Fatigue (material)
From Academic Kids

Mechanical failure modes 

Buckling 
Corrosion 
Creep 
Fatigue 
Fracture 
Melting 
Thermal shock 
Wear 
In materials science, fatigue is a process by which a material is weakened by cyclic loading. The resulting stress may be below the ultimate tensile stress, or even the yield stress of the material, yet still cause catastrophic failure.
Contents 
Characteristics of fatigue failures
The following characteristics are common to fatigue in all materials:
 The process starts with a microscopic crack, called the initiation site, which then widens with each subsequent movement, a phenomenon analysed in the topic of fracture mechanics.
 Failure is essentially probabilistic. The number of cycles required for failure varies between homogeneous material samples. Analysis demands the techniques of survival analysis.
 The greater the applied stress, the shorter the life.
 Damage is cumulative. Materials do not recover when rested.
 Fatigue life is influenced by a variety of factors, such as temperature and surface finish, in complicated ways.
 Some materials, for example steel and titanium, exhibit a fatigue limit, a limit below which repeated stress has no effect. Most others, for example aluminium, exhibit no such limit and even infinitesimally small stresses will eventually cause failure.
Timeline of fatigue history
 1829: Wilhelm Albert first discusses the phenomenon on observing the failure of iron minehoist chains in Clausthal mines.
 1839: The term fatigue becomes current when JeanVictor Poncelet describes metals as being tired in his lectures at the military school at Metz.
 1843: William John Macquorn Rankine recognises the importance of stress concentration in his investigation of railroad axle failures following the Versailles accident.
 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.
 1860: The first systematic investigations of fatigue life by Sir William Fairbairn and August Wöhler. Wöhler's study of railroad axles leads him to the idea of a fatigue limit and to propose the use of SN curves in mechanical design.
Ewing_and_Humfrey_fatigue_cracks.JPG
 1903: Sir James Alfred Ewing demonstrates the origin of fatigue failure in microscopic cracks.
 1910: O. H. Basquin clarifies the shape of a typical SN curve.
 1939: Invention of the strain gauge at BaldwinLimaHamilton catalyses fatigue research.
 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 crackgrowth 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. Matsuiski devise the rainflowcounting algorithm and enable the reliable application of Miner's rule to random loadings.
 1970: W. Elber elucidates the mechanisms and importance of crack closure.
 1975: S. Pearson observes that propagation of small cracks is sometimes surprisingly arrested in the early stages of growth.
Highcycle fatigue
Historically, most attention has focused on situations that require more than 10^{4} cycles to failure where stress is low and deformation primarily elastic.
The SN curve
In highcycle fatigue situations, materials performance is commonly characterised by an SN curve, also known as a Wöhler curve. This is a graph of the magnitude of a cyclical stress (S) against the cycles to failure (N).
figure to be done!
SN 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). Analysis of fatigue data requires techniques from statistics, especially survival analysis and linear regression.
Probabilistic nature of fatigue
As coupons sampled from a homogeneous frame will manifest variation in their number of cycles to failure, the SN curve should more properly be an SNP 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 and Weibull distribution.
Complex loadings
Rainflow_fig2.PNG
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:
 Reduce the complex loading to a series of simple cyclic loadings using a technique such as rainflow analysis;
 Create an histogram of cyclic stress from the rainflow analysis;
 For each stress level, calculate the degree of cummulative damage incurred from the SN curve; and
 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 PalmgrenMiner 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:
 <math>\sum_{i=1}^k \frac {n_i} {N_i} = C <math>
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 percentage 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:
 It fails to recognise the probabilistic nature of fatigue and there is no simple way to relate life predicted by the rule with the charateristics of a probability distribution.
 There is sometimes an effect in the order in which the reversals occur. In some circumstances, cycles of high stress followed by low stress cause more damage than would be predicted by the rule.
Lowcycle 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. Lowcycle fatigue is usually characterised by the CoffinManson relation (popularised by L. F. Coffin in 1979 based on S. S. Manson's 1960 work):
 <math>\frac {\Delta \epsilon_p} {2} = \epsilon_f '(2N)^c<math>
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 0.5 to 0.7 for metals.
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.
 Crack nucleation;
 Stage I crackgrowth;
 Stage II crackgrowth; and
 Ultimate ductile failure.
Factors that affect fatiguelife
Magnitude of stress and Quality of the surface
Design against fatigue
Dependable design against fatiguefailure requires thorough education and supervised experience in mechanical engineering or materials science. There are three principle approaches to life assurance for mechanical parts that display increasing degrees of sophistication:
 Design to keep stress below threshold of fatigue limit (infinite lifetime concept);
 Design (conservatively) for a fixed life after which the user is instructed to replace the part with a new one (a socalled lifed part, finite lifetime concept, or "safelife" design practice);
 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 crackgrowth between inspections. This is often referred to as damage tolerant design or "retirementforcause".
Famous fatigue failures
Versailles accident
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. 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 and Rankine's investigation highlighted the importance of stress concentration for the first time.
De Havilland Comet
Metal fatigue came strongly to the notice of aircraft engineers in 1954 after three de Havilland Comet passenger jets had broken up in midair and crashed within a single year. 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. All aircraft windows were immediately redesigned with rounded corners.
Others
 Capsize of the oil platform Alexander Kielland
 Loss of United Airlines Flight 232, Japan Airlines Flight 123, and China Airlines Flight 611
 The Boston Molasses Disaster has been attributed to a fatigue failure
See also
Fatigue Testing (http://www.zwick.com.sg)
Bibliography
 Andrew, W. (1995) Fatigue and Tribological Properties of Plastics and Elastomers, ISBN 1884207154
 Dieter, G. E. (1988) Mechanical Metallurgy, ISBN 0071004068
 Little, R. E. & Jebe, E. H. (1975) Statistical design of fatigue experiments ISBN 0470541156de:Materialermüdung