**Introduction:**

**Sources of Fatigue:**

- Thermal Expansion & Contraction
- Vibration due to Occasional loading
- Pressure variation within Piping system
- Motion wave.
- Due to Flow induced Vibration

**Factors Affecting the Fatigue Behavior:**

- Type and Nature of Loading.
- Size of Component and stress or strain Distribution.
- Surface finish and Directional Properties.
- Stress or Strain Concentration.
- Mean stress or Strain.
- Environmental Effects.
- Metallurgical Factors and Material Properties.
- Strain Rate and Frequency Effects.

**Characteristics of Low Cycle Fatigue:**

- Characterized by high loads and a small no. of cycles before failure.
- Here failure occurs only with stress levels in the plastic range, i.e. significant plastic strain occurs during each cycle.
- The stresses which cause fatigue failure in the piping are the peak stresses.
- In piping design, most of the loading cycles encountered would be of the low cycle type

**Characteristics of High Cycle Fatigue:**

- Characterized by high no. of cycles (Preferable N>10^4) with relatively low stress levels and the deformation is in elastic range.
- This type of fatigue failure used in the design of rotating machinery.
- This type of fatigue results from strain cycles in the elastic range.
- A stress level, endurance limit, may be applied an infinite times without failure, is calculated.

**Failure Criteria:**

- Fatigue failure, or cracking under repeated stress much lower than the ultimate tensile strength, is shown in most metals and alloys that exhibit some ductility in static tests. The magnitude of the applied alternating stress range is the controlling fatigue life parameter.
- Failure depends upon the number of repetitions of a given range of stress rather than the total time under load. The speed of loading is a factor of secondary importance, except at elevated temperatures.
- Some metals, including ferrous alloys, have a safe range of stress. Below this stress, called the “endurance limit or fatigue limit”, failure does not occur irrespective of the number of stress cycles.
- Notches, grooves, or other discontinuities of section greatly decrease the stress amplitude that can be sustained for a given number of cycles.
- The range of stress necessary to produce failure in a fixed number of cycles usually decrease as the mean tension stress of the loading cycle is increased.
- Examination of fatigue fracture shows evidence of microscopic deformation, ever in the apparently brittle region of origin and propagates of the crack. The plastic deformation that accompanies a spreading fatigue crack is usually limited in extent to regions very near the crack.

**Analysis Requirement:**

- Designate the specified number of times each type of stress cycle of types 1,2,3,…,n, will be Repeated during the life of the component as n1, n2, n3,……., nn, respectively. In determining n1, n2, n3,……., nn, consideration shall be given to the superposition of cycles of various origins which produce the greatest total alternating stress range. For example , if one type of stress cycle produce 1000 cycles of a stress variation from zero to +60,000 psi and another type of stress cycle produces 10,000 cycles of a stress variation from zero to -50,000 psi, the two cycles to be considered are shown below:

- cycle type 1: n1=1000 and Salt1= (60000+50000)/2
- cycle type 2: n2=9000 and Salt2= (0+50000)/2
- For each type of stress cycle, determine the alternating stress intensity Salt, which for our application is one half of the range between the expansion stress cycles (as shown above). These alternating stress intensities are designated as Salt1, Salt2, Saltn.
- On the applicable design fatigue curve find the permissible number of cycles for each Salt computed. These are designated as N1, N2, …….Nn.
- For each stress cycle calculate the usage factor U1, U2, …….Un where U1= n1/N1, U2= n2/N2,……..Un=nn/Nn.
- Calculate the cumulative usage factor U as U=U1+U2+…….+Un.
- The cumulative usage factor shall not exceed 1.0