I do not operate engines lean of peak. We did not operated lean of peak when we flew pistons transatlantic. I would rather waste a little fuel, and have to flight plan more carefully, then to cause engine stress for a very minor benefit, and actualy have an engine problem (particularly there). Fuel is cheaper than a broken engine!
One won't break the engine if one operates it properly.
Studies in the past determined that the ideal range for detonation occurs within about 11% of stoichiometric, or peak mixture...that's 11% rich, not lean. This is only at high power settings. It's nearly impossible to cause detonation uner normal operating cruise conditions...and both Continental and Lycoming have pernitted and even recommended peak operation at cruise power settings between 65% and 75% power for a long time...again, a big part of the reason that you'll find recommendations against leaning below three or four thousand feet...above those altitudes in a normally aspirated engine you aren't going to achieve adequate power to cause detonation. It's simply idiot-proofing the operating practices against ham-fisted pilots who don't know how to operate their engines.
I think the admonition not to use carb heat at high power due to detonation risk is a hangover from the days of the big radials, where the combination of charge-temperature rise from both the supercharger and carb heat very definitely could take you into detonation territory.
In large radial operation, we adjusted carburetor heat by the carb air temperature gauge; it's absolutely true that applying too much carb heat at high temperatures in a large radial can cause all kinds of woes, but it's not done that way. The carb is adjusted specific to a narrow temperature range individually for each engine, by watching the carb air temperature gauge. Then again, it's well to remember that part of the normal induction of most large radials is a supercharger that comprises the back part of the engine case...even if the engine isn't turbocharged. In that respect the radial is different, though that factor is inconsequential when considering operation at the cylinder and at the carburetor with respect to carb heat at lower power settings...settings which approximate what you're seeing in say, an 0-320 or 0-520. Simply put, when running a radial below barometric (below about 29" Hg Mp at sea level, for example), it's operated in the same manner as the engine in your Skyhawk or Warrior or Cherokee.
The carburetion on a large radial is different; it's a pressure carburetor rather than a float carburetor, but that doesn't make a difference in the way the carb heat is used, either...so yes, the carb heat techniques on a radial engine, being a piston engine, apply to a small flat horizontally opposed engine, too. Mixture techniques, too. A big difference is that the big pressure strom carburetors utilized autorich and autolean settings...which were routinely overridden for manual leaning in flight. I often set mixture in cruise at night by the color of the flame out the exhaust first, and then final adjustments by instrumentation.
While you can't do that on a light single or twin (see exhaust flame), you can safely operate at peak at reduced power, and no, carburetor heat isn't going to tear the engine apart. The ideal would be a carb air temp gauge, but for cost and simplicity most light airplanes are equipped with a very crude carb air box (which typically leaks on most airplanes after a while anyway). It's either full on or full off...and if you need carb heat during takeoff, during climb, during cruise, during descent, then use it.
You can think of it this way; while the greatest possibility of detonation occurs at higher power settings, and one may reasonably guess that the greatest harm might occur with at high power settings, think about why you're applying the carb heat in the first place. If you have carb ice, then you need carb heat, period. When is the greatest potential for icing? When the greatest temperature drop occurs...which occurs at high power settings when the greatest airflow takes place through the venturi. Does carb ice form at high power settings? You bet, and carb heat is needed to get rid of it.
Carb ice is common during ground operations, too, but forms a little differently, for the same reason that carb fuction at idle is different than with an open throttle. Idle fuel is obtained from a different fuel jet, with a different, independent fixed-mixture setting, by utilizing calibrated airflow leakage past the throttle plate in the carburetor. Rather than using high airflow to create a pressure drop through a venturi to draw fuel into the induction airstream, the low manifold pressure and a calibrated leak past the throttle plate combine to draw fuel in a different place than with the open throttle...and ice forms in a different place and in a different manner. Carburetor icing and heat useage therefore, is a different subject when considering throttle open and throttle closed operation.
