# How to Calculate Fatigue Analysis?

## Measuring strain and stress spectrum

### 1. Measure the stress concentration area and arrange the strain gauge

The stress concentration area can be determined by simulation (finite element) or test (a layer of paint is applied on the prototype, and the load is applied after the paint is dry, and the stress concentration is at the place where the paint is peeled off), and then three strain gauges are arranged in the stress concentration area according to the left figure below:

Because the material is isotropic, the x and y directions are not necessarily horizontal and vertical, but the two must be vertical, and the middle one must be at an angle of 45 ° with the x and y directions.

### 2. Calculate the stress according to the measured strain and material properties

The three strains measured are recorded as ε x,ε y, ε xy.

Two principal stresses (assuming only elastic deformation):

Where E is the elastic modulus of the material and µ is the Poisson’s ratio.

Based on these two principal stresses, the equivalent stress that may be required by some methods can be calculated (the main purpose is to convert the multi-component stress state into a numerical value to facilitate the application of fatigue data of materials), such as Mises equivalent stress:

Or maximum shear stress:

The strain time spectrum is actually measured, and the stress (or equivalent stress time spectrum) can be calculated by the above formula.

### 3. Decomposition spectrum

It is to decompose the above measured stress (strain) – time spectrum and calculate the times under different stress (including amplitude and average value) cycles, so as to calculate the accumulated damage.

The most commonly used method is the rainflow counting method.

## Get material data

If the load frequency is not high, a group of simple fatigue tests can be carried out (sinusoidal stress, tension and compression or bending, with national standards):

A stress life (i.e. number of cycles) curve is obtained, which is the so-called S-N curve:

If the load frequency is high or the temperature changes greatly, the S-N load under different average stresses and temperatures shall be measured for interpolation calculation, because the average stress has an impact on the life.

According to different empirical formulas (such as Goodman’s criterion, Gerber’s criterion, etc.) and other material properties (such as tensile strength, failure strength, etc.), the corresponding fatigue life when the average stress is not zero can also be calculated from the ordinary S-N curve (i.e., the average stress is 0).

If the material data is extremely limited, or the company is very poor and lazy to do fatigue test, the fatigue performance can also be estimated from the strength of the material.

If plastic strain occurs, the cumulative damage is generally based on the strain life curve (i.e., E-N curve), so the strain load needs to be applied.

## Damage calculation

Up to now, fatigue analysis is basically based on empirical formula, and there is no completely unified theory.

There are many calculation methods for damage accumulation, the most commonly used is linear cumulative damage (i.e. miner’s criterion), but the results are not conservative and the calculated life is high.

The accumulation criterion with high accuracy is bilinear, and the calculation is easier than “failure curve method”, so it is a good compromise choice.

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