2. Reference solution#
2.1. Benchmark results#
The results are experimental [ref 1]. The measured values are the stress amplitudes after stabilization:
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\(\frac{\Delta {\varepsilon }_{\mathit{xx}}}{2}\) |
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FRI15 |
0.0034 |
0 |
0 |
413 |
413 |
-5 |
0.0058 |
0 |
237 |
0 |
FRI15 |
0.0034 |
0 |
0 |
398 |
398 |
-5 |
0.0058 |
0 |
231 |
1 |
So we get the following averages \(\frac{\Delta {\sigma }_{\mathit{xx}}}{2}\mathrm{=}405.5\mathit{MPa}\) and \(\frac{\Delta {\sigma }_{\mathit{xy}}}{2}\mathrm{=}234\mathit{MPa}\),
which, like \({\sigma }_{\mathit{xx}}\mathit{moy}\mathrm{=}\mathrm{-}5\mathit{Mpa}\), and \({\sigma }_{\mathit{xx}}\mathit{moy}\mathrm{=}\mathrm{0,5}\mathit{Mpa}\) leads to:
\({\sigma }_{\mathit{xx}}\mathit{max}\mathrm{=}400.5\mathit{MPa}\), \({\sigma }_{\mathit{xx}}\mathit{min}\mathrm{=}\mathrm{-}410.5\mathit{MPa}\)
\({\sigma }_{\mathit{xy}}\mathit{max}\mathrm{=}234.5\mathit{MPa}\), \({\sigma }_{\mathit{xy}}\mathit{min}\mathrm{=}\mathrm{-}233.5\mathit{MPa}\)
2.2. Uncertainty about the solution#
The uncertainty resulting from the variability of the experimental results is 2%. That which comes from the identification of material parameters can be estimated at 5% to 10% (cf. [ref. 2]).
2.3. Bibliographical references#
« Multiaxial fatigue evaluation using discriminating strain paths » Nima Shamsaei, Ali Fatemi, Darrell F. Socie International Journal of Fatigue 33 (2011) 597—609
J.M. PROIX « Viscoplastic behavior taking into account the non-proportionality of the load » EDF R&D-CR- AMA12 -284, 12/12/12