Dear colleagues!
If calculate strain energy density at static loading as an area under the stress-strain curve and at cyclic loading as a difference of areas of hysteresis loops of two consequent loading cycles summarized by the number of cycles till fracture, how close the values should be?
How to calculate strain energy density at fatigue fracture from experimental cyclic stress-strain curve (hysteresis loop)?
Any references on this topic?
you can create matlab code to read your hysteresis loops and give you the total area for all cycles, average......
now for your first question, it depends. what is the material you are testing, what is the strain rate ( material young's modulus) will be affected by the strain rate you are using.
in other words let's assume material X fails statically at load N "yield point load", then when applying dynamic load it will fail at a value more than N in general.
Good luck
Thank you for the answer, Younis!
Mathlab is good idea.
I should add some details to my question:
Material is 0.65%C carbon spring steel 65Г (analogues1066,
1566 Ck67, 080A67, 65Mn, 65G) in as-delivered state, without heat treatment.
I’m considering low-cycle fatigue conditions, so strain is far more than yielding point. All the calculations were performed in terms of local strains, measured by digital image correlation technique (DIC).
The stress rate at cyclic loading is close to -1 (tension+ compression) so the hysteresis loop has a zero-crossing.
In my calculation the summarized strain energy density at mentioned conditions is just 30% more than obtained from true stress-strain (not engineering curve) curve for this material.
Is this accidental?
How does this correspond to existing theories of fatigue fracture?
what is your cyclic strain, if its above 2% it should be the other way!
I believe you already studied this material, sending you this PDF and I hope it will help
https://www.efatigue.com/training/Chapter_5.pdf
In my research, for solder alloy SnAgCu we found that cycling will cause change in the microstructure (recrystallization) and change in the material behavior (hardening/softening)
here is one of the articles I did while working on the topic
https://www.researchgate.net/publication/276242058_Damage_Evolution_in_Lead_Free_Solder_Joints_in_Isothermal_Fatigue
I hope it help, and good luck
Article Damage Evolution in Lead Free Solder Joints in Isothermal Fatigue
Thank you, Younis! Yes, I’m familiar with the theory in PDF you’ve sent and I’ll study your article.
In my tests strain was up to 6-7%, so I used true stress-strain curve.
The research is described in this article
https://www.researchgate.net/publication/309428603_Strain_energy_density_of_steel_evaluation_at_cyclic_loading
(it is not translated into English so far, but I hope you can get the main point from the descriptions to the figures).
The calculation in the article was performed for representative volume of material ahead of fatigue crack tip in the center of the wide plate. Now I’m going to do the same for smooth specimen undergoing cyclic loading at stress ratio 0.3. The aim is to calculate the life-time of a specimen using energy approach described in the article. The problem is that local stress rate in this case will be not -1, but close to the external loading rate (0.3) so the hysteresis loop will be deferent and I’ll need to modify the calculation algorithm.
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