Fatigue (material)


In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of the fracture surface. The crack will continue to grow until it reaches a critical size, which occurs when the stress intensity factor of the crack exceeds the fracture toughness of the material, producing rapid propagation and typically complete fracture of the structure.
Fatigue has traditionally been associated with the failure of metal components which led to the term metal fatigue. In the nineteenth century, the sudden failing of metal railway axles was thought to be caused by the metal crystallising because of the brittle appearance of the fracture surface, but this has since been disproved. Most materials, such as composites, plastics and ceramics, seem to experience some sort of fatigue-related failure.
To aid in predicting the fatigue life of a component, fatigue tests are carried out using coupons to measure the rate of crack growth by applying constant amplitude cyclic loading and averaging the measured growth of a crack over thousands of cycles. There are also special cases that need to be considered where the rate of crack growth is significantly different compared to that obtained from constant amplitude testing, such as the reduced rate of growth that occurs for small loads near the threshold or after the application of an overload, and the increased rate of crack growth associated with short cracks or after the application of an underload.
If the loads are above a certain threshold, microscopic cracks will begin to initiate at stress concentrations such as holes, persistent slip bands, composite interfaces or grain boundaries in metals. The stress values that cause fatigue damage are typically much less than the yield strength of the material.

Stages of fatigue

Historically, fatigue has been separated into regions of high cycle fatigue that require more than 104 cycles to failure where stress is low and primarily elastic and low cycle fatigue where there is significant plasticity. Experiments have shown that low cycle fatigue is also crack growth.
Fatigue failures, both for high and low cycles, all follow the same basic steps: crack initiation, crack growth stages I and II, and finally ultimate failure. To begin the process, cracks must nucleate within a material. This process can occur either at stress risers in metallic samples or at areas with a high void density in polymer samples. These cracks propagate slowly at first during stage I crack growth along crystallographic planes, where shear stresses are highest. Once the cracks reach a critical size they propagate quickly during stage II crack growth in a direction perpendicular to the applied force. These cracks can eventually lead to the ultimate failure of the material, often in a brittle catastrophic fashion.

Crack initiation

The formation of initial cracks preceding fatigue failure is a separate process consisting of four discrete steps in metallic samples. The material will develop cell structures and harden in response to the applied load. This causes the amplitude of the applied stress to increase given the new restraints on strain. These newly formed cell structures will eventually break down with the formation of persistent slip bands. Slip in the material is localized at these PSBs, and the exaggerated slip can now serve as a stress concentrator for a crack to form. Nucleation and growth of a crack to a detectable size accounts for most of the cracking process. It is for this reason that cyclic fatigue failures seem to occur so suddenly where the bulk of the changes in the material are not visible without destructive testing. Even in normally ductile materials, fatigue failures will resemble sudden brittle failures.
PSB-induced slip planes result in intrusions and extrusions along the surface of a material, often occurring in pairs. This slip is not a microstructural change within the material, but rather a propagation of dislocations within the material. Instead of a smooth interface, the intrusions and extrusions will cause the surface of the material to resemble the edge of a deck of cards, where not all cards are perfectly aligned. Slip-induced intrusions and extrusions create extremely fine surface structures on the material. With surface structure size inversely related to stress concentration factors, PSB-induced surface slip can cause fractures to initiate.
These steps can also be bypassed entirely if the cracks form at a pre-existing stress concentrator such as from an inclusion in the material or from a geometric stress concentrator caused by a sharp internal corner or fillet.

Crack growth

Most of the fatigue life is generally consumed in the crack growth phase. The rate of growth is primarily driven by the range of cyclic loading although additional factors such as mean stress, environment, overloads and underloads can also affect the rate of growth. Crack growth may stop if the loads are small enough to fall below a critical threshold.
Fatigue cracks can grow from material or manufacturing defects from as small as 10 μm.
When the rate of growth becomes large enough, fatigue striations can be seen on the fracture surface. Striations mark the position of the crack tip and the width of each striation represents the growth from one loading cycle. Striations are a result of plasticity at the crack tip.
When the stress intensity exceeds a critical value known as the fracture toughness, unsustainable fast fracture will occur, usually by a process of microvoid coalescence. Prior to final fracture, the fracture surface may contain a mixture of areas of fatigue and fast fracture.

