The most common Ti alloy used in bicycles is 6%AL 4% V
The frame material in the original post though is 3AL
and as I warned early on in the post "strength" is a vague definition. However, if I look at all the bicycle failures I've examined, it has always been through cracking. Therefore I choose to compare strengths in fracture toughness. I could use fatigue limits, but a frame builder can easily compensate for that and alu builders of course do. This particular Ti alloy has a fracture toughness roughly correspondent to it's density, if you compare aluminium, titatnium and steel.
But you can't pick just 1 form of failure and base a complete argument around that, as you you are clearly intelligent enough to know that it's never that simple. I don't think comparing fracture toughness is entirely an accurate way of doing it either, as fracture toughness is the resistance to brittle failure in a material that already has a crack. We need to look at other material properties to see when that crack will occur. And, unfortunately, there are several unknowns that can cause the cracks, frame geometry, build process, etc.
At the moment the only figures I can find for fracture toughness of 4130 steel is that it is classified as an ultra high strength steel, which would mean it is in excess of 100MPa which is identical to that of 3AL Titanium (at half the density)
However, even if we were to use Young's modulus, where it more or less matches that of steel
The young's modulus of 4130 steel (which is as close as I can find to the composition of 531 tubes), is nearly double that of 3AL titanium (207 vs 100). So if you compare these, then you will need nearly equal weights of 4130 steel and 3AL titanium, to get the same "stiffness".
Yield is probably more important, I admit, than ultimate tensile strength. As the frame will be pretty useless if it yields. But, the yield strength of 4130 is around the 500MPa mark, which matches 3AL with 500MPa yield also.
Given the above, depending on the frame builder, you should be able to build an identical bike that is just as resistant to brittle failure once a crack has formed, just as likely to yield. But, will not be anywhere near as stiff,
depending on the geometry that could be used to create a bike with more compliance than a steel equivalent, though this I assume will effect power transfer (Though I have no real information yet to back this up). But with a much lighter frame
OR
You can have a titanium frame that is the equivalent weight and stiffness of steel, but is far, far stronger, in nearly all the definitions of the terms.
My very premise to the debate is that Ti is an inappropriate material for the job.
I will agree with this, but I think I agree for different reasons. It is only inappropriate because it has no clear benefits.
If you want something lighter than steel, but stiff. Then get carbon
If you want something lighter than steel, but more compliant. Then get aluminium
The only benefit, is if you was in the market to buy a bike for a lifetime, then it's strength properties for an equal mass, and it's resistance to corrosion would make it a good choice. But, there is plenty of old steel frames around that work pefectly well. So steel is a suitable choice here.
Ti is an exotic material, for those who want to buy it. There are better performing materials, or suitably performing materials available at lower prices.
