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### Fluctuating stresses:

Fluctuating stresses are the cause of fatigue failure. The stress magnitude is lower than the ultimate tensile strength of the material. Engineering components are subjected to an external force that is not static in nature whose magnitude is changing with respect to the time and the stresses induced by these forces are termed as fluctuating stresses. The fluctuating in any mechanical component is easily understood by the help of a sine-wave curve.

The variations of the stresses are categorized into three types which are Fluctuating stresses, Repeated stresses and Reversed stresses. The sine wave is constructed between stress and time. The fluctuating or alternating stress is varying in the sinusoidal form with respect to the time. The fluctuating stress has two values i.e. minimum and maximum which is easily understood with the help of diagrams. The stress varies from zero value to the maximum value. In the calculation of the fluctuating stresses, the tensile stress is considered as positive and compressive stresses are negative. The mean stress and the amplitude of the stress can be easily calculated with the help of the following formulas.
Ïƒm =   (Ïƒmax + Ïƒmin)

Ïƒa  =   (Ïƒmax – Ïƒmin)
Ïƒm is the mean stress and Ïƒa is the stress amplitude. Ïƒmax and Ïƒmin are the maximum and minimum stresses respectively.
In the case of Repeated stress, the value of minimum stress is zero i.e. Ïƒmin = 0 and in Reversed stresses, the mean stress is zero i.e. Ïƒm = 0.

### Failures due to fatigue:

Sometimes we use this method to cut the wire by bending and unbending for few times. The cyclically repeated force causes failure and wire break in two pieces. This is a very common example of fatigue failure.  Fatigue failure is defined as the time-dependent fracture under cyclic loading. Fatigue failure is different from static failure. The region of the crack is subjected to stress concentration. This crack is elongated due to the cycling loading conditions of fluctuating stresses as a result of the form of deformation of the engineering components.
The fatigue or endurance limit describes the life of the mechanical component which is defined as the maximum amplitude of completely reversed stress that the standard component can sustain for an infinite number of cycles without the fatigue failure. The fatigue life is another term that is used with the endurance limit for a better understanding of the life of the components. The fatigue life is defined as the number of stress cycles that a standard component can be completed during the test before any crack appears. If the value of the induced stress in the component is less than or equal to the endurance limit than the component has infinite life (≥ whereas if the value of the induced stress is greater than endurance limit than the component has finite life ( to cycles ).