How many times can 1/2 inch copper pipes be frozen-thawed.
Our hot-cold lines were frozen for over two days, have thawed on their own and show no signs of a leak (we can see the pipes in the basement).
This happened to us a couple of times in the past, but never for so long

How many times can 1/2 inch copper pipes be frozen-thawed.
That is not a pertinent question. When water freezes it expands. That expansion is what causes the pipe to burst. You have been very fortunate if your pipes have frozen repeatedly and not burst. You need to provide heat in the basement to prevent freezing or you need to install heat tapes on the pipes. When a pipe burst you not only have to repair the pipes but you usually have water damage when the pipes thaw.
It would be unusual for pipes in a basement to freeze because the heat from the house usually keeps the basement above freezing. Are you sure that they are freezing in the basement. If the pipe come up from the basement in an exterior wall that is a more likely place fro them to freeze.
Heat tapes and insulation are easy to install and not expensive. Much less expensive than repairing busted pipes.

We can't give a definite answer because we don't know the grade of your pipe. Each time it froze it became more damaged. Like Harold said, you are very lucky and are now on borrowed time. I guess it maight be helpful to tell you they will burts the very next time theyr freeze so get some heat on then.

Good morning,

Thanks for your advice.
The pipes are in fact in an exterior wall and are visible in the basement before they go into the wall. Other pipes in that same part of the basement did not freeze so it is obvious that the problem area is the pipes that go to the top floor via the exterior wall.

My questions are whether a certain grade of copper pipe can be frozen without rupturing and if maximum expansion of ice occurs at one degree below freezing or if ice in pipes continue to expand as temperature keeps droping (ie: maximum expansion of ice at 40 degrees below freezing?)

Thanks,
Lynne

Yes and no. Yes a pipe can freeze without rupturing and the expansion continues to take place the colder the pipe gets but not forever. At a certain point, well into freezing, the water will slowly stop expanding any further. What exactly is your concern in your home?