A mathematical validation of a computer code performing FEM based fatigue analysis is, in general, not possible because of the following:
An unique fatigue analysis method does not exist.
Many approaches have been developed over the years, and many will still be developed in the future:
multiple stress-based and strain-based fatigue parameters are available in literature;
critical plane or alternative approaches;
multiple cyclic plasticity models;
different damage cumulation models;
A huge amount of papers are available in literature claiming the goodness of certain methods on the basis of adherence to dedicated experimental data. These highlight the fact some methods could be more appropriate than other depending on the problem being solved (type of geometry, loading modes, …) and/or material parameters (and in some cases also calibration factors) being used.
(With LIFING, the analyst can choose among a list of many of the most acknowledged analysis techniques).
When a fatigue solver is used, a specific set of material parameters is adopted. However material fatigue data are characterized by a significant scatter. This means that, even if an ideal unique fatigue analysis parameter/approach would exist, results being produced would be ‘deterministically’ related to the specific material parameters used, therefore comparison with test data will inevitably show an ‘error’ due to the difference between the real material behaviour (of the used test specimen) and the modelled one.
The fatigue damage, or life, calculated on the basis of a FEM is strictly dependent on the FEM quality (mesh size, element type and order, boundary conditions, …). This means that two different FE Models of the same structure, solved with the same fatigue solver, using same approach and same material data, will show different fatigue results.
Because of the above, when a FEM assisted fatigue analysis is performed, the analyst must ensure that calculated results are valid within an acceptable error. This can be done if experimental data, for the problem being analysed, exist. The analyst can ‘calibrate’ results accordingly and apply appropriate scatter factors to the calculated results.
The LIFING ‘validation’ presented here must be looked from the perspective outlined above, that is:
It is not a rigorous mathematical validation because a reference fatigue theoretical solution to be used for validating the implemented algorithms does not exist.
Calculated results are based on analysis methods which are considered more appropriate, however any of the available methods can be used, which will deliver their own related results (which will be affected by the assumptions and limitations embedded in the method).
Deviations between analysis and test data results must be judged considering appropriate scatter bands.
Tension-Torsion Loading of a Notched Shaft
The Society of Automotive Engineers (SAE) Fatigue Design and Evaluation Committee coordinated an extensive testing program of a notched shaft subjected to tension and torsion loading. Results are documented in Multiaxial Fatigue: Analysis and Experiments, AE-14, G.E. Leese, D.F. Socie, Society of Automotive Engineers, Warrendale, PA, 1989.
Material is steel SAE 1045 Hot rolled in normalized condition.
The geometry is shown in the sketch on the right.
The FEM is so characterized:
Used elements are 2nd order HEXA; at the notch the element size is 0.78x1.43 mm.
The model is ground constrained in the middle section of the left side cylindrical part and loaded at the middle section of the right side cylindrical part.
LIFING is used to run the analysis for those tests that are done minimum twice.
Tests with only bending applied is solved by using the Smith-Watson-Topper fatigue parameter and cyclic plasticity is solved using Dowling method.
Tests with torsion or combined bending and torsion is solved with Fatemi-Socie fatigue parameter. Cyclic plasticity is solved in these cases with the Köttegen-Barkey-Socie Pseudo-Material method.
The chart on the left shows the comparison between test and analytical results.
More details are provided in the LIFING Validation documentation.