Acceleration and retardation

The following effects change the rate of growth:
  • Mean stress effect: Higher mean stress increases the rate of crack growth.
  • Environment: Increased moisture increases the rate of crack growth. In the case of aluminium, cracks generally grow from the surface, where water vapour from the atmosphere is able to reach the tip of the crack and dissociate into atomic hydrogen which causes hydrogen embrittlement. Cracks growing internally are isolated from the atmosphere and grow in a vacuum where the rate of growth is typically an order of magnitude slower than a surface crack.
  • Short crack effect: In 1975, Pearson observed that short cracks grow faster than expected. Possible reasons for the short crack effect include the presence of the T-stress, the tri-axial stress state at the crack tip, the lack of crack closure associated with short cracks and the large plastic zone in comparison to the crack length. In addition, long cracks typically experience a threshold which short cracks do not have. There are a number of criteria for short cracks:
  • * cracks are typically smaller than 1 mm,
  • * cracks are smaller than the material microstructure size such as the grain size, or
  • * crack length is small compared to the plastic zone.
  • Underloads: Small numbers of underloads increase the rate of growth and may counteract the effect of overloads.
  • Overloads: Initially overloads lead to a small increase in the rate of growth followed by a long reduction in the rate of growth.

    Characteristics of fatigue

  • In metal alloys, and for the simplifying case when there are no macroscopic or microscopic discontinuities, the process starts with dislocation movements at the microscopic level, 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 are common locations at which the fatigue process begins.
  • Fatigue is a process that has a degree of randomness, often showing considerable scatter even in seemingly identical samples in well controlled environments.
  • Fatigue is usually associated with tensile stresses but fatigue cracks have been reported due to compressive loads.
  • The greater the applied stress range, the shorter the life.
  • Fatigue life scatter tends to increase for longer fatigue lives.
  • Damage is irreversible. 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, etc.
  • Some materials exhibit a theoretical fatigue limit below which continued loading does not lead to fatigue failure.
  • High cycle fatigue strength 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 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 research history

  • 1837: Wilhelm Albert publishes the first article on fatigue. He devised a test machine for conveyor chains used in the Clausthal mines.
  • 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 rail accident was caused by fatigue failure of a locomotive axle.
  • 1843: Joseph Glynn reports on the fatigue of an 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: F. Braithwaite reports on common service fatigue failures and coins the term fatigue.
  • 1860: Systematic fatigue testing undertaken by Sir William Fairbairn and August Wöhler.
  • 1870: A. 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.
  • 1903: Sir James Alfred Ewing demonstrates the origin of fatigue failure in microscopic cracks.
  • 1910: O. H. Basquin proposes a log-log relationship for S-N curves, using Wöhler's test data.
  • 1940: Sidney M. Cadwell publishes first rigorous study of fatigue in rubber.
  • 1945: A. M. Miner popularises Palmgren's linear damage hypothesis as a practical design tool.
  • 1952: W. Weibull An S-N curve model.
  • 1954: The world's first commercial jetliner, the de Havilland Comet, suffers disaster as three planes break up in mid-air, causing de Havilland and all other manufacturers to redesign high altitude aircraft and in particular replace square apertures like windows with oval ones.
  • 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.
  • 1970: Smith, Watson, and Topper developed a mean stress correction model, where the fatigue damage in a cycle is determined by the product of the maximum stress and strain amplitude.
  • 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.
  • 1973: M. W. Brown and K. J. Miller observe that fatigue life under multiaxial conditions is governed by the experience of the plane receiving the most damage, and that both tension and shear loads on the critical plane must be considered.