Monotonic or Cyclic Stress-Strain Curve for FE Fatigue?

[AeroStructAnalyst]

Hi all and the experts in house,
I have two questions regarding FE Fatigue;
In order to do fatigue analysis in most Axial FE Fatigue codes, various Unit load cases are often created based on 'Linear' FEA assumptions - (usually linear material model based on monotonic material Stress-Strain curve) and depending on the 'peak' load case in the time history, the Unit load cases Linear FEA nodal stresses is 'factored' and superimposed to create the nodal stresses for that given 'peak' load in the time history.

For Axial S-N fatigue, using the user defined or code default S-N curve, the allowable cycles is derived based on these deduced 'superimposed' nodal stresses (derived from the Linear FEA) at each 'peak' in the time history, taking into account various reduction factors. Using the required number of cycles, the damage at each node is calculated, and the fatigue life is derived accordingly.

For Axial e-N fatigue, some deductions are carried out to account for notch effects and the likes. and using the user defined e-N curve, or code default e-N curve,the number of reversals to failure is deduced and the fatigue life, hence fatigue life is derived accordingly knowing the required number of cycles.

My question is this; given the cyclic nature of fatigue, should the Linear FE be based on monotonic or cyclic material properties?

My second question is perhaps really not appropriate for S-N fatigue since the basis is 'elastic stresses'. For Low Cycle Fatigue, hence e-N fatigue, where high plastic strains is likely, how is the plastic shake down (or otherwise) taken into account given that the 'superimposed' nodal stresses for each given 'peak' in the time history are derived using 'Unit load' FEA stresses which are also derived based on 'Monotonic' stress-strain material properties? Is the assumption that the e-N curve by nature already accounts for this plastic shake down?

 

[rb1957]

"given the cyclic nature of fatigue, should the Linear FE be based on monotonic or cyclic material properties?" ... if you're fatigueing typical materials (Al alloy) then most cyclic stress should be elastic. in any case, i'm curious what this "cyclic material property" is ? i'm aware that strain hardening happens, but i'd've thought the effect was negligible for the elastic range ??

your 2nd question somewhat confused me ... if you're dealing with plastic stresses, then you need to use a NL FEA. not sure what "plastic shake down" means. if you're into the plastic zone, then you can't use unit loads, since they don't extrapolate (beyond the elastic zone). if you've got e-N data that should be usable, it should account for plasticity but you'll need to read into it with a plastic strain ...

Quando Omni Flunkus Moritati

 

[bxtsafe]

AeroStructAnalyst,

I did not understand your first question. So, I'll just answer the second one.

The e-N curve have 4 parameters associated to it (S'f , b , e'f , c) . It is important to have in mind that the e-N curve ALREADY ACCOUNTS for the "plastic shake down". You can realize it by searching for how the e-N curve is obtained. I recommend the book "Fatigue Testing and Analysis, Theory and Practice" of "Yung-Li Lee et al.".

We can use the S-N method ONLY for High Cycle Fatigue, i.e., problems for which the applied stresses are BELLOW the material yield strength.

Otherwise, we can use the e-N method for BOTH High Cycle Fatigue AND Low Cycle Fatigue (i.e. problems for which the applied stresses are ABOVE the material yield strength). The majority of the analysts use the S-N method for problems of High Cycle Fatigue because this method requires just 2 variables ( "S'f" and "b") to solve the fatigue problem.

When you have a component that is under cyclic loading and the stresses are above the Material Yield Strength the usual method is:
A) Do a Transient NONLINEAR Analysis, using the MONOTONIC stress-strain to account for plasticity.
B) After that, you have to do a Rainflow Counting to identify the fatigue loading cycles.
C) After, for each cycle (identified in the previous step) you have to apply the e-N method to calculate the Fatigue Damage caused by that cycle.

The previous explanation is the pragmatic way to solve a fatigue problem. Although, Transient Nonlinear Analyses are very very time consuming. So, there are another way to do it:
A) Do a Transient LINEAR Analysis, using just the Modulus of Elasticity and the Poisson ration of the material analysed.
B) After that, you have to do a Rainflow Counting to identify the fatigue loading cycles.
C) After, for each cycle (identified in the previous step) you have to apply the NEUBER's RULE. This rule is a technique used to calculate the TRUE stress and TRUE strain values of a point from the NOMINAL stress and NOMINAL strain values, which were obtained from a Linear FEA. See "

http://fcp.mechse.illinois.edu/media/pdfs/1_Notches.pdf"

for more information on Neuber's Rule)
D) Use the TRUE stresses and TRUE strains of each cycle in the e-N method to calculate the Fatigue Damage caused by that cycle. We have to remember that the values of strain that should be input on the e-N method must be the TRUE values.

Cheers.