What is S–N curve?

Short Answer:

The S–N curve (also known as the Wöhler curve) is a graph that shows the relationship between the stress amplitude (S) applied to a material and the number of cycles to failure (N) under cyclic loading. It is obtained from fatigue tests and helps to predict how long a material can last when repeatedly loaded and unloaded.

In simple words, the S–N curve shows how the fatigue life of a material decreases as the applied stress increases. It is widely used in designing mechanical parts like shafts, gears, and springs that are subjected to repeated or fluctuating stresses during operation.

Detailed Explanation:

S–N Curve

The S–N curve is one of the most important graphical representations in the study of fatigue behavior of materials. It describes how materials fail under repeated or fluctuating stresses over time. “S” stands for the stress amplitude applied to the specimen, and “N” stands for the number of cycles to failure.

This curve is also known as the Wöhler curve, named after August Wöhler, a German engineer who first studied the effect of repeated loading on metals in the 19th century. The S–N curve provides valuable information about how long a material can endure under different stress levels before fatigue failure occurs.

The concept of the S–N curve is very important in mechanical design, as many machine components (such as shafts, connecting rods, and aircraft wings) are subjected to cyclic loading and must be designed to avoid fatigue failure over their expected life.

Construction of S–N Curve

To obtain an S–N curve, a fatigue test is performed on specimens of the material under controlled cyclic loading conditions. The procedure is as follows:

  1. Specimen Preparation:
    A smooth, polished test specimen of standard size and shape is prepared to minimize surface defects.
  2. Fatigue Testing:
    The specimen is subjected to repeated or cyclic loading using testing machines such as rotating bending machines or axial fatigue testing machines.
  3. Stress Variation:
    Different specimens are tested at different stress amplitudes, and the number of cycles (N) it takes for each specimen to fail is recorded.
  4. Plotting the Curve:
    The results are plotted on a graph with stress amplitude (S) on the vertical axis and number of cycles to failure (N) on the horizontal axis (on a logarithmic scale).
  5. Curve Shape:
    The resulting curve typically slopes downward from left to right, showing that as stress decreases, the number of cycles to failure increases.

Shape and Characteristics of S–N Curve

  • The S–N curve starts with a high stress and low cycle region where failure occurs quickly.
  • As the stress level decreases, the number of cycles before failure increases significantly.
  • For ferrous materials (like steels), the curve becomes horizontal beyond a certain point, meaning the material can endure an infinite number of cycles below a certain stress level — this stress level is called the endurance limit.
  • For non-ferrous materials (like aluminum, copper, or magnesium), the curve keeps sloping downward, meaning these materials do not have a true endurance limit — they eventually fail if the stress is applied long enough.

Thus, the S–N curve helps engineers determine both the fatigue strength and the endurance limit of materials.

Typical Regions of the S–N Curve

  1. Low-Cycle Fatigue (High-Stress Region):
    • Occurs when the applied stress is high (near or above the yield strength).
    • The material fails in a small number of cycles (usually fewer than  cycles).
    • Deformation is mostly plastic in nature.
    • Common in applications involving shock loading or overload.
  2. High-Cycle Fatigue (Low-Stress Region):
    • Occurs when the applied stress is low (below the yield strength).
    • The number of cycles to failure is large (usually between  and ).
    • Deformation is mainly elastic.
    • Common in rotating machinery, aircraft parts, and automotive components.

Significance of S–N Curve

  1. Predicts Fatigue Life:
    • The curve helps determine how long a component can last under a given stress level before failure occurs.
  2. Determines Endurance Limit:
    • For materials like steel, it identifies the limiting stress below which the material can withstand infinite cycles.
  3. Guides Safe Design:
    • Engineers use S–N curves to set safe stress limits and apply factors of safety in design.
  4. Material Selection:
    • Helps compare different materials for fatigue resistance in cyclic loading conditions.
  5. Failure Prevention:
    • By understanding the fatigue characteristics, failures due to repeated loading can be minimized or completely avoided.

Factors Affecting S–N Curve

Several factors influence the position and shape of the S–N curve:

  1. Material Type:
    • Steels show a clear endurance limit, while non-ferrous metals do not.
  2. Surface Finish:
    • Rough or scratched surfaces reduce fatigue life. Polished surfaces improve it.
  3. Size of Specimen:
    • Larger specimens tend to have lower fatigue strength due to higher stress concentrations.
  4. Temperature:
    • High temperatures reduce fatigue resistance, while low temperatures may increase it.
  5. Mean Stress:
    • A higher mean stress (static component) reduces fatigue life.
  6. Environment:
    • Corrosive environments accelerate fatigue failure (known as corrosion fatigue).
  7. Residual Stresses:
    • Compressive residual stresses (from processes like shot peening) improve fatigue resistance.

Applications of S–N Curve

The S–N curve is used in the design and analysis of components that are subjected to repeated loading during service, such as:

  • Aircraft structures and wings.
  • Engine parts (crankshafts, connecting rods).
  • Rotating shafts and spindles.
  • Springs and gears.
  • Bridges and railway components.

By using the S–N curve data, engineers can ensure that these components operate safely below their fatigue limits for long durations without failure.

Conclusion

The S–N curve is a graphical representation that shows how the fatigue life of a material varies with applied cyclic stress. It helps determine the endurance limit, fatigue strength, and safe stress levels for components under fluctuating loading. The curve typically shows that as the stress amplitude decreases, the number of cycles to failure increases. For ferrous materials, it becomes horizontal beyond a certain limit, indicating infinite life. The S–N curve is an essential tool in mechanical design for ensuring the safety, durability, and reliability of components operating under repeated stresses.