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Fracture of Rubber

Zhigang Suo's picture

A rubber band can be stretched several times its original length. This large deformation may hide its brittleness: the strain to rupture can be markedly reduced by the presence of a crack. This lecture describes fracture mechanic of highly deformable materials, such as rubbers and gels.

Demonstrate in class the effect of a crack on a rubber band. Use a wide rubber band. Show the class that the rubber band can be stretched several times its original length. Then use scissors to cut a crack into the rubber band. Pull the rubber band to rupture. Note that the strain to rupture is markedly reduced by the crack. Pass the scissors and some rubber bands around. Invite every student to try.

These notes belong to a course on fracture mechanics


Li Han's picture

Zhigang, in class, you touch upon the crack tip field for rubber (by Caltech?). If assuming neohookean material model, does the "same k, same fracture process"-type argument still apply? In other word, is there still an annulus zone where non-linear elastic solution can approximate well the stress field, like the William's solution in the linear elastic case?

Li Han

Zhigang Suo's picture

Yes.  See details reviewed in the paper by Krishnan, Hui and Long (2008) listed at the end of the class notes.

Jung W. Hong's picture

Dear Zhigang,

This is a very good note for me.

I will use it for the discussion with my students, especially for the validation of my numerical schemes.





Zhigang Suo's picture

Rivlin wrote a remarkably detailed autobiogrpphic postscript to his collected papers.  You can read much of it for free at Google Book.  Of direct relevance to our
lecture are the following passages from Rivlin's autobiography:

“With regard to the problem of tearing, my first idea was to examine the validity of a criterion of the Griffith type, according to which an existing tear in a test-piece held at constant extension will grow if the elastic energy thereby released exceeds the increase in the surface energy. Griffith was concerned with glass, for which the elastic deformations are small, so that classical elasticity theory can be used to calculate the energy release. In the case of vulcanized rubber the large deformations involved rendered similar calculations impossible at the time, although such calculations were carried out much later by Lindley using finite-element methods. We therefore devised experiments in which the necessity for elaborate calculations was avoided. My (not very firm) expectation was that the Griffith criterion would not apply. I was therefore somewhat surprised when we found it possible, by measuring force required to tear a test-piece with a preexisting cut, to calculate a characteristic tearing energy that could be used to predict the tearing force for test pieces for which the forces were orders of magnitude different. This characteristic energy was, however, many orders of magnitude greater than one would expect for a surface energy. We interpreted it as the energy expended in the irreversible processes that take place in a neighborhood of the crack prior to its formation.

“Although the work was not published until 1953, it was substantially completed by the summer of 1950, and I lectured on it in George Irwin’s department at the Naval Research Laboratory in the fall of 1950.”

In the course, I have divided the fracture mechanics of rubber into two lectures:

Dear Zhigang, 

Thanks for your helpful notes. I learned a lot from them when studying the course of fracture mechanics.

While reading the note, I found a small mistake.  On page 4, the energy release rate G for the "simple extension" test should be equal to  2*F*lambda/t-2*W*a instead of its negative, 2*W*a-2*F*lambda/t.


Zhigang Suo's picture

Thank you very much!  I'll post updated notes when I teach the course again in the Spring of 2014.



Please i would like to ask you a question about orthodontic ligature. I serach to model it in abaqus but i don't know how to choose the behavior low to introduce it in abaqus. All that i know about this material is that it is an elastomer. Can anyone help me please? 

thanks a lot 

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