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Representative curves of applied stress vs number of cycles for steel (showing an endurance limit) and aluminium (showing no such limit).

The fatigue limit, also known as the endurance limit or fatigue strength, is the stress level below which an infinite number of loading cycles can be applied to a material without causing fatigue failure.^[1]

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Ferrous alloys and titanium alloys^[2] have a distinct limit. Other structural metals, such as aluminium and copper, do not have a distinct limit and will eventually fail even from small stress amplitudes. In these cases, the term endurance strength is used. Endurance strength is defined as the maximum value of completely reversed bending stress that a material can withstand for a finite number of cycles without a fatigue failure.

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Definitions[edit]

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The ASTM defines fatigue strength, ${displaystyle S_{N_{f}}}$ , as the value of stress at which failure occurs after ${displaystyle N_{f}}$ cycles, and fatigue limit, ${displaystyle S_{f}}$ , as the limiting value of stress at which failure occurs as ${displaystyle N_{f}}$ becomes very large. ASTM does not define endurance limit, the stress value below which the material will withstand many load cycles,^[1] but implies that it is similar to fatigue limit.^[3]

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Some authors use endurance limit, ${displaystyle S_{e}}$ , for the stress below which failure never occurs, even for an indefinitely large number of loading cycles, as in the case of steel; and fatigue limit or fatigue strength, ${displaystyle S_{f}}$ , for the stress at which failure occurs after a specified number of loading cycles, such as 500 million, as in the case of aluminium.^[1]^[4]^[5] Other authors do not differentiate between the expressions even if they do differentiate between the two types of materials.^[6]^[7]^[8]

Typical values[edit]

Typical values of the limit ( ${displaystyle S_{e}}$ ) for steels are 1/2 the ultimate tensile strength, to a maximum of 290 MPa (42 ksi). For iron, aluminium, and copper alloys, ${displaystyle S_{e}}$ is typically 0.4 times the ultimate tensile strength. Maximum typical values for irons are 170 MPa (24 ksi), aluminums 130 MPa (19 ksi), and coppers 97 MPa (14 ksi).^[2]Note that these values are for smooth 'un-notched' test specimens. The endurance limit for notched specimens (and thus for many practical design situations) is significantly lower.

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For polymeric materials, the fatigue limit has been shown to reflect the intrinsic strength of the covalent bonds in polymer chains that must be ruptured in order to extend a crack. So long as other thermo chemical processes do not break the polymer chain (i.e. ageing or ozone attack), a polymer may operate indefinitely without crack growth when loads are kept below the intrinsic strength.^[9]^[10]

The concept of fatigue limit, and thus standards based on a fatigue limit such as ISO 281:2007 rolling bearing lifetime prediction, remains controversial, at least in the US.^[11]^[12]

History[edit]

The concept of endurance limit was introduced in 1870 by August Wöhler.^[13] However, recent research suggests that endurance limits do not exist for metallic materials, that if enough stress cycles are performed, even the smallest stress will eventually produce fatigue failure.^[5]^[14]

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References[edit]

^ ^a^b^cBeer, Ferdinand P.; E. Russell Johnston Jr. (1992). Mechanics of Materials (2 ed.). McGraw-Hill, Inc. p. 51. ISBN978-0-07-837340-4.
^ ^a^b'Metal Fatigue and Endurance'. Archived from the original on 2012-04-15. Retrieved 2008-04-18.
^Stephens, Ralph I. (2001). Metal Fatigue in Engineering (2nd ed.). John Wiley & Sons, Inc. p. 69. ISBN978-0-471-51059-8.
^Budynas, Richard G. (1999). Advanced Strength and Applied Stress Analysis (2nd ed.). McGraw-Hill, Inc. pp. 532–533. ISBN978-0-07-008985-3.
^ ^a^b