Fault Current Test for Earthing Electrode

will there be any change in readings on account of Rod having been earlier subjected to fault current of 40 kA True RMS.

Probably not (as long as the rod returns to the same temperature of the first test before the second test is conducted). You may notice a slight increase in resistance due to surface tarnishing if the metal has discoloured, but only if you haven't cleaned the current-carrying contact surfaces properly.

If however there are any joints, fittings, weak points, etc connected to the rod which are also being tested (ie- carrying the short circuit current) then the extra stress of additional short circuit tests may cause these to increase in resistance or fail altogether.

If you are testing earth electrodes you should also be testing with the associated cable (or bonded metal) and fittings connected otherwise the test is meaningless, the connection will highly likely be the weak point and will fail before the solid earthing rod.

My another related query is : whether 40 mm x 3000 mm long and 40 mm x 1200 mm long rod will withstand same fault current levels during testing.

Most likely yes, the current is still the same the only real difference to consider is the reduced thermal mass.

What exactly is the purpose of the test and what standard are you testing to?

They must have one Hell of a test set...P=RxI²

Short circuit test rigs of this size are extremely impressive. I have had our smaller 11kV powered MW-sized short-circuit test rig up to about 24kA for 3 seconds.

Nothing like doubling the power usage of our local industrial estate for a very short time.

The first blast of current might well vaporize enough of the water out of the immediately surrounding soil to increase the voltage drop on the second test. Not a lot I hope, or else lightning rods would not protect on successive strokes, which they are frequently required to do. A search on lightning protection would likely produce several scholarly papers in this civil / electrical engineering boundary.