Cycles to failure

$$\text{Ramberg-Osgood equation:} \hspace{41mm} \varepsilon_{tot} = \underbrace{\frac{\sigma}{E}}_{\text{elastic}} + \underbrace{\left(\frac{\sigma}{K}\right)^{\frac{1}{n}}}_{\text{plastic}}$$ $$\text{Coffin-Manson equation:} \hspace{46mm} \varepsilon_{tot} = \underbrace{\frac{\sigma_f}{E}\left(2N_f\right)^b}_{\text{elastic}} + \underbrace{\varepsilon_f\left(2N_f\right)^c}_{\text{plastic}}$$ I was wondering about a situation where the cycles were not of constant stress/strain and not given by a SN curve or strain life diagram. How do you get the ultimate tensile strength after a number of cycles with changing stress and strain at each cycle?

• That makes it quite difficult, particularly since fatigue failure is statistical to begin with. – Jon Custer Aug 18 '20 at 14:05