Register to reply

Cracked glass

by lost.and.lonely.physicist@gmail.com
Tags: cracked, glass, solved
Share this thread:
George Hammond
#19
Oct12-06, 05:01 AM
P: n/a
On Sun, 2 Oct 2005 19:55:34 +0000 (UTC),
"lost.and.lonely.physicist@gmail.com"
<lost.and.lonely.physicist@gmail.com> wrote:

>Hello everyone
>
>A cafe I visit often has large glass windows. Recently, one of them
>cracked - it appears that something went thru it, puncturing a small
>hole, causing the entire rectangular piece of glass to crack (but not
>shatter) into a cobweb-like pattern, centered around the hole.
>
>I'm curious how one might describe such a phenomenon -- both the
>cobweb-like pattern of cracked glass, how it formed in the first place,
>in what way the formation of the pattern is dependent on boundary
>conditions (the glass window is held in a rectangular wooden frame) and
>what sort of aggregate properties one might be able to derive out of
>such a seemingly complicated system.
>
>Thanks for any insight.


[Hammond]
I have little insight on broken glass other than this.
Obviously the cracks in a mirror, binocular lens, or a pair of glasses
would occur where the stress tensor exceeded the elastic limit of the
glass.
The stress tensor would do so where the deformation of the glass
was maximum (the basic stress=strain equation being obtained by
setting the deformation equal to the stress tensor with the elastic
constants of proportionality.
Since the deformation due to the impact of a projectile can be
expected to look like an extended "dent" as it were... the stress
tensor can be calculated from that deformation... and the "cracks"
themselves will be determined by the stress tensor.. and will
basically conform to the shape of the deformation. In the case of a
"dent" type of deformation, obviously the crack pattern will be a
radial "spider web" type of pattern... due to the (r, theta)
2-variable polar coordinate symmetry of the deformation and which is
most commonly seen in glass that has been hit by a low speed
projectile such as a stone.
The boundary conditions (clamped vs free) will of course
affect the solutions, and thus the deformation and stress tensor.
Obviously the deformation will be greater on the diagonals of a
square so that the cracks can be expected to be greater diagonally
in a window pane.
The problem is complicated because the glass is subjected to both
inertial and mechanical restraint (mass restraint vs. spring
restraint)... and thus there is both a lo-speed and hi-speed solution.
A high speed projectile will not "deform" the glass, but will rather
speed straight thru it, the glass being "inertially restrained" (mass
restrained, rather than spring restrained). In that simple case the
crack pattern can be expected to leave a nearly circular hole with
little or no cracking... however existing stress in the glass due to
clamping at the boundary almost always results in catastrophic long
radial cracks, most usually in the diagonal direction toward the
corners. This is probably the most common scenario of breakage
pattern... a small hole from a high speed projectile (which under
perfect conditions would not cause any cracks at all.. just a small
hole)... however, there almost always is considerable clamping stess
already in the window, most of it corner to corner, so there usually
results a catastrophic diagonal crack in the window. This is very
common in automobile windshields hit by high speed stones.
A low speed projectile, such as a baseball or, or a drivers head, on
the other hand can be expected to cause "deformation cracking" and a
large scale pattern of spider web crackingk (or "cob web" cracking
such as you mentioned.
On the other hand, most plate glass fractures are overwhelmed by
"prexisting stress" cracking that run the full length of the window
(usually diagonally), and are mainly due to clamping stress at the
window boundaries, or even due to stress in the glass itself due to
manufacturing processes (heating/cooling).
I am sure there are extensive analyses of glass pane breakage
patterns in the literature... or even online.

===========================
George Hammond's Website
http://geocities.com/scientific_proof_of_god
===========================

uchchwhash@hotmail.com
#20
Oct12-06, 05:01 AM
P: n/a
in case this post remains unanswered, ... I would very much like to
learn about it too!

uchchwhash@hotmail.com
#21
Oct12-06, 05:01 AM
P: n/a
in case this post remains unanswered, ... I would very much like to
learn about it too!

uchchwhash@hotmail.com
#22
Oct12-06, 05:01 AM
P: n/a
in case this post remains unanswered, ... I would very much like to
learn about it too!

uchchwhash@hotmail.com
#23
Oct12-06, 05:01 AM
P: n/a
in case this post remains unanswered, ... I would very much like to
learn about it too!

uchchwhash@hotmail.com
#24
Oct12-06, 05:01 AM
P: n/a
in case this post remains unanswered, ... I would very much like to
learn about it too!

uchchwhash@hotmail.com
#25
Oct12-06, 05:01 AM
P: n/a
in case this post remains unanswered, ... I would very much like to
learn about it too!

uchchwhash@hotmail.com
#26
Oct12-06, 05:01 AM
P: n/a
in case this post remains unanswered, ... I would very much like to
learn about it too!

uchchwhash@hotmail.com
#27
Oct12-06, 05:01 AM
P: n/a
in case this post remains unanswered, ... I would very much like to
learn about it too!

uchchwhash@hotmail.com
#28
Oct12-06, 05:01 AM
P: n/a
in case this post remains unanswered, ... I would very much like to
learn about it too!

