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    3D Triaxial Displacement Secondary Creep (NAFEMS Test 6(b))

    The secondary creep validation case belongs to solid mechanics. This test case aims to validate the following parameters:

    • Creep material behavior
    • Standard and reduced integration elements
    • Automatic time stepping

    The simulation results were compared to the results presented in [NAFEMS]\(^1\).

    Geometry

    The geometry consists of a cube with an edge length \(l\) = 0.1 \(m\).

    geometry of the cube used in secondary creep validation case
    Figure 1: Simple cube geometry used in this validation case

    The coordinates for the points in the cube geometry are as tabulated below:

    ABCDEFGH
    x00.10.1000.100.1
    y000.10.1000.10.1
    z00000.10.10.10.1
    Table 1: Cube dimensions in meters

    Analysis Type and Mesh

    Tool Type: Code Aster

    Analysis Type: Nonlinear static

    Mesh and Element Types: The mesh for cases A through D is a second-order tetrahedral mesh, generated in SimScale by the standard algorithm.

    CaseMesh TypeNumber of NodesElement TypeCreep FormulationElement Technology
    AStandard2352nd order tetrahedralNortonStandard
    BStandard2352nd order tetrahedralNortonReduced integration
    CStandard2352nd order tetrahedralTime HardeningStandard
    DStandard2352nd order tetrahedralTime HardeningReduced integration
    Table 2: Overview of the validation cases. The element technology integration and creep formulation change between the cases.

    Find below the standard mesh used for cases A through D:

    generated second order mesh in simscale which has 235 nodes for secondary creep validation
    Figure 2: Generated second order mesh with SimScale for cases A through D

    Simulation Setup

    Material:

    • Steel (linear elastic)
      • Isotropic: \(E\) = 200 \(GPa\)
      • \(\nu\) = 0.3
      • \(\rho\) = 7870 \(kg/m³\)
      • Creep formulation:

    Boundary Conditions:

    • Constraints:
      • Fixed value:
        • Face ADEH: \(d_x\) = 0 \(m\)
        • Face ABFE: \(d_y\) = 0 \(m\)
        • Face ABCD: \(d_z\) = 0 \(m\)
      • Displacement in x-direction
        • Face BCGF: \(d_x\) = 0.3 \(mm\)
      • Displacement in y-direction
        • Face CDHG: \(d_y\) = 0.2 \(mm\)
      • Displacement in z-direction
        • Face EFGH: \(d_z\) =0.1 \(mm\)

    Advanced Automatic Time Stepping

    For all cases, the following advanced automatic time stepping settings were defined under Simulation control:

    • Retiming event: Field change
    • Target field component: Internal variable V1 (accumulated unelastic strain)
    • Threshold value: 0.00005
    • Timestep calculation: Mixed
    • Field change target: 0.00004

    Result Comparison

    The secondary creep movement validation is done by comparing the stress (\(\sigma_{xx}\)) after a creep time of 1000 hours. Below you will find the SimScale and reference results from [NAFEMS]\(^1\):

    CaseNAFEMS R27 \([MPa]\)SimScale \([MPa]\)Error [%]
    A1007.71008.230.053
    B1007.71008.230.053
    C1007.71008.230.053
    D1007.71008.230.053
    Table 3: Stress comparison between the reference and the simulation results

    In all configurations, the results obtained with SimScale show a good agreement with the reference values. The displacement of the geometry can be seen below:

    visualization of displacement of a cube
    Figure 3: Displacement observed in case A

    Note

    If you still encounter problems validating your simulation, then please post the issue on our forum or contact us.

    Last updated: July 21st, 2021

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