4. C modeling#
In this modeling, the extended finite element method (\(\text{X-FEM}\)) is used. A radius of geometric enrichment is defined with a number of element layers equal to 3.
4.1. Characteristics of the mesh#
The domain is meshed with linear triangles (mesh TRIA3). We maintain the refinement of the previous models, namely 100 quadrangles (divided into 2 triangles) along the \(X\) axis and 100 quadrangles (divided into 2 triangles) along the \(Y\) axis. The crack is not meshed.
Figure 4.1-1 : mesh with triangles
4.2. Tested sizes and results#
The crack is inclined according to 3 angular values: \(\theta \mathrm{=}0°,30°,60°\)
For each angle of inclination, the stress intensity factors are tested as in models \(A\) and \(B\), by the \(G\mathrm{-}\mathit{thêta}\) method and by the method of extrapolation of displacement jumps.
For method \(G-\mathrm{thêta}\) (command CALC_G), the following theta field crowns are chosen: \({R}_{\mathrm{inf}}=\mathrm{0,1}a\) and \({R}_{\text{sup}}=\mathrm{0,3}a\).
4.2.1. Results for \(\theta \mathrm{=}0°\)#
Identification |
Reference |
Tolerance |
CALC_G |
||
C1 + background1: K1 |
2.5725 105 |
|
C1 + background2: K1 |
2.5725 105 |
|
C1 + background1: K2 |
0 |
257 |
C1 + background2: K2 |
0 |
257 |
C1 + background1: G |
0.29 |
|
C1 + background2: G |
0.29 |
|
C2 + background1: K1 |
2.5725 105 |
|
C2 + background2: K1 |
2.5725 105 |
|
C2 + background1: K2 |
0 |
257 |
C2 + background2: K2 |
0 |
257 |
C2 + background1: G |
0.29 |
|
C2 + background2: G |
0.29 |
|
POST_K1_K2_K3 |
||
C1 + background1: K1 |
2.5725 105 |
|
C1 + background2: K1 |
2.5725 105 |
|
C1 + background1: K2 |
0 |
514.5 |
C1 + background2: K2 |
0 |
514.5 |
C2 + background1: K1 |
2.5725 105 |
|
C2 + background2: K1 |
2.5725 105 |
|
C2 + background1: K2 |
0 |
514.5 |
C2 + background2: K2 |
0 |
514.5 |
The zero values of \({K}_{2}\) are tested in absolute terms with a tolerance equal to \({K}_{1}^{\mathit{ref}}\mathrm{/}1000\) for CALC_G and a tolerance equal to \({K}_{1}^{\mathit{ref}}\mathrm{/}500\) for POST_K1_K2_K3.
4.2.2. Results for \(\theta \mathrm{=}30°\)#
Identification |
Reference |
Tolerance |
CALC_G |
||
C1 + background1: K1 |
1.9294 105 |
|
C1 + background2: K1 |
1.9294 105 |
|
C1 + background1: K2 |
1.1139.105 |
|
C1 + background2: K2 |
1.1139.105 |
|
C1 + background1: G |
0.215 |
|
C1 + background2: G |
0.215 |
|
C2 + background1: K1 |
1.9294 105 |
|
C2 + background2: K1 |
1.9294 105 |
|
C2 + background1: K2 |
1.1139.105 |
|
C2 + background2: K2 |
1.1139.105 |
|
C2 + background1: G |
0.215 |
|
C2 + background2: G |
0.215 |
|
POST_K1_K2_K3 |
||
C1 + background1: K1 |
1.9294 105 |
|
C1 + background2: K1 |
1.9294 105 |
|
C1 + background1: K2 |
1.1139.105 |
|
C1 + background2: K2 |
1.1139.105 |
|
C2 + background1: K1 |
1.9294 105 |
|
C2 + background2: K1 |
1.9294 105 |
|
C2 + background1: K2 |
1.1139.105 |
|
C2 + background2: K2 |
1.1139.105 |
|
4.2.3. Results for \(\theta \mathrm{=}60°\)#
Identification |
Reference |
Tolerance |
CALC_G |
||
C1 + background1: K1 |
6.4312105 |
|
C1 + background2: K1 |
6.4312105 |
|
C1 + background1: K2 |
1.1139.105 |
|
C1 + background2: K2 |
1.1139.105 |
|
C1 + background1: G |
7,1692 10-2 |
|
C1 + background2: G |
7,1692 10-2 |
|
C2 + background1: K1 |
6.4312105 |
|
C2 + background2: K1 |
6.4312105 |
|
C2 + background1: K2 |
1.1139.105 |
|
C2 + background2: K2 |
1.1139.105 |
|
C2 + background1: G |
7,1692 10-2 |
|
C2 + background2: G |
7,1692 10-2 |
|
POST_K1_K2_K3 |
||
C1 + background1: K1 |
6.4312105 |
|
C1 + background2: K1 |
6.4312105 |
|
C1 + background1: K2 |
1.1139.105 |
|
C1 + background2: K2 |
1.1139.105 |
|
C2 + background1: K1 |
6.4312105 |
|
C2 + background2: K1 |
6.4312105 |
|
C2 + background1: K2 |
1.1139.105 |
|
C2 + background2: K2 |
1.1139.105 |
|