Combining Creep Material Models

This model illustrates how to combine different creep models to accurately represent the material behavior. An example for such a material model combination is to add a Norton-Bailey’s law with a Norton’s law as described in the equation

Model Definition

This model is a modification of the application library model Thermally Induced Creep. The same geometry, hollow sphere, load, inner pressure and thermal gradient, are used here. The parameters of Norton’s law are also reused and govern secondary creep. The primary creep data, which differentiates the two models, is defined as

Parameter A2 = 10 h-1 accounts for the stress normalization of the equivalent stress, σe, in MPa and time, t, in hours. The other parameters are n2 = 3.5, m = 0.5, and

f2(T) = e-12500/T, where T defines the temperature in K .

Results and Discussion

Figure 1 shows the von Mises stress at 108 h when both primary creep and secondary creep are active. The largest equivalent stress, found in the center of the sphere, demonstrates that the relaxation take place starting from the inner radius and continuing toward the outer boundary. Without creep due to the internal pressure, the largest stresses are found on the inner radius and decreases toward the outer radius instead.

Figure 1: Distribution of von Mises stress at t = 108 h.

To compare the both creep models, secondary creep against combined creep, see Figure 2 where the time history of the equivalent stress is shown at three different locations. It is clear that the primary creep relaxes the inner boundary earlier than the secondary creep; compare the turquoise and blue lines. Over time, both creep models converge to the same result. This is expected because the influence of the primary creep fades away with time.

The creep strain can also be plotted for primary and secondary creep separately. The primary creep strain increases earlier than secondary creep, as shown in Figure 3. Lastly, the history of the stress profile is shown in Figure 4. Relaxation causes the propagation from the inner to the outer radius of the position of the peak stress.

Figure 2: History of von Mises stress at radius 205 mm, 350 mm, and 495 mm, of the secondary creep only (solid lines), and with primary creep included (dashed lines).

Figure 3: History of primary and secondary creep strain at radius 205 mm, 350 mm, and 495 mm.

Figure 4: von Mises stress versus radius at t = 1, 104, 105, 107, 108, and 1010 hours with primary creep included.

Modeling in COMSOL Multiphysics

In COMSOL Multiphysics you can add several nodes under the same Linear Elastic Material feature. Each creep node can define its unique creep model.

The Norton-Bailey’s law is defied in Nonlinear Structural Materials Module with

In order to normalize the equivalent stress in MPa and the time in h, set the reference stress σref = 1 MPa and the reference time tref = 1 h. Set the time shift tshift to 1 min in order to avoid the singularity that occurs at t = 0. Considering the long time scale of the analysis this has a negligible effect on the results.

Nonlinear_Structural_Materials_Module/Creep/combined_creep

Modeling Instructions

From the menu, choose .

Browse to the model’s Application Libraries folder and double-click the file thermally_induced_creep.mph.

Component 1 (comp1)

In the window, expand the node.

Solid Mechanics (solid)

Linear Elastic Material 1