# Fatigue life hand calculations based on static FEA results

• FEAnalyst
In summary, FEA can be used to calculate stress concentrations and determine whether a part will fail due to fatigue. However, it’s likely that hand calculations are not possible and one must rely on the safety factor obtained analytically.
FEAnalyst
TL;DR Summary
How can one calculate fatigue life for a complex model based on results obtained from linear static FEA ?
Hi,
advanced FEA programs allow their users to perform fatigue analyses. However, there are still many programs where such simulations can't be performed. I've heard that in such case one can use results obtained from regular linear static FEA to calculate fatigue life manually. Theoretically maximum stress (Mises or principal ?) could be compared with Wöhler curve of the material to obtain minimum fatigue life. However, there are two main issues:
- how to do it in case of geometrically complex models (machine parts) subjected to complex loading (not just simple tension/compression, bending or torsion) ?
- how to do it in case of loading other than fully reversed so that we have to account for mean stress effects ?

Is it possible to account for these factors in hand calculations based on stress from linear static FEA ? If yes then how to do it and which formulas should I use ? Where can I find some examples ?

My copy of Fundamentals of Machine Component Design by Juvinall and Marshek has a chapter on fatigue with a section on fatigue of components with non-zero mean stress. There is too much to summarize in a PF post, so I recommend getting a copy of that book. I have used it to design a number of highly stressed components, none of which failed by fatigue.

Use the FEA to get the maximum and minimum tensile stresses, then use Juvinall and Marshek. Keep in mind that appropriate discretization of complex parts calculates the stress concentration for you, so there is no need to apply a stress concentration factor.

FEAnalyst
Thank you very much for reply. The problem is that the approach described in Juvinall's book (involving Goodman's diagram) allows you to obtain the safety factor and determine whether the part will fail or not due to fatigue under a given load. However, what I want to calculate is the fatigue life (how many cycles can the part withstand). Is it possible to do it with hand calculations ?

I don't think so. Here's my reasoning:
1) The scatter plots in Juvinall are from carefully prepared fatigue test specimens. Complex machine parts add a level of complexity that will increase the scatter.
2) The scatter plots in MIL-HDBK-5: same comments.
3) I once took a graduate course in fatigue. I no longer have the textbook, but do not recall any practical way to estimate fatigue life for arbitrary loadings in complex parts.
4) Effect of loading history. Hazy recollection: The British Comet airliners that exploded due to fatigue leading to uncontrolled crack propagation. Their ground test fuselage was at 14,000 pressurization cycles with no signs of failure while the real airplanes failed catastrophically at 1400 cycles. The test fuselage survived because of an initial overpressure test that caused yielding in a stress concentration, which reduced peak tensile stresses in normal loading.
5) Material property variation. A friend's father made precision rifle barrels. He once got, unknowingly, a batch of commercial grade steel instead of the aerospace grade. The alloy and heat treat were right, but wrong quality level. He found this out the hard way when some barrels blew up.

Thanks again. Indeed it’s very likely that such calculations are not possible and one can only obtain the safety factor analytically. However, I wonder how FEA solves fatigue analyses then (if we ignore all complex effects such as damage cummulation). I think that it simply compares the stresses in each element with Wohler curve and uses mesn stress correction. Maybe this could be done manually too.

jrmichler

## What is fatigue life?

Fatigue life refers to the number of cycles or repetitions that a material can withstand before it fails under a specific load or stress level. It is an important consideration in engineering and design, as it helps determine the durability and reliability of a component or structure.

## What is a static FEA?

A static FEA (Finite Element Analysis) is a computer simulation method used to analyze the structural behavior of a component or structure under a static load. It divides the structure into smaller elements and uses mathematical equations to calculate stress and strain at each point, providing a visual representation of the stress distribution.

## How are fatigue life hand calculations based on static FEA results performed?

To calculate fatigue life based on static FEA results, the stress values obtained from the simulation are used as inputs in the fatigue analysis equations. These equations take into account factors such as material properties, load cycles, and stress concentration to estimate the number of cycles the component can withstand before failure.

## What are the limitations of fatigue life hand calculations based on static FEA results?

One limitation is that the accuracy of the results depends on the accuracy of the inputs, such as material properties and load conditions. Additionally, hand calculations may not take into account all the complexities of real-world conditions, such as varying loads and stress concentrations. Therefore, they should be used as a preliminary estimation and validated with physical testing.

## How can fatigue life be improved based on static FEA results?

To improve fatigue life, engineers can make design changes based on the stress distribution obtained from the FEA analysis. This can involve adjusting the geometry, changing material properties, or adding reinforcements to areas with high stress concentrations. Additionally, conducting multiple iterations of the FEA analysis can help optimize the design for better fatigue life.

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