Nick Maclaren
#29
Oct12-06, 05:01 AM
P: n/a
In article <1128237092.487607.99630@g43g2000cwa.googlegroups.com>,
"lost.and.lonely.physicist@gmail.com" <lost.and.lonely.physicist@gmail.com> writes:
|>
|> A cafe I visit often has large glass windows. Recently, one of them
|> cracked - it appears that something went thru it, puncturing a small
|> hole, causing the entire rectangular piece of glass to crack (but not
|> shatter) into a cobweb-like pattern, centered around the hole.

Don't forget to wear your Kevlar underwear, when you next visit,
then :-)

|> I'm curious how one might describe such a phenomenon -- both the
|> cobweb-like pattern of cracked glass, how it formed in the first place,
|> in what way the formation of the pattern is dependent on boundary
|> conditions (the glass window is held in a rectangular wooden frame) and
|> what sort of aggregate properties one might be able to derive out of
|> such a seemingly complicated system.

At a simplistic level, it is easy. The basic shape of the breaks
is caused by the distortion caused by the 'bullet' and the frame,
and the detailed locations are caused by random weaknesses in the
near-uniform glass. You can actually get a long way using only
school (i.e. not university) physics and mathematics.

The radials are caused by crack propagation, which happens because
the maximum stress is at the end of a crack, and the cross-breaks
by where the glass breaks in a 'dry stick' fashion. The shape of
the frame comes in because of the way that it controls the way the
glass distorts.

So far, so good. Once you start getting down to detailed analysis,
it gets much hairier, and you need to ask the people who work on
safety glass design for that. But I believe that a lot is still
pragmatic engineering, of the sort where they can predict what will
happen, know the basic principles of why, but not the details.

Regards,
Nick Maclaren.


Nick Maclaren
#30
Oct12-06, 05:01 AM
P: n/a
In article <1128237092.487607.99630@g43g2000cwa.googlegroups.com>,
"lost.and.lonely.physicist@gmail.com" <lost.and.lonely.physicist@gmail.com> writes:
|>
|> A cafe I visit often has large glass windows. Recently, one of them
|> cracked - it appears that something went thru it, puncturing a small
|> hole, causing the entire rectangular piece of glass to crack (but not
|> shatter) into a cobweb-like pattern, centered around the hole.

Don't forget to wear your Kevlar underwear, when you next visit,
then :-)

|> I'm curious how one might describe such a phenomenon -- both the
|> cobweb-like pattern of cracked glass, how it formed in the first place,
|> in what way the formation of the pattern is dependent on boundary
|> conditions (the glass window is held in a rectangular wooden frame) and
|> what sort of aggregate properties one might be able to derive out of
|> such a seemingly complicated system.

At a simplistic level, it is easy. The basic shape of the breaks
is caused by the distortion caused by the 'bullet' and the frame,
and the detailed locations are caused by random weaknesses in the
near-uniform glass. You can actually get a long way using only
school (i.e. not university) physics and mathematics.

The radials are caused by crack propagation, which happens because
the maximum stress is at the end of a crack, and the cross-breaks
by where the glass breaks in a 'dry stick' fashion. The shape of
the frame comes in because of the way that it controls the way the
glass distorts.

So far, so good. Once you start getting down to detailed analysis,
it gets much hairier, and you need to ask the people who work on
safety glass design for that. But I believe that a lot is still
pragmatic engineering, of the sort where they can predict what will
happen, know the basic principles of why, but not the details.

Regards,
Nick Maclaren.

Nick Maclaren
#31
Oct12-06, 05:01 AM
P: n/a
In article <1128237092.487607.99630@g43g2000cwa.googlegroups.com>,
"lost.and.lonely.physicist@gmail.com" <lost.and.lonely.physicist@gmail.com> writes:
|>
|> A cafe I visit often has large glass windows. Recently, one of them
|> cracked - it appears that something went thru it, puncturing a small
|> hole, causing the entire rectangular piece of glass to crack (but not
|> shatter) into a cobweb-like pattern, centered around the hole.

Don't forget to wear your Kevlar underwear, when you next visit,
then :-)

|> I'm curious how one might describe such a phenomenon -- both the
|> cobweb-like pattern of cracked glass, how it formed in the first place,
|> in what way the formation of the pattern is dependent on boundary
|> conditions (the glass window is held in a rectangular wooden frame) and
|> what sort of aggregate properties one might be able to derive out of
|> such a seemingly complicated system.

