Paper as strong as steel?

December 30, 2015 | 12:00
Experimental equipment for measuring frictional forces. © Frédéric Restagno & Christophe Poulard
Experimental equipment for measuring frictional forces. © Frédéric Restagno & Christophe Poulard
Interleave one by one the pages of two phone books and then try and separate them by pulling on the covers. Impossible!
This assembly is so strong it is even possible to suspend a car with it. According to a model reproducing the forces of tension and friction in play, researchers at the Laboratory of Solid Physics (CNRS, University of South Paris), the Gulliver Laboratory (CNRS/ESPCI ParisTech), the Laboratory of Papermaking Processes (CNRS / Grenoble INP) and McMaster University in Canada have shown that when one pulls vertically on the ends of two interleaved directories, part of the vertical force is converted to a horizontal force which presses on the pages. The pages thus stick to each other by the effect of friction. This enormous frictional force resists the tension forces to the point where , we read, you could throw yourself into the void on an elastic cord held onto two interleaved directories (but don’t try this at home – leave it to the researchers!). They have measured the force necessary to separate the pages as a function of the number of pages, the thickness of the paper and the overlap distance.

The analysis reveals the importance of the combination of these three parameters. It seems that the strength of the assembly rises much more rapidly than the number of pages. Once you have reached the number of pages necessary to resist a tension force, then just multiplying the number of pages by ten, if the pages overlap sufficiently, increases the strength of the assembled directories by a factor of 10 000.

This study enables the measure of the coefficients of friction with very small forces, allowing understanding of the mechanical behaviours of more complex interleaved systems, such as textiles or muscles. And it may perhaps one day lead to the development of new biomimetic materials.
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