On Tue, 18 May 2021 16:38:33 -0700, Jeff Liebermann
wrote:

On Tue, 18 May 2021 08:16:38 -0700 (PDT), Tom Kunich
wrote:

Titanium in most cases doesn't get anywhere near the required
stress limits to fatigue since it is so damned strong to begin
with. This is why I said that if the Ti frameset doesn't fail
in the first month or so it will last virtually forever.

"The Fatigue of Titanium and Titanium Alloys"
http://www.metalspiping.com/the-fatigue-of-titanium-and-titanium-alloys.html
"Fatigue life tells us how long a titanium component survives at a
particular stress, while fatigue strength is the maximum stress a
titanium component endures without occurrence of fatigue cracks after
a large numbers of cycles, such as 10^8."

You'll find that if you stress titanium enough times (such as 10^8
times), it will crack. If you attach a few strain gauges to the
various tubes of a titanium frame, and use a data logger to count the
number of stress cycles, you might find that 10^8 cycles (100,000,000
cycles) arrives fairly soon, especially when every bump in the road is
considered a stress cycle.

Hmmm... I could probably guestimate the Ti frame life. A 700c wheel
is very close to 2 meters circumference. In 1 km, that's 500 wheel
revolutions. Pulling a number out of my hat, I would guess(tm) about
1 stress cycle per revolution, or 500 bumps per km. 10^8 bumps would
require riding:
1*10^8 bumps / 500 bumps/km = 200,000 km
At 100 km/week, that would take:
200,000km / 100km/week = 2,000 weeks
2,000 weeks / 52 weeks/year = 38 years
of riding before your titanium frame falls apart. I expected less,
but 38 years seems acceptable. If you want a better number, attach on
the strain gauges and provide a number for how many bumps per km your
experience while riding.

http://www.metalspiping.com/the-fati...um-alloys.html
The point that you are missing in your calculation is the severity of
the stress imposed. At a stress of 900 MPa (130,533.96 psi) the
titanium sample broke after a bit less then 10^4 cycles and at a
stress of 600 MPa (87,022 psi) it required ~10^7 cycles.

Another point is that the strength and fatigue failure of titanium
varies greatly depending on the alloy. the numbers above are obviously
for an alloy of titanium but pure titanium fails as low as 275 MPa
(39,885 psi) for 10^7 cycles in the annealed condition and as cold
rolled at 300 MPa (43,511 psi) for 10^7 cycles.

So, if a titanium alloy you may be able to hit 10,000,000 bumps at a
force of 87,022 psi before the bicycle breaks :-)
--
Cheers,

John B.