Bill,
Titanium is generally more brittle than aluminum and steel.
I have seen more titanium lacrosse shafts (6al 4v, similar alloy used in the SR-1) snap than all other materials (aluminum alloys, steel alloys, composites, scandium alloys) combined.
The SR-71 uses titanium only because the other option that can handle the heat was stainless steel (too heavy).
95% of the Ti source used to build the SR-71 was rejected because it was too brittle.
The extreme heat generated by air friction actually helped the Ti withstand the vibrations by annealing it (making it softer for those who don't know the term).
The SR-71 doesn't just take off and pop into mach 3 nor does it handle like an F-16 (because it would fall apart if it did).
Ductility of 6AL 4V titanium is about 14%, the ductility of low carbon steels is around 25%.
You may be confusing "brittleness" with "weakness."
No one here ever said Ti was weak.
You may want to go back to the books and get the facts yourself.
This info comes from a metallurgist friend.