Benchmark solution
=====================


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

The reference solution was obtained by experimental method :ref:`4 <RefNumPara__9929_1168901107>`. In this article, a numerical simulation is also carried out.


Benchmark results
----------------------


The Paris-type fatigue propagation law resulting from the tests is as follows:
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:math:`\frac{\mathit{da}}{\mathit{dN}}\mathrm{=}C{(\Delta K)}^{m}` with :math:`C\mathrm{=}{10}^{\mathrm{-}\mathrm{9,2}}` and :math:`m\mathrm{=}\mathrm{3,5}`. The values of the coefficients of the Paris law are given for :math:`\Delta K` in :math:`\mathit{MPa}\mathrm{.}\sqrt{m}` and a speed :math:`\frac{\mathit{da}}{\mathit{dN}}` in :math:`m\mathrm{/}\mathit{cycle}`.
------------------------------------------------------------------------------ -

After 4000 cycles, the deepest point of the crack bottom experimentally reached coast :math:`y\mathrm{=}173\mu m`. The present experimental crack background is calculated numerically after 4000 cycles.


.. image:: images/10000000000002A70000021A9ABF1FF0C39F932A.png
    :width: 5.1201in
    :height: 3.1835in


.. _RefImage_10000000000002A70000021A9ABF1FF0C39F932A.png:

Figure2.1 1: Crack bottom


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



.. _RefNumPara__9929_1168901107:

1. E. Ferrié, J.Y. Buffière, W. Ludwig, W. Ludwig, A., Graouil, A., A., A., Graouil, A., L., Edwards, L., Fatigue, Crack Propagation: In situ visualization using X-ray microtomography and 3D simulation using the extended finite element method, Acta Materialia 54, pp. 1111-1122, 2006