The resistance of fatigue of a material is measured by the endurance limit. The endurance limit, also known as the fatigue limit, is the maximum stress level that a material can withstand for an infinite number of cycles without failing. It is an important property in engineering as it determines the durability and reliability of a material under cyclic loading conditions.

Explanation:
1. What is endurance limit?
The endurance limit is the maximum stress level at which a material can withstand cyclic loading indefinitely without failure. It represents the fatigue strength of the material and is typically determined through fatigue testing.

2. Importance of endurance limit:
The endurance limit is a critical parameter in designing components and structures that are subjected to cyclic loading. It helps engineers determine the maximum stress level that a material can endure without experiencing fatigue failure. This information is crucial in ensuring the longevity and reliability of structures and machinery.

3. Difference between endurance limit and ultimate tensile strength:
While the ultimate tensile strength (UTS) represents the maximum stress a material can withstand before it breaks under tension, the endurance limit focuses on the material's resistance to cyclic loading. The UTS is determined through a single tensile test, whereas the endurance limit is determined through fatigue testing, which involves subjecting the material to repeated cycles of stress.

4. Elastic limit and Young's modulus:
The elastic limit is the maximum stress level a material can endure without experiencing permanent deformation. It is different from the endurance limit, which focuses on fatigue failure. Young's modulus, on the other hand, represents the stiffness or rigidity of a material and is not directly related to its fatigue resistance.

5. Determining the endurance limit:
The endurance limit is typically determined through fatigue testing, where a specimen of the material is subjected to repeated cycles of stress. The stress levels applied during the test are gradually increased until fatigue failure occurs. The number of cycles the material can withstand without failure is recorded, and the endurance limit is defined as the stress level below which the material can endure an infinite number of cycles without failure.

In conclusion, the endurance limit is the measure of a material's resistance to fatigue failure under cyclic loading conditions. It is determined through fatigue testing and represents the maximum stress level that a material can endure indefinitely without failure. The endurance limit is essential in designing reliable and durable structures and components.