4. B modeling#
4.1. Characteristics of modeling#
Method SIMPLEXE is used by PROPA_FISS to solve the crack propagation equations. No auxiliary grids are used.
4.2. Characteristics of the mesh#
The same mesh as that of modeling A. is used.
4.3. Tested sizes and results#
The values of \({K}_{I}\) and \({K}_{\mathit{II}}\) for the two depths of the crack are tested after each propagation. To check if these values are correct, a relative tolerance equal to 5% is used for the values of \({K}_{I}\). On the other hand, to check whether the value of \({K}_{\mathit{II}}\) is zero, an absolute tolerance (threshold value) linked to the value of \({K}_{I}\) is used: it is considered that \({K}_{\mathit{II}}\) is zero if its value is less than 1% of the value of \({K}_{I}\). Indeed, in this case we can overlook the value of \({K}_{\mathit{II}}\).
We test the maximum value of \({K}_{I}\) and \({K}_{\mathit{II}}\) between the two bottoms of the crack.
Propagation |
Max \({K}_{I}\) [\(\mathit{Pa}\sqrt{\mathit{mm}}\)] |
\({K}_{I}\) reference [\(\mathit{Pa}\sqrt{\mathit{mm}}\)] |
Tolerance [%] |
1 |
2.2914E+07 |
2.2997E+07 |
5.0 |
2 |
2.5803E+07 |
2.5878E+07 |
5.0 |
3 |
2.8809E+07 |
2.8894E+07 |
5.0 |
Propagation |
Max \({K}_{\mathit{II}}\) [\(\mathit{Pa}\sqrt{\mathit{mm}}\)] |
\({K}_{I}\) reference [\(\mathit{Pa}\sqrt{\mathit{mm}}\)] |
\({K}_{\mathit{II}}\) threshold [\(\mathit{Pa}\sqrt{\mathit{mm}}\)] |
1 |
7.4881E+03 |
2.2997E+07 |
2.2997E+05 |
2 |
4.028E+03 |
2.5878E+07 |
2.5878E+05 |
3 |
2.0639E+04 |
2.8894E+07 |
2.8894E+05 |
4.4. notes#
All values tested are within the tolerances used. This means that method SIMPLEXE correctly calculates both the position of the two crack bottoms and the level sets.
The error obtained on the values of \({K}_{I}\) is almost zero and the values of \({K}_{\mathrm{II}}\) are always in the order of 0.1% of the values of \({K}_{I}\). The results obtained are therefore very satisfactory.