Hi guys
I don’t know if anyone here is somewhat comfortable with fracture mechanics, and more specifically fatigue crack growth equations. One of the most common laws is Paris’ law, but it doesn’t really account for the stress ratio (R).



According to “Mechanical Metallurgy” by George E. Dieter, a better approximation of the crack growth rate that does account for the stress ratio is:




α is a geometric factor that depends on the crack length (a) as well, that’s why most commercial programs use a numerical approach. For my sake, I’ll assume that α is constant.

So the above crack growth equation can be rewritten as




Where I have a problem is integrating the formula to estimate the number of cycles until rupture. Basically, I want to isolate ΔN (Nf-Ni) where N is the number of cycles.

This is what I’ve come to, but my calculus knowledge is rusty, so I’m not sure if what I’ve done is good or not.



Where ac and a0 and the limits of the integral, where a0 is the initial crack length and ac is the critical crack length.


If someone could check the math on that, I’d really appreciate it!

I'm a french canadian by the way, so pardon my english