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 (which physically represents the case of an increase in the surface roughness and increase in the size of the beam).

Detailed Explanation:
The actual endurance limit ($S_e$) of a machine member differs from the endurance limit ($S_e^{\text{'}}$) determined in standard laboratory tests. To account for these differences, Marin's equation is used:
$S_e=k_a·k_b·k_c·k_d·k_e·k_f·S_e^{\text{'}}$
where:
• $k_a$ is the surface condition modification factor.
• $k_b$ is the size modification factor.

1. Influence of Surface Roughness ($k_a$):
Fatigue failures almost always originate from surface defects. A rougher surface contains microscopic scratches, tool marks, and grooves that act as stress concentrators (stress raisers). An increase in surface roughness increases local stress concentration, which facilitates crack initiation under cyclic loading. Consequently, the surface factor $k_a$ decreases, thereby lowering the endurance limit.

2. Influence of Beam Size ($k_b$):
When a beam is subjected to pure bending, the stress is non-uniform, reaching its maximum at the outermost fibers. A larger beam has a greater volume of material subjected to high stress levels. Statistically, a larger volume has a higher probability of containing micro-defects or material flaws that can trigger fatigue failure. As a result, the size factor $k_b$ decreases as the dimensions of the beam increase, leading to a lower endurance limit.