Opps sorry just realised your completely correct but I will leave the post anyway. I was on day 5 of 6 sector days on earlies.
The youngs modulus doesn't change and after yield there is residual stress in the structure and the hardness changes. It is one of the of the ways you test that something has yielded. And as the metal becomes harder it becomes more brittle which effects its post yield behaviour.
For abdg, its a rockwell hardness tester
PCE-2000 (type D impact) hardness tester that we use and the change in hardness tells you how much its yielded by. You can also acid etch the surface and look at the metal grain. And if you really want to get fancy you stick a x-ray diffractometer on it and that will give you a real reading of the residual stress in the metal.
Basically the stress strain curve shifts to the right but it never returns to the original zero strain. The yield point increases which is sometimes used to work harden for use so the strength is increased. The classic example of this is high pressure piping systems and the teeth on digger buckets. Both cases the metal is quite mallable when installed but after the work up in the pipe system and using it after the install the metal properties change allowing alot higher pressures to be carried. The digger teeth you can grind them and weld them before using them but after a couple of hours work you can't touch them with a grinder and if you weld them they will just shatter.
For a given load you first have to over come the residual stress then you will start deflecting. The material next to that will be deforming as it did before which will set up a discontinuity which will act as a stress concentrator.
So if you deflect a yielded bit of metal by say 5mm it will require a different force to deflecting a none yielded bit of metal by 5mm. So I would call that a change in stiffness but to be honest its more a discussion on definitions than anything else and the US engineers do use different terminology to european ones.
Stiffness - Wikipedia, the free encyclopedia