What is the difference between the 'adhesive splice' and the 'adhesive bonding'?
Structurally, as long as you've got sufficient core-shear and skin-endload connectivity it should be ok. Just foaming adhesive (possibly referred to as a 'core splice') should work for shear. Make sure you have adequate pressure applied. You don't want the core splice to be too thick, so try to keep the gap between the pieces of core controlled. A maximum gap of 1/2", and preferably less. Make sure enough foaming adhevive is put in to fill it (duh! Manufacturer's data sheet should guide as to amount of foaming, but experience probably more important). If the core is honeycomb the gap should be a rough average.
You show the original skins overlapping your 'adhesive splice.' Is the intent to 'core out' some of the original core material? Having a big gap will increase the chances of an undersirable outcome. There's very little support given to the skins by the adhesive as it foams. I don't actualy know what the internal foam pressure is but I'd be surprised it's a couple of psi.
Your shear overlaps should of course be adequate. While the overlaps shown aren't too bad, often 0.5"
per ply would be used and in an overlap patch each ply should probably have an overlap of 20t or so. A simple pyramid patch (usually match the parent layup properties plus one overall 45° ply) would be probably be ok (I assume composite skin—if Al or similar no need for such elaboration). While just cure under vacuum might be enough, 30–50 psi (keep it as low as the original cure of the honeycomb panel) in an autoclave would help. NB: in diagram had to add the '-'s at line start as for some reason it made multiple spaces into one space in the preview window.
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------- ____/________\____
-- ____/__________________\____
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-| | | | | | | |..| | | | | | |
-| | | | | | | |..| | | | | | |
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Well, I *think* this monospaced 'diagram' make senses. The 'preview' area is a bit variable.
Some people would splice the core as a separate op from putting the patch on. That way there's no chance of a composite patch sinking into the gap between the original skins and the splice is easy to clean up and inspect.
I think you'd only need a separate block of core if the gap to be filled was a bit big. To sort of reiterate, if it's more than 1/4" to 1/2" I'd think about making it even bigger and putting in some core like (1). You run the risk of inadequate through-thickness support during cure otherwise.
Your second para concerning qualification depends a lot on what rules this is being done under. Is it a production aerospace concession? A field aircraft repair? A public walkway bridge handrail? A bit of your garden shed? Etc. I personally would always expect some sensible calcs to be done, but that's my background and there may well be no need. Even with aircraft, it used to be the case that a lot of repair was done based on common sense and replacement of area (I may well be out of date here; this is pretty remote memories from the '80s).
I don't have any documents explicitly covering repair of sandwich. The usual suspects such as the DIAB and Hexcel manuals will help, but you may already have seen these.
You might also check out Care and Repair of Advanced Composites by Armstrong. A bunch of $/£/€, but worth it.
With regard to 'mixing' phenolic and epoxy, certainly after they are cured they may be bonded together, although the bond to the phenolic won't be as good as you might think (very roughly halve values for bonding cured epoxy with epoxy adhesives). Co-bonding (with either the epoxy or the phenolic uncured and the other cured) should sort of work, with a similar reservation on the shear strength. People with more experience than I of things like aircraft interiors may well know more. Also of course beware that epoxy will be more dangerous in any environment where it might burn.