What is maximum displacement for aircraft engine?
There is no standard.  Even for a single plane and a single engine, there will be literally hundreds of different possible displacements depending on the condition. The engine manufacturer will split these into several categories.  

First would be static versus dynamic loads. Static loads are the loads (or displacements) caused by gravity, thrust load, maneuvers or wind.  Dynamic loads are transient events caused by rotor unbalance, bird impacts, blade loss, etc.

The second category is the severity of the load.  There are several levels here.  First is a fatigue load.  The engine will experience this level of load (or displacement) on virtually every flight.  Therefore, all parts must be able to withstand this load and not have a fatigue failure.  The second level is a "limit" load.  This would be experienced by the engine say once every 4000 or 5000 flights.  E.g. a very rapid maneuver or a particularly hard landing. For this level, fatigue is not a concern, because the engine won't experience it very often.  Just have to make sure no parts yield.  Final level is "ultimate" load.  This is the highest load that will ever be experienced by any engine in the lifetime of the entire fleet (e.g. a fan blade out condition).  Yielding may be allowed here, as long as nothing breaks.

Depending on what you are looking for, the answers could vary between 0.001 inch and several inches. I'm not sure that you will be able to find exact values, as the airframer and engine manufacturers will regard this as proprietary information.