Endurance limit of a beam subjected to pure bending decreases with

The correct option is: Endurance limit of a beam subjected to pure bending decreases with.

To understand why this is correct, we analyze how the fatigue endurance limit of a material is influenced by external modifying factors (Marin factors) such as surface condition and size.

The endurance limit of a mechanical component is given by the Marin equation:
$S_e=k_a{k}_b{k}_c{k}_d{k}_e{k}_f{S}_e^{\prime }$
where:
• $k_a$ is the surface condition modification factor.
• $k_b$ is the size modification factor.
• $S_e^{\prime }$ is the rotary-beam test specimen endurance limit.

1. Effect of Surface Roughness:
Surface roughness introduces microscopic irregularities (valleys and scratches) on the outer layer of the beam. These irregularities act as localized stress raisers (stress concentration zones) under bending loads. Since fatigue cracks almost always initiate at the surface, increasing the surface roughness makes it easier for cracks to form, thereby decreasing the endurance limit (reducing the value of $k_a$).

2. Effect of Size:
As the size of the beam increases, a larger volume and surface area of the material are subjected to high stresses. According to statistical weakest-link theories, a larger volume has a higher probability of containing critical material defects, dislocations, or voids that can initiate fatigue failure. Therefore, as the size increases, the size factor $k_b$ decreases, resulting in a lower endurance limit.

Thus, the fatigue endurance limit of a beam subjected to pure bending decreases with an increase in surface roughness and an increase in the size of the beam.