I don't understand the premise of your question. If you stick to the minimum test pressure, then "Permanent Visible Distortion" wont occur.
The purpose of the code is to efficiently design equipment and provide minimum pressure test requirements which the vessel is certain to pass if fabricated correctly, and then go on to operate safely.
Your question doesn't relate to the core purpose of the code. I don't understand why you would ask it. Is there a reason why you would exceed the minimum test pressure?
If it is just a question of interest, then the most accurate way of learning how a vessel will behave and distort when the minimum test pressure is exceeded would be to conduct an elastic-plastic analysis of the over pressure test. But even then, knowing if the distortion you can see on your computer screen would be "visible" in a the real world (and therefore a failure) requires real world experience of intentionally failing vessels. After you have failed a few in the real world with "visible distortion", you can perhaps gain the experience to reasonably accurately predict failure on an elastic plastic analysis with out the need to do the real world test.