In this paper a numerical approach coupling independent path integrals, such as M-integral, to compute the crack driving forces namely the stress intensity factors, and empirical models, for instance Paris-Erdogan’s law, to assess the cumulative fatigue damage (i.e. crack size) during the crack growth process, is proposed. The M-integral derived from Nother’s theorem combines the real and virtual mechanical deformation and stress fields. A finite element routine is developed in order to compute the energy release rate according to the stress intensity factors. Results are given for a simple standard Al7075-T6 tensile test specimen. Finally, numerical estimates are compared to experimental data for various crack length in order to prove the efficiency and the accuracy of the proposed model.