Re: stress vs. strain determines crack limit

"seferiad" <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
....
> Let's say I have a bunch of fibers that perfectly obey Weibull statistics
> when  I do dynamic pull testing to destruction for the fibers. The
> distribution when plotted on Weibull gives a slope = m (it doesn't matter
> what m is....
> 
> I have two "ideal" Instron machines. One machine pulls with a constant
> stress rate and the other machine pulls with a constant strain rate.

"Instron" machines are deflection devices. I take what you say to mean
test type 1 is constant rate of force increase (ie. proportional to
nominal engineering stress rate) & test type 2 is constant rate of
deflection increase(ie. constant nominal engineering strain rate).

Before going on to your question of wiebull distributions for these
two types of tests let's think about the tests themselves.

Consider a large number of non-interacting parallel fibers in a
bundle.

Test type 2: (constant deflection rate)-as deflection increases some
of the fibers break so the total force is for a particular deflection
is less than that expected if no fibers break; ie. the nominal stress
is LESS than predicted by the (initial modulus)*(strain) by the
fraction f of fibers remaining.  That is, (actual stress) =
f*(predicted stress). "f" is in effect a fiber's survival probability
at the actual stress on the surviving fibers.

Test type 1: (constant force rate) -as force increases & some of the
fibers break the deflection at a particular nominal stress is MORE
than that expected by the inverse fraction 1/f of fibers broken. That
is, (actual strain)=(predicted strain)/f. Again, f is the fiber's
probability of survival at the actual stress on the surviving fibers.

Note that in either case the fraction of fibers broken can be
estimated by taking the ratio of the observation to the linear
prediction.

> If I now plot these two Weibull distributions:  %Failure vs. Stress (or
> Strain)
....

Now things get a little confusing for me because I don't know exactly
what you intend to plot.

The first test I described (the constant deflection rate test) yields
data that are easily compared with weibull predictions. (force
observed)/(force predicted) is the fraction of surviving fibers and
(engineering strain)*(initial modulus)*time/(initial number of fibers)
is the fiber stress.

I hope this helps. Perhaps your response might clarify your question.
Am I addressing the matter that concerns you?