the stress state ("stress intensity" near the tip of a crack caused

This relationship was later modified (by Forman, 1967[1]) 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.

Low-cycle fatigue

Where the stress is high enough for plastic deformation to occur, the account in terms of stress is less useful and the strain in the material offers a simpler description. Low-cycle fatigue is usually characterised by the Coffin-Manson relation (published independently by L. F. Coffin in 1954 and S. Year 1954 ( MCMLIV) was a Common year starting on Friday (link will display full 1954 Gregorian calendar) S. Manson 1953):

-where:

• Δε_p /2 is the plastic strain amplitude;
• ε_f' 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. Year 1953 ( MCMLIII) was a Common year starting on Thursday (link will display full calendar of the Gregorian calendar. 5 to -0. 7 for metals.

A similar relationship for materials such as Zirconium, used in the nuclear industry, is due to W. J. O'Donnell and B. F. Langer (Nuclear Science and Engineering, vol 20, pp 1-12, 1964).

Fatigue and fracture mechanics

The account above is purely phenomenological and, though it allows life prediction and design assurance, it does not enable life improvement or design optimisation. For the latter purposes, an exposition of the causes and processes of fatigue is necessary. Such an explanation is given by fracture mechanics 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 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. Shot peening is a Process used to produce a Compressive residual stress layer and modify mechanical properties of Metals It entails impacting Such techniques for producing surface stress are often referred to as peening, whatever the mechanism used to produce the stress. Peening is the process of working a Metal 's surface to improve its material properties usually by mechanical means such as hammer blows or by blasting with shot ( Laser peening and ultrasonic impact treatment can also produce this surface compressive stress and can increase the fatigue life of the component. Laser peening is the process of hardening or Peening metal using a powerful Laser. 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, and other manufacturing processes involving heat or deformation can produce high levels of tensile residual stress, which decreases the fatigue strength. Residual stresses are stresses that remain after the original cause of the stresses (external forces heat gradient has been removed

• Size and distribution of internal defects. Casting defects such as gas porosity and shrinkage voids can significantly reduce fatigue strength.

• 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. Corrosion fatigue is fatigue in a corrosive environment It is the mechanical degradation of a material under the joint action of Corrosion and cyclic loading

• Temperature. Higher temperatures generally decreases fatigue strength.

Design against fatigue

Dependable design against fatigue-failure requires thorough education and supervised experience in structural engineering, mechanical engineering, or materials science. Structural engineering is a field of Engineering dealing with the analysis and design of Structures that support or resist loads Structural engineering is Mechanical Engineering is an Engineering discipline that involves the application of principles of physics for analysis Design, Manufacturing Materials Science or Materials Engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of Science and There are three principal approaches to life assurance for mechanical parts that display increasing degrees of sophistication:

1. Design to keep stress below threshold of fatigue limit (infinite lifetime concept);
2. 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);
3. 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. Nondestructive testing ( NDT) also called nondestructive examination ( NDE) and nondestructive inspection ( NDI) is testing that does 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. Drilling is the process of using a Drill bit in a Drill to produce cylindrical holes in solid materials such as wood or metal ^[5] 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. A stress concentration (often called stress raisers or stress risers) is a location in an object where stress is concentrated There is thus the possibility of a new crack starting in the side of the hole. It is always far better to replace the cracked part entirely. Several disasters have been caused by botched repairs to cracked structures, such as JAL 123. Japan Airlines Flight 123 was a Japan Airlines domestic flight from Tokyo International Airport (Haneda to Osaka International Airport (Itami

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. A helicopter rotor is the rotating part of a Helicopter which generates an aerodynamic Force. A propeller is essentially a type of fan which transmits power by converting Rotational motion into Thrust for propulsion of a vehicle such as an Composite materials (or composites for short are engineered Materials made from two or more constituent materials with significantly different physical or chemical 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.

Infamous fatigue failures

Versailles train crash

Drawing of a fatigue failure in an axle, 1843. One of the worst rail disasters of the 19th century the Versailles train crash, occurred on May 8 1842 at Meudon ( Versailles) France.

On May 8, 1842 one of the trains carrying revellers on their return from Versailles to Paris, having witnessed the celebrations of the birthday of Louis Philippe, derailed and caught fire. Events 589 - Reccared summons the Third Council of Toledo 1450 - Jack Cade's Rebellion: Kentishmen Year 1842 ( MDCCCXLII) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian Calendar (or a Common Versailles (vɛʀsaj in French) formerly de facto capital of the kingdom of France, is now a wealthy suburb of Paris and is still an important Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city Louis Philippe ( 6 October 1773 &ndash 26 August 1850) was King of the French from 1830 to 1848 in what was known as the Fire is the heat and light energy released during a Chemical reaction, in particular a combustion reaction. Though the resulting conflagration mutilated the dead beyond recognition or enumeration, it is estimated that 53 perished and around 40 were seriously injured.

