For many decades, “Rocket Science” was the most glamorous form of engineering in most people’s imaginations. It dealt with big and grand things like rocket launchers and space suits. What many didn’t realize is that engineering rockets, just like engineering a car, airplane, or even a vacuum cleaner, is as much about big grand ideas as it is about the performance of the tiniest rubber part.
Most people had probably never heard of an “O-ring”— until the failure of one was blamed for the Challenger disaster in January, 1986. In the subsequent televised failure investigation, (the late) Professor Richard Feynman of California Institute of Technology dipped a small O-ring into a glass of ice water to dramatize its change in properties with temperature.
The example in the figure above demonstrates only one of the complexities involved in analyzing 2-D rubber contact, where an axisymmetric model of an O-ring seal is first compressed by three rigid surfaces, then loaded uniformly with a distributed pressure. The O-ring has an inner radius of 10 cm and an outer radius of 13.5 cm, and is bounded by three contact surfaces. During the first 20 increments, the top surface moves down in the radial direction of a total distance of 0.2 cm, compressing the O-ring. During the subsequent 50 increments, a total pressure load of 2 MPa is applied in the Z-direction, compressing the O-ring against the opposite contact surface. The deformed shapes, equivalent Cauchy stress contours and the final contact force distribution are shown below. The Ogden material parameters are assigned values of:
At the end of increment 70, the originally circular cross-section of the O-ring has filled the rectangular region on the right while remaining circular on the left (where the pressure loading is applied).
This type of elastomeric analysis may encounter instability problems because of the large compressive stresses; the solution algorithm in the FEA code must be able to pinpoint such difficulties during the analysis and follow alternative paths. Otherwise, the FEA code may give incorrect results!
The O-ring is also analyzed using a 2-term Mooney-Rivlin model. It is found that the CPU and memory usage are about the same per iteration as for the 3-term Ogden model.
For this type of rubber contact analysis, the nonlinear FEA code must be able to handle “deformable-to-rigid” contact, the incompressibility of the material, friction, mesh distortions (especially at the two corners), and potential instability problems as the analysis progresses. The important point to note about this example is that the applied pressure is many times larger than the shear stiffness. Although the analysis is 2-D, the solution of this rubber problem is not trivial.