Step 1: Compare fatigue with static failure.
A component can fail statically when a single large load exceeds its ultimate strength, but fatigue is a different phenomenon altogether, it happens at stress levels well below the yield or ultimate strength of the material.
Step 2: Rule out the other loading types.
A sudden shock load or a constant steady load produces a single point on the stress life curve and does not by itself create the microscopic cracks associated with fatigue. A gradually applied load also does not cycle the stress up and down, so it cannot initiate the crack growth mechanism either.
Step 3: Explain the actual mechanism.
Fatigue develops because a stress that rises and falls repeatedly, over thousands or millions of cycles, initiates a microcrack at a stress concentration point such as a notch, fillet or surface flaw, and then slowly propagates it cycle by cycle until the remaining cross section suddenly snaps. This is why components are designed against an endurance limit read off the S-N curve, not just against the ultimate tensile strength.
\[ \boxed{\text{Repeated application of stress}} \]