winLIFE QUICK CHECK (Endurance Limit Certification)

 

Many FEM users wish to make fatigue life predictions. They often, however, have hardly any information on the load spectrum, the S-N curves, surface, isotropy etc. Despite this, they still wish to make at least a rough estimate on whether any fatigue strength problems are to be expected. The Endurance Limit Certification can help to answer such questions. If it is possible to safely show that in a worst-cast-scenario the stress is below the endurance limit, then this result is often sufficient and more extensive fatigue strength tests can be dispensed with.

 

The endurance limit certification cannot give you the fatigue life, but a prediction as to whether the worst-case-scenario is below the endurance limit and if so, by how much. If the endurance limit certification is not fulfilled, then it will be necessary to carry out much more detailed fatigue life tests. For these, you will need, in particular, the loads and their time relation.

Proof of Safety against Endurance Limit

 

The program module winLIFE QUICK CHECK provides the functionality for the endurance limit certification. Results can be achieved with very little action by the user. The proof is based on FEM calculations and for every load Fi (force, torque, temperature), which has an effect on the component you must have a static FEM-calculation for the maximum value (upper load Foi).

 

For each load having an effect on the component, only

 

-          the mean load and amplitude or

-          a constant load

 

is taken into account. The number of load cycles is not considered in the calculation. The stress tensors of however many nodes you require – e.g. all surface nodes – are used for the analysis.

 

To describe the material you only need the endurance limit and its dependence on the mean stress.

 

To calculate the safety against the endurance limit, a calculation of all possible combinations of the stress tensors is carried out and superimposed. The process is shown in the following picture.

 

The maximum and minimum occurring principal stress is ascertained from the results of all the superpositions. From this, a principal mean stress and a principal stress amplitude are calculated and then transformed into an equivalent amplitude Sa,equ  with the aid of the mean stress sensitivity M. The endurance limit SDW of the S-N curve is divided by the equivalent amplitude which gives you the safety against endurance limit. The reciprocal value of the safety against the endurance limit is the degree of efficiency a = Sa,equ/SDW.


The maximum load (= upper load) Foi for each individual loading condition i must be put on the FE-model. The results of the FE calculation are the stress tensors Ski,o for each node  To obtain the lower load Fui use the following formula with the stress ratio R and Foi

 

Fui = Foi * Ri

The stress tensor for the lower load can be calculated simply with the aid of the following formula:

 

 

Now the permutations p(i) of all imaginable load combinations are calculated just in case the stresses were superposed unfavourably. In this way, the result takes into account the worst case and is therefore on the safe side. In order to define the most unfavourable stress superposition, the following load condition combinations must be examined.

 

 

Load type

Number of combinations to be examined

Variation 1

Variation 2

 

alternating (R=-1)

2

+1

-1

 

pulsating (R=0)

2

+1

0

 

constant  (R=1)

1

+1

 

 

any R

2

+1

-1

 

 

A simple example for a pure pull-push loading is shown in the following diagram and it makes the procedure clear. If you only consider the condition on the surface then there will be an even stress condition. This can be shown simply in a Mohr`s circle and the principal stress is obvious.

 

 

Within every node, each stress tensor Skiu und Skio has a largest and a smallest principal stress. Since the time path of the loads i is not known, winLIFE QUICK CHECK examines all imaginable load condition combinations and looks for the largest and the smallest of all the combinations. Using the principal stress as a damage relevant size makes it much easier but this is sufficient for an estimate.

The largest and the smallest principal stresses SHmax and SHmin are used to determine the amplitude and the mean stress using the following formula:

 

Sm,k= (SHmax,k + SHmin,k)/2

 

Sa,k =(SHmax,k - SHmin,k)/2


An equivalent alternating stress Sa,equ,k  is then calculated from the stress amplitude and the mean stress with the aid of the amplitude transformation. The endurance limit SDW divided by this alternating stress amplitude then gives you the safety against endurance limit. The reciprocal value of the safety against the endurance limit is the degree of efficiency a = Sa,equ,k /SDW. The results of the safety against endurance limit and the degree of efficiency are written in the winLIFE export file and can either be shown on the screen or printed out

 

If the degree of efficiency is < 1 then you can presume that it is not necessary to calculate the fatigue life.

 

If the degree of efficiency is nearly or even above 1, then a more detailed analysis and a fatigue life prediction is necessary.