Titanium alloys may have low strength - lower then Aluminium ones, although only when the % of titanium is higher than 98% - those almost pure Titanium alloys are used only in medicine, as are extremely resistant to corrosion. Not useful for aviation industry though - here are usually alloys with less than 90% Titanium, with the rest being Aluminium, Vanadium, Chromium etc. Those alloys are very tough, light, and both corrosion and heat resistant. The only reason why aircrafts are not made entirely of Titanium alloys (Black Bird and X-15 excluded) is because of high cost of the TiO ore, and manufacturing - as it is not very efficient - milling is very expensive because of high material strength, welding was not possible on the wider scale until 1990s, and casting is problematic because of other materials usage, and time.
I played with few things made of titanium alloys, and those were almost indestructible. Also take a look at the wreckage pictures of F-14s - main central wing spar that is also a main fuel tank and the whole aircraft hang from it - is always intact. I can't imagine that Titanium parts designed with aviation industry safety factors could be broken under normal operation loads, although as we all know it happened few times already, but I don't believe the material selection had anything to do with it.