At a simplistic level, it is easy. The basic shape of the breaks
is caused by the distortion caused by the 'bullet' and the frame,
and the detailed locations are caused by random weaknesses in the
near-uniform glass. You can actually get a long way using only
school (i.e. not university) physics and mathematics.

The radials are caused by crack propagation, which happens because
the maximum stress is at the end of a crack, and the cross-breaks
by where the glass breaks in a 'dry stick' fashion. The shape of
the frame comes in because of the way that it controls the way the
glass distorts.

So far, so good. Once you start getting down to detailed analysis,
it gets much hairier, and you need to ask the people who work on
safety glass design for that. But I believe that a lot is still
pragmatic engineering, of the sort where they can predict what will
happen, know the basic principles of why, but not the details.

Regards,
Nick Maclaren.

Nick Maclaren
#32
Oct12-06, 05:01 AM
P: n/a
In article <1128237092.487607.99630@g43g2000cwa.googlegroups.com>,
"lost.and.lonely.physicist@gmail.com" <lost.and.lonely.physicist@gmail.com> writes:
|>
|> A cafe I visit often has large glass windows. Recently, one of them
|> cracked - it appears that something went thru it, puncturing a small
|> hole, causing the entire rectangular piece of glass to crack (but not
|> shatter) into a cobweb-like pattern, centered around the hole.

Don't forget to wear your Kevlar underwear, when you next visit,
then :-)

|> I'm curious how one might describe such a phenomenon -- both the
|> cobweb-like pattern of cracked glass, how it formed in the first place,
|> in what way the formation of the pattern is dependent on boundary
|> conditions (the glass window is held in a rectangular wooden frame) and
|> what sort of aggregate properties one might be able to derive out of
|> such a seemingly complicated system.

At a simplistic level, it is easy. The basic shape of the breaks
is caused by the distortion caused by the 'bullet' and the frame,
and the detailed locations are caused by random weaknesses in the
near-uniform glass. You can actually get a long way using only
school (i.e. not university) physics and mathematics.

The radials are caused by crack propagation, which happens because
the maximum stress is at the end of a crack, and the cross-breaks
by where the glass breaks in a 'dry stick' fashion. The shape of
the frame comes in because of the way that it controls the way the
glass distorts.

So far, so good. Once you start getting down to detailed analysis,
it gets much hairier, and you need to ask the people who work on
safety glass design for that. But I believe that a lot is still
pragmatic engineering, of the sort where they can predict what will
happen, know the basic principles of why, but not the details.

Regards,
Nick Maclaren.

Nick Maclaren
#33
Oct12-06, 05:01 AM
P: n/a
In article <1128237092.487607.99630@g43g2000cwa.googlegroups.com>,
"lost.and.lonely.physicist@gmail.com" <lost.and.lonely.physicist@gmail.com> writes:
|>
|> A cafe I visit often has large glass windows. Recently, one of them
|> cracked - it appears that something went thru it, puncturing a small
|> hole, causing the entire rectangular piece of glass to crack (but not
|> shatter) into a cobweb-like pattern, centered around the hole.

Don't forget to wear your Kevlar underwear, when you next visit,
then :-)

|> I'm curious how one might describe such a phenomenon -- both the
|> cobweb-like pattern of cracked glass, how it formed in the first place,
|> in what way the formation of the pattern is dependent on boundary
|> conditions (the glass window is held in a rectangular wooden frame) and
|> what sort of aggregate properties one might be able to derive out of
|> such a seemingly complicated system.

At a simplistic level, it is easy. The basic shape of the breaks
is caused by the distortion caused by the 'bullet' and the frame,
and the detailed locations are caused by random weaknesses in the
near-uniform glass. You can actually get a long way using only
school (i.e. not university) physics and mathematics.

The radials are caused by crack propagation, which happens because
the maximum stress is at the end of a crack, and the cross-breaks
by where the glass breaks in a 'dry stick' fashion. The shape of
the frame comes in because of the way that it controls the way the
glass distorts.

So far, so good. Once you start getting down to detailed analysis,
it gets much hairier, and you need to ask the people who work on
safety glass design for that. But I believe that a lot is still
pragmatic engineering, of the sort where they can predict what will
happen, know the basic principles of why, but not the details.

Regards,
Nick Maclaren.

Nick Maclaren
#34
Oct12-06, 05:01 AM
P: n/a
In article <1128237092.487607.99630@g43g2000cwa.googlegroups.com>,
"lost.and.lonely.physicist@gmail.com" <lost.and.lonely.physicist@gmail.com> writes:
|>
|> A cafe I visit often has large glass windows. Recently, one of them
|> cracked - it appears that something went thru it, puncturing a small
|> hole, causing the entire rectangular piece of glass to crack (but not
|> shatter) into a cobweb-like pattern, centered around the hole.

