The path independent J integral proposed by Rice (1968) [41] describes the stress-strain field at the tip of the crack under elastic-plastic loading. Since the integral can be taken far from the crack tip and then information about the crack tip may be deduced, this allows an extension of fracture mechanics associated with elastic fatigue fracture from linear elastic to elastic-plastic behaviour.
From experiment, under certain theoretical conditions, it has been shown that the governing equation for crack growth can be written in a form similar to Paris-Erdogan,
where 
is the J-integral range, and m is determined
from experiment. It should be remembered that the J integral
methods have strong analytical basis, which differs from the
totally empirical Paris-Erdogan.