Re: stress vs. strain determines crack limit

"seferiad" <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> 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? .....

While this is a kind of "chicken and egg" question, Over the years
I've found it most instructive to consider strain as the primary
variable when considering mechanics of materials.

There are a number of reasons for this, perhaps the most important
being that if one puts strain on the left hand side of the equation,
the right hand side is a sum of simple influence terms.

Strain = Compliance*Stress + ExpansionCoefficient*Temperature + ..etc.

Another indicator is that the deformation behavior of various
materials varies widely with applied stress and does not vary much
with applied strain; for example, yield of materials occurs in a
fairly small range of strains.

At the atomic level the coherence of a material is dictated by
distances between the atoms.  Failure is the consequence of atoms
being drawn so far apart that they rearrange themselves into a new
configuration.

While such considerations cannot assign primacy to intimately tangled
variables like stress and strain, they can sometimes help simplify
certain problems.