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An approximation in closed form for the integral of Oore–Burns for cracks similar to a star domain
Author(s) -
Livieri P.,
Segala F.
Publication year - 2018
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/ffe.12629
Subject(s) - ellipse , mathematical analysis , mathematics , weight function , star (game theory) , stress intensity factor , integral equation , fourier transform , domain (mathematical analysis) , stress field , computation , asymptotic expansion , fracture mechanics , geometry , structural engineering , engineering , algorithm , finite element method
In this paper, we give an explicit new formulation for the three‐dimensional mode I weight function of Oore–Burns in the case where the crack border agrees with a star domain. Analysis in the complex field allows us to establish the asymptotic behaviour of the Riemann sums of the Oore–Burns integral in terms of the Fourier expansion of the crack border. The new approach gives remarkable accuracy in the computation of the Oore–Burns integral with the advantage of reducing the size of the mesh. Furthermore, the asymptotic behaviour of the stress intensity factor at the tip of an elliptical crack subjected to uniform tensile stress is carefully evaluated. The obtained analytical equation shows that the error of the Oore–Burns integral tends to zero when the ratio between the ellipse axes tends to zero as further confirmation of its goodness of fit.