page_title: Fatigue (material)
section_title: Strain-life (ε-N) method
hierarchical_section_title: Fatigue (material) / Predicting fatigue life / Stress-life and strain-life methods / Strain-life (ε-N) method
caption_attribution_description: English: graph showing fatigue failure as a function of strain amplitude
context_page_description: In materials science, fatigue is the weakening of a material caused by cyclic loading that results in progressive and localized structural damage and the growth of cracks. Once a fatigue crack has initiated, each loading cycle will grow the crack a small amount, 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 seem to experience some sort of fatigue-related failure such as composites, plastics and ceramics.
context_section_description: When strains are no longer elastic, such as in the presence of stress concentrations, the total strain can be used instead of stress as a similitude parameter. This is known as the strain-life method. The total strain amplitude  is the sum of the elastic strain amplitude  and the plastic strain amplitude  and is given by
  .
  Basquin's equation for the elastic strain amplitude is
  where  is Young's modulus.
  The relation for high cycle fatigue can be expressed using the elastic strain amplitude
  where  is a parameter that scales with tensile strength obtained by fitting experimental data,  is the number of cycles to failure and  is the slope of the log-log curve again determined by curve fitting.
  In 1954, Coffin and Manson proposed that the fatigue life of a component was related to the plastic strain amplitude using:
  .
  The equations can be combined to account for high cycle and low cycle fatigue giving
  .
caption: Graph showing fatigue failure as a function of strain amplitude.
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