Analytical evaluation of J-integral for elliptical and parabolic notches under mode I and mode II loading |
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Authors: | Paolo Livieri Fausto Segala |
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Affiliation: | (1) Department of Engineering, University of Ferrara, Via Saragat 1, 44100 Ferrara, Italy;(2) Department of Physics, University of Ferrara, Via Saragat 1, 44100 Ferrara, Italy |
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Abstract: | In the present work the J-integral (indicated here as JVρ
because two parallel flanks are not present) was calculated by using, along the free border, the exact analytical stress
distribution for the ellipse and the asymptotic one for parabolic notches. The material was assumed as homogeneous isotropic
and linear elastic. First, for an ellipse under remote tensile loading, the expression of JVρ
has been analytically calculated on the basis of Inglis’ equations. The equations have been used to prove that, in terms
of J-integral, the crack is the limit case of an equivalent elliptic notch. Furthermore, by distinguishing the symmetric and
skew-symmetric terms, the well-known Stress Intensity Factors (SIF) of mode I and II for a crack in a wide plate under tension
are obtained by adding a limiting condition. Second, by means of Creager–Paris’ equations, JVρ
has been analytically calculated for a parabolic notch of assigned tip notch radius ρ. The asymptotic value of JVρ
and the relationship between the peak stress and the relative SIF are the same as the ellipse. Finally, as an engineering
application, we provide an accurate formula for the evaluation of the Notch Stress Intensity Factors of a crack, mainly subjected
to tensile stress, from the peak stress of the equivalent ellipse under the same loading. |
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Keywords: | J-integral Notches Stress intensity factors Stress concentration |
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