The AFU and Urban Legend Archive Science Glass Flow glass flow math Select a topic - - - - - - - - Home Searches AFU FAQ - - - - - - - - AFU Animals Books Celebrities Classic Collegiate Death Disney Drugs Food GIF Language Legal Medical Misc Movies Politics Products Religion Science Sex Songs TV - - - - - - - - Other sites

From: s-sehlhorst@ds.mc.ti.com (Scott Sehlhorst)
Newsgroups: alt.folklore.urban
Subject: Glass flow, the answer.
Date: Wed, 21 Jun 1995 17:06:49

NNTP-Posting-Host: 157.87.224.38
X-Newsreader: Trumpet for Windows [Version 1.0 Rev Final Beta #11]

Enough already.
Here's the bottom line.
File it at cathouse. Also reference my other posts, which pointed towards but did not include the solution.

From:
_Elastic-Plastic Problems_, B.D. Annin and G.P. Cherepanov, c 1988, The American Society of Mechanical Engineers, 345 East 47th St, NYNY 10017

Translation of:Uprugo-plasticheska[i]a zadacha. QA931.A613 1988 531'.3823'015 88-70032
ISBN 0-7918-0000-8

Note: The equations are nearly unintelligible in ascii, so I will only reference them by author/eq# in the derivation of the solution, and will only try and asciify the bottom line.

Discussion is of elastic-plastic and pure plastic behavior of materials.

Guber-Mises condition (eq#1.3.12) defines shear type plastic deformation in metals and polymers.

Schleiher-Mohr condition is best applicable to granular materials and rocks, (like amorphous solids, like glass), and describes the onset of plastic deformation.

An example of the Guber-Mises is carried through, with support of the equations put forth by Reuss (1930) for pure shear, and Prandtl (1924) for plane stress, resulting in Prandtl-Reuss eq's.

Further discussion of boundary problem definitions and references to Melan's work (1939) lead to the formulation of the Mises maximum principle (1974), leading to the incremental theory of plasticity, and then the associated law, which is recognized as "the most general and substantiated theory."[p11]

In section 1.4, the Haar-Karman principle further goes on to define the conditions under sufficiently smooth surfaces. As everyone knows, the H-K principle becomes the Castigliano principle of linear elasticity once the entire body deforms elastically. That of course is not relevant to this thread, but does serve to define the scope of the theory. I digress.

In equations (#1.4.8), known as Hencky's relations, the tensor fields are defined. The Tresca plasticity condition (1.3.11) is applied, where tau-s is the yield limit for pure shear, and this is continued in the solution of "eq#1.4.6 under conditions (1.4.2), (1.2.4)", returning to the HaarKarman series of equations.

Again, common knowledge, the Haar-Karman equations have different forms depending upon the number of principle stresses that meat or exceed tau-s.

Since gravity is the only vector, I am taking the liberty of assuming that a single stress (that caused by gravity) is relevant. This state is called a "semi-plastic state". If two principle stresses are greater that or equal to tau-s, then we have a state of "total plasticity", but gravity can't create that, so I don't get the simplified equation.

Eq#1.4.12 is what I'm trying to type in ascii as follows:

      s2=Ev                      E
         -----------(e1+e2+e3) +---e2
         (1+v)(1-2v)            1+v

where s2 = the principle stress due to gravity

       E = The Young's Modulus for glass is 4 to 14 e10^3 kg/mm^2
           (today's glass falls in the range of 5.5 to 9 e10^3 kg/mm^2)
           (so don't use that old impure glass crap to disprove!)
      en = the principle strains
       v = Poisson's ratio (0.244 for glass)

Stress concentration factors (from cracks, etc) impact measures of glass strength, but not the material properties relevant to flow calculations, so don't waste your breath. I'll get back to it, just wait.

Glass material yield stress is around 3500 kg/mm^2. Glass would have to be subjected to stresses IN EXCESS of that amount, in a sustained fashion for this to begin to occur.

Because of material flaws and crack propogation principles, and the breakdown of crystal bonds (in localized ways) as a mechanism of crack propogation, you can't ever load the glass to its yield stress.

The highest observed macro stress level acheived is only 20% of that, and was done to a glass fiber (as close to flawless as we can get).

Therefore, we can not apply a yield stress to the glass that could cause it to flow without first breaking our sample.

If, somehow, magically, you could apply a stress to an unflawed sample, then the observed plastic deformation (e2) would be roughly 1/15000 the magnitude of the applied stress (in kg/mm^2).

So even if you could magically apply a yielding stress, then you would not be able to measure the deformation.

This applies to glasses below 600C (or 270C for infinite time lengths).

This should be enough for the FAQ!
Scott "A fortune teller told me I'd be famous someday" Sehlhorst