What term describes the number of cycles required to cause failure for a given stress level?

The term that describes the number of cycles required to cause failure for a given stress level is fatigue life. Fatigue life quantifies how long a material or component can endure repetitive loading before experiencing failure. This concept is crucial in mechanical design, as it informs engineers about the reliability of materials and components under cyclic loads.

When a component is subjected to fluctuating stresses, it undergoes fatigue, which can lead to microscopic cracks that propagate over time, ultimately resulting in a failure. Understanding the fatigue life helps in predicting how many load cycles a component can withstand before it broke down, enabling the design of safer and more durable structures.

In contrast, the other terms refer to related but distinct concepts. Endurance refers to the ability of a material to withstand cyclic loading without failing, which is often associated with a specific stress level, but does not directly quantify the cycles to failure. Fatigue, while directly related to the phenomenon of failure over time under repeated loading, does not specifically denote the number of cycles. Rupture refers to a more instantaneous failure condition, typically under static loads rather than cyclic stresses. Hence, fatigue life is the most accurate descriptor for the cycles to failure under a certain stress level.