Re: stress vs. strain determines crack limit

In article <[EMAIL PROTECTED]>, jbuch <[EMAIL PROTECTED]>
writes
>seferiad wrote:
..snip..
>> 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.
...snip...
>I suggest that you do some basic reading on both "Brittle Fracture" and 
>Fracture Mechanics.
>
..snip..
>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."
..snip..

Agreed.
However, in linear elastic fracture mechanics (LEFM)
it is not really necessary to understand the mechanics
of the fracture process. All we need to appreciate 
is that the region immediately surrounding the crack
tip is subjected to highly non-linear fields of stress
and strain. However, outside that, we have the unique
K-controlled "square root r" elastic fields of stress 
and strain. So, the stress intensity factor, K, tells 
you all you need to know about the loading of that crack 
region and when it well eventually fail: K_applied=K_mat.

In elastic-plastic fracture mechanics, a similar 
'control' of the stresses and strains in the crack 
tip region is considered to be achieved by means of the 
parameter J (J-integral),

As stated by the previous poster, in reality the material 
ahead of the crack tip fails in a manner which depends 
on the particular micromechanics of the material. 
So, cracks in ductile steels grow by microvoid initiation, 
growth and coalescence to give ductile tearing. In a simple
micromechanical model , this requires a combination of 
plastic strain and stress triaxiality to achieve. 

Cracks in ferritic steels on the lower shelf and in the 
ductile-brittle transition are considered to fail by 
cleavage. A simple micromechanical model of cleavage 
requires a critical stress to be achieved over a 
characteristic distance ahead of, or volume 
surrounding, the crack tip. 

Returning to the original question, it can be argued that
strain is what is imposed on the material and stress is 
its response to it. On balance I would prefer to regard 
strain as the "independent variable", but engineers
are used to working with stress so this tends to be 
more commonly used.

Anyway, just my 'two penny worth' to the thread.

Regards
Martin
--
http://www.analysis.demon.co.uk
http://www.fracturetraining.co.uk