The derailment had been the result of a broken locomotive axle. A locomotive is a railway Vehicle that provides the motive power for a Train. Rankine's investigation of broken axles in Britain highlighted the importance of stress concentration, and the mechanism of crack growth with repeated loading. William John Macquorn Rankine FRS ( July 5, 1820 &ndash December 24, 1872) was a Scottish engineer and A stress concentration (often called stress raisers or stress risers) is a location in an object where stress is concentrated

De Havilland Comet

Metal fatigue became apparent to aircraft engineers in 1954 after three de Havilland Comet passenger jets had broken up in mid-air and crashed within a single year. Year 1954 ( MCMLIV) was a Common year starting on Friday (link will display full 1954 Gregorian calendar) WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout Investigators from the Royal Aircraft Establishment at Farnborough in England told a public enquiry that the sharp corners around the plane's window openings (actually the forward ADF antenna window in the roof) acted as initiation sites for cracks. The Royal Aircraft Establishment (RAE England, was a British research establishment latterly under the UK Ministry of Defence Farnborough is a Town in the Rushmoor district of Hampshire, England. England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland A stress concentration (often called stress raisers or stress risers) is a location in an object where stress is concentrated The skin of the aircraft was also too thin, and cracks from manufacturing stresses were present at the corners. All aircraft windows were immediately redesigned with rounded corners.

Others

• The Liberty Ships during World War II
• The 1980 capsize of the oil platform Alexander Kielland
• United Airlines Flight 232, Japan Airlines Flight 123, China Airlines Flight 611, Los Angeles Airways Flight 417, and El Al Flight 1862
• The 1957 plane crash of the "Mt. Pinatubo", presidential plane of Philippine President Ramon Magsaysay who died in the crash along with 24 others. History and service In 1936 the American Merchant Marine Act was passed to subsidize the annual construction of 50 commercial merchant vessels to be used in wartime by World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including United Airlines Flight 232 was a scheduled flight operated by United Airlines between Denver and Philadelphia via Chicago. Japan Airlines Flight 123 was a Japan Airlines domestic flight from Tokyo International Airport (Haneda to Osaka International Airport (Itami China Airlines Flight 611 Callsign Dynasty 611 (CAL611 CI611 was a 747 on a regularly scheduled flight from Chiang Kai Shek International Airport (now Los Angeles Airways Flight 417 crashed on August 14, 1968 in the city of Compton, California. On October 4, 1992, El Al Flight 1862, a Boeing 747 cargo plane of the Israeli airline El Al, crashed into the Groeneveen and The 1957 crash of a Douglas C-47 plane named "Mt Pinatubo" on the slopes of Mount Manunggal Cebu, Philippines, killed the 7th President of the The President of the Philippines is the head of state and government of the Republic of the Philippines. Ramon del Fierro Magsaysay ( August 31, 1907 - March 17, 1957) was the third President of the Third Republic of the Philippines
• The 1919 Boston Molasses Disaster has been attributed to a fatigue failure
• The 1998 Eschede train disaster (crash of an InterCityExpress train). Boston Molasses Disaster, also known as the Great Molasses Flood and the Great Boston Molasses Tragedy, occurred on January 15 1919, in the Year 1998 ( MCMXCVIII) was a Common year starting on Thursday (link will display full 1998 Gregorian calendar) The Eschede train disaster was one of the world's deadliest high-speed train accidents The InterCityExpress or ICE (German pronunciation) is a system of high-speed trains predominantly running in Germany and neighbouring countries
• The 2005 crash of Chalk's Ocean Airways Flight 101

See also

• Air safety
• Corrosion fatigue
• Embedment
• Fracture mechanics
• Forensic engineering
• Forensic materials engineering
• Fractography
• Kalitta Air
• Materials science
• Peening
• Shock (mechanics)
• Structural failure
• Ultrasonic Impact Treatment
• Vibration

References

• Andrew, W. A news release, media release, press release or press statement is a written or recorded Communication directed at members of the News The Dorland J Henderson Memorial Bridge, familiarly known as the Manahawkin Bay Bridge, is a steel girder Bridge that spans Manahawkin Bay, New Jersey ( is a state in the Mid-Atlantic and Northeastern regions of the United States. (1995) Fatigue and Tribological Properties of Plastics and Elastomers, ISBN 1-884207-15-4
• Dieter, G. E. (1988) Mechanical Metallurgy, ISBN 0-07-100406-8
• Little, R. E. & Jebe, E. H. (1975) Statistical design of fatigue experiments ISBN 0-470-54115-6

External links

• Fatigue by Shawn M. Kelly
• SAE Fatigue, Design, and Evaluation Committee website
• A collection of fatigue knowledge and calculators
• Article regarding Fatigue Testing of Bolted Joints
• Examples of fatigued metal products