Don't forget to wear your Kevlar underwear, when you next visit,
then :-)

|> I'm curious how one might describe such a phenomenon -- both the
|> cobweb-like pattern of cracked glass, how it formed in the first place,
|> in what way the formation of the pattern is dependent on boundary
|> conditions (the glass window is held in a rectangular wooden frame) and
|> what sort of aggregate properties one might be able to derive out of
|> such a seemingly complicated system.

At a simplistic level, it is easy. The basic shape of the breaks
is caused by the distortion caused by the 'bullet' and the frame,
and the detailed locations are caused by random weaknesses in the
near-uniform glass. You can actually get a long way using only
school (i.e. not university) physics and mathematics.

The radials are caused by crack propagation, which happens because
the maximum stress is at the end of a crack, and the cross-breaks
by where the glass breaks in a 'dry stick' fashion. The shape of
the frame comes in because of the way that it controls the way the
glass distorts.

So far, so good. Once you start getting down to detailed analysis,
it gets much hairier, and you need to ask the people who work on
safety glass design for that. But I believe that a lot is still
pragmatic engineering, of the sort where they can predict what will
happen, know the basic principles of why, but not the details.

Regards,
Nick Maclaren.

Nick Maclaren
#35
Oct12-06, 05:01 AM
P: n/a
In article <1128237092.487607.99630@g43g2000cwa.googlegroups.com>,
"lost.and.lonely.physicist@gmail.com" <lost.and.lonely.physicist@gmail.com> writes:
|>
|> A cafe I visit often has large glass windows. Recently, one of them
|> cracked - it appears that something went thru it, puncturing a small
|> hole, causing the entire rectangular piece of glass to crack (but not
|> shatter) into a cobweb-like pattern, centered around the hole.

Don't forget to wear your Kevlar underwear, when you next visit,
then :-)

|> I'm curious how one might describe such a phenomenon -- both the
|> cobweb-like pattern of cracked glass, how it formed in the first place,
|> in what way the formation of the pattern is dependent on boundary
|> conditions (the glass window is held in a rectangular wooden frame) and
|> what sort of aggregate properties one might be able to derive out of
|> such a seemingly complicated system.

At a simplistic level, it is easy. The basic shape of the breaks
is caused by the distortion caused by the 'bullet' and the frame,
and the detailed locations are caused by random weaknesses in the
near-uniform glass. You can actually get a long way using only
school (i.e. not university) physics and mathematics.

The radials are caused by crack propagation, which happens because
the maximum stress is at the end of a crack, and the cross-breaks
by where the glass breaks in a 'dry stick' fashion. The shape of
the frame comes in because of the way that it controls the way the
glass distorts.

So far, so good. Once you start getting down to detailed analysis,
it gets much hairier, and you need to ask the people who work on
safety glass design for that. But I believe that a lot is still
pragmatic engineering, of the sort where they can predict what will
happen, know the basic principles of why, but not the details.

Regards,
Nick Maclaren.

Nick Maclaren
#36
Oct12-06, 05:01 AM
P: n/a
In article <1128237092.487607.99630@g43g2000cwa.googlegroups.com>,
"lost.and.lonely.physicist@gmail.com" <lost.and.lonely.physicist@gmail.com> writes:
|>
|> A cafe I visit often has large glass windows. Recently, one of them
|> cracked - it appears that something went thru it, puncturing a small
|> hole, causing the entire rectangular piece of glass to crack (but not
|> shatter) into a cobweb-like pattern, centered around the hole.

Don't forget to wear your Kevlar underwear, when you next visit,
then :-)

|> I'm curious how one might describe such a phenomenon -- both the
|> cobweb-like pattern of cracked glass, how it formed in the first place,
|> in what way the formation of the pattern is dependent on boundary
|> conditions (the glass window is held in a rectangular wooden frame) and
|> what sort of aggregate properties one might be able to derive out of
|> such a seemingly complicated system.

At a simplistic level, it is easy. The basic shape of the breaks
is caused by the distortion caused by the 'bullet' and the frame,
and the detailed locations are caused by random weaknesses in the
near-uniform glass. You can actually get a long way using only
school (i.e. not university) physics and mathematics.

The radials are caused by crack propagation, which happens because
the maximum stress is at the end of a crack, and the cross-breaks
by where the glass breaks in a 'dry stick' fashion. The shape of
the frame comes in because of the way that it controls the way the
glass distorts.

So far, so good. Once you start getting down to detailed analysis,
it gets much hairier, and you need to ask the people who work on
safety glass design for that. But I believe that a lot is still
pragmatic engineering, of the sort where they can predict what will
happen, know the basic principles of why, but not the details.

Regards,
Nick Maclaren.


Register to reply