Abstract
As often done in design practice, the Wohler 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 N∞=2·106 or N∞=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 Wohler’s 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 Wohler coefficient, k’, is found as a function of the intrinsic Wohler coefficient k of the material and the size of the crack or notch. We find that for a notched structure, k<k’<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.
Highlights
I t is well known that initiation and propagation of cracks are well distinct phenomena, and depend strongly on the material, geometry and load levels
At low load levels, where we expect fatigue failure at high cycle numbers (HCF, High Cycle Fatigue) practically the whole life is expended in enucleating the crack, rather than propagating: the latter phase only takes the final few cycles
At high load levels, cyclic plastic deformation takes place rapidly leading to failure
Summary
I t is well known that initiation and propagation of cracks are well distinct phenomena, and depend strongly on the material, geometry and load levels (for a review see for example Fleck et al [1]). The scope of the present paper is to try to “unify” crudely various concepts for static and fatigue design, without any intention to give radically new methodologies, or empirical formulae, but with the simpler scope of examining various ranges of validity and overlap between the theories which often are treated separately, and with principally the suggestion to use interpolation between robust estimates of limit conditions and the use of all the material properties which are available, rather than extrapolation from a single methodology using a limited set of material properties, independently on how refined the methodology may appear to be This is not necessarily limited to preliminary calculations, and when there is possibility of some experimental investigations, as a simpler route for understanding of the behaviour in fatigue of a notched component. The entire spectrum of possible behaviour can be described in a single diagram strength vs. notch/crack size
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