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# 3D Triaxial Load Secondary Creep (NAFEMS Test 6(a))

This triaxial load 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 of SimScale were compared to the analytical results derived from [NAFEMS_R27]$$^1$$.

## Geometry

The geometry consists of a cube with edge length $$l$$ = 0.1 $$m$$.

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

## Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Nonlinear static

Mesh and Element Types: The mesh for cases A through F is a second-order hexahedral one-element mesh. It was created locally and imported to SimScale. For cases G through J, the standard algorithm was used to generate a second-order tetrahedral mesh.

The secondary creep formulation and element technology vary from case to case. The table below contains an overview of the configurations:

Find below the mesh used for case G. It’s a standard mesh with second-order tetrahedral cells. Figure 2: Second-order standard mesh used for cases G through J in this secondary creep validation.

## Simulation Setup

Material:

• Steel (linear elastic)
• $$E$$ = 200 $$GPa$$
• $$\nu$$ = 0.3
• $$\rho$$ = 7870 $$kg/m³$$
• Three creep formulations are used. Find here the parameters for each of them.
• Norton:
• A = 8.6805556e-48 $$1/s$$
• N = 5
• Time hardening:
• A = 8.6805556e-48 $$1/s$$
• N = 5
• M = 0
• Strain hardening:
• A = 8.6805556e-48 $$1/s$$
• N = 5
• M = 0

Boundary Conditions:

• Constraints
• $$d_x$$ = 0 on face ADHE;
• $$d_y$$ = 0 on face ABFE;
• $$d_z$$ = 0 on face ABCD.
• $$t_x$$ = 300 $$MPa$$ on face BCGF;
• $$t_y$$ = 200 $$MPa$$ on face CDHG;
• $$t_z$$ = 100 $$MPa$$ on face EFGH.

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

• Retime event: field change;
• Target field component: internal variable V1 (accumulated unelastic strain);
• Threshold value: 0.0001;
• Time step calculation type: mixed;
• Field change target value: 0.00008.

## Reference Solution

The equations used to solve the problem are derived in [NAFEMS_R27]$$^1$$. As SimScale uses SI units, the reference solution was adopted to a time unit of seconds instead of hours.

$$\epsilon_{xx}^c = – \epsilon_{zz}^c = \frac{0.004218}{3600} t \tag{1}$$

$$\epsilon_{eff}^c = \frac{0.004871}{3600} t \tag{2}$$

$$\epsilon_{yy}^c = 0.0 \tag{3}$$

## Result Comparison

Find below a comparison between SimScale’s results and the analytical solution presented in [NAFEMS_R27]$$^1$$ for the average creep strain $$\epsilon_{xx}^c$$ of the cube. The creep time is 3.6e6 $$s$$ (equivalent to 1000 hours):

In Figure 3, we can see how $$\epsilon_{xx}^c$$, $$\epsilon_{yy}^c$$, and $$\epsilon_{zz}^c$$ are evolving for case D.

$$\epsilon_{yy}^c$$ and $$\epsilon_{zz}^c$$ also show very good agreement with the analytical solution, having an error of 0% and 0.0178%, respectively.