The analysis of stress relaxation due to internal creep

Usually, the analysis of stress relaxation is performed only to estimate the effects on the supports and nozzle connections. Note that at elevated temperatures if the deformation is constant, the stress resisting that deformation will decrease with time.

Creep is permanent deformation over time; fatigue is crack propagation over time. Both occur due to applied loads and both can lead to failure. Creep is characterized by looking at the elongation of the sample; fatigue, by elongation of the crack.

Creep is a constant stress situation that is below yield. It is extremely prevalent in higher temperature conditions. Creep is usually tested with a wire of a given size that has a constant load and the elongation is measured over time. Be careful not to mistake creep with stress relaxation.

Fatigue is due to cyclic/alternating loading that can be at any stress level. The loading is repeated until the number of cycles imparted causes failure. This is expressed in S-N curves for particular materials. A material is usually said to have an infinite fatigue endurance limit if it can withstand 10^6 cycles at the particular alternating stress level.

Modeling Relaxation in Rohr2

Since creep relaxation is a very slow process, the analysis can be limited to one hot load case in which the system will remain for most of the operation time.

To generate only the thermal load case, the dead load contribution should be removed. For this reason the factor of “-1” is given for the load case “Dead load” (refer to the snapshot) on the following page.In case of a non-linear calculation of the thermal expansion one would usually create a load case “Operating” which includes thermal expansion but also gravity so that the friction on the supports can be determined correctly. Therefore, one first needs to remove the gravity effect from the combined load case “Operating” to create the temperature effect alone, i.e., the load case “Thermal.”

Snapshot showing the generation of the load case “Relaxation”Note that the operation with “RELX” changes the sign of the loads but does not operate on the anchor movements.

Thus, it is assumed that stress relaxation does not affect the anchor movements only that the loads have their sign changed.

Now one needs to create a new load case “StressRelease” having the combination between “Relaxation” and “Dead load” which corresponds to the system after the long hot operation and then cooling down including the weight.

Finally, the existing superposition load case “Operation” is modified so that it also includes (takes into account) the relaxed state (StressRelease). This is done by first moving the load cases “Relaxation” and “StressRelease” in the position above “Operation”. Then, the load case ”Operation” is selected and the key “Edit” is pressed to open the window with the assigned load cases. Afterwards, the load case “StressRelease” is added in the list.

The load case “StressRelease” can also be include in the output table. This can be achieved by selecting the option “Output table”. Then, select “New” and specify the load case (StressRelease) to be added in the table.

The above snapshot shows the load case “StressRelease” included in the output table.