I am involved in a research project in which we use slumped sheet
glass (alkaline free borosilicate glass .3 mm thick) in telescopes. 
The glass is cut using a scriber, leaving microcracks in each cut
edge.  I am looking for a quantitative answer (whether in the form of
an equation or a graph) that directly relates the number of
microcracks to the decrease in overall bending strength of the glass.

I have searched the web, as well as various school libraries, for a
scientific paper that addresses this issue.  I have found many, but
none of them are quantitative.  They all come to the same
conclusion--that edge defects do in fact have significant effects on
bending strength.  However, I need an exact scientific method in order
to convince a committee to invest money in a wire cutter which would
greatly improve the edge condition.

I have already searched the Corning glassware site, the Schott glass
site (where we order the glass from), Columbia University Libraries
(which has a pretty comprehensive website), and various scientfic
journal databases online.  I have also read through mechanical
engineering and material science texts discussing fracture toughness,
but was unable to come up with a congruent method.

I am a student, so I cannot afford to offer a high price, however,
receiving this information (the sooner, the better) would greatly
contribute to the efforts of our research team.

---

Request for Question Clarification by hedgie-ga on 22 Aug 2003 02:31 PDT

The growth of a crack has been studied and a
complex equation describing it does exist. However,
that does not translate into what you asking
for: Number of cracks is nor sufficient to
dtermine the strength. One would need a statistical
measure of the crack size distribution. Would
you consider either of the above as an answer?

To convince a comittee a more practical, engineering
approach, may be more effective,than "exact scientific method"
 such as comparing cost of polishing to the cost of a 
different cutter.

---

Clarification of Question by sblowen-ga on 30 Aug 2003 17:26 PDT

Hedgie,

Rather than comparing the "cost of polishing to the cost of a
different cutter," we are trying to prove whether or not we need to
change anything at all.  We have a hot wire-cutter which produces a
very smooth edge with almost no microcracks.  However, much money
would be needed to make the machine more effecient and user friendly. 
What the committe would like to see is proof that the microcracks in
our existing glass (cut with the scriber) decreases bending strength
significantly enough to invest money in the wire-cutter (or even
polishing, if that turns out to be a more efficient means).

The only reason I asked for a "quantitative answer that directly
relates the number of microcracks to the decrease in overall bending
strength of the glass" is because our research director mentioned once
seeing such an existing method (but I have not been able to find it). 
Saying that such a method does not exist is definitely helpful, but I
still need a quantitative way of measuring the bending strength of our
glass with microcracks vs. that of the same piece with a smooth edge.

Can you elaborate on "a statistical measure of the crack size
distribution"?  This sounds like it might be very helpful.

Please let me know if any further clarification is necessary.  And
thank you for your time and effort.

hello again,  sblowen

 Thanks forthe clarification, it helps. 
  The literature on  'cracks and material strength'
 is extensive and the challenge is to find the needle 
which will serve your purpose, in the haystack of
 specialized studies which are available on the web,
which is a small fraction of the total.

 Since no one picked up the challenge so far,
I will go ahead and list few links  which appear to be relevant. 


Here is a bit of  overview and history:   

   " As early as the 1920s, the strength of glass and other
brittle materials was understood to be limited by the
presence of small cracks. Under stress, the small cracks
would grow into larger cracks until reaching a critical
size, at which point the material would fracture
catastrophically. It also was well known that humid
environments reduced the strength more severely than
did dry environments... .."
http://nvl.nist.gov/pub/nistpubs/sp958-lide/181-183.pdf.     


Simple Model of the crack propagation
    www.poco.phy.cam.ac.uk/~rbb11/EIS.pdf
 
Griffith's contribution :   (energy balance)
 
Griffith's criterion was based on the observation that glass is not
internally
 homogeneous but rather contain pores ... 
       http://www.geosc.psu.edu/~engelder/geosc465/lect14.rtf

 
  A bit of theory and some basic equations   (Griffith-Irwin)
  www.utm.edu/departments/engin/lemaster/
Machine%20Design/Lecture%2012.pdf


  Limitations of the Griffith approach
    http://www.mpg.de/english/illustrationsDocumentation/documentation/pressReleases/2000/news15_00.htm




 Empirical study of slow crack propagation in glass
 http://www.physics.usyd.edu.au/apphys/crack.html


  Lot of the material can be found in subscription journals
  such as:
 

 J . Appl. Physics (subscription required)
  J E Flitcroft and R D Adams
 Dept. of Mech. Engng., Univ. of Bristol, Bristol, UK

 ".. Shear crack propagation has been studied in unidirectional glass
and carbon
 fiber reinforced plastics.."


 or monographs 
  http://www.solid.ikp.liu.se/solidbook/lawn.htm   

    Since growth of cracks depends on local stress, solution of the
Navier-Stokes eq.
  for the structure is often necessary in engineering design studies.
That probably is
more then you want to do in your case, but as an illustration, this
link may be of interest:
                simu.ulb.ac.be/newsletters/N3VI.pdf


Search Terms
Crack Propagation  
Griffith Theory
 crack propagation, Navier Stokes


hedgie

This is sort of tough sell.  Nobody studies the strength of cracked
glass because the results end up so messy.  You can predict your
results will be unpredictable.  Makes for frustrating research.

I do remember one paper that advocated polished edges to improve glass
strength.  Add polished edges to your searches and I'm sure you'll
find it.

Are you using sf float?  I would call places like Glass Fab and ask
the people with experience for their advice.

I once saw some interesting formulas in these books.  You can
interlibrary loan them from MIT:

1. Formulas for Stress and Strain, 5th ed., Raymond J. Roark and
Warren C. Young, p572.
2. The Properties of Glass, 2nd ed., George W. Morey, p338.