Material fatigue

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Hard shell of a ski boot broken due to material fatigue

The fatigue describes a slowly progressive injury process in a material under ambient conditions such as varying mechanical load, changing temperature, UV radiation, ionizing radiation , possibly with the additional action of a corrosive medium.

Material fatigue means that even a statically uncritical load (still in the elastic range, i.e. still below the yield point of the material) can lead to malfunction (fatigue crack formation) or even to total failure ( fatigue fracture ) of a component if it acts often enough on the component.

Parts subject to cyclical loads therefore generally have a limited service life . For this reason, a service life assessment, calculation or tests must be carried out on critical components before use, which allow an assessment of the durability of the component. Components that can theoretically withstand an unlimited number of cycles (because they consist of certain, suitable materials) are called fatigue-resistant .

Simple example: The holder of a ballpoint pen can be bent back and forth elastically several times. However, as the number of bending operations increases, the likelihood of breakage increases. The expression "constant dripping wears away the stone" or the philosophical law of "turning quantitative changes into qualitative ones" describes this phenomenon.

A close look at the fracture pattern of a component shows whether a force or fatigue fracture is present. Conclusions must be drawn from this in order to avoid component failure in the future.


One distinguishes

Isothermal mechanical fatigue

The process that ultimately leads to the failure of a component or material due to the formation of a crack, reaching a certain crack length or fatigue fracture is referred to as mechanical material fatigue of metallic materials . The process begins with local dislocation movements that occur even with loads below the yield point, especially on the component surface at cross-sectional transitions and surface notches or in the volume of material inhomogeneities such as inclusions, pores, precipitations, dispersions, etc. due to local excessive stresses.

Repeated loading results in statistically randomly distributed areas of local plastic deformations. In the further course of the load, dislocation configurations are formed , which can have a damaging effect by concentrating plastic deformations on very small areas.

The further behavior under cyclical loading is strongly dependent on the material and its history. Fatigue sliding bands , so-called persistent sliding bands , usually form in material areas close to the surface , which then form so-called ex- and intrusions on the component surface at 45 ° to the direction of loading (highest shear stress and therefore preferred direction of the dislocation movement, Mohr stress circle ) . These act like sharp notches and initiate micro-cracks that run parallel to the sliding bands. After a few micrometers (often around twice the grain diameter of the structure) the cracks swivel around and run at 90 ° to the direction of stress.

When a certain crack length is reached, one speaks of macro cracks or so-called technical cracks, which spread depending on the crack geometry, the type of stress (crack mode) and the height. If the crack reaches the so-called critical crack length, the component fails due to unstable crack propagation (force fracture) in the remaining cross-section.

Historical events

  • 1822: Thomas Tredgold publishes A Practical Essay on the Strength of Cast Iron and other Metals
  • 1829: Julius Albert observes failures in iron chain links in mine elevators in the Clausthal mines
  • 1839: In his lectures at the military school in Metz, Jean Victor Poncelet introduces the concept of fatigue in metals and compares it to the slackness of a person
  • 1843: William John Macquorn Rankine recognizes the importance of the concentration of stress in his investigations into failures of railway axles in the Versailles train accident
  • 1849: Eaton Hodgkinson investigates the limit up to which one can load steel structures without endangering safety
  • 1860: August Wöhler examines railway axles and suggests that the load limits of components be plotted in a diagram in order to enable future strength designs
  • 1875: The Amstetten locomotive derails due to a broken tire due to material fatigue . The investigation of the accident is considered to be the beginning of modern materials testing and standardization
  • 1903: Sir James Alfred Ewing discovers microscopic cracks as the origin of fatigue failure
  • 1910: OH Basquin defines the shape of a typical Wöhler curve
  • 1938: Edward E. Simmons invents the strain gauge , accelerating all research in the field of fatigue
  • 1945: AM Miner favors A. Palmgrens (1924) linear damage accumulation theory as a practicable interpretation tool
  • 1954: Material fatigue leads to an initially puzzling series of crashes of De Havilland DH.106 Comet jets, the first commercial passenger jets.
  • 1954: LF Coffin and SS Manson explain the crack growth on the basis of plastic expansion at the crack tip
  • 1961: PC Paris contrasts Miner's phenomenological considerations with his theoretical considerations based on the crack growth of individual cracks
  • 1968: Tatsuo Endo and M. Matsuiski derive the Rainflow algorithm for counting random oscillation cycles and thus enable the reliable application of Miner's laws
  • 1970: W. Elber discovers the mechanisms of crack closure
  • 1975: S. Pearson observes occasional stoppage of crack growth in the early growth phases of short cracks
  • 1975: J. Köhler confirms the statistical influence of size from the extreme value theory according to W. Weibull and EJ Gumbel
  • 1998: A broken tire due to material fatigue leads to the ICE accident in Eschede , the world's worst accident involving a high-speed train

