L. Calabri

Bio: L. Calabri is an academic researcher from Northwestern University. The author has contributed to research in topics: Nanoindentation & Resonance. The author has an hindex of 9, co-authored 17 publications receiving 446 citations.

Modulus, Fracture Strength, and Brittle vs. Plastic Response of the Outer Shell of Arc-grown Multi-walled Carbon Nanotubes

Abstract: The fracture strengths and elastic moduli of arc-grown multi-walled carbon nanotubes (MWCNTs) were measured by tensile loading inside of a scanning electron microscope (SEM). Eighteen tensile tests were performed on 14 MWCNTs with three of them being tested multiple times (3×, 2×, and 2×, respectively). All the MWCNTs fractured in the “sword-in-sheath” mode. The diameters of the MWCNTs were measured in a transmission electron microscope (TEM), and the outer diameter with an assumed 0.34 nm shell thickness was used to convert measured load-displacement data to stress and strain values. An unusual yielding before fracture was observed in two tensile loading experiments. The 18 outer shell fracture strength values ranged from 10 to 66 GPa, and the 18 Young's modulus values, obtained from a linear fit of the stress–strain data, ranged from 620 to 1,200 GPa, with a mean of 940 GPa. The possible influence of stress concentration at the clamps is discussed.

AFM nanoindentation: tip shape and tip radius of curvature effect on the hardness measurement

Abstract: AFM nanoindentation is nowadays not so widespread for the study of mechanical properties of materials at the nanoscale. 'Nanoindenter' machines are presently more accurate and more standardized. However, AFM could provide interesting features such as imaging the indentation impression right after the load application. In this work a new method for nanoindentation via AFM is proposed. The use of AFM allows hardness measurement with standard sharp AFM probes and a simultaneous high-resolution imaging (which is not achievable with standard indenters—cube corner and Berkovich). How the shape of the indenter and the tip radius of curvature affect the hardness measurement is here analysed with three different approaches: experiments, numerical simulations and theoretical models. In particular the effect of the tip radius of curvature, which is not negligible for the real indenters, has been considered both in the nature of the indentation process, than in the practice of imaging with AFM. A final theoretical model has been developed, that includes the effect of the tip radius of curvature as well as variable corner angle. Through this model we have been able to define a correction factor which permits us to evaluate the actual hardness of the material, once the radius of curvature of the tip is measured.

Nanoindentation shape effect: experiments, simulations and modelling

Abstract: AFM nanoindentation is nowadays commonly used for the study of mechanical properties of materials at the nanoscale. The investigation of surface hardness of a material using AFM means that the probe has to be able to indent the surface, but also to image it. Usually standard indenters are not sharp enough to obtain high-resolution images, but on the other hand measuring the hardness behaviour of a material with a non-standard sharp indenter gives only comparative results affected by a significant deviation from the commonly used hardness scales. In this paper we try to understand how the shape of the indenter affects the hardness measurement, in order to find a relationship between the measured hardness of a material and the corner angle of a pyramidal indenter. To achieve this we performed a full experimental campaign, indenting the same material with three focused ion beam (FIB) nanofabricated probes with a highly altered corner angle. We then compared the results obtained experimentally with those obtained by numerical simulations, using the finite element method (FEM), and by theoretical models, using a general scaling law for nanoindentation available for indenters with a variable size and shape. The comparison between these three approaches (experimental, numerical and theoretical approaches) reveals a good agreement and allowed us to find a theoretical relationship which links the measured hardness value with the shape of the indenter. The same theoretical approach has also been used to fit the hardness experimental results considering the indentation size effect. In this case we compare the measured data, changing the applied load.

American Society for Testing and Materials

Abstract: The American Society for Testing and Materials (ASTM) is an independent organization devoted to the development of standards.

