2. Benchmark solution#

2.1. Calculation method used for the reference solution#

The reference solution was obtained by experimental method 4. In this article, a numerical simulation is also carried out.

2.2. Benchmark results#

2.3. The Paris-type fatigue propagation law resulting from the tests is as follows:#

\(\frac{\mathit{da}}{\mathit{dN}}\mathrm{=}C{(\Delta K)}^{m}\) with \(C\mathrm{=}{10}^{\mathrm{-}\mathrm{9,2}}\) and \(m\mathrm{=}\mathrm{3,5}\). The values of the coefficients of the Paris law are given for \(\Delta K\) in \(\mathit{MPa}\mathrm{.}\sqrt{m}\) and a speed \(\frac{\mathit{da}}{\mathit{dN}}\) in \(m\mathrm{/}\mathit{cycle}\). —————————————————————————— -

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

_images/10000000000002A70000021A9ABF1FF0C39F932A.png

Figure2.1 1: Crack bottom

2.4. Bibliographical references#

    1. 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