On notch and crack size effects in fatigue, Paris law and implications for Whler curves - Michele Ciavarella; A. Papangelo (Fracture and Structural Integrity)
As often done in design practice, the Whler curve of a specimen, in the absence of more direct information, can be crudely retrieved by interpolating with a power-law curve between static strength at a given conventional low number of cycles N0 (of the order of 10-103), and the fatigue limit at a infinite life, also conventional, typically N8=2?106 or N8=107 cycles. These assumptions introduce some uncertainty, but otherwise both the static regime and the infinite life are relatively well known. Specifically, by elaborating on recent unified treatments of notch and crack effects on infinite life, and using similar concepts to the static failure cases, an interpolation procedure is suggested for the finite life region. Considering two ratios, i.e. toughness to fatigue threshold FK=KIc/DKth, and static strength to endurance limit, FR =sR /Ds0, qualitative trends are obtained for the finite life region. Paris and Whlers coefficients fundamentally depend on these two ratios, which can be also defined sensitivities of materials to fatigue when cracked and uncracked, respectively: higher sensitivity means stringent need for design for fatigue. A generalized Whler coefficient, k, is found as a function of the intrinsic Whler coefficient k of the material and the size of the crack or notch. We find that for a notched structure, k min k min m, as a function of size of the notch: in particular, k=k holds for small notches, then k decreases up to a limiting value _which depends upon Kt for mildly notched structures, or on FK and FR only for severe notch or crack_. A perhaps surprising return to the original slope k is found for very large blunt notches. Finally, Paris law should hold for a distinctly cracked structure, i.e. having a long-crack; indeed, Paris coefficient m is coincident with the limiting value of k lim. The scope of this note is only qualitative and aims at a discussion over unified treatments in fatigue