3. Modeling A#
Modeling A corresponds to the case a/b = 0.4.
3.1. Characteristics of modeling#
Z
R
Full mesh
Zoom of the crack point
3.2. Characteristics of the mesh#
1756 knots and 569 elements including 529 QUA8 and 40 TRI6
3.3. Tested features#
In this test, the mechanical result post-processed by the operator CALC_G comes from a CREA_RESU. As this type of result contains only displacements and no constraints, it is necessary to calculate these constraints within the CALC_G operator from the displacement fields. This operation is carried out by choosing to calculate the option G_ EPSI.
3.4. Definition of crown radii#
Several successive pairs of radii for the lower and upper integration rings are retained. These rays should be specified in the CALC_G keyword factor THETA:
Crown No. 1 |
Crown No. 2 |
Crown No. 2 |
Crown No. 3 |
Crown No. 4 |
||
ring |
1.E-6 |
2.5E-5 |
5.E-5 |
7.5E-5 |
7.5E-5 |
|
rsup |
2.5E-5 |
5.E-5 |
7.5E-5 |
1.E-4 |
3.5. Benchmark solutions#
For a ratio a/b = 0.4 (and a = 10-3 m), the reference solution for KI is:
\({K}_{I}=4.7419\text{MPa}\cdot \sqrt{(\text{m})}\)
To calculate the energy return rate, we use the formulas of IRWIN in plane deformations:
\({G}_{\mathrm{réf}}=\frac{1-{\nu }^{2}}{E}({K}_{I}^{2}+{K}_{\mathrm{II}}^{2})\), with \({K}_{\mathrm{II}}^{2}=0\)
either:
\({G}_{\mathrm{réf}}={\mathrm{1.0231.10}}^{2}{\text{J.m}}^{-2}\)
3.6. Tested sizes and results#
Parameter |
Unit |
Option |
Option |
Crown |
Aster |
% Tolerance |
G |
J.m-1 |
G_ EPSI |
crown No. 1 |
1,0231.102 |
0,9701.10 2 |
6 |
G |
J.m-1 |
G_ EPSI |
crown No. 2 |
1,0231.102 |
1,0051.10 2 |
2 |
G |
J.m-1 |
G_ EPSI |
crown No. 3 |
1,0231.10 2 |
1,0055.10 2 |
2 |
G |
J.m-1 |
G_ EPSI |
crown No. 4 |
1,0231.102 |
1.01.102 |
2 |
K1 |
|
K |
crown No. 1 |
4.7419 |
4.4145 |
8 |
K1 |
|
K |
crown No. 2 |
4.7419 |
4.7571 |
2 |
K1 |
|
K |
crown No. 3 |
4.7419 |
4.7913 |
2 |
K1 |
|
K |
crown No. 4 |
4.7419 |
4.8244 |
2 |