Question

The S-N curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit? 

 

• A. \(S_{ut}\)
• B. \(S_2\)
• C. \(S_3\)
• D. \(S_4\)

Hint:

For S-N curves of steel, always look for the "knee" where the curve flattens out. The stress value of this flat, horizontal line is the endurance limit. Not all materials (e.g., aluminum alloys) have a distinct endurance limit; their S-N curves continue to slope downwards.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
An S-N curve (Stress vs. Number of cycles) is a graphical representation of the fatigue life of a material. It plots the cyclic stress amplitude (\(S\)) against the number of cycles to failure (\(N\)). The endurance limit (or fatigue limit), denoted \(S_e\), is a specific feature of S-N curves for certain materials like ferrous alloys (e.g., steel). It is the stress level below which the material can withstand an infinite number of load cycles without failing due to fatigue.
Step 2: Detailed Explanation:
1. The S-N curve typically starts at the Ultimate Tensile Strength (\(S_{ut}\)) for a very low number of cycles.
2. As the number of cycles increases, the fatigue strength (the stress the material can withstand for that number of cycles) decreases. This is the downward sloping part of the curve (regions 1, 2, 3).
3. For materials like steel, after a certain number of cycles (typically \(10^6\) to \(10^7\)), the curve becomes horizontal.
4. This horizontal portion indicates that if the applied stress is at or below this level, the material will not fail, no matter how many cycles are applied. This stress level is the endurance limit.
5. In the given graph, the curve slopes downwards from \(S_{ut}\) through \(S_1\), \(S_2\), and \(S_3\). Beyond \(N_3\), the curve becomes horizontal at the stress level \(S_4\).
6. Therefore, \(S_4\) represents the endurance limit of the steel.
Step 3: Final Answer:
The endurance limit is given by \(S_4\).
Step 4: Why This is Correct:
By definition, the endurance limit is the stress value at which the S-N curve becomes asymptomatic or horizontal. In the provided diagram, this occurs at the stress level \(S_4\). Stresses above \(S_4\) lead to failure after a finite number of cycles, while stresses at or below \(S_4\) are presumed to lead to an infinite life.