Ab initio calculation of ideal strength and phonon instability of graphene under tension

Abstract: Graphene-based $s{p}^{2}$-carbon nanostructures such as carbon nanotubes and nanofibers can fail near their ideal strengths due to their exceedingly small dimensions. We have calculated the phonon spectra of graphene as a function of uniaxial tension by density functional perturbation theory to assess the first occurrence of phonon instability on the strain path, which controls the strength of a defect-free crystal at $0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Uniaxial tensile strain is applied in the $x$ (nearest-neighbor) and $y$ (second nearest-neighbor) directions, related to tensile deformation of zigzag and armchair nanotubes, respectively. The Young's modulus $E=1050\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ and Poisson's ratio $\ensuremath{ u}=0.186$ from our small-strain results are in good agreement with previous calculations. We find that in both $x$ and $y$ uniaxial tensions, phonon instabilities occur near the center of the Brillouin zone, at (${\ensuremath{\epsilon}}_{xx}=0.194$, ${\ensuremath{\sigma}}_{xx}=110\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${\ensuremath{\epsilon}}_{yy}=\ensuremath{-}0.016$) and (${\ensuremath{\epsilon}}_{yy}=0.266$, ${\ensuremath{\sigma}}_{yy}=121\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${\ensuremath{\epsilon}}_{xx}=\ensuremath{-}0.027$), respectively. Both soft phonons are longitudinal elastic waves in the pulling direction, suggesting that brittle cleavage fracture may be an inherent behavior of graphene and carbon nanotubes at low temperatures. We also predict that a phonon band gap will appear in highly stretched graphene, which could be a useful spectroscopic signature for highly stressed carbon nanotubes.

Measurements of near-ultimate strength for multiwalled carbon nanotubes and irradiation-induced crosslinking improvements.

Abstract: The excellent mechanical properties of carbon nanotubes are being exploited in a growing number of applications from ballistic armour to nanoelectronics. However, measurements of these properties have not achieved the values predicted by theory due to a combination of artifacts introduced during sample preparation and inadequate measurements. Here we report multiwalled carbon nanotubes with a mean fracture strength >100 GPa, which exceeds earlier observations by a factor of approximately three. These results are in excellent agreement with quantum-mechanical estimates for nanotubes containing only an occasional vacancy defect, and are ∼80% of the values expected for defect-free tubes. This performance is made possible by omitting chemical treatments from the sample preparation process, thus avoiding the formation of defects. High-resolution imaging was used to directly determine the number of fractured shells and the chirality of the outer shell. Electron irradiation at 200 keV for 10, 100 and 1,800 s led to improvements in the maximum sustainable loads by factors of 2.4, 7.9 and 11.6 compared with non-irradiated samples of similar diameter. This effect is attributed to crosslinking between the shells. Computer simulations also illustrate the effects of various irradiation-induced crosslinking defects on load sharing between the shells. The mechanical properties of carbon nanotubes rarely match the values predicted by theory owing to a combination of artefacts introduced during sample preparation and inadequate measurements. However, by avoiding chemical treatments and using high-resolution imaging, it is possible to obtain values of the mean fracture strength that exceed previous values by approximately a factor of three.

Dispersion of Carbon Nanotubes: Mixing, Sonication, Stabilization, and Composite Properties

Abstract: Advances in functionality and reliability of carbon nanotube (CNT) composite materials require careful formulation of processing methods to ultimately realize the desired properties. To date, controlled dispersion of CNTs in a solution or a composite matrix remains a challenge, due to the strong van der Waals binding energies associated with the CNT aggregates. There is also insufficiently defined correlation between the microstructure and the physical properties of the composite. Here, we offer a review of the dispersion processes of pristine (non-covalently functionalized) CNTs in a solvent or a polymer solution. We summarize and adapt relevant theoretical analysis to guide the dispersion design and selection, from the processes of mixing/sonication, to the application of surfactants for stabilization, to the final testing of composite properties. The same approaches are expected to be also applicable to the fabrication of other composite materials involving homogeneously dispersed nanoparticles.