Fatigue

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. The nominal maximum stress values that cause such damage may be much less than the strength of the material, typically quoted as the ultimate tensile stress limit, or the yield stress limit.

Fatigue occurs when a material is subjected to repeated loading and unloading. After a finite number of cycles, microscopic cracks will begin to *initiate* at stress concentrations such as holes, *persistent slip bands* (PSBs),  composites interfaces or grain boundaries in metals.

Once a 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 failures, both for high and low cycle, all follow the same basic steps process of crack initiation, stage I crack growth, stage II crack growth, and finally ultimate failure. To begin the process cracks must nucleate within a material. This process can occur either at stress risers in metallic samples or at areas with a high void density in polymer samples. These cracks propagate slowly at first during *stage I* crack growth along crystallographic planes, where shear stresses are highest. Once the cracks reach a critical size they propagate quickly during *stage II* crack growth in a direction perpendicular to the applied force. These cracks can eventually lead to the ultimate failure of the material, often in a brittle catastrophic fashion.

## Characteristics of fatigue

* In metal alloys, and for the simplifying case when there are no macroscopic or microscopic discontinuities, the process starts with dislocation movements at the microscopic level, which eventually form persistent slip bands that become the nucleus of short cracks.
* Macroscopic and microscopic discontinuities (at the crystalline grain scale) as well as component design features which cause stress concentrations (holes, keyways, sharp changes of load direction etc.) are common locations at which the fatigue process begins.
* Fatigue is a process that has a degree of randomness (stochastic), often showing considerable scatter even in seemingly identical samples in well controlled environments.
* Fatigue is usually associated with tensile stresses but fatigue cracks have been reported due to compressive loads.
* The greater the applied stress range, the shorter the life.
* Fatigue life scatter tends to increase for longer fatigue lives.
* Damage is irreversible. Materials do not recover when rested.
* Fatigue life is influenced by a variety of factors, such as temperature, surface finish, metallurgical microstructure, presence of oxidizing or inert chemicals, residual stresses, scuffing contact (fretting), etc.
* Some materials (e.g., some steel and titanium alloys) exhibit a theoretical fatigue limit below which continued loading does not lead to fatigue failure.
* High cycle fatigue strength (about 104 to 108 cycles) can be described by stress-based parameters. A load-controlled servo-hydraulic test rig is commonly used in these tests, with frequencies of around 20–50 Hz. Other sorts of machines—like resonant magnetic machines—can also be used, to achieve frequencies up to 250 Hz.
* Low-cycle fatigue (loading that typically causes failure in less than 104 cycles) is associated with localized plastic behavior in metals; thus, a strain-based parameter should be used for fatigue life prediction in metals. Testing is conducted with constant strain amplitudes typically at 0.01–5 Hz.

## Fatigue limit

**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, called the endurance limit, which is the amplitude of stress below which the material can withstand an infinite number of cycles without 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, the term endurance strength is used.

Fatigue limit is used in plotting S-N curves and the Goodman diagram.

### Typical values

Typical values of the limit (Se) for steels are 1/2 the ultimate tensile strength, to a maximum of 290 MPa (42 ksi). For iron, aluminium, and copper alloys, Se 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). 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.