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Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene

Jeffrey Kysar's picture

We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m–1) and –690 Nm–1, respectively. The breaking strength is 42 N m–1 and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Young's modulus of E = 1.0 terapascals, third-order elastic stiffness of D = –2.0 terapascals, and intrinsic strength of {sigma}int = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.

Lee, C.; Wei, X.; Kysar, J. W.; and Hone, J. (2008) “Measurement of the Elastic
Properties and Intrinsic Strength of Monolayer Graphene” Science, 321, 385-388.

http://www.sciencemag.org/cgi/content/full/321/5887/385

Comments

Luoyu Roy Xu's picture

Dear Jeff,

Congratulation
on such important achievement! I'd propose one issue on strength measurements
based on your nice work. For engineering materials, usually we make specimens
such as dogbone specimens to get a uniform stress field across the test region
before failure. However, during an indentation experiment, the stress field is
highly non-uniform from the beginning to failure.  I believe the strength data from these two
approaches will lead to different results (even for the same material).
Probably the variation of the indentation approach is larger than that of the
dogbone approach (of course, we have to employ indentation approaches for
small-size specimens).

 Roy

Jeffrey Kysar's picture

Dear Roy,

 Thank you for taking the time to look through our paper. You are, of course, correct to say that the stress field is heterogeneous throughout the specimen.

 One can think of our monolayer graphene specimens as being "drumheads" that are one atomic layer thick and have a diameter of either 1 micron or 1.5 microns. The AFM tip we used to deflect the center of the graphene film had a tip radius of either about 15 nm or 25 nm, depending upon the tip. (Incidently, we had to use a diamond AFM tip for the experiments because conventional silicon AFM tips broke at loads smaller than that required to break the monolayer graphene)

 Computer simulations of graphene up to the point of failure suggest that its breaking strength is highly dependent upon the initial defect structure, hence we can think of it as a brittle material. In addition, the strain at the point of breaking in the simulations was very high--upwards of 20%. Therefore, specimens with random distributions of defects would be expected to have a very wide distribution of breaking forces which could be quantified using Weibull statistics.

 We did a mechanics analysis of the stress and strain distribution throughout the deflected graphene film. The strain exceeded 5% in only about the inner 1% of the film's area, which amounts to an area of only a few thousand square nanometers of highly strained material. Previous experiments using STM had shown that monolayer graphene taken from the same source as ours did not contain any defects whatsoever in regions of many hundreds of square nanometers. Therefore, we hoped that the highest stressed region of the graphene film would be defect-free as well.

 The distribution of breaking forces from about two dozen different graphene films was Gaussian rather than Weibull. The very high Weibull modulus of the breaking force (and hence breaking stress) of our experiments strongly suggests that the graphene is defect-free, at least in the region of highest strain. For that reason, we claim that our experiment are able to sample the "intrinsic" strength of defect-free, pristine graphene.

 To return to your comment of a possible difference in breaking strength of homogeneously and heterogeneously strained specimens, in principle, the intrinsic breaking strength is the same irrespective of the specimen geometry and strain distribution. However, since graphene is a brittle material, the actual breaking force of any given specimen will depend upon the initial defect structure. A homogeneously deformed specimen would presumably have a greater propensity for defects because it would have free edges, and hence a lower breaking force due to the stress concentrations around the defects.

Sincerely,

 Jeff

mohammed yahya abdellah ahmad
assistant lecturer, South valley University
Faculty of Engineering, Qena

hi every body
i have a problem with abaqus for 3 months ,
i model composite laminates using XFEM, but all time get the following error message;
37296 elements have fewer than the required number of integration
points. The elements are identified in element set
ErrElemMissingIntegPoints.
any one can help me
thank you
best regards
Mohammed

 

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