3. Modeling A#
3.1. Characteristics of modeling#
For this modeling, the 3 topological parameters of the crack block are:
\(\mathrm{NS}\): number of sectors on \(90°\)
\(\mathrm{NC}\): number of crowns
\(\mathrm{rt}\): the radius of the largest crown (with a: half length of the crack)
\(\mathit{NS}\mathrm{=}8\)
\(\mathit{NC}\mathrm{=}4\)
\(\mathit{rt}\mathrm{=}\mathrm{0,001}\mathrm{\times }a\)
The values of the upper and lower radii, to be specified in the CALC_G command, are:
Crown 1 |
Crown 2 |
Crown 3 |
Crown 3 |
Crown 4 |
Crown 5 |
Crown 6 |
|
\(\text{Rinf}\) |
3,75E—5 |
7,500E—5 |
7,500E—5 |
1,500E—4 |
1,875E—4 |
2,250E—4 |
2,250E—4 |
\(\text{Rsup}\) |
7,50E—5 |
1,125E—4 |
1,500E—4 |
1,875E—4 |
2,250E—4 |
3,000E—4 |
3,000E—4 |
3.2. Characteristics of the mesh#
Half-mesh; mesh radiating at the right end of the crack.
3831 knots,
1516 elements,
884 TRI6,
632 QUA8.
3.3. Quantities tested and results of modeling A#
Identification |
Reference |
Aster |
% difference |
\({K}_{\mathit{II}}\), crown #1 |
2.2347E+7 |
2.2814E+7 |
2.09 |
\({K}_{\mathit{II}}\), crown #2 |
2.2347E+7 |
2.2813E+7 |
2.08 |
\({K}_{\mathit{II}}\), crown #3 |
2,2347E+7 |
2,2814E+7 |
2,09 |
\({K}_{\mathit{II}}\), crown no. 4 |
2.2347E+7 |
2.2814E+7 |
2.09 |
\({K}_{\mathit{II}}\), crown no. 5 |
2,2347E+7 |
2,2817E+7 |
2,10 |
\({K}_{\mathit{II}}\), crown #6 |
2.2347E+7 |
2.2818E+7 |
2.11 |
\(G\), crown No. 1 |
2.4969E+3 |
2.5984E+3 |
4.07 |
\(G\), crown #2 |
2.4969E+3 |
2.5990E+3 |
4.09 |
\(G\), crown #3 |
2,4969E+3 |
2,5992E+3 |
4,10 |
\(G\), crown no. 4 |
2.4969E+3 |
2,5993E+3 |
4,10 |
\(G\), crown no. 5 |
2.4969E+3 |
2.6013E+3 |
4.18 |
\(G\), crown #6 |
2.4969E+3 |
2.5985E+3 |
4.07 |
3.4. notes#
In the reference, the author assumes \({K}_{I}\mathrm{=}0\), but he does not check it after the fact. In view of the deformations resulting from Code_Aster, the coefficient \({K}_{I}\) is different from zero, but it remains very low compared to \({K}_{\mathit{II}}\) (the crack slides more than it opens).
With regard to the energy return rate \(G\), if we assume that \({K}_{I}\mathrm{=}0\), we derive the reference value from the formula of IRWIN in plane constraints:
\({G}_{\mathit{ref}}\mathrm{=}(1\mathrm{/}E)\mathrm{\times }{K}_{\mathit{II}}^{2}\)