I think you are looking for the phrase "notch failure". This is only an issue with CP (commercially pure) titanium...failing along a stress riser. CP is made for chemical piping applications. Teledynes, and a lot of early titanium bikes, were made of CP. The builders realized the problem early and went to alloyed Titanium, like Ti-6AL-4V or 35AL-2V. These alloys are not prone to notch failure.