Ogre, a sci-fi tabletop wargame from 1977, used the development of an extraordinarily strong composite armor called 'biphase carbide' (BPC) as a technobabble justification for the widespread deployment of nuclear munitions in conventional warfare and a resurgence of tanks as the primary combatants of world powers. The intro to the game states that the armor is so light that even a ground-effect vehicle can carry several centimeters of protection, which is still enough to require 'the equivalent of a ton of TNT' to breach. Armored vehicles protected by layers of BPC are effectively invulnerable to anything short of a contact nuclear detonation.
It seems to me that widespread development of this material would have implications beyond being used simply as armor. While the game is deliberately vague about the material beyond stating that it's both very tough and very light, I'd think that a material that is so strong that it requires tactical nukes to breach while being lighter than steel should be useful for more than just armoring tanks. The focus of the game is on the AI-controlled supertanks, but I'm curious as to what the wider applications of this material would be. Lighter engines? More stable architecture? Should the implied materials science translate to civil applications, or do properties that make for good armor not necessarily have wider uses (eg, nobody makes buildings out of Chobham)? Or am I missing some obvious, world-changing application?
What would be the world-changing implications of widespread access to an extremely strong, but extremely light composite material?
Edit: It has been pointed out to me that this question is vague, so let's add some hypothetical rules for this material. I'm not a materials scientist so please bear with me.
I've read that carbon fiber is currently about eight times more expensive than steel, and that price has thus far limited its adoption, so let's put the overall price for manufacturing (tooling, production costs, etc) at roughly four times that of steel. So cheaper than carbon fiber, and much more capable for the same roles (high strength, light weight), but still more expensive than steel.
It's not particularly difficult to produce, or reliant on exotic materials. I'll say comparable to carbon fiber.
It's not able to survive sitting on a nuke. It's strong enough to render conventional weapons ineffective, not invulnerable. Given that the Chobham armor of an M1 Abrams is speculated to be around five times more effective than a steel equivalent, I'll say that this material is fifty times tougher than steel per unit mass.
Its density is a fifth that of steel, so a given volume of this material is ten times stronger than steel at a fifth the mass.
Given the above, I know that this is pretty much an impossible wonder-material. Let's say it runs on the magic of handwavium and try to focus on the implications rather than the physical implausibility.
These are all ballpark figures, but I think may help narrow down the parameters. It's more expensive than steel, but far stronger despite less density. It has limits, especially cost-related, but it's physical capabilities are pretty high. So, what are the practical applications? Where will this technology change the world in immediately noticeable ways?