Fatigue Life Of Material


Title

An axial residual compressive stress due to a manufacturing process is present on the outer surface.

Description/Problem

An axial residual compressive stress due to a manufacturing process is present on the outer surface of a rotating shaft subjected to bending. Under a given [(Page 21 of 429) - Chapter-1 Stress and Strain S K Mondal’s] bending load, the fatigue life of the shaft in the presence of the residual compressive stress is: [GATE-2008]
(a) Decreased
(b) Increased or decreased, depending on the external bending load
(c) Neither decreased nor increased
(d) Increased

Solution:

Fatigue life is the duration till which any material is able to withstand all types of compressive and tensile stress before showing any type of distortion or damage in its mechanical shape. It is calculated as the number of stress cycles that an object or material can handle before the failure. Most of the time, nominal maximum stress value is taken into account for calculating fatigue life whose value is generally less than the ultimate tensile stress limits. Yield stress limit also helps in the accurate calculation of fatigue life.

According to the description, an axial residual compressive stress due to a manufacturing process is generated on the outer surface of a rotating shaft. It is subjected to bending.

Diagrammatically we can represent the event like the following –


The above figure clearly shows the normal distribution of stresses acting over the surface of the rotating beam as stated in the description. As it is told to be subjected to bending, it is a cantilever-loaded rotating beam. The top surface of the beam is subjected to tensile stress while the lower part is under compressive stress. This results in bending in the direction of rotation of the beam.


The pattern of residual stress generated and induced can be seen in the above diagram. It is compressive in nature.


Fatigue life is the duration till which any structure or body is able to bear the forces and stresses acting over it. The above graph can clarify that only under constant compressive or tensile force or stress can a fracture result. The residual tensile stress is the major factor in the decrease of fatigue life. The beam is under the constant alternative effect of compressive and tensile stress respectively. This reduces the net resultant force acting over the surface of the beam and increases the plasticity. Hence, it reduces the plastic deformation.


The pattern of the net stress obtained at the time of loading the surface treated beam can be seen in the above diagram. A considerable reduction in the magnitude of the tensile stress is seen. This is the reason for increased fatigue life.



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