4. B modeling#
Modeling B corresponds to the case a/b = 0.01.
4.1. Characteristics of modeling#
Full mesh
Zoom
Zoom of the crack point
4.2. Characteristics of the mesh#
2095 nodes and 680 elements including 640 QUA8 and 40 TRI6
4.3. Features tested#
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.
4.4. 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. 0 |
Crown No. 1 |
Crown No. 1 |
Crown No. 2 |
Crown No. 3 |
Crown No. 4 |
||
ring |
1.E-6 |
1.5E-5 |
1.75E-5 |
2.E-5 |
2.25E-5 |
||
rsup |
2.5E-5 |
1.75E-5 |
1.75E-5 |
2.25E-5 |
2.5E-5 |
2.5E-5 |
4.5. Reference solutions#
For an a/b ratio = 0.01 (and a = 2.5.10-5 m), the reference solution for KI is:
\({K}_{I}=0.9609\text{MPa}\cdot \sqrt{(\text{m})}\)
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:
\({G}_{\mathrm{réf}}=4.2019{\text{J.m}}^{-2}\)
4.6. Tested sizes and results#
Parameter |
Unit |
Option |
Option |
Crown |
Aster |
% Tolerance |
G |
J.m-1 |
G_ EPSI |
crown No. 1 |
4.2019 |
4.1567 |
2 |
G |
J.m-1 |
G_ EPSI |
crown No. 2 |
4.2019 |
4.1554 |
2 |
G |
J.m-1 |
G_ EPSI |
crown No. 3 |
4.2019 |
4.1544 |
2 |
G |
J.m-1 |
G_ EPSI |
crown No. 4 |
4.2019 |
4.1554 |
2 |
K1 |
|
K |
crown No. 0 |
0.9609 |
0.9653 |
2 |