Information and insight from fracture mechanics experts

Load Interaction Models - Retardation Models - Something to think about

It goes without saying that load interaction is important if the life prediction is to represent reality and not simply be a go no go measure.  Often times go no go is good enough.  But a lot of the time in the management of aging fleets, a real life prediction can be the difference between retirement or return to service.
Retardation can account for 70 percent of the life and that in it self should create wonder!  Well where does this miraculous life enhancement come from?  The neat thing is that nobody really knows.  It is true that few men created (made up) some useful models based upon rational guesses.  These models have been tweaked for years and that’s what makes them so very useful.  They can be tuned to the specific aircraft, usage, and component.  All that’s needed is an attempt at the real spectrum, and the testing equivalent and a test lab.  The number of coupons is left as an exercise.  Of course another avenue is to have service history of cracking and a detail record of how the aircraft was used.  At one time we referred to this as correlating to flying fatigue test articles.  This is because even the OEM has to assume how the customer is going to use the aircraft, and they test to their assumption, reality is sometimes different.
So what?  I suppose any one who has even a cursory knowledge of fracture has come across the notion of the fictional “plastic radius.”  It is fictional because the extent of plasticity at a crack tip is definitely not shaped like a radius, so much for the physics of the problem.  A lot of smoke and mirrors and late night sections have been spent on the subject of the plastic radius in all its manifestations, from plane strain plane stress, fracture toughness coupon requirements, to net section yield as a crack propagates. 
It is no surprise that load interaction investigators got hooked on the notion of a plastic interaction zone which increases and/or decreases with spectra level and crack length, some later even attempted account for plasticity in the wake of the crack along the flanks.  Simply amazing rational insights but not yet reality.  The point of this is that current state of load interaction models all rely on the notion of plasticity, some “out and out” some “inferred” but all do. 
If one digs into the subject even a little he will quickly realize that the benefit arising from plasticity IS dependent upon constraint.  The assumed closure mechanism that all the load interaction models are based on either at the crack tip or along the flanks as the case may be is totally dependent on there being enough elastic material surrounding the crack to provide sufficient strength to squeeze or constrain the plastic deformed region back into its original (undeformed) shape (volume). 
The “how much is needed” is why I started this note.  I don’t know the answer but I know its important and possibly the real mechanism of retardation.  But one thing I do know is that when the crack is approaching a free edge, either the part or another hole, there certainly is not sufficient elastic material surrounding it to create the constraint or closure forces.  Without closure forces there is no retardation. 
So you may grab one of the interaction models and do a fantastic job of modeling the cracking scenario and make a perfect prediction but you may be off and in the wrong direction!  Why, all the interaction models assume that there is “enough” elastic material surrounding the crack tip.  There are of course mitigating circumstances such as very little life available due to the steepness of the beta and/or the load level of the spectra.
So caution is urged in applying load interaction models carte blanche to the crack growth problems.  Edge ligament cracking is a prefect example of retardation decaying, as are those pesky continuing damage cracks into adjacent holes.  It seems then the only time that the current load interaction models are fully effective is out in the middle of a panel with no discontinuities.
And we haven’t discussed relaxation of the plastic zone with time under self weight, perhaps for aircraft that sit on the ramp for weeks between flights. What happens to the load interaction then?
I can’t remember anyone really pointing out this subtle nuisance … so I thought I might.

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