What are S-N curves, and how are they used in fatigue analysis?

Short Answer:

S-N curves, also known as Wöhler curves, show the relationship between the stress (S) applied to a material and the number of cycles (N) it can survive before failing due to fatigue. These curves help engineers understand how long a material can last under repeated loading conditions.

In fatigue analysis, S-N curves are used to predict the life of components. By knowing the stress level a part experiences, the curve can tell how many cycles it will last before failure. This is very helpful in designing safe and long-lasting mechanical parts like shafts, beams, and machine components.

Detailed Explanation:

S-N curves and their use in fatigue analysis

In mechanical engineering, many machine parts work under repeated or cyclic loads. These loads are not constant, and they keep changing during the operation. Over time, such changes can cause small cracks to form in the material, which grow and lead to failure. This type of failure is called fatigue failure. To study and prevent this, engineers use a special graph known as the S-N curve.

What is an S-N curve?

An S-N curve is a graph that shows the relationship between:

  • S: the stress amplitude (how much stress is applied), and
  • N: the number of cycles to failure (how many times the stress is applied before the part breaks).

These curves are made using experiments where a sample material is tested under repeated loading until it fails. Different stress levels are applied, and the number of cycles until breakage is recorded for each case. When this data is plotted, it creates a downward-sloping curve that helps engineers understand the fatigue behavior of the material.

This curve is also called a Wöhler curve, named after August Wöhler, who first studied fatigue in railway axles.

How are S-N curves used in fatigue analysis?

S-N curves are a very important tool in fatigue analysis. Here’s how engineers use them:

  1. Predicting fatigue life
    Suppose a machine part is going to be subjected to a certain repeated stress. By checking the S-N curve of the material, engineers can find out how many cycles that part can survive before failure. This is called fatigue life estimation. For example, if the part experiences 200 MPa stress, and the S-N curve shows failure after 500,000 cycles at that level, then the part needs to be replaced or maintained before reaching that cycle count.
  2. Deciding safe stress levels
    Instead of predicting life, sometimes engineers fix the number of cycles the part should survive (e.g., 10⁶ cycles for one year of operation). Then they use the S-N curve to find the maximum stress the material can safely handle for that many cycles. This helps in setting design limits and safety margins.
  3. Comparing materials
    Different materials have different S-N curves. Stronger materials like alloy steel may show longer life under stress compared to weaker materials like aluminum. Engineers compare curves to select the best material for fatigue-prone components.
  4. Detecting endurance limit
    Some S-N curves become flat after a certain point, meaning the material can survive infinite cycles if the stress is below a certain value. This point is called the endurance limit. Materials like steel show this behavior, and engineers design such parts to work below this stress for long life.

Features of an S-N curve

  1. Logarithmic scale: The number of cycles (N) is usually shown on a logarithmic scale to cover a wide range from 100 to millions of cycles.
  2. S-N slope: The curve slopes downwards, meaning that higher stress leads to failure in fewer cycles.
  3. Knee point: In materials with endurance limit, the curve flattens at the end. This is the safe zone for infinite life.
  4. Scatter: Real test results do not follow one single line. There is variation due to different samples, surface finishes, or testing conditions.

Practical example

Let’s say a crankshaft in a car engine experiences a repeated load of 150 MPa. The S-N curve for its steel material shows that it can survive up to 1 million cycles at this stress. If the car’s engine rotates 1000 times per minute, and the crankshaft is loaded in every rotation, it would take about 1000 minutes (around 17 hours) to reach 1 million cycles. If the stress is reduced to 100 MPa, the S-N curve might show 10 million cycles, increasing the life significantly.

This shows how reducing stress or choosing a better material improves fatigue life.

Conclusion

S-N curves are essential tools in mechanical design to study how materials behave under repeated stress. They help engineers predict how long a component will last (fatigue life) or decide how much stress is safe for long-term use. By using S-N curves properly, engineers can prevent sudden failures, ensure safety, and design more reliable machines. These curves are especially important for parts like gears, shafts, aircraft wings, and rotating machines that face continuous loading and unloading during their life.