3. Modeling A#
3.1. Characteristics of modeling#
Boundary conditions:
\(\mathit{N1}\): \(\mathit{N2}\): |
|
Charging:
Traction on the \(\mathrm{[}34\mathrm{]}\) side (SEG2 mesh) + assignment of the same temperature on all knots
The total number of increments is 20 (10 increments between \(t\mathrm{=}\mathrm{0s}\) and \(\mathrm{1s}\), 10 increments between \(t\mathrm{=}\mathrm{1s}\) and \(\mathrm{2s}\))
Behavior:
For mechanical calculation, the keyword META_LEMA_ANI is used, with the following parameters (see [R4.04.05] and [R4.04.05]):
\(\mathit{YoungModulus}=80000\mathit{MPa}\)
\(\mathit{PoissonRatio}=0.35\)
\({\alpha }_{f}=0.\)
\({\alpha }_{c}=0.00004\)
\({a}_{3}=\mathrm{253,5497}\mathit{MPa}\)
\({m}_{3}=0.\)
\({n}_{3}=4.39\)
\({Q}_{3}=0.K\)
\({M}_{\mathit{rrrr}}^{3}=1.\)
\({M}_{\theta \theta \theta \theta }^{3}=1.\)
\({M}_{\mathit{zzzz}}^{3}=1.\)
\({M}_{r\theta r\theta }^{3}=0.75\)
\({M}_{\mathit{rzrz}}^{3}=0.75\)
\({M}_{\mathrm{\theta }z\mathrm{\theta }z}^{3}=0.75\)
\(\mathit{TDEQ}=809.\)
\(K=1.135E-2\)
\(\text{NEQ}=2.187\)
\(T1C=831.\)
\(T2C=0.0\)
\(\text{QSR\_K}=14614\)
\(\mathit{AC}=1.58E-4\)
\(M=\mathrm{4,7}\)
\(T1R=949.1\)
\(T2R=\mathrm{0,0}\)
\(\mathit{AR}=-5.725\)
\(\mathit{BR}=\mathrm{0,05}\)
The parameters corresponding to the cold phase and to the \(\alpha \beta\) mixture do not play a role and are taken to be arbitrary.
3.2. Characteristics of the mesh#
Number of knots: 4
Number of meshes: 2
1 QUAD4
1 SEG2
3.3. Tested sizes and results#
The stresses and deformations are compared with the B model.
Identification |
Reference |
Reference type |
Tolerance |
\(t=0.3\) Constraints \(\mathit{SIGYY}\) (\(\mathit{N3}\)) |
-91.7598 |
Other_Aster (B modeling) |
1.00% |
\(t=0.8\) Constraints \(\mathit{SIGYY}\) (\(\mathit{N3}\)) |
-92.5802 |
Other_Aster (B modeling) |
1.00% |
\(t=1.3\) Constraints \(\mathit{SIGYY}\) (\(\mathit{N3}\)) |
70.1846 |
Other_Aster (B modeling) |
1.00% |
\(t=2.0\) Constraints \(\mathit{SIGYY}\) (\(\mathit{N3}\)) |
84.4144 |
Other_Aster (B modeling) |
1.00% |
Identification |
Reference |
Reference type |
Tolerance |
\(t=1.3\) Total deformations \(\mathit{EPYY}\) (\(\mathit{N3}\)) |
0.006 |
Other_Aster (B modeling) |
0.0001% |
\(t=2.0\) Total deformations \(\mathit{EPYY}\) (\(\mathit{N3}\)) |
0.02 |
Other_Aster (B modeling) |
0.0001% |
Identification |
Reference |
Reference type |
Tolerance |
\(t=0.8\) Beta phase proportion (\(V6\)) |
1.0 |
Analytical |
0.0001% |
\(t=1.3\) Beta phase proportion (\(V6\)) |
1.0 |
Analytical |
0.0001% |
\(t=2.0\) Beta phase proportion (\(V6\)) |
1.0 |
Analytical |
0.0001% |
Identification |
Reference |
Reference type |
Tolerance |
\(t=0.8\) Thermal Deformations \(V7\) (\(\mathit{N3}\)) |
0.0096 |
Analytical |
0.0001% |
\(t=1.3\) Thermal Deformations \(V7\) (\(\mathit{N3}\)) |
0.0156 |
Analytics |
0.0001% |
\(t=2.0\) Thermal Deformations \(V7\) (\(\mathit{N3}\)) |
0.024 |
Analytical |
0.0001% |
Identification |
Reference |
Reference type |
Tolerance |
\(t=0.8\) Hill equivalent stress \(V8\) (\(\mathit{N3}\)) |
92.5802 |
Other_Aster (B modeling) |
0.0001% |
\(t=1.3\) Hill equivalent stress \(V8\) (\(\mathit{N3}\)) |
70.1846 |
Other_Aster (B modeling) |
0.0001% |
\(t=2.0\) Hill equivalent stress \(V8\) (\(\mathit{N3}\)) |
84.4144 |
Other_Aster (B modeling) |
0.0001% |
Identification |
Reference |
Reference type |
Tolerance |
\(t=0.8\) Beta phase viscous stress \(V11\) (\(\mathit{N3}\)) |
92.5802 |
Other_Aster (B modeling) |
0.0001% |
\(t=1.3\) Beta phase viscous stress \(V11\) (\(\mathit{N3}\)) |
70.1846 |
Other_Aster (B modeling) |
0.0001% |
\(t=2.0\) Beta phase viscous stress \(V11\) (\(\mathit{N3}\)) |
84.4144 |
Other_Aster (B modeling) |
0.0001% |
Identification |
Reference |
Reference type |
Tolerance |
\(t=0.8\) Phase Change Indicator \(V12\) (\(\mathit{N3}\)) |
0.0 |
Analytics |
0.0001% |
\(t=1.3\) Phase Change Indicator \(V12\) (\(\mathit{N3}\)) |
0.0 |
Analytics |
0.0001% |
\(t=2.0\) Phase Change Indicator \(V12\) (\(\mathit{N3}\)) |
0.0 |
Analytics |
0.0001% |
Identification |
Reference |
Reference type |
Tolerance |
\(t=1.3\) Mechanical deformations \(\mathit{EPSYY}\) (\(N3\)) |
-0.0096 |
Other_Aster (B modeling) |
0.0001% |
\(t=2.0\) Mechanical deformations \(\mathit{EPSYY}\) (\(N3\)) |
-0.004 |
Other_Aster (B modeling) |
0.0001% |
Identification |
Reference |
Reference type |
Tolerance |
\(t=1.3\) Anelastic deformations \(\mathit{EPSYY}\) (\(N3\)) |
-0.0105 |
Other_Aster (B modeling) |
0.0001% |
\(t=2.0\) Anelastic deformations \(\mathit{EPSYY}\) (\(N3\)) |
-0.0051 |
Other_Aster (B modeling) |
0.0001% |