# Simcenter 3D Solutions Why aren't my Specialist Durability results for Maximum Stress, Minimum Stress, Mean Stress and Maximum Stress Amplitude forming a cycle?

2024-05-13T14:40:51.000-0400
Simcenter 3D

## Summary

Simcenter 3D Specialist Durability offers not only cyclic fatigue damage and fatigue life as results, the user can also get plots for stress results (Maximum Stress, Minimum Stress, Mean Stress and Maximum Stress Amplitude). These results can be used for a quick check by testing if they form a cycle, the biggest cycle in the loading: Max. Stress = Mean Stress + Max. Stress Amplitude and Min. Stress = Mean Stress - Max. Stress Amplitude This is not always true though! Check below for more information about when this test should work and when not - and why not.

## Details

We investigate a simple model, a plate with a hole in the middle.

On the smaller side in +y-direction, the plate is clamped. On the opposite side one unit load per corner is applied. Furthermore the weight is applied as a static load. In the calculation, we only use the force on the left side and we apply a simple swelling loading with r-ratio of 0.5.

The signal only consist of three data points, and it's changing from 0.5 to 1.0 and back to 0.5.

It's being applied to the unit load case result of "FORCE_LEFT" in a superposition load event and the connection is then multiplied with a scaling factor of 50.

The Superposition Event is used in a Specialist Solution using the Stress Life Approach with common calculation parameters.

The Specialist Solution is then calculated and as results a layout of the different stress results processed during the loading are shown.

The results are as follows:

View Port top left: Max. Stress on Top/Bottom

View Port top right: Min. Stress on Top/Bottom

View Port bottom left: Mean Stress on Top/Bottom

View Port bottom right: Max. Stress Amplitude on Top/Bottom

We take the maximum values from Max. Stress, Mean Stress and Max. Stress Amplitude and the minimum value from Min. Stress.

They are all located on Node 155 of Element 131 (see annotation flags in the results plots).

We can now enter the values in the formulas below describing a cycle.

Max. Stress = Mean Stress + Max. Stress Amplitude

567.16 = 425.37 + 141.79        [MPa]

Correct.

Min. Stress = Mean Stress - Max. Stress Amplitude

-567.16 = 425.37 - 141.79        [MPa]

Not correct.

The minimum stress in the plot is far lower than mean stress minus the maximum stress amplitude from the plots. We'd expect to see a minimum stress of (567.16 MPa / 2) = 283.58 MPa for this cycle, which is alternating between a factor of 0.5 and 1.0. The value we get for the minimum stress has the same absolute value than the maximum stress.

This can be explained by the results displayed being for Top and for Bottom of the shell elements.

We bend the plate that is clamped at one end and loaded orthogonally to the mid-plane at the other end. Thus, we have tension on one side and the same amount of compression on the other side. Combining values from different sides (Top and Bottom) in the same formula for a cycle won't work. We need to use results on the same location (Node, Element) and from the same side (Top or Bottom).

Thus, we change the plots and limit the Element Result Location to Top only.

The values for the Maximum extreme values we read from Max. Stress, Mean Stress and Max. Amplitude Stress remain the same as before, they were on position Top. The extreme values of the Min. Stress result moved away from the previous locations. Custom annotations on Element 131 are needed to retrieve the desired value to be used in the formula.

The values are taken from Node 155 of Element 131, Element Result Location Top.

Entering the values in the formulas below describing a cycle:

Max. Stress = Mean Stress + Max. Stress Amplitude

567.16 = 425.37 + 141.79        [MPa]

Correct.

Min. Stress = Mean Stress - Max. Stress Amplitude

-5.29 = 425.37 - 141.79        [MPa]

Still not correct.

The minimum stress in the plot is still not matching Mean Stress minus Max. Amplitude Stress (and our expected value of 283.58 MPa).

Here is a look at the documentation, in which it's listed what the different stress results types show.

The stress results shown in the results plots are the maxima and minima encountered during the loading.

And it's also stated that it's important to take into account the local stress state used in the calculation.

When the critical plane approach is used, Max. Stress and Min. Stress are calculated across all planes. The overall maximum and minimum can occur in different planes and thus, (Max. Stress - Min. Stress / 2) may not be equal to Max. Amplitude Stress.

We did use the Critical Plane Approach in the Solution. Thus, we may have been looking at results from different critical planes.

Simcenter 3D Specialist Durability offers the Function Definition that allows to show the components of the stress tensor before projection and the projected stress for selected locations. A Function Definition on Node 155 Element 131 will allow to review the stress in the candidate critical planes at this location.

Looking through the different results for the projected stress in different candidate planes, we find that indeed the extreme values are in different planes (marked by "Projection Index").

The plane "Projection Index 8" contains the Max. Stress value from the plots (567.16 MPa), the absolute maximum over all planes.

The minimum in the plane is then the expected value of 283.58 MPa.

The plane "Projection Index 17" contains the Min. Stress value from the plots (-5.29 MPa), the absolute minimum over all planes for the Element Result Location Top.

The maximum in the plane is -2.64 MPa.

While in some cases it is possible to check the stress results from Specialist Durability via formulas using them to describe the largest cycle, the user needs to take into account that the results must be on the same location, which doesn't only mean same node and element, but in case of shell elements also the same side (Top or Bottom).

Furthermore, the Local Stress State is important. An equivalent stress method only produces one set of stress results during the projection of the stress tensor, whereas the Critical Plane Approach generates 18 different sets and the software searches for the extreme values in all of them. Depending on the loading this may lead to Maximum Stress and Minimum Stress not being from the same critical plane.

Thus, the check to use the stress results from the Specialist Durability results (Maximum Stress, Minimum Stress, Mean Stress and Maximum Stress Amplitude) to fill in the formulas describing one cycle may work if the user ensures to look at results at the same location and if they use an equivalent stress method.

Since the Critical Plane Approach is often used, users should be aware that using the formulas:

Max. Stress = Mean Stress + Max. Stress Amplitude
and
Min. Stress = Mean Stress - Max. Stress Amplitude

to check, may be misleading since Max. Stress and Min. Stress may be from different critical planes.

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Durability