Fatigue failure is frequently caused by the machine component being loaded repeatedly or cyclically. The fatigue failure is brought on by repetitive or fatigued loading. The stress fluctuation in a piece of machinery leads to fatigue failure. Therefore, “fatigue life” refers to the number of stress cycles a component can withstand before failing as a system. The process to determine a component’s fatigue life is as follows.
There are several tests to determine the fatigue life of any material. The small-scale fatigue test or the rotating-beam test is the most common to calculate fatigue life. In the case of a rotating-beam test, the specimen is placed in alternating compression, and the tension stresses of equal magnitude are rotated.
The following is a brief description of the rotating-beam test:
Fatigue Life Equation Calculation
In the case of a new engineering component’s design with a particular material, calculating the component’s fatigue life is essential. The fracture toughness data is combined, therefore, in most cases, to find out the fatigue life of the component by analysing the data of the fatigue crack growth.
An equation for determining fatigue life can be created by integrating the fatigue crack growth rate equation between the initial crack (flaw) size ao and the critical crack (flaw) size. The equation is produced while determining the fatigue failure after the number of cycles to failure Nf is found. Therefore, one can easily determine fatigue failure.
The formula for the fatigue growth rate is
According to the formula mentioned above, da/dN = fatigue crack growth rate (Units: mm/cycle or in./cycle)
ΔK = stress-intensity factor range (ΔK = Kmax − Kmin ), MPa√m or ksi√in
A, m = constants and are considered as functions of the environment, frequency, material, stress ratio, and temperature
The Stress intensity in the formula is considered as facto KI, pronounced “Kay-one” in the case of mode 1.
However, one must remember that the critical stress intensity factor or the KIC pronounced “kay-one-see” is known as Fracture toughness. The KI and the KIC are entirely different, and one should not be confused about these two.
The stress intensity factor for Mode 1 is KI = Y σ √(πa).
In the formula mentioned above,
KI = stress-intensity factor
σ = applied nominal stress
a = edge crack length or half of an internal through-length crack’s
Y = geometric constant without dimensions of the order of 1
The formula for the stress intensity factor is: ΔK = Yσ√πa = Y σ π1/2 a1/2.
The formula is followed by ΔKm = Ym σm πm/2 am/2.
While one substitutes the value in the above Fatigue Crack Growth Rate equation, it will be:
When the above equation is rearranged, the crack size, from the initial crack size ao to the final crack size at failure, is considered along with the fatigue failure Nf.
Therefore,
The standard integration formula is, thus,
Or
The equation can be rewritten as
While the calculation is rearranged to get the fatigue life in cycles Nf, the formula is as follows,
Summing up
Hence, it is the final fatigue life equation formula. You can apply the formula to calculate the fatigue life equation in any material.