Most Durable Frame Material? (for fully loaded long-distance international touring)
Is it one of the hardened steels? Titanium? Other?
One issue would be the material itself, another issue would be the welds, lugs, or other methods of connection, and their durability.
Which is least likely to fail over the long haul, including longterm travel on rough roads?
Repairability is another issue, but the main question of interest is: which is least likely to fail in the first place (assuming reasonably light weight)?
IMO, lugged and brazed double butted steel or welded CrMo steel
on a really long tour, I don't think you should ignore the fact that you can get steel repaired. From the failures I've seen on CGOAB, I would use a high strength steel oversize tubing and very carefully select the other frame parts. In particular, dropouts seem to have a fairly high failure rate.
Steel is pretty much a given, I would ride other materials, but for your criteria steel would be the best.
Carbon probably could be good also because it is repairable, without heat sources, and it is extremely durable when properly handled. The prime example of the latter is the way carbon has come on as the toughness winner in archery. Arrows hit things at 300+ fps, and they don't always survive, but carbon has risen from the most fragile material the the toughest of the lot. The problem for bikes is that few if any users of carbon are doing the work with durability as the main issue. Carbon tends to fail spectacularly when clever prototypes hit the real world, so it would only be great once the first few thousand frames had been around the world and back, and even then the real advantage over steel might end up being slight. "better" materials aren't always the best choice in every case. Carbon is the obvious choice for golf club shafts, but it has proven very tough to implement. Here is an interesting example of carbon repairability:
Start about 3:30
I don't see any particular reason to favour lugs and butted tubes. Welding is totally proven in this kind of application. So are lugs and brazed joints. Just isn't a major issue as far as I can see.
Butted tubes can make a lot of sense but if you run the numbers, the weight saving is pretty minimal so even butted tubes may not be necesarry. A lot of the fancy tubes in tube sets, other than the main triangle are not really butted. They have wall thickness differences but not in the same way as in the main tubes. A lot of it has to do with getting tapers into the tubes for various reasons, but it isn't the heat wall thickness issue you see with the main tubes from what I can see. If one could find appropriate straight wall tubes it has some advantages for all the braze ons, and stuff like S&S. Maybe advantages is going too far, but it might do no harm. I'm looking at it from a large rider perspetive. Start to talk about 1.1-.8-1.1 tubes, or whatever, and good old .9 straight wall starts to look pretty good.
One thing about round the world trips is that they are high mileage low time duration events. 3 years, say, is not a lot of time if one is worried about stuff like rust, one of the few ways in which 4130 type tubes are not supreme.
For a world tour I would put a lot of effort into the design, the fit, and not too much into the material, 4130 type steels would suit me fine.
I don't think the high tensile steels are necesarry for the kind of structure one finds in a touring bike. On the other hand, more conventional tube sizings made in high tensile steel wouldn't be a bad thing. Realism has to come into it though. Finding a top maker of touring bikes who has ample extreme steel experience in the real world you are contemplating would not probably be the easiest find.
Ti in bikes is no longer regarded by most as the ideal material it once was. There is at least one guy on the touring forum who has been riding a BG Ti touring bike for decades and really likes it. One thing though, if you think lugs, butted tubes or in-field repairability are top priorities, it probably isn't the best material for you.
I don't know what you are thinking about lugs vs. welds, but most of these materials are designed to be welded in the first place. And these materials started being welded back before the first world war, bikes included. Lugs are totaly proven, and if they add a lot of beauty and satisfaction to your ride, then go for it, but it isn't a durability issue, and I am not sure it ever was. It is difficult to weld very light tubbing and maintain perfect alignment. But modern methods have totaly solved that problem. TIG has it's aesthetic and structural advantages, they just aren't as well understood. If your perfect touring bike includes classic geometry then you will have the choice of either method, if you end up with materials like Ti, Al and odd geometries, you will be better off with TIG. To me brazing is more about the molded joint look, I see little advantage to it on the main joints, it is high heat, and weight relative to TIG, well proven though. All bikes will probably have some brazing on them it is a very important secondary process for nearly all builders, if one can even consider stuff like drops secondary.
let me refine my comment about repair a little: as long as you stay away from stainless, you can get steel repaired by anyone with a torch and some brass. That can be important if you want to continue your tour. In most places, you aren't going to find someone with a TIG.
Somewhere on the touring board I did a long piece on welding in the field and what steps one could take to raise the potential for success. And of course, one can also use carbon fiber and epoxy, at least for certain repairs...
Would have made a good sticky for the touring board if it was written a little better.