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LIMITATIONS ON THE USE OF THE STRESS INTENSITY FACTOR, K , AS A FRACTURE PARAMETER IN THE FATIGUE PROPAGATION OF SHORT CRACKS
Author(s) -
Kfouri A. P.
Publication year - 1997
Publication title -
fatigue and fracture of engineering materials and structures
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.887
H-Index - 84
eISSN - 1460-2695
pISSN - 8756-758X
DOI - 10.1111/j.1460-2695.1997.tb01521.x
Subject(s) - stress intensity factor , fracture mechanics , fracture (geology) , stress concentration , stress (linguistics) , materials science , finite element method , structural engineering , point (geometry) , paris' law , crack closure , mechanics , mathematics , mathematical analysis , geometry , composite material , engineering , physics , linguistics , philosophy
— It is well known that for very short cracks the stress intensity factor K is not a suitable parameter to estimate the stress level over the small but finite Stage II process zone activation region of size r s near the crack tip, within which crack growth events take place. A critical appreciation of the reasons for the limitations on the applicability of Δ K as a fatigue crack propagation (FCP) parameter, when the crack length a is of the same order of magnitude or smaller than the size of the ‘fatigue‐fracture activation region’, r s is presented. As an alternative to Δ K the range Δσ s of the cyclic normal stress at a point situated at the fixed distance s = r s /2, ahead of the crack tip, inside the fatigue‐fracture activation region, is proposed. It is observed that the limitation on the use of Δ K when the crack is short, is mathematical (and not physical) but this inconvenience is easily circumvented if the stress Δσ s at the prescribed distance is used instead of Δ K since nowadays Δσ s can be obtained numerically by using finite element methods (FEM). It follows that the parameter Δσ s is not restricted by the mathematical limitations on Δ K and so it would seem that there is, a priori , no reason why the validity of the parameter Δσ s cannot be extended to short cracks. It is shown that if the Paris law is expressed in terms of Δσ s (πr r s ) ½ instead of Δ K the validity of the modified Paris law can be extended to short cracks. A coherent estimate of the value of the fatigue‐fracture activation region r s is derived in terms of the fatigue limit Δσ FL obtained from S‐N tests and of the threshold value Δ K th obtained from tests on long cracks where both relate to Stage II crack growth that ends in failure, namely, r s = (Δ K th /Δσ FL ) 2 /π. An overall, threshold diagram is presented based on the simple criterion that, for sustained Stage II FCP, Δσ s must be greater than Δσ FL . The study is based on a simple continuum mechanics approach and its purpose is the investigation of the suitability of both Δ K and Δσ s to characterise the crack driving force that activates complex fracture processes at the microstructure's scale. The investigation pertains to conditions that lead to the ultimate failure of the component at values of Δσ s > Δσ FL .