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I read that brittle materials tend to have an observed strength much less than its theoretical strength because they tend to have surface cracks and whatever tension is applied gets greatly magnified at the tip of the crack. I once saw a web page that said it was predicted that glass has a theoretical strength of 31 GPa.

Apparently, people seem to think only nanotubes can be made strong enough for a space elevator and graphite can't. More details can be seen in this question's edit history, but what I wonder is:

Has there been research on improving the strength of graphene-based materials?

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    $\begingroup$ Hi Timothy, you are tending to ask questions about generic research. You are attempting to reduce it down to two simple questions which is good, but I think based on what you are asking you will not get a satisfactory answer. I also think this falls more towards Physics rather that matter modeling, but I think it should be reworked rather than transferred. $\endgroup$ Feb 16 at 3:16
  • $\begingroup$ @TristanMaxson That is my question. I want to ask the question I have, not a question I don't have. I don't see how my question can be made clearer than it is. I think it's not worth closing. We don't want to assume definitely it can never be answered. Maybe the world is going to slowly become smarter and then it will be so easy for researchers to figure out how to answer those questions. When questions get closed that were clear, they can't be answered. Then we don't learn when somebody would have had the capability to answer them. It's also useful for research on which clear questions $\endgroup$
    – Timothy
    Feb 16 at 4:39
  • $\begingroup$ actually can be answered to give them a chance to answer them and not make them unable to be answered by closing them. $\endgroup$
    – Timothy
    Feb 16 at 4:39
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    $\begingroup$ You give a lot of unrelated information to your question. Your entire question could be summed up as "What research has been done on improving the strength of graphite/graphene based materials". Since graphene is known for strength, you can probably assume there has been some work, but you should put in more effort to ask a narrower question. Right now it is very broad and somewhat off topic for this SE. $\endgroup$ Feb 16 at 7:06
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    $\begingroup$ I suspect that you are not too familiar with the research process, you should contact people involved in these materials and talk to them directly if you want to contribute. This forum is more for people doing active research or hobby research and asking about how to model the materials. $\endgroup$ Feb 16 at 20:11
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There has indeed been quite a lot of research in this area, as is readily uncovered by searching for "improving the strength of graphene" in your search engine of choice; for example, this 2017 review https://www.sciencedirect.com/science/article/pii/S0079642517300968.

Graphene is often highlighted as having high mechanical strength, but this usually refers to its tensile strength and is not always the critical factor in mechanical applications. Do you only need the material to support tension, or also compression? What about shear stress? Some relevant considerations:

  • Graphene is a 2D material, only a single atom thick, so in order for it to be useful for macroscopic applications requiring high tensile strength, many sheets would need to be used.

  • Graphene sheets only interact very weakly, via van der Waals interactions. The sheets can slide very easily (which is why graphite is so good for pencils, lubrication etc) and cannot support even moderate shear stresses (in the out-of-plane direction). If you need high shear strength, then you need to do something to the graphene sheets, for example induce corrugation: https://www.sciencedirect.com/science/article/pii/S0008622320306230

  • Real graphene sheets are not infinite, they have edges. These edges are chemically reactive and need to be passivated or they will reconstruct. One alternative is to fold the sheet so that, for example, the left-hand edge wraps over and binds to the right-hand edge. This can maintain the pristine structure and high tensile strength of the graphene. The resultant structure is a carbon nanotube, which is one reason why these are of interest in mechanical applications.

  • Graphene sheets are strong under tension, but buckle easily under compression (nanotubes are stronger in this respect).

  • Pristine, single-crystal graphene is difficult to create in large quantities, e.g. using CVD, and polycrystalline graphene has a much wider spread of mechanical strengths. Not all of the defects and grains are detrimental, but understanding the nanostructure and implications is challenging for modelling due to the long-range interactions between point defects and the extremely soft flexural phonon modes which lead to large thermal effects (see e.g. https://www.nature.com/articles/nphys3183)

There are many, many more studies in this area, both experimental and modelling, but I hope this has given you a flavour of it at least.

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