Measuring strain and stress spectrum
1. Measure the stress concentration area and arrange the strain gauge
The stress concentration area can be determined through simulation using finite element analysis or by conducting a test. In the test method, a layer of paint is applied to the prototype, and the load is applied after the paint has dried.
The stress concentration is identified at the location where the paint peels off. Once the stress concentration area is determined, three strain gauges can be arranged in that area as shown in the left figure below:
Since the material is isotropic, the x and y directions may not necessarily be horizontal and vertical, but they must be perpendicular to each other, and the third direction must be at an angle of 45° with both 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 the two principal stresses, one can calculate the equivalent stress using various methods (primarily to convert the multi-component stress state into a numerical value for easy application of material fatigue data). One such method is the 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
The objective is to decompose the stress (or strain) – time spectrum obtained above and determine the duration of different stress cycles (including amplitude and average value), in order to compute the accumulated damage.
The rainflow counting method is the most widely employed approach for this purpose.
Get material data
If the load frequency is not high, a set of simple fatigue tests can be conducted according to national standards. These tests may include sinusoidal stress, tension and compression, or bending.
A stress life (i.e. number of cycles) curve is obtained, which is the so-called S-N curve:
When the load frequency is high or there are significant temperature changes, it is necessary to measure the S-N load under various average stresses and temperatures for interpolation calculation. This is because the average stress has an impact on the life.
Fatigue life can also be calculated from ordinary S-N curve when the average stress is not zero, using different empirical formulas such as Goodman’s criterion, Gerber’s criterion, and other material properties like tensile strength and failure strength.
In cases where material data is limited or the company is unwilling to conduct fatigue tests, the fatigue performance can be estimated from the material strength.
When plastic strain occurs, the cumulative damage is usually based on the strain life curve (i.e., E-N curve), which requires the application of strain load.
Damage calculation
Currently, fatigue analysis relies mainly on empirical formulas, and a completely unified theory does not yet exist.
Several calculation methods exist for damage accumulation, with linear cumulative damage (also known as Miner’s criterion) being the most widely used. However, the results are not always conservative and may overestimate the calculated life.
The accumulation criterion with high accuracy is bilinear, and the calculation is easier than the “failure curve method”, making it a good compromise choice.
