Re: stress vs. strain determines crack limit

seferiad wrote:
> Hello,
> With respect to classic power-law crack growth in brittle materials,  the
> critical limit is given by
>
> K = Y*S*a^1/2,  where Y is a constant, S is the applied stress, and a is the
> crack length (which is taken as a square root).
>
> My question is : What is the true independent variable (i.e., stress or
> strain) that determines when the material fractures?  This equation suggests
> that it is the stress, since the strain is not given, but that might be more
> for convenience since we tend to measure stress, not strain.
>
> Assuming the stress-strain relationship were perfectly linear it wouldn't
> matter, but since materials fracture in a regime in which the stress-strain
> is not linear, it changes the interpretation of fracture data.
>
> Thanks,
> Jay
I suggest that you do some basic reading on both "Brittle Fracture" and 
Fracture Mechanics.

The original Griffith papers were based on the basic concept of fracture 
being controlled by the development of stresses at the crack tip 
sufficiently large to cause atomic rupture.

If you think about the Griffith model carefully, then you will realize 
that if you are in a strain controlled situation, then you may have to 
do a little more clever thinking to translate that strain control into 
the key concept of stress development at the crack tip.

If you proceed to the next generation of ideas by Irwin, you find the 
key concept now is the strain energy release rate, and it must be 
sufficently large to overcome the plastic work of fracture.

Then, if you think more about it, you will realize that if you are in a 
strain controlled loading situation, your job is to translate the body 
mechanics down to understanding the crack tip strain energy release rate.

So, if you ask "Is fracture stress controlled or strain controlled?", 
the answer is something like:
___ "NO, you have to still understand the mechanics of each case."

Fracture has been a sort of intellectual pain in the anus for several 
centuries.

It still is far from being put in the can and stuck on the shelf as a 
cookbook sort of thing, which too many engineers desire greatly today, 
and have desired greatly for more than a century. None of this stops 
people from trying, though.

Jim


--
...............................


Keepsake gift for young girls.
Unique and personal one-of-a-kind.
Builds strong minds 12 ways.
Guaranteed satisfaction
- courteous money back
- keep bonus gifts

 http://www.alicebook.com