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


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

The reference solution is a digital solution from the note [:ref:`bib1 <bib1>`]. The purpose of this note was to validate simplified methods in fracture mechanics. The results of this note were obtained with code_aster version 3.

     [:ref:`bib1 <bib1>`] gives the value of :math:`{J}_{\text{fond}}` for various load levels :math:`m`.

     :math:`m=\frac{M}{4{\sigma }_{\gamma }{R}^{2}t}`

The results are given in the following table:


.. csv-table::

    ":math:`M(\mathit{Nmm})` "," :math:`m` "," :math:`{J}_{\text{fond}}(\mathit{KJ}/m\mathrm{²})` "," :math:`{J}_{\text{fond}}^{e}(\mathit{KJ}/m\mathrm{²})`"
    "", "", "", ""
    "5.216 109", "2.013", "9.8102", "1.91101"




     Where:

     :math:`{J}_{\text{fond}}(\mathit{KJ}/m\mathrm{²})` is the value of the integral J at the bottom of the crack for an elasto-plastic behavior law.

     :math:`{J}_{\text{fond}}^{e}(\mathit{KJ}/m\mathrm{²})` is the value of the integral J at the bottom of the crack for a linear elastic behavior law.


Bibliography
-------------


1. P. CAMBERFOR — Y. GUELORGET: FICHE 3479- Calculations of straight pipes with semi-elliptical and axisymmetric circumferential defects: moment loads and pressure+moment. Team management EDF. Thermal and nuclear studies and projects department. 1998.