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.
