Introduction
Fatigue life can be defined as the operational life of a mechanical component before it is subjected to a fatigue failure. Fatigue life is an important factor in the design and implementation of many engineering systems such as those found in aerospace engineering, civil engineering, manufacturing, and the military. Developing a reliable method to predict fatigue life can help to reduce the risks associated with unexpected component failure.
The Need for Predicting Fatigue Life
A major concern in designing and implementing mechanical/structural components is that these components must be able to withstand a number of load cycles before they will experience fatigue crack growth and subsequent fracture. Therefore, predicting the fatigue life of a component is essential in order to achieve a reliable and long-lasting operational life. Many structures that operate in challenging environments must be designed with sufficient margin of safety in order to reduce the risk of unexpected fatigue fracture.
Fatigue Life Theory
Fatigue life is typically characterized by the number of load cycles required before rapid failure occurs. A fatigue life curve is used to map the relationship between the number of load cycles and the probability of failure. The base of the curve is determined by the fatigue strength of the material and the slope of the curve is primarily determined by the applied load.
In order to predict fatigue life, a number of theories have been developed to mathematically describe the relationship between the number of load cycles, the applied load, and the fatigue strength of the material. These theories include the Stress-Life (S-N) theory, the Strain-Life (e-N) theory, and the Modified Goodman Theory.
The Stress-Life (S-N) Theory
The stress-life (S-N) theory is generally used to predict fatigue life in most aerospace components. The stress-life (S-N) theory is based on the number of cycles to failure of a particular material under a specific load. The theory assumes that a material fails when the number of load cycles, N, reaches a critical value, commonly referred to as the fatigue limit or fatigue strength, S. The fatigue limit is the maximum stress (in ksi) that a material can safely withstand before failure.
The fatigue life can be calculated using the following equation:
N=dfrac{S_{f}}{S-K}
Where,
N = Number of cycles to failure,
S_f = Nominal stress,
S = Material fatigue strength,
K = Nature of loading.
The Strain-Life (e-N) Theory
The strain-life (e-N) theory is based on the number of cycles to failure of a particular material under a specific strain. The theory assumes that a material fails when the number of load cycles, N, reaches a critical value, commonly referred to as the fatigue limit or fatigue strength, e. The fatigue limit is the maximum strain that a material can safely withstand before failure.
The fatigue life can be calculated using the following equation:
N=dfrac{e_{f}}{e-K}
Where,
N = Number of cycles to failure,
e_f = Nominal strain,
e = Material fatigue strength,
K = Nature of loading.
The Modified Goodman Theory
The modified Goodman theory is an empirical method used to estimate the fatigue life of isothermal mechanical components. The theory is based on the number of cycles to failure of a particular material at a given temperature. The modified Goodman theory assumes that a material fails when the number of cycles, N, reaches a critical value.
The fatigue life can be calculated using the following equation:
N=A dfrac{S^{b}T^{c}}{K^d}
Where,
A = Constant,
S = Nominal stress,
T = Temperature,
K = Stress concentration factor,
b = Constant,
c = Constant,
d = Constant.
Conclusion
In conclusion, there are a number of methods available to predict fatigue life. The stress-life (S-N) theory, the strain-life (e-N) theory, and the modified Goodman theory are all reliable methods for predicting fatigue life. The selection of the appropriate fatigue life prediction method depends on the application and the operational environment. With the availability of accurate fatigue life predictions, engineers are able to design and implement reliable mechanical/structural components that can withstand a large number of load cycles before experiencing fatigue crack growth and subsequent fracture.
