Another book for your library: Cellular Solids, Structure and Properties

logo_smallThis book (ISBN: 9780521499118) at a 2nd edition is written by Lorna J. GibsonMassachusetts Institute of Technology and Michael F. Ashby from the University of CambridgeThe last author is famous by the following statement:

When modern man builds large load-bearing structures, he uses dense solids; steel, concrete, glass.When nature does the same, she generally uses cellular materials; wood, bone, coral. There must be good reasons for it.

The book contains much more than thermal insulation and gives a theoretical foundation for the elastic properties of foams. These properties are used in cellular glass engineering and process calculation.

I learned that the stress relaxation behavior does not depend on the geometry / density of the cell structure but solely on the basic material, glass in this case. But the Poisson ratio depends completely on the geometry and is 0.33 for an open cell structure with regular round cells, while it is 0.28 for solid glass.

Both facts are important for the calculation of the annealing temperature curve for cellular glass, already one reason to buy this excellent book.


Cellular glass is smart

logo_smallIf we put a compressive stress on cellular glass, we would expect random phenomena of breaking cells. With piezo-electric sensors on the material, we are able to registrate these breaking cells, because they all emit acoustic waves in the structure. This measurement technique is acoustic emission and it is used to study the behaviour of steel welds, rocks, concrete, … . In that way, we can check whether the phenomena are random or not.

But in the case of many heterogeneous brittle materials, the distribution of amplitudes of these waves show a power law correlation. A Physical Review paper shows that this is also the case for cellular glass like it happens also for earthquakes. In the latter case, we speak about the Richter-Gutenberg law. For earthquakes, there is also the Omori law for the time interval between the after shocks. This distribution is also a nice power law and it is also present in cellular glass over many decades from microseconds to several minutes. In region with many earthquakes, there is also another power law about the distribution of distance between the epicentra of consecutive earthquakes. These three power laws in magnitude, time and space domain have the same coefficients for cellular glass as the earthquakes around San Francisco.

It is clear that the breaking of cellular glass under a compressive load is not a random but instead a correlated process, which has a limited but not negligible predictability. And this predictability allows us to define a safety factor between the short time compressive strength (1 min) and the long term mechanical stability. For cellular glass, a safety factor 3 is generally accepted  and the above description is a method to prove that.

Solid glass has a much higher safety factor because one crack gives always complete failure while in the case of cellular glass, the interaction between the cells halts microcopic cracks inducing the low safety factor. This means that under a certain load under the safety factor, cellular glass does not not creep at all, while XPS, EPS, PIR, PUR and other foams always keep creeping and are never stable. This interaction between the brittle cells, as demonstrated with acoustic emission, gives cellular glass its perfect mechanical stability. Cellular glass is indeed smart …