"S-N Curve/Wohler Curve"

Hi Everyone!!

"S-N Curve is a plot of the magnitude of an alternating stress versus the number of cycles to failure for a given material"

How is S-N Curve created for a given material?

Consider a rotating beam specimen for a 4-Point bending test and start to rotate.

As it rotates it will experience compression (C) at the top portion and then as it rotates further it will reach to neutral axis (NA) where there is no stress and later when it rotates and reach at bottom portion, it experiences tension (T). This is 1 complete Cycle and called as Fully Reversible Cycle. So, S-N diagram holds good for fully reversible loading.

So, if load applied to the specimen is equal to the ultimate strength then it will fail immediately. As we decrease the load progressively and check how many cycles it can sustain then it will plot the curve as below. This is called S-N curve.

In order to simplify the curve in linear relation, it is usually plotted in log scale as shown below, so that we can check relative effects.

There are three parameters that separate the plastic, elastic and infinite life regions:

• Ultimate Strength: Stress level required to fail with one cycle.
• Yield Strength: Dividing line between elastic and plastic region.
• Endurance Limit: If all cycles are below this stress level amplitude, no failures occur.

Elastic Region:-

In the elastic region, the relationship between stress and strain remains linear. When a cycle is applied and removed, the material returns to its original shape or length. This region is also referred to as the “High Cycle Fatigue” region, because a high number of stress cycles, at a low amplitude, can cause the specimen to fail.

Typical factors that influence the performance of a material in the elastic region are residual stresses and geometric considerations. For example, a severe geometry change in the material may be more likely to have a crack initiate than a smooth geometry change.

Plastic Region:-

In the plastic region, the material experiences high stress levels, causing the shape or geometry to change due to the repeated application of stress cycles. This region is also referred to as the “Low Cycle Fatigue” region of the SN-Curve, where a low number of stress cycles, with a high amplitude, result in failure.

Material plasticity and geometry are big influences on the number of cycles to failure in the plastic region.

Calculating fatigue life or damage in the plastic region of a material with a SN-Curve is probably avoided. If cyclic stress levels are in the plastic region, a strain life approach would typically be recommended, which includes an E-N (Strain vs Number of cycles) as part of the analysis. Strain life also takes into account the order or sequence in which loads are applied.

Endurance limit:-

The maximum value of fully reversible loading test that material can withstand without any failure.

"As long as stress is below endurance limit, it will have infinite life"

Note: - Non-ferrous alloys like Aluminium does not have Endurance limit because S-N curve for Aluminium will progressively decrease with increase in number of cycles as shown below.

How to consider Endurance limit for Non-ferrous alloys??

• Usually it is considered as the Stress that gives 10^7 cycles, Or
• Endurance limit = 0.3 – 0.5 Sut (if S-N curve is not available)

This is all about S-N Curve, Now question arises:-

How to decide which methodology is appropriate?? High Cycle Fatigue (HCF) or Low Cycle Fatigue (LCF)

Perform Static analysis and check stresses Vs Yield strength.

• Components subjected to stresses lower than yield strength do not experience plastic deformation and have relatively long life. This type of service is commonly referred to as high-cycle fatigue.
• Components subjected to stresses greater than yield strength experience plastic deformation and have relatively short lives. This type of service is commonly referred to as low-cycle fatigue. 

I hope this article will provide basic idea about S-N Curve and it's use.

Have a Nice long Happy Weekend!!

One Quote to end it on positive note,

"Life is like a Mirror. Smile at it and It smiles back at you"