# How is the assumption that stress and strain are elastic everywhere is valid for STRESS-LIFE method for fatigue life calculation?

Stress life method is generally employed for high-cycle fatigue (HCF) applications. while HCF region is approximated by $$\sigma=a(N)^b$$ which gives a linear graph on log-log scale, for steels it starts from $$0.9\sigma_{ut}$$ up to $$0.5\sigma_{ut}$$. I presume that $$0.9\sigma_{ut}> \sigma_{y}$$ and in such a case how is my assumption of elastic strain and stress everywhere is valid. $$\sigma_{ut}$$ and $$\sigma_{y}$$ are the ultimate strength and yield strength of steel respectively.

• Check out the Comet - a real example. Jun 25 at 7:01
• Please provide the source material for a better understand of your concerns.
– r13
Jun 25 at 16:44
• I am not certain that there is an explicit assumption that material remains in the elastic region during fatigue testing. Could you provide the exact quote for that statement? If it states that explicitly, then your concerns are valid, but I don't think that's the case. Jun 25 at 17:39
• If the loading causes nonlinear material behavior, you will not have high cycle fatigue by the usual definition of HCF - i.e. at least $10^4$ cycles to failure and often at least $10^7$. Jun 26 at 1:07
• I was referring to the following video youtu.be/Alvl5f8blgI .@7:20 the professor states the above assumption. Jun 26 at 14:40

Note "High Cycle Fatigue (HCF)" failure is characterized by high repetitive cycles (N), usually equal to or greater than $$10^4$$, and low-stress (S) in the elastic zone.