The following is transcript of a YouTube video by Dr Ronald Wagner posted here with his permission. It has been edited for clarity and formatted as an article.
In this video I do an analysis of the Ocean Gate Titan incident. The submersible Titan imploded on June 18, 2023. It’s basically a carbon fiber cylinder and two titanium hemispheres and some panels that cover the electronics.
For this video, I prepared a Abaqus Python script which creates the submersible. It is available here but you have to be a Patreon which requires a small fee. The model is made from all the data I could find in the Internet. The script creates the whole submersible, all important details, I think.
Here we have the CFRP cylinder and here are the heavy edge rings made of titanium and here are titanium hemispheres and then we have here an acrylic window.
And I want to show you the manufacturing of the CFRP so you can see the mandrel of the filament winding process. We can see the manufacturing, the filament. The cylinder has a thickness of 127 millimeters which is actually very thick for composite structure and the ply layup is a cross ply so we have alternating zero and 90 degree fibers.
[Ed. note: The laminate schedule is taken from a video and description of a cylyndrical hull being manufactured by Spencer Composites. The actual cylinder hull on the Titan when it imploded was made by Electroimpact, which used a different machine and may have had a different laminate schedule.]
Here you can see the titanium heavy edge ring that is bonded to the carbon fiber cylinder. I have to say is that as soon as I saw that both parts are only glued together, I thought to myself I would never take a dive with this submersible.
Back to the model. Here we have the Titan shell model. It is a continuous shell model and it's pretty thick as you can see here. And in my opinion there are several weak points. First off, I would say A) the connection between the heavy edge ring and carbon fiber cylinder, B) the window and C) the carbon fiber cylinder.
Here we can see the boundary conditions in the loading of the submersible. The loading is just a pressure load. It's actually not that easy to define the boundary conditions for a submersible. I have chosen here four points and defined the boundary conditions that exist so all degrees of freedom are locked.
The next step was a linear buckling analysis. I have performed two analyses and we can see the results. Here the first eigenvalue is 100. And in all unit systems this would be like 100. So, the remains of the Titanic are at an approximate depth of 4,000 meters and there the pressure vessel needs to withstand about 40 megapascals.
Here I have also run the same model but with a finer mesh and here we basically also have 100 megapascals. So, in terms of linear analysis or linear geometry and linear material, the submersible would easily withstand the pressure load at a depth of 4,000 meters.
The next step is performing a nonlinear analysis in terms of geometry and material in order to check the material strength of the titanium and the material strength of the composite. I have checked the use case of titanium. It is between 240 and in extreme cases for specific alloys 1,200 megapascals. So, pretty big range. And I think it's not that important because we think the bottleneck of the structure is the composite. So, I have prepared this. We are at 40 megapascals and the failure criterion here for the composite is the Hashin criterion is below one. So the composite at 40 megapascals would withstand the pressure load.
Let's increase it until we reach one. So if this simulation, it reaches one then we have basically a failure indicator for compression. So we can see that highest levels are in the interface between the titanium and the composite and you can see we have now reached one for fiber compression damage. In tension we have nothing and matrix compression damage is also close to one. So we will say that the failure compression load is like 57 or 58 megapascals and then we are underwater and for under water conditions we have a knock down factor for the mysterious things in carbon fiber and that is 0.75. If you multiply 57 megapascals we get like 42 megapascals. Which is still safe at this depth but I think it would not be certified. And we should also keep in mind that we have not considered any kind of imperfection in the whole structure. And also, we have not really modeled the adhesive zone which may reduce the allowable stress even further.
Now a short summary. So we have a linear buckling pressure of 100 megapascals for our structure and we only need to stay in like 40, so that's fine. But the material failure buckling pressure is like 57 megapascals and if we consider wet CFRP it's already 42. So very close to the target and then there are, in my opinion, those three most important failure modes. First the fracture of the window, then the fracture of the carbon fiber cylinder and last, the failure of the cylinder/titanium interface. In the following I will show some simulation results regarding those three modes.
We apply the pressure load and then we can see what happens. What breaks first? The cylinder, the connection, the acrylic window? As you can see already the window fractures and sends its debris to damage the cylinder. So I've modeled the contact. This is definitely a weak point of the submersible. But it entirely depends on the material parameters, which I just have taken from the Internet, the elastic properties, the yield stress. And I modeled the fracture of the acrylic window as ductile damage but with zero fracture energy basically and a very short fracture strain. So, it should behave similar to acrylic.
In this simulation I have defined the acrylic window in a way that it cannot basically get damaged in order to see which part of the structure fails after the window. So let's check it out. Again, we increase the pressure load. And then what happens? We have very high stresses in the interface between the titanium ring and the CFRP pieces. Then you can see the CFRP piece fractures.
At the CFRP pieces, not in the interface, is also a weak point. The material parameters of CFRP which I have used are from a publication of the submersible so they should be somewhat realistic.
Here is a final simulation result which shows the somewhat realistic implosion of the submersible. Again, the pressure load increases and you have here high stresses at the edge links and then the cylinder implodes and you have all kinds of debris flying around.
And another interesting detail is that here the steps are in milliseconds. One step is a millisecond and your brain needs like 13 milliseconds to process information from your eye. So that means you will need like 13 milliseconds in order to get an image of what your eyes saw. But as you can see here, if we go forward 13 milliseconds they would be already dead like 10 milliseconds ago. It happens so fast. And in order to process pain, it's like 100 milliseconds. So as the news said, they wouldn't really feel anything or have seen anything coming. They would just be instantly dead.
Next: The Titan Submersible Simulation Gets More Realistic
Notes and Corrections
August 7, 2023. Added link to revised analysis.
August 4, 2023. Analyst Ronald Wagner has updated the simulation to match Titan geometry and be consistent with the titanium rings found intact after the implosion.
August 4, 2023. Added note about cylindrical hull being created by Electroimpact.