Vibratory stress

Qualitative representation of the Wöhler curve
The Haigh diagram is a diagram for determining fatigue strength

Material fatigue can occur as a result of oscillating, dynamic loads. The stress at which a dynamically loaded component breaks is, however, well below the tensile strength and usually also below the yield point of the material used. The fatigue strength of materials or components is determined in a Wöhler test . For this purpose, the test bodies are loaded cyclically, mostly with a sinusoidal load-time function. The test runs until a defined failure (breakage, crack) occurs or a specified number of limit cycles is reached. Test specimens that reach the limit number of cycles without recognizable failure are referred to as runners.

The results of the experiment are entered in a double logarithmic diagram. The nominal stress amplitude S a is usually plotted against the tolerable number of cycles in the Wöhler diagram. The resulting curve is called the Wöhler curve or Wöhler line . The three areas K, Z and D are entered in the adjacent Wöhler curve.

  • K is the range of short-term strength or short-term fatigue strength below approx. 10 4 to 10 5 cycles. This type of fatigue occurs at high plastic strain amplitudes, which lead to early failure. The Coffin-Manson plot is usually used to illustrate this area more precisely .
  • Z is the range of fatigue strength or fatigue strength between 10 4 and, depending on the material, approximately 2 · 10 6 vibration cycles, in which the Wöhler curve runs almost straight in the double logarithmic representation.
  • D is the subsequent area of ​​the so-called fatigue strength . In ferritic-pearlitic steels, the fatigue strength range begins at approx. 1–5 · 10 6 . With austenitic steels and automotive base materials (e.g. aluminum, gold, copper), the tolerable amplitude continues to decrease. There is no “real” fatigue strength here. Therefore, the tolerable amplitude at 10 7 load changes is usually referred to as the fatigue strength. If a component is subject to constant corrosion or greatly increased temperatures, fatigue strength can no longer be expected. To determine the fatigue strength, graphs such as the Haigh diagram or the Smith diagram are used.

Below the fatigue strength S aD , a component can in principle withstand any number of oscillation cycles . Loads above the fatigue strength cause the component to fail after a certain number of cycles. The number of endurance cycles of a component under operational load (variable load amplitudes) up to failure can be predicted within the scope of statistical accuracy with the help of the Wöhler curve. To do this, the methods of linear damage accumulation according to Palmgren, Langer and Miner are used. One speaks here of the operationally stable dimensioning of a component. Fatigue strength is used today in almost all areas of technology for lightweight construction.

See also


  • S. Suresh: Fatigue of Materials . Cambridge University Press, 1998.
  • Bernhard Ilschner : High-temperature plasticity . Springer-Verlag, 1973.
  • Joachim Rösler, Harald Harders, Martin Bäker: Mechanical behavior of materials . Teubner, 2006.
  • Richard M. Christensen: The theory of materials failure. Oxford Univ. Press, Oxford 2013, ISBN 978-0-19-966211-1 .

Web links

Wiktionary: Material fatigue  - explanations of meanings, word origins, synonyms, translations

Individual evidence

  1. W. Olivier, R. Jaeger, M. Möser, K. Müller: Damage analysis of a failure due to implant fracture . In: Implantologie Journal , 7 (6), 2003, Oemus Media Leipzig, pp. 34-36, ISSN  1435-6139
  2. K. Müller, W. Olivier, R. Jaeger, M. Möser: Damage analyzes on endosseous titanium implants . ( Memento of the original from April 28, 2015 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF) Poster session, DGI Conference Göttingen 27. – 29. November 2003 @1@ 2Template: Webachiv / IABot /
  3. ^ Georg Jacobs: Machine design . Mainz Verlag, Aachen 2015, ISBN 3-86130-748-0 , p. 19-21 .