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Discussion of fracture paper #31 - Toughness of a rigid foam

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A most readworthy paper, "Static and dynamic mode I fracture toughness of rigid PUR foams under room and cryogenic temperatures" by E. Linul, L. Marşavina, C. Vălean, R. Bănică, Engineering Fracture Mechanics, 225, 15 February 2020, 106274, 1-10, is selected for this ESIS blog. It has received a lot of attention and was for an extended period of time one of the most read papers in EFM. The attention is earned because of the clear and concise writing about an intricate material that did not yet get as much focus as it deserves. 

As the title says, the paper concerns fracture mechanical testing of a solid polyurethane foam. The material has a closed pore structure. It is frequently used in the transport sector for its low density. It also have desirable performance at compression, giving a continuous and almost constant mechanical resistance. The beneficial properties are taken advantage of in applications such as sandwich composites, shock absorbers, packaging materials etc.

I have no professional experience of the material but I have come across it a few times and I recognise its character. The excellent description in the introductions confirms the feeling of something that I am familiar with, i.e., the crushing under compressive load and the brittle fracture in tension. Judging from the listed yield stresses given in the paper, I guess that one can manually make an indent e.g. with a finger.

Before fracture the material may be treated as linear elastic with the elastic limit reached only in a small region at the crack tip, which is controlled by the stress intensity faktor KI. The linear extent of the non-linear region is supposed to be below at most a tenth, or so, of the crack length. The exact limit depends of course on the specific geometry. 

The ASTM convention described in STP 410 by Brown and Srawley in 1966, claims for structural steels that ligaments, thickness, and crack length should not be less than 2.5(KIc/yield stress)2. It is not mentioned in the paper but the results show that the specimen in all cases fullfil these requirements with an almost four-folded safety, i.e. ligament, thickness and crack length exceed 9.6(KIc/yield stress)2. 

The validity of the obtained toughnesses KIc becomes important when it is applied to real structures with cracks that could be too small. This is not within the scope of the present paper. When is a crack too short for linear fracture mechanics? It may not be the most urgent thing to study, but I guess that it has to be checked before the results are put into general use. I am particularly excited over how it compares with the STP 410 recommendations. 

When the scale of yielding or damage becomes excessive the fracture process region generally loses its KI autonomy. It happens when the shielding of the fracture process region increases which leads to an increased energy release rate required for crack growth. An analysis would require a more elaborate continuum mechanical model in combination with a box or line model of the fracture process region. The material model would be a challenge I guess. 

I did a minor literature search for both establishing the limits of linear fracture mechanics and application of non-linear models beyond these limits for solid foam materials but didn't find anything definite. I could have missed some. Who knows?

Per Ståhle 

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