Usually max power is time limited for jet/piston engines to 10 or 5 minutes. Can anybody explain the reason? What will happen if those limits are exceeded?
Maybe Catastrophic Failure...
Any number published by an engine maker (or any aviation part maker for that matter) is the numbers they have tested it to. Thus if Continental or GE claims a 2000 hour TBO but puts a 5 minute limit on max power, that in turn means that the 2000TBO number is based on operations within these published limitations. Exceeding these limitations may cause TBO to arrive sooner than expected and could possibly cause undesired operating characteristics. It is of course possible that if you drive the engine at max power for a time greater than suggested, it will throw itself to pieces. However, this is unlikely.
In some cases there are physical limits based on the materials used in the engine. If exceeding maximum run time provides a way to generate internal temperatures that exceed the limits of an internal part you could very well have an issue very quickly. From my experience with piston engines it's generally a wear and heat fatigue issue when flogging the engine at max power. That being said if the POH calls for a maximum of 5 minutes at full power and you spend 5 minutes and 30 seconds at full power on a climb out chances are you will be fine. If you do this routinely you may find that your engine hits TBO long before the published numbers.
This article also alludes to the fact that there may be other limiting factors such as the strength of the gear box the engine is connected to.
The shp of a turboprop engine is restricted by the strength of the gearbox that drives the propeller, and by the ability of the airplane to handle the thrust developed by the prop.
On any note I would think that most manufacturers publish numbers that are on the conservative side for many reasons.
Since this question is highly related to TBO number you should check out this article about some common myths around engine overhauling numbers and engine wear in general.
TBO: Time Between Overhaul. This is generally the lifetime of an engine. Although some people commonly think this is a legal number it is only manufacturer suggestion and you are free to exceed it (and plenty of people do).
POH: Pilots Operating Handbook. The document that outlines the limits and safe operation of a given airframe.
I suspect that the answer might vary from aircraft to aircraft and engine to engine, so I'll answer specifically for an aircraft/engine combination I am familiar with.
The Lycoming O-360, of various models, was chosen by Robinson to power the R22 series. This engine is widely used in fixed wing and rotaries, is more or less bullet proof when cared for properly and is serviced by a market with a good spares supply and availability of skilled mechanics and overhaul centres.
For the R22 Beta II, the engine is capable of producing 180 HP but Robinson said we only need 130 HP, maybe 140 HP at most but can you make it lighter? I forget the numbers - they came from an interview with Frank Robinson, I'm sure Google will lead you to accurate ones.
Lycoming responded by making several changes without changing the major replaceable components including thinning the cylinder walls and making the cooling fins somewhat smaller. This means that the engine is less capable of dispersing heat and consequently, cannot run at maximum power for long.
Eventually, they certified it at 145 HP (less than the maximum - i.e. "derated"). The POH (Pilots Operating Handbook) allows using the maximum derated power, 145 HP, for short periods, from memory, 5 minutes. The engine life and reliability are only good if these limits are not exceeded.
There are also limits on how much power the drive train, including the gearbox, tail rotor drive shaft and tail rotor gearbox, can handle which place limits on the maximum power the engine can safely produce.
In an emergency, it is possible at sea level to exceed the 145 derated maximum since there is no physical device to stop you putting the collective into your armpit or opening the throttle wide but there is a good chance that doing so will damage the drive train or blades and if exceeded, a maintenance inspection is mandatory. Using the whole 180 HP will lead to damage and has been implicated in accidents.
For gas turbine engines, the three measurements to watch are:
MTO: Maximum TakeOff thrust. (no more than 5 minutes)
MCT: Maximum Continuous Thrust. (okay, unless the turbine overspeeds or overheats)
MCL: Maximum CLimb thrust. (often the same as MCT)
Those three limits are the ones established by the engine manufacturer during extended lifecycle testing as sustainable while maintaining the engine's established time between overhaul. Exceed them, and the aircraft maintenance person must consider a shortened TBO if they don't want to risk an in flight failure.
And, yes, the manufacturer used up a pile of engines establishing those limits.
On piston engines, heat is the big enemy. Exceeding RPM isn't usually a concern, as most props become inefficient when the blades go supersonic, so overspeeding a piston engine is counterproductive. Overheated parts become weaker, and wear faster even if they don't break immediately. In particular the cylinder heads (and gaskets) will likely be the first to fail in an overheat situation.
Why is it possible to exceed those limits on aircraft engines? In his book Fate Is The Hunter, Ernest Gann describes it most eloquently, when talking about backfiring the engines on a DC2 to clear off ice that was closing the air intakes to the engines, causing them to lose power: This is terrible abuse of the engines, but not as bad as asking them to fly through a mountain. (anyone who holds a pilot's license should read that chapter on the icing incident... it's scary)
Unlimited overboost is there in case of dire emergency, when the choice may be either overhaul the engines prematurely, or crash the plane.