Discussion of fracture paper #40 - Icicle or carrot, which one has isotropic fracture properties?

Around 20 years ago, I gave a fracture mechanics lecture and talked about crack initiation that happens in the plane with the largest tensile stress. True, at least if the material has isotropic properties. The students already knew where an isotropic material would give the largest stress at bending and torsion. I planned to make a desktop experiment with an icicle and a carrot. This was during the autumn with an abundance of icicles everywhere. The carrot, I found at home.

I asked the students which one would be the anisotropic one. The majority said the carrot but one student, whom I already, halfway into the course, considered to be the smartest in the class, voted for the icicle. I asked why and she said, "Because you asked. If it is the carrot it would be boring". She was the smarter one and I was the fool. The bending and twisting gave the expected isotropic result for the carrot but not for the icicle. 

It has been known since Laudise and Barns study from 1979, that the major part of the icicle is a single crystal. For all icicles I tested, the bending gave zig-zag crack paths and the torsion almost always resulted in a cup-cone fracture. For the latter, I still do not have a good explanation.

The interesting paper that brought these memories back is

"Thickness-independent fracture in columnar freshwater ice: An experimental study" by I.E. Gharamti, W. Ahmad, O. Poulakka, and J. Tuhkuri  in Engineering Fracture Mechanics, vol. 298, 2024, https://doi.org/10.1016/j.engfracmech.2024.109906.

It is a readworthy paper. It is only related to my in-class experiment via the freshwater ice. The study is very interesting and the motivation is marine applications. According to the authors, the tested ice is polycrystalline which is no surprise since the test specimens are measured in cubic metres and huge as compared with my middle finger-sized icicles.

What we learn is that the ice in general is polycrystalline and may be assumed to be isotropic. The experiments show that there is no detected influence of the ice thickness on the fracture behaviour. As I understand it the implication is that the material does not change properties as it grows thicker and the thickness change leads to a proportional increase in load-carrying capacity.

The expected transition from plane strain to plane stress occurs for specimens with thicknesses that are around, or smaller than the characteristic length scale of the cohesive zone ahead of the crack tip. In the paper, it is called the fictive crack based on Hillerborg's notation for non-linear regions in concrete or similar materials. A more widespread and earlier introduced denotation is Barenblatt process region. 

The experiments were performed on specimens with pretty large thicknesses. With estimated process zone sizes being small as compared with the specimen thicknesses, the plane strain to plane stress transition that occurs for thin specimens is avoided. 

I have friends from the north of Sweden who claim that one or two inches of ice is enough to carry a human. It should depend on weight and shoe size. Since I am a Swede and the authors from the neighbouring country Finland share the same Baltic Sea water, it would be interesting to know if one or two inches is enough also on the Finnish side.

Only a couple of inches sounds risky. Also, it would involve the plane stress transition and the present linear scaling would possibly fail. It would be interesting to hear if anyone knows if a switch to plane stress leads to reduced or increased safety.

It would be interesting to hear from anyone who would like to discuss or provide comments or thoughts, regarding the subject, the method, or anything related. Perhaps the authors can cast some light on the Swedish sufficient ice thickness guess. If anyone wishes to comment and does not have an iMechanica account and fails to register, please email me at per.stahle@solid.lth.se and I will post your comments in your name. If the paper is not open-access it will be that in a couple of days. 

Per Ståhle