Reference solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

In [:ref:`bib1 <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:

:math:`{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 :math:`\theta`, in the figure below.


.. image:: images/10000000000007E0000005684CB762FE86C059B2.png
    :width: 6.4528in
    :height: 3.9701in


.. _RefImage_10000000000007E0000005684CB762FE86C059B2.png:

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

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


Uncertainty about the solution
---------------------------


Bibliographical references
---------------------------


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