It becomes a little more complex, however. I see far too many instructors that teach their students to reduce power to idle abeam the numbers and make a prolonged idle descent. This is hard on engines. Often the drill is to reduce to idle power by closing the throttle, apply carburetor heat, and leave it on through the descent. This is poor airmanship and poor practice, and really should be reserved only for training for engine failures. It's a time when backlash issues come into play in the engine (timing can change as much as 20 degrees or more over time with a worn woodruff key in a mag driveshaft, for example, strictly due to backlash), piston ring flutter occurs, and though few realize it, idle mixture changes substantially (resulting in a leaner idle mixture than on the ground at idle). Prolonged operation during a descent at idle is a bad idea and poor practice.
Likewise, operation with the carb heat simply left on, mindlessly, while doing prolonged idle descents is also bad idea. Use of carb heat of it's own accord isn't a bad idea, but for heaven's sake, know why it's being used and what it's doing. Simply applying the heat because the instructor said to apply it there is never wise...especially since the instructor is probably only doing what he does because he saw someone else do it...the heritage of inexperience. It's that same heritage that teaches us that peak or lean of peak operations are dangerous, and a host of other myths that pervade the hangar talk that goes on today. (Along with destructive practices like pulling the propeller through to "limber up the oil" as part of a preflight, etc).
This is all very interesting, but isn't the reason for setting the carb heat to cold at the decision height to give full power in the event of a go-around? Nothing to do with damaging the engine..... (apart from possibly ingesting undesirable stuff when on the ground).
Well, yes, and no. You're right that the chief concern is making sure you have adequate power to go around. I cringe when I see idle descents made to a go-around. Going from a nice, cool or cold engine to full power on the go-around is not good for the engine for a host of reasons. However, when you need to go around, you want that power available, and carb heat robs power. If you're operating an airplane close to sea level and you're operating very lean, and at high power settings, you can put yourself into a regime where it can contribute to detonation, but it's difficult to do...nearly impossible with most properly maintained light airplane engines with leaded fuels. Further, contrary to some of the incorrect information that's been posted in the thread, you have NOTHING to fear from "increased cylinder pressures or temperatures" resulting from carb heat...doesn't occur, and presents no hazard.
Use of carburetor heat is there for two reasons; to help remove the ice that may have formed and to prevent it's formation by operating the carburetor in the ideal temperature range. That range isn't very big, and what manufacturers do when giving a simple butterfly carb air box with no carb air temperature gauge, is take a shotgun approach. Rather than provide you with the means to properly set carb temp, they shotgun it with extra heat in a form of overkill...apply enough to melt everything.
During a power transition, however, you pass through the ideal ranges and the less than ideal ranges, as airflow through the carb is changing, and the temperature in the cowl area (from whence the heated carb air comes) is changing...and you not only pass through the ideal carb air temp range for avoiding ice...but quite possibly both sides of that range where the ideal temperature and conditions for FORMING ice occur...you can cause ice to form.
I've seen this occur during a go-around during the right humid conditions following a rain, while doing flight training with student's, before. Application of power to go around produced a smooth transition to the climb, followed shortly thereafter by an engine failure with a very rapid buildup of carb ice. Reapplication of heat as we set up for the forced landing on the remaining runway, resulted in a restoration of power. This isn't common in my experience, but I've certainly experienced it. Use carburetor heat when and where you need it, but don't use it indiscriminately.
Having said all this, if you have instructions for your aircraft specifying a carb heat-on descent for landing, then do that, but take the time to get to know your system and the why's of what you're doing. Tools such as mixture and carb heat are NOT absolutes; just like the ideal application of carb heat is partial heat (which can only be done in conjunction with a carburetor air temperature gauge), the same applies to mixture. It's there to be adjusted, to be used as needed, and to be used with care and judgement. It's there to give you options...not simply there to be thrown on or off with abandon, or by rote.