High-cycle method
In: Fatigue calculation methods
Existence of a high-cycle method is a purely virtual construct. This group of method is separated only in order to define scope of results that can be achieved. High-cycle fatigue can be studied in many other books. What the meaning of high-cycle method should be here is, that these methods confront the actual load history with lifetimes around the fatigue limit only.
This is a relatively rough simplification. First, one very often hears, that existence of fatigue limit is unproven. Nevertheless, this point can be at least evaluated as a conventional fatigue limit e.g. on 10e6 or 10e7 number of cycles. Second, the high-cycle fatigue region starts at a bit lower number of cycles and reaches beyond the fatigue limit point (giga-cycle fatigue). A more precise description of high-cycle region should comprise of the whole area and not with one specific point. Thus we distinguish two types of methods here:
* fatigue limit oriented methods
* limited lifetime oriented methods
Fatigue Limit Oriented Methods
The commonly used formula in this group of criteria can be rewritten as a combination of shear C and normal stress N on some plane or planes:
or with wholly general left hand side (LHS):
,
where the f-1 corresponds to fatigue limit in fully reversed tension-compression. The fatigue index is then defined as:
If it is lower than one, the local loading is lower than fatigue limit. If the fatigue limit separates the region of infinite life (which is not wholly true), than the local place should withstand infinite loading of the range given. Higher values correspond to the other case – the component would break.
Since the multiaxial fatigue criteria are usually tested towards experimentally gained complex fatigue limits, the fatigue index of an ideal criterion should be every time equal to one for these experiments. This usually is not the case, so the fatigue index error was defined to be:
Values of fatigue index error lower than zero correspond to non-conservative solution, higher values mark a conservative prediction.
Note: Results of similar analyses, which have been until now systematically evaluated for the most criteria implemented in PragTic, can be found in the freely accessible FatLim database tool.
The methods of this category implemented in PragTic are:
* Carpinteri & Spagnoli method with SWT modification
* Carpinteri & Spagnoli method with SWT and MD modifications
* Gonçalves, Araújo & Mamiya (GAM) method
* Ninic method with SWT modification
All of them produce the resulting fatigue index, not the final damage. The methods focus on description of fatigue behaviour under constant amplitude loading. Thus no rain-flow decomposition and no cumulative rule is applied within them - the maximum loads are input into the damage parameter.
Limited Lifetime Oriented Methods
There is only one criterion in PragTic today, which could be related to high-cycle fatigue in its complete meaning:
* Findley criterion revised by Socie.
Here the result of computation correspond to value of damage, reciprocal value of which is number of cycles till the crack initiates. The method is based on the e-N curve and thus the problematic definition of behaviour of the S-N curve near the fatigue limit is avoided. PragTic utilizes the conservative expectation that the maximum values from the complete load history are confronted with the fatigue limit - the method is again oriented towards the constant amplitude loading similarly to the previous group of the criteria.
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