2. Reference solution#

2.1. Calculation method used for the reference solution#

In [bib1], a reference solution is given, based on an integral boundary equation method. The value of the stress intensity factor in mode I is then:

\({K}_{I}\mathrm{=}\frac{3+\nu }{4}\mathrm{\cdot }\rho {\omega }^{2}({R}_{2}^{2}+\frac{1\mathrm{-}\nu }{3+\nu }{R}_{1}^{2})\mathrm{\cdot }\sqrt{\pi b}\mathrm{\cdot }{F}_{I}\) where the geometric correction factor is given, as a function of the parametric angle of the ellipse \(\theta\), in the figure below.

_images/10000000000007E0000005684CB762FE86C059B2.png

The ratio \(a\mathrm{/}t\) chosen corresponds to the upper curve (squares).

Since the maximum difference between the marked points and the curve is \(\text{2\%}\), the reading error on the curve is less than the maximum error announced (\(\text{5\%}\)).

However, we are not using this reference because it seems to be wrong.

As a reference, we use the numerical results obtained from calculations using the ANSYS software.

2.2. Uncertainty about the solution#

2.3. Bibliographical references#

    1. MURAKAMI: Stress Intensity Factors Handbook, box 9.39, pages 786-791. The Society of Materials Science, Japan, Pergamon Press, 1987.