3. Modeling A#
3.1. Characteristics of modeling#
It is a three-dimensional model. The mesh was made using procedure GIBI of cracked block \(\mathrm{3D}\) [bib1]. Only an eighth of the structure (and therefore a quarter of the crack front) has been represented, with a quarter of this front being discretized into 16 sectors.
3.2. Characteristics of the mesh#
The mesh is composed of quadratic elements
Number of meshes and types: 624 PENTA15, 5600 HEXA20
3.3. Tested sizes and results#
The values tested are those of the local energy restoration rate at points \(A\) and \(B\) using the various integration crowns and the two methods for defining the fields \(\theta\):
Identification |
Reference |
\(\text{\%}\) Tolerance |
\(G\) local discretization LEGENDRE (degree 5 ) |
||
\(G\) Mini/Maxi 1 |
1.13210-1 |
2%/2% |
\(G\) Mini/Maxi2 |
1.13210-1 |
2%/2% |
\(G\) Mini/Maxi3 |
1.13210-1 |
3%/2% |
\(G\) Mini/Maxi4 |
1.13210-1 |
2%/2% |
\(G\) Mini/Maxi 5 |
1.13210-1 |
2%/2% |
\(G\) local discretization LINEAIRE |
||
\(G\) Mini/Maxi1 |
1.13210-1 |
3%/2% |
\(G\) Mini/Maxi2 |
1.13210-1 |
3%/1% |
\(G\) Mini/Maxi3 |
1.13210-1 |
6%/4% |
\(G\) Mini/Maxi4 |
1.13210-1 |
4%/2% |
\(G\) Mini/Maxi 5 |
1.13210-1 |
4%/2% |
\(K\) discretization LEGENDRE (degree 5 ) |
||
\(K\) Mini/Maxi1 |
1.5773105 |
3%/4% |
\(K\) Mini/Maxi2 |
1.5773105 |
6%/7% |
\(K\) Mini/Maxi3 |
1.5773105 |
4%/9% |
\(K\) Mini/Maxi 5 |
1.5773105 |
4%/9% |
\(K\) discretization LINEAIRE |
||
\(K\) Mini/Maxi1 |
1.5773105 |
1%/8% |
\(K\) Mini/Maxi2 |
1.5773105 |
3%/25% |
\(K\) Mini/Maxi3 |
1.5773105 |
7%/34% |
\(K\) Mini/Maxi 5 |
1.5773105 |
7%/34% |
Crown 1: |
\(\mathrm{Rinf}=0.07\) |
|
Crown 2: |
\(\mathrm{Rinf}=0.2\) |
|
Crown 3: |
\(\mathrm{Rinf}=\mathrm{0.4.}\) |
|
Crown 4: |
\(\mathrm{Rinf}=0.07\) |
|
Crown 5: Rinf and Rsup are automatically determined by CALC_G.
Where
The supports of the local \(\theta\) field correspond to the first three crowns of the global field.
3.4. notes#
The reference value is the value of the local energy return rate: \({G}_{\mathrm{réf}}=5.66{10}^{-8}J/{m}^{2}\).
The results of local \(G\) are only given for points \(A\) and \(B\) respectively located on a plane of symmetry and in the middle of the crack front. The results for point \(B\) (middle of the forehead) show a difference of around \(\text{3\%}\) compared to the reference result. The results for point \(A\) are less good (the difference is between \(\text{3\%}\) and \(\text{13.5\%}\)), which is a usual observation for estimating the local \(G\) for points located on a plane of symmetry.