# Fatigue life of a simple beam

• FEAnalyst
In summary, it seems that it is not possible to calculate fatigue life for complex models analytically, based on static FEA results. However, it is possible to calculate fatigue life for a simple case of a beam subjected to bending using a simplified procedure.
FEAnalyst
TL;DR Summary
Is it possible to calculate the fatigue life of a simple beam analytically?
Hi,

some time ago I wondered if it's possible to calculate fatigue life (number of cycles to failure) for complex models analytically, based on static FEA results: https://www.physicsforums.com/threa...culations-based-on-static-fea-results.994264/

Unfortunately, it seems that it's not doable. However, now I would like to perform such calculations for a simple case of a beam subjected to bending. Let's assume that the beam is simply-supported and has uniformly distributed load (UDL) acting on it. Let's assume that the beam is 1 m long, has square cross-section (40x40 mm) and is made of steel. Force resultant of applied UDL is 8000 N. Thus the maximum stress is around 94 MPa. I used bilinear stress-life curve approximation with 2 data points: transition (stress: 200 MPa, life: 1000 cycles) and endurance (stress: 75 MPa, life: 100000 cycles). Direct reading of fatigue life for stress of 93.75 MPa gives the following result (interpolated linearly): 85150 cycles to failure.
I performed a numerical analysis in SolidWorks Simulation to check this. Static stress result is correct but the result of fatigue simulation is around 40000 cycles to failure. What may cause the difference ? Does it mean that it's not possible to calculate faitgue life even in such a simple case ? Or maybe I should use different approach than simply reading from stress-life curve ? I'll just add that mean stress effect wasn't included here (because I assumed fully-reversed loading) and that I enabled fatigue calculation based on von Mises stress (instead of stress intensity) in SolidWorks Simulation. I also specified 1000000 as the number of cycles for this study.

You should research the standard fatigue test using an R.R. Moore machine. This is the way most fatigue data is acquired.

I think the short answer to your question is simply "no." There is always some scatter in fatigue data due to small imperfections in the material, the specimen geometry, and the test process.

These factors could make the analytical results inaccurate when compared with real life experiments. But what about the comparison with finite element analysis ? Numerical simulation software uses the same input data (stress-life curve) and in this case it doesn't apply any advanced techniques such as mean stress correction. So how does it calculate the fatigue life and why couldn't it be done analytically?

Well, I really don't know. After all, you are the FEAnalyst, not me. It would seem logical that anything that can be done in a finite number of computer steps could also be done (in principle) with a finite number of pencil and paper steps. Someone who does FEA would surely know how that works, I would think.

I know the procedure followed by one of the fatigue analysis programs that I use at work because it's described in the documentation. However, I can't find any details about the approach used in another FEA software, the one that I used when solving this simple case of a beam. I'll keep searching and asking, maybe I will find out how this particular software works. It must use some simplified procedure since it's just a CAD-embedded FEA module, not a separate fatigue analysis code.

It seems likely that it would simply be an implementation of one of the standard approaches used for machine design such as the Goodman line.

I've decided to go back to this and I've finally found the reason of the difference between fatigue analysis results and direct reading from stress-life curve. I just made a mistake when reading the fatigue life for particular stress amplitude from S-N curve - I forgot that this is log-log curve and performed the reading like for linear axes. Now the reading is pretty much the same as the value obtained from analysis (around 35 000 cycles).
Maybe someone will find this solution useful in the future.

Tom.G

## 1. What is the definition of fatigue life for a simple beam?

Fatigue life refers to the number of cycles or repetitions of loading that a simple beam can withstand before it fails due to fatigue. It is a measure of the durability and strength of the beam under repeated loading.

## 2. How is the fatigue life of a simple beam calculated?

The fatigue life of a simple beam is typically calculated using a fatigue curve or S-N curve, which plots the stress amplitude against the number of cycles to failure. The point where the curve intersects the required stress level is used to determine the fatigue life of the beam.

## 3. What factors can affect the fatigue life of a simple beam?

Several factors can affect the fatigue life of a simple beam, including the material properties, geometry, loading conditions, and surface conditions. Other factors such as temperature, environment, and manufacturing processes can also play a role.

## 4. How can the fatigue life of a simple beam be improved?

The fatigue life of a simple beam can be improved through various methods, such as using higher strength materials, reducing stress concentrations, improving surface finish, and implementing design changes to reduce stress levels. Regular maintenance and inspections can also help to prolong the fatigue life of a beam.

## 5. Why is it important to consider the fatigue life of a simple beam?

Considering the fatigue life of a simple beam is crucial because fatigue failure is one of the most common causes of structural failure. It is especially important in applications where the beam is subjected to repeated loading, such as in bridges, buildings, and machines. Understanding the fatigue life can help ensure the safety and reliability of the structure and prevent costly failures.

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