The brazing done by Caterham and many other race chassis builders is called Bronze welding.
I think terminology varies. My recollection is that brazing refers to work that does not melt the base metal.
Elewayne did you use a gas type flux? I've heard that they use something that connects to the torch's hoses and fluxes thru the flame. It's not common gear in the US though, so far as I know.
Since the fillet is larger then the gage of the metal I'm not sure very exotic material is required for 1018 square tube. I'm interested in this, but researching is tiring. There are many types of brazing materials, in a variety of shapes and sizes. When you go to the suppliers sites, you can be confronted with a list of 40 types for similar purposes.
I've only used fairly generally available rods and also some silver soldering and copper/phosphorous rods.
Elewayne how much gas does it take to weld a frame? Please do get us the type you used. I know my local Lincoln dealer has a few types and said they would order rods too. They didn't have nickel/bronze MIG wire, but it seems silicon bronze is becoming available. Maybe that had a problem though, perhaps brittle?
Some are better for fillets and others for wicking into joints. This is generally in the description. One clue is the range given for the melting point. Materials with a large range say 100-200 degrees from starting to melt to completely melted will make better fillets. The "solidus" temperature is when it hardens and the "liquidous" temperature is fully melted.
As for Charles original question about frame tubing size, if you build a Locost out of birdcage size tubing, it needs to look like a birdcage to work - if that makes sense. If you used larger then normal tubing you have less tubes. So a Cobra with 2 4" tubes or a Locost with one or two dozen 1" tubes or a birdcage with more then a hundred ( ? ) tubes. If you carry this to it's logical extent, that's how you get monocoque cars out of sheet metal. A Lotus Elan or Europa sort of has 1 tube as it's backbone.