## What is Fatigue Limit?

The fatigue limit or endurance limit is the stress level below which an infinite number of loading cycles can be applied to a material without causing fatigue failure.

Some metals such as ferrous alloys and titanium alloys have a distinct limit, whereas others such as aluminum and copper do not and will eventually fail even from small stress amplitudes.

Where materials do not have a distinct limit the term fatigue strength or endurance strength is used and is defined as the maximum value of completely reversed bending stress that a material can withstand for a specified number of cycles without a fatigue failure.

Fatigue life is affected by cyclic stresses, residual stresses, material properties, internal defects, grain size, temperature, design geometry, surface quality, oxidation, corrosion, etc. For some materials, notably steel and titanium, there is a theoretical value for stress amplitude below which the material will not fail for any number of cycles, called a fatigue limit, endurance limit, or fatigue strength.

Engineers use a number of methods to determine the fatigue life of a material. One of the most useful is the stress-life method is commonly characterized by an S-N curve, also known as a Wöhler curve. This method is illustrated in the figure It plots applied stress (S) against component life or number of cycles to failure (N).

As the stress decreases from some high value, component life increases slowly at first and then quite rapidly. Because fatigue like brittle fracture has such a variable nature, the data used to plot the curve will be treated statistically. The scatter in results is a consequence of the fatigue sensitivity to a number of test and material parameters that are impossible to control precisely.

## Who Discover a Fatigue Limit?

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 and that if enough stress cycles are performed, even the smallest stress will eventually produce fatigue failure.

## Definitions

The following terms are defined for the S-N curve:

**Fatigue Limit.**Fatigue limit (also sometimes called the endurance limit) is the stress level, below which fatigue failure does not occur. This limit exists only for some ferrous (iron-based) and titanium alloys, for which the S–N curve becomes horizontal at higher N values. Other structural metals, such as aluminum and copper, do not have a distinct limit and will eventually fail even from small stress amplitudes. Typical values of the limit for steels are 1/2 the ultimate tensile strength, to a maximum of 290 MPa (42 ksi).**Fatigue Strength.**The ASTM defines fatigue strength, SNf, as the value of stress at which failure occurs after some specified number of cycles (e.g., 107 cycles) For example, the fatigue strength for annealed Ti-6Al-4V titanium alloy is about 240 MPa at 107 cycles and the stress concentration factor = 3.3.**Fatigue Life.**Fatigue life characterizes a material’s fatigue behavior. It is the number of cycles to cause failure at a specified stress level, as taken from the S–N plot

The process of fatigue failure is characterized by three distinct steps:

- Crack initiation, in which a small crack forms at some point of high-stress concentration.
- Crack propagation, during which this crack advances incrementally with each stress cycle. Most of the fatigue life is generally consumed in the crack growth phase.
- Ultimate failure occurs very rapidly once the advancing crack has reached a critical size.

Cracks associated with fatigue failure almost always initiate (or nucleate) on the surface of a component at some point of stress concentration. Anything which leads to stress concentration, and the development of cracks, will reduce fatigue life.

Therefore, increasing the degree of surface finish, polishing as compared to grinding, improves fatigue life. Increasing the strength and hardness of the surface layers of metal components will also improve fatigue life.

## Typical values

Typical values of the limit (S_{e}) for steels are one-half the ultimate tensile strength, to a maximum of 290 MPa (42 ksi). For iron, aluminum, and copper alloys, (S_{e}) is typically 0.4 times the ultimate tensile strength.

Maximum typical values for irons are 170 MPa (24 ksi), aluminum 130 MPa (19 ksi), and coppers 97 MPa (14 ksi). Note that these values are for smooth “un-notched” test specimens. The endurance limit for notched specimens is significantly lower.

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, a polymer may operate indefinitely without crack growth when loads are kept below the intrinsic strength.