Are you refering to the 737 and A-310 accidents, or a more generic scenario. And/or are you refering to the classic S & C  "ruddwer lock" phenomenon?

My interest in rudder limiter functions and possible rudder reversal in the A300-600 AA crash at Belle harbor, NY in October 2001. Mu question is would excessive rudder movement have caused the vertical fin to delaminate and depart from the aircraft.

Aviation Week magazine has had many articles on the accident and subject. Are you familar with them?

Assume the airplane is put in  a steady heading sideslip by opposite application of rudder and aileron. If the rudder is rapidly moved from its deflected position while the airplane is still in the sideslip, high fin loads can be applied (the fin is now at a high "angle of attack"). The FARs do not specifically require the airplane structure to be designed to withstand a full rudder "reversal" (from max throw in the deflected/one direction to max throw in opposite direction)while in a sideslip. From memory, it must(I think) be designed to handle a rapid movement back to neutral. Many airplanes have rudder limiters for either/both fin load or S&C considerations. These result in some sort of a max rudder throw vs speed schedule. Often flaps, LE devices, gear position also are part of the scheduling.  A few (I believe) also have a sideslip angle input to the schedule. Others are "hinge moment limited" in that the force to deflect the rudder is limited in some way. Usually the deflection limiters allow full throw up to some intermediate speed so as to have a good low Vmc in the takeoff and landing speed regime. Often the max possible loads occur at or just above the max speed for full throw. Its a very complex topic. Hope this helps a bit.

Thank you very helpful info. Do you think that the 737 accidents were caused by the rapid and full movement of the rudder. By full movement i mean perhaps beyond what the Rudder Limiter should have allowed.

No. There is no evidence the fin separated. NTSB surmised cause was a very subtle rudder hyd power package failure which put in a large large rudder throw resulting in loss of control. Boeing is now redesigning control system at cost to it and operators of several tens of millions of dollars.

davidjh answers are perfect. I would just add that the 737 accidents (there were two - one in the US, one in the Far East)were caused by rudder runaway caused by an internal failure of the rudder PCU (the hydraulic servo actuator). The cause was found by an ALPA (Airline Pilots Association) investigation team.
As for the rudder reversal that caused the airframe failure of the A300-600, FAR 25 only considers loads due to a single sideslip to maximum rudder deflection followed by rudders back to neutral. Loads due to reversion of rudder deflection from maximum to one side to maximum to the other side when sideslip is at it maximum can lead to airframe failure for some aircraft, depending on speed.
Normally T tail aircraft are less susceptible to that because the fin must already be capable of withstanding asymmetric loads on the horizontal tail, so they have very strong vertical tails.

It is unlikely that many airplanes can withstand a commanded full rudder reversal at maximum sideslip.  The loads in this condition are enormous and well beyond the design requirement.  The rudder is usually the most powerful control on an airplane (the B-52 is a possible exception, it has a tiny rudder for the size of the airplane).

While the fin of a T-tail has to carry the symmetric and asymmetric loads of the horizontal tail as well, these do not entail the kind of bending and torsion loads that a full rudder reversal would cause.  Besides, the horizontal tail loads are there in a sideslip, including the asymmetric loads on the horizontal due to the sideslip, so that any strength available for those loads is already being used.

I personally wonder whether the existing fin structural design criterion is adequate.  It appears that most pilots are unaware of the damage they can do by commanding a rudder reversal in an airplane without a rudder limiter (only airplanes with powered controls have rudder limiters, and I would guess that not all of those have them).

One final point on powered rudder control systems.  The control algorithms generally assume that the airframe is completely intact.  In the event that the rudder or fin becomes partially compromised due to internal structural failure (e.g., fatigue, delamination, or corrosion) or if the rudder position sensor malfunctions or becomes loose, the control system may drive the rudder into oscillations that could cause the fin to separate and/or induce flutter modes in the airplane.  There are supposed to be failsafe features, but one wonders.....

RE the A300 Accident: I wanted to add a caution about taking the Aviation Week aero data or the NTSB releases at face value. The claim by both sources is that ultimate structural loads can be exceeded by combinations of aircraft sideslip and rudder movements that do not exceed the deflection limit of 10 degrees.  Of course during accelerated flight any number of scenarios make this possible but it is unclear how this would happen in the normal flight envelope around 250 knots. I would suggest that it would be very hard to exceed the load limits by using any number of 10 degree rudder inputs in anything short of a departure or violent spin manuever.
When all is said, I think a prexisting flaw in the composite material will turn out to be a more likely possibility to account for the tail breaking off.