2. Benchmark solution#
2.1. Tested sizes#
The quantities of interest are the cracking times obtained by the index method and by the BaBy (Barbier-Bystricky) model [1].
The crack time (in hours) of the index model is given by the following expression:
\({t}_{f}=\frac{10000}{{i}_{T}\mathrm{.}{i}_{M}\mathrm{.}{i}_{\sigma }}\)
where
\({i}_{T}={\mathrm{9,49.10}}^{15.}\mathrm{exp}(\frac{-22000}{T+\mathrm{273,15}})\) with \(T\) in °C. For \(T=350°C\), \({i}_{T}=\mathrm{4,41}\)
\({i}_{M}=1\)
\({i}_{\sigma }={\mathrm{2,44.10}}^{-11}{\sigma }^{4}\), with \(\sigma\) the biggest main constraint (expressed as \(\mathit{MPa}\))
The cracking time of the BaBy model is obtained by solving a coupled mechanical-corrosion problem. A simplified version of solving the problem consists in decoupling the equations and treating the corrosion equations only by post-processing a non-linear mechanical calculation. This is the strategy adopted in modeling A.
From the stress field \(\sigma\), the evolution of the cumulative plastic deformation \(p\) and the concentration of corrosive agent \({c}_{h}\) is determined during post-treatment:
\(\begin{array}{c}\dot{p}={(\frac{{\Vert \sigma \Vert }_{\mathit{VM}}}{K(T)(1-{c}_{h})})}^{n}\mathrm{.}{p}^{-n/m}\\ \dot{{c}_{h}}=\frac{3}{2}\beta \dot{p}\frac{⟨1/3\mathit{tr}\sigma ⟩}{{\Vert \sigma \Vert }_{\mathit{VM}}}\end{array}\)
then the time to crack is the time such as \({c}_{h}({t}_{f})=1\).
Parameter \(\beta\) is a material parameter identified from a creep experiment alone.
Here, \(\beta =\mathrm{889,5}\).
2.2. Bibliographical references#
Barbier, P. Bystricky, Application of the BaBy model to the prediction of diffusion times by Stress Corrosion of Alloy 600 in the primary environment, Note EDF R&D HT-2C/97/048/A, March 1998