Fatigue limit, endurance limit, and fatigue strength are all expressions used to describe a property of materials: the amplitude (or range) of cyclic stress that can be applied to the material without causing fatigue failure. Ferrous alloys and titanium alloys have a distinct limit, an amplitude below which there appears to be no number of cycles that will cause failure. 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, a number of cycles (usually 107) is chosen to represent the fatigue life of the material.
The ASTM defines fatigue strength, SNf, as the value of stress at which failure occurs after Nf cycles, and fatigue limit, Sf, as the limiting value of stress at which failure occurs as Nf becomes very large. ASTM does not define endurance limit, the stress value below which the material will withstand many load cycles, but implies that it is similar to fatigue limit.
Some authors use endurance limit, Se, 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, Sf, for the stress at which failure occurs after a specified number of loading cycles, such as 500 million, as in the case of aluminium. Other authors do not differentiate between the expressions even if they do differentiate between the two types of materials.
Typical values of the limit (Se) for steels are 1/2 the ultimate tensile strength, to a maximum of 100 ksi (690 MPa). For iron, aluminium, and copper alloys, Se is typically 0.4 times the ultimate tensile strength. Maximum typical values for irons are 24 ksi (165 MPa), aluminums 19 ksi (131 MPa), and coppers 14 ksi (96.5 MPa). 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.
The concept of endurance limit was introduced in 1870 by August Wöhler. 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.
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 thermochemical processes do not break the polymer chain (ie ageing or ozone attack), a polymer may operate indefinitely without crack growth when loads are kept below the intrinsic strength.  
- Tension-compression testing : Samples are repeatedly switched between a tensile and a compressive load.
- Tension-tension testing. Samples are placed under an oscillatory tension amplitude.
- Beer, Ferdinand P.; E. Russell Johnston, Jr. (1992). Mechanics of Materials (2nd ed.). McGraw-Hill, Inc. p. 51. ISBN 0-07-837340-9.
- "Metal Fatigue and Endurance". Retrieved 2008-04-18.
- Stephens, Ralph I. (2001). Metal Fatigue in Engineering (2nd ed.). John Wiley & Sons, Inc. p. 69. ISBN 0-471-51059-9.
- Budynas, Richard G. (1999). Advanced Strength and Applied Stress Analysis (2nd ed.). McGraw-Hill, Inc. pp. 532–533. ISBN 0-07-008985-X.
- Askeland, Donald R.; Pradeep P. Phule (2003). The Science and Engineering of Materials (4th ed.). Brooks/Cole. p. 287. ISBN 0-534-95373-5.
- Hibbeler, R. C. (2003). Mechanics of Materials (5th ed.). Pearson Education, Inc. p. 110. ISBN 0-13-008181-7.
- Dowling, Norman E. (1998). Mechanical Behavior of Materials (2nd ed.). Printice-Hall, Inc. p. 365. ISBN 0-13-905720-X.
- Barber, J. R. (2001). Intermediate Mechanics of Materials. McGraw-Hill. p. 65. ISBN 0-07-232519-4.
- W. Schutz (1996). A history of fatigue. Engineering Fracture Mechanics 54: 263-300. DOI
- Bathias, C. (1999). "There is no infinite fatigue life in metallic materials". Fatigue & Fracture of Engineering Materials & Structures 22 (7): 559–565. doi:10.1046/j.1460-2695.1999.00183.x.
- Lake, G. J.; P. B. Lindley (1965). "The mechanical fatigue limit for rubber". Journal of Applied Polymer Science 9 (4): 1233–1251. doi:10.1002/app.1965.070090405.
- Lake, G. J.; A. G. Thomas (1967). "The strength of highly elastic materials". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 300 (1460): 108–119. doi:10.1098/rspa.1967.0160.
- Nunomura; et al. Fahmy M. Haggag, W. L. Server, eds. Small Specimen Test Techniques Applied to Nuclear Reactor Vessel Thermal Annealing and Plant Life Extension. ISBN 0803118694.