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.

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Geometry

• Cube edge length l = 0.100 m

Analysis type and Domain

Tool Type : Code_Aster

Analysis Type : Static – nonlinear

Mesh and Element types :

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

• 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]: