Multi-axial fatigue analysis program development

In the principal stress approach, stresses are separated into two directions (parallel and normal). 

1. The algorithm starts by calculating the first and the second principal stress directions. 

2. The next step is to group principal stresses by principal directions. The DNV standard allows 10° of principal stress variation. Therefore, time series larger than this should be grouped before analysis. 

3. The fatigue damage is then calculated for each group. The average principal stress direction for each group can be used as the representative principal direction of each group.

4. The unidirectional cracks in the angle range ±60° relative to the perpendicular to the weld direction are added to the damage and all unidirectional cracks outside the angle range ±45° are added to the damage

5. Then the larger of the two will be the final damage. 

Critical plane approach refers to the calculation of damage parameters on specific planes, which are prone to cause failure.  In this module, an in-plane critical plane approach is adopted. 

1. The algorithm starts by generating stress states corresponding to different in-plane angles. The stress states are calculated using Mohr's circle. 

2. Cycle counting is first performed on a normal stress channel using a simple uniaxial rainflow counting algorithm.  

3. As normal stress cycles are identified, the algorithm extracts the maximum and minimum shear stress values for each cycle. 

4. The effective stress range is computed using the multi-axial fatigue criterion

5. Fatigue damages is calculated for each planes with the effective stress ranges by Palmgren-Miner rule. 

6. The largest of the damages will be the final damage.