1. Reference problem#
1.1. Geometry#
Each test is carried out on a smooth cylindrical test piece. For obvious reasons of symmetries, an axisymmetric 2D modeling of a quarter of the structure is sufficient.
1.2. Material properties#
The behavior of the material studied is described by a Von Mises elasto-plastic law with linear isotropic work hardening, “VMIS_ISOT_LINE”. The deformations used in the behavior relationship are linearized deformations.
Poisson’s ratio does not depend on temperature, \(\nu =\mathrm{0,3}\).
The values of the Young’s modulus \(E\), the tangent modulus \({E}_{t}\) and the elastic limit are given in the following table:
Temperature \([°C]\) |
—150 |
—100 |
—50 |
—50 |
\(E[\mathrm{MPa}]\) |
200000 |
200000 |
200000 |
|
\(\mathrm{Et}[\mathrm{MPa}]\) |
2000 |
2000 |
2000 |
|
\({\sigma }_{Y}[\mathrm{MPa}]\) |
750 |
700 |
700 |
650 |
1.3. Boundary conditions and loads#
With reference to the figure in §1.1, the limit and load conditions are as follows:
On segment \(\mathrm{BC}\) (\(Y={L}_{0}\)), displacement imposed in the direction \(\mathrm{OY}\):
\(T[°C]\) |
Displacement ( \(l-{l}_{0}\) ) at break for a reference length \({l}_{0}\) of \(203.5\mathrm{mm}\) \([\mathrm{mm}]\) The results for each temperature are in ascending order |
||||||||||||||
-50 |
10.68 |
28.78 |
30.31 |
31.66 |
32,53 |
33,90 |
34.38 |
35.82 |
36.69 |
37.09 |
37.37 |
37.49 |
38.45 |
39.77 |
44,39 |
-100 |
20,57 |
21.68 |
23,32 |
24,37 |
24.66 |
25.59 |
25.84 |
27.51 |
28.44 |
29.30 |
29.68 |
30.16 |
30.18 |
30,20 |
30.95 |
-150 |
11.33 |
14.70 |
14.79 |
14.90 |
18.62 |
18.87 |
19.00 |
19.37 |
19.61 |
20,07 |
21,19 |
22.79 |
23,28 |
24.17 |
24,41 |
On segment \(\mathrm{OA}\) (\(Y=0\)) blocked movements following the direction \(\mathrm{OY}\).
On segment \(\mathrm{OB}\) (\(X=0\)) blocked movements following the direction \(\mathrm{OX}\).
1.4. Initial conditions#
Zero stresses and deformations.