3D triaxial load secondary creep (NAFEMS Test 6(a))
Overview
The aim of this test case is to validate the following functionalities:
- creep material behavior
- standard and reduced integration elements
- automatic time stepping
The simulation results of SimScale were compared to the analytical results in [NAFEMS_R27]. The tetrahedral meshes used were created with the parametrized-tetrahedralization-tool on the SimScale platform.
Import validation project into workspace
Geometry
- Cube edge length l = 0.100 m
Analysis type and Domain
Tool Type : Code_Aster
Analysis Type : Static – nonlinear
Mesh and Element types :
| Case | Mesh type | Number of nodes | Creep formulation | Element type |
|---|---|---|---|---|
| (A) | 2nd order hex | 20 | Norton | 3D standard |
| (B) | 2nd order hex | 20 | Norton | 3D reduced |
| (C) | 2nd order hex | 20 | Time Hardening | 3D standard |
| (D) | 2nd order hex | 20 | Time Hardening | 3D reduced |
| (E) | 2nd order hex | 20 | Strain Hardening | 3D standard |
| (F) | 2nd order hex | 20 | Strain Hardening | 3D reduced |
| (G) | 2nd order tet | 21 | Norton | 3D standard |
| (H) | 2nd order tet | 21 | Norton | 3D reduced |
| (I) | 2nd order tet | 21 | Time Hardening | 3D standard |
| (J) | 2nd order tet | 21 | Time Hardening | 3D reduced |
Simulation Setup
Material:
-
- linear elastic, isotropic: $$E = 210 GPa$$, $$\nu = 0.3$$
- creep formulation:
– Norton, A = 8.6805556e-48, n = 5
– Time Hardening, A = 8.6805556e-48, n = 5, m = 0
Important Information
The material Data of the reference was given in MPa, mm and h units and were converted to SI units using the following relation:
$$A_{SI} = rac{1}{3600} cdot rac{1}{10^{6n}} cdot A_{MPa;h}$$
$$A_{SI} = \frac{1}{3600} \cdot \frac{1}{10^{6n}} \cdot A_{MPa\;h}$$
Constraints:
- face ADEH: $$d_x = 0.0m$$ mm
- face ABFE: $$d_y= 0.0m$$
- face ABCD: $$d_z=0.0m$$
Loads:
- face BCGF: $$\sigma_{xx}=300 MPa$$
- face CDHG: $$\sigma_{yy}=200 MPa$$
- face EFGH: $$\sigma_{zz}=100 MPa$$
Advanced Automatic Time Stepping:
- Retiming Event: Field Change
- Target Field component: internal variable V1 (accumulated unelastic strain)
- Threshold value: 0.001
- Timestep Calculation Type: mixed
- Field Change Target Value: 0.0008
Reference Solution
$$\epsilon_{xx}^c = – \epsilon_{zz}^c = \frac{0.004218}{3600} t$$
$$\epsilon_{eff}^c = \frac{0.004871}{3600} t$$
$$\epsilon_{yy}^c = 0.0$$
The equations used to solve the problem are derived in [NAFEMS_R27]. As the SimScale solution is calculated using SI units, the reference solution was adopted to a time unit of seconds instead of hours.
Results
Comparison of the average creep strain $$\epsilon_{xx}^c$$ of the cube after a creep time of 3.6e6 s (1000 h) with the analytical solution presented in [NAFEMS_R27]:
| Case | time [s] | [NAFEMS_R27] | SimScale | Error (%) |
|---|---|---|---|---|
| (A) | 3600000 | 4.218 | 4.21875 | -0.0178 |
| (B) | 3600000 | 4.218 | 4.21875 | -0.0178 |
| (C) | 3600000 | 4.218 | 4.21875 | -0.0178 |
| (D) | 3600000 | 4.218 | 4.21875 | -0.0178 |
| (E) | 3600000 | 4.218 | 4.21875 | -0.0178 |
| (F) | 3600000 | 4.218 | 4.21875 | -0.0178 |
| (G) | 3600000 | 4.218 | 4.21875 | -0.0178 |
| (H) | 3600000 | 4.218 | 4.21875 | -0.0178 |
| (I) | 3600000 | 4.218 | 4.21875 | -0.0178 |
| (J) | 3600000 | 4.218 | 4.21875 | -0.0178 |