On unified crack propagation laws. (15th February 2019) - Papangelo, A.; Guarino, R.; Pugno, N.; Ciavarella, M.
Highlights: A unified crack propagation law is proposed, which holds for the propagation of short and long cracks. When integrated, the proposed law is compatible with the standard SN curve of uncracked specimens. The proposed unified law compares satisfactorily with experimental data from literature. Abstract: The anomalous propagation of short cracks shows generally exponential fatigue crack growth but the dependence on stress range at high stress levels is not compatible with Paris' law with exponent m = 2 . Indeed, some authors have shown that the standard uncracked SN curve is obtained mostly from short crack propagation, assuming that the crack size a increases with the number of cycles N as da dN = H Δ σ h a where h is close to the exponent of the Basquin's power law SN curve. We therefore propose a general equation for crack growth which for short cracks has the latter form, and for long cracks returns to the Paris' law. We show generalized SN curves, generalized Kitagawa–Takahashi diagrams, and discuss the application to some experimental data. The problem of short cracks remains however controversial, as we discuss with reference to some examples.