I would like to be able to predict when a part will fail. I define a failure for this case as a complete fracture of the part which allows the component to separate into two pieces. I have looked at some of the non-linear static examples and set up a simple problem but don't really see how to get there from here.

If I model a cylindrical hollow aluminum tube that is 48" long x 4" dia. X .25" thick I can restrain one end and apply a load to the other end. I can also depict this problem on paper and solve for the bending stress and displacement which matches the SolidWorks solution very closely. That's the good news. How do I use the simulation to predict when the part will actually fracture? Can I do that? Obviously stress in excess of the tensile strength is a problem but I would like to quantify what value is required to fail the part.

When i vary loads on the example described above I seem to continue to get linear results even as the stress in the part goes well above the tensile strength. Shouldn't the displacement and stress be non-linear by definition?

I picture is attached. Any insight would be appreciated.

Well, I am going to assume the part is made out a ductile metal. If we imagine what happens when this thing i s loaded we get the following sequence of events:

A NL static analysis can probably take you a ways along either of these paths but all the way down either is quite tricky for any code. Ideally you would need a cohesive failure model for your elements to have them "fracture" SWX Sim Premium does not have this capability but some codes do. It maybe able to go post buckling, if that happens but how far would probably be dependent on element distortion levels and incremental strain levels - my guess is not too far along but probaly past the initial buckling load.

Usually the magnitude of the onset of one of the above failure condition is sufficient to estimate ultimate strength. Any of those work for you?