Mesh and Element Types: For this validation case, a single second-order tetrahedral mesh was created in SimScale with the standard algorithm.

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

Case

Mesh Type

Nodes

Element Type

Creep Formulation

Element Technology

(A)

Standard

235

2nd order tetrahedral

Norton

Standard

(B)

Standard

235

2nd order tetrahedral

Norton

Reduced integration

(C)

Standard

235

2nd order tetrahedral

Time hardening

Standard

(D)

Standard

235

2nd order tetrahedral

Time hardening

Reduced integration

Table 2: Overview of the mesh, creep formulation, and element technology used for each case.

Find below the second-order standard mesh used in this validation case:

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.

Surface loads

\(t_x\) = 300 \(MPa\) on face BCGF;

\(t_y\) = 200 \(MPa\) on face CDHG;

\(t_z\) = 100 \(MPa\) on face EFGH.

Advanced Automatic Time Stepping

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 targetvalue: 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):

Case

[NAFEMS_R27]

SimScale

Error (%)

(A)

4.218

4.21875

0.0178

(B)

4.218

4.21875

0.0178

(C)

4.218

4.21875

0.0178

(D)

4.218

4.21875

0.0178

Table 3: Comparison of SimScale’s results against the analytical solution for this secondary creep validation case.

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.

Last updated: July 21st, 2021

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