3. Modeling A#
3.1. Characteristics of modeling#
\(A\mathrm{=}\mathit{N01099}\) (\(s=0.\))
\(B=\mathrm{N01259}\) (\(s=26.68\))
\(C=\mathrm{N01179}\) (\(s=\mathrm{18,0}\); \(\mathrm{\alpha }=\mathrm{0,77}\approx \mathrm{\pi }/4\))
Loading: Unit pressure distributed on the face of the block opposite the plane of the lip:
\(P=\mathrm{1.MPa}\) in the \(Z\mathrm{=}\mathrm{1250.mm}\) plan.
3.2. Characteristics of the mesh#
Number of knots: 20567
Number of meshes and types: 160 PENTA15, 175 PYRAM13, 175, 9383 TETRA10 and 1290 HEXA20
3.3. Tested sizes and results#
The values tested are:
the local energy release rate \(g\) in all the nodes at the bottom of the crack (option G of CALC_G). These values are tested for integration rings defined by variable radii (R_ INF_FO and R_ SUP_FO) or by the number of layers (NB_COUCHE_INF and NB_COUCHE_SUP).
the local energy recovery rate \(g\) for points A and B at the bottom of the crack with the calculation operator POST_K1_K2_K3.
the stress intensity factor \({K}_{I}\), calculated at the same nodes of the crack bottom as the energy release rate (options K and KJ of CALC_G). In the case of the KJ option, we also highlight that when the calculated G value is negative, we have \({K}_{J}=0\) (by convention).
the \({G}_{\mathit{IRWIN}}\) energy return rate calculated from \({K}_{I}\) and the Irwin formula
In the case of the refund rate \({G}_{\mathit{IRWIN}}\), we ensure that when the value of G calculated
The mesh includes only one of the lips of the crack, it is therefore necessary to use the keyword “SYME” to automatically multiply by 2 in the Aster calculation the energy restoration rate calculated by virtual extension of the single lip.
Identification |
Reference |
\(\text{\%}\) tolerance |
\(g(A)\) crown \({C}_{1}\) (“LEGENDRE”) |
7.171 10-5 |
1 |
\(g(A)\) crown \({C}_{2}\) (“LEGENDRE”) |
7.171 10-5 |
1 |
\(g(A)\) crown \({C}_{1}\) (” LINEAIRE “) |
7.171 10-5 |
1 |
\(g(A)\) crown \({C}_{2}\) (” LINEAIRE “) |
7.171 10-5 |
1 |
\({G}_{\mathit{IRWIN}}(A)\) crown \({C}_{2}\) (” LEGENDRE “) |
7.171 10-5 |
1 |
\({G}_{\mathit{IRWIN}}(A)\) crown \({C}_{2}\) (” LINEAIRE “) |
7.171 10-5 |
1 |
\({G}_{\mathit{IRWIN}}(A)\) POST_K1_K2_K3 |
7.171 10-5 |
4 |
\(g(B)\) crown \({C}_{1}\) (“LEGENDRE”) |
1.721 10-5 |
10 |
\(g(B)\) crown \({C}_{2}\) (“LEGENDRE”) |
1.721 10-5 |
10 |
\(g(B)\) crown \({C}_{1}\) (” LINEAIRE “) |
1.721 10-5 |
1 |
\(g(B)\) crown \({C}_{2}\) (” LINEAIRE “) |
1.721 10-5 |
1 |
\({G}_{\mathit{IRWIN}}(B)\) crown \({C}_{2}\) (” LEGENDRE “) |
1.721 10-5 |
4 |
\({G}_{\mathit{IRWIN}}(B)\) crown \({C}_{2}\) (” LINEAIRE “) |
1.721 10-5 |
6 |
\({G}_{\mathit{IRWIN}}(B)\) POST_K1_K2_K3 |
1.721 10-5 |
3 |
\(g(C)\) crown \({C}_{1}\) (“LEGENDRE”) |
5.215 10-5 |
1 |
\(g(C)\) crown \({C}_{2}\) (“LEGENDRE”) |
5.215 10-5 |
1 |
\(g(C)\) crown \({C}_{1}\) (” LINEAIRE “) |
5.215 10-5 |
1 |
\(g(C)\) crown \({C}_{2}\) (” LINEAIRE “) |
5.215 10-5 |
1 |
Identification |
Reference |
\(\text{\%}\) tolerance |
\({K}_{J}(A)\) crown \({C}_{1}\) (“LEGENDRE”) |
4.067 |
1 |
\({K}_{J}(A)\) crown \({C}_{2}\) (“LEGENDRE”) |
4.067 |
1 |
\({K}_{I}(A)\) crown \({C}_{2}\) (” LINEAIRE “) |
4.067 |
1 |
\({K}_{I}(A)\) crown \({C}_{2}\) (” LEGENDRE “) |
4.067 |
1 |
\({K}_{J}(B)\) crown \({C}_{1}\) (“LEGENDRE”) |
1.992 |
10 |
\({K}_{J}(B)\) crown \({C}_{2}\) (“LEGENDRE”) |
1.992 |
10 |
\({K}_{I}(B)\) crown \({C}_{2}\) (“LEGENDRE”) |
1.992 |
2 |
\({K}_{I}(B)\) crown \({C}_{2}\) (” LINEAIRE “) |
1.992 |
5 |
\({K}_{J}(C)\) crown \({C}_{1}\) (“LEGENDRE”) |
3.469 |
1 |
\({K}_{J}(C)\) crown \({C}_{2}\) (“LEGENDRE”) |
3.469 |
1 |
\({K}_{J}(A)\) crown \({C}_{2}\) (” LINEAIRE “, “ NB_POINTS_FOND ****) ** |
0.0 |