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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

Geometry of the Cube
  • 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
Mesh used for the SimScale cases (G) – (J)

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]:

Comparison of the creep strain $$\epsilon_{xx}